PASSAGES FROM THE LIFE OF A PHILOSOPHER, by Charles Babbage

B. H. Babbage, del.

Impression from a woodcut of a small portion of Mr. Babbage’s Difference Engine No. 1, the property of Government, at present deposited in the Museum at South Kensington.

• It was commenced 1823.
• This portion put together 1833.
• The construction abandoned 1842.
• This plate was printed June, 1853.
• This portion was in the Exhibition 1862.

PASSAGES
FROM
THE LIFE OF A PHILOSOPHER.
BY
CHARLES BABBAGE, ESQ., M.A.,
F.R.S., F.R.S.E., F.R.A.S., F. STAT. S., HON. M.R.I.A., M.C.P.S., COMMANDER OF THE ITALIAN ORDER OF ST. MAURICE AND ST. LAZARUS, INST. IMP. (ACAD. MORAL.) PARIS CORR., ACAD. AMER. ART. ET SC. BOSTON, REG. ŒCON. BORUSS., PHYS. HIST. NAT. GENEV., ACAD. REG. MONAC., HAFN., MASSIL., ET DIVION., SOCIUS. ACAD. IMP. ET REG. PETROP., NEAP., BRUX., PATAV., GEORG. FLOREN, LYNCEI ROM., MUT., PHILOMATH. PARIS, SOC. CORR., ETC.

“I’m a phi­los­o­pher. Confound them all—

Birds, beasts, and men; but no, not womankind.”—Don Juan.

“I now gave my mind to philosophy: the great object of my ambition was to make out a complete system of the universe, including and comprehending the origin, causes, consequences, and termination of all things. Instead of countenance, encouragement, and applause, which I should have received from every one who has the true dignity of an oyster at heart, I was exposed to calumny and misrep­re­sen­ta­tion. While engaged in my great work on the universe, some even went so far as to accuse me of infidelity;—such is the malignity of oysters.”—“Autobiography of an Oyster” deciphered by the aid of photography in the shell of a phi­los­o­pher of that race,—recently scolloped.

LONDON:

LONGMAN, GREEN, LONGMAN, ROBERTS, & GREEN.

1864.

[The right of Translation is reserved.]

DEDICATION.

TO VICTOR EMMANUEL II., KING OF ITALY.

SIRE,

IN dedicating this volume to your Majesty, I am also doing an act of justice to the memory of your illustrious father.

In 1840, the King, Charles Albert, invited the learned of Italy to assemble in his capital. At the request of her most gifted Analyst, I brought with me the drawings and explanations of the Analytical Engine. These were thoroughly examined and their truth acknowledged by Italy’s choicest sons.

To the King, your father, I am indebted for the first public and official acknowledgment of this invention.

I am happy in thus expressing my deep sense of that obligation to his son, the Sovereign of united Italy, the country of Archimedes and of Galileo.

I am, Sire,
With the highest respect,

Your Majesty’s faithful Servant,

CHARLES BABBAGE.

PREFACE.

SOME men write their lives to save themselves from ennui, careless of the amount they inflict on their readers.

Others write their personal history, lest some kind friend should survive them, and, in showing off his own talent, unwittingly show them up.

Others, again, write their own life from a different motive—from fear that the vampires of literature might make it their prey.

I have frequently had applications to write my life, both from my countrymen and from foreigners. Some caterers for the public offered to pay me for it. Others required that I should pay them for its insertion; others offered to insert it without charge. One proposed to give me a quarter of a column gratis, and as many additional lines of eloge as I chose to write and pay for at ten-pence per line. To many of these I sent a list of my works, with the remark that they formed the best life of an author; but nobody cared to insert them.

I have no desire to write my own biography, as long as I have strength and means to do better work.

The remarkable circumstances attending those Calculating Machines, on which I have spent so large a portion of my life, make me wish to place on record some account of their past history. As, however, such a work would be utterly uninteresting to the greater part of my countrymen, I thought it might be rendered less unpalatable by relating some of my experience amongst various classes of society, widely differing from each other, in which I have oc­ca­sion­al­ly mixed.

This volume does not aspire to the name of an autobiography. It relates a variety of isolated circumstances in which I have taken part—some of them arranged in the order of time, and others grouped together in separate chapters, from similarity of subject.

The selection has been made in some cases from the importance of the matter. In others, from the celebrity of the persons concerned; whilst several of them furnish interesting illustrations of human character.

CONTENTS.

• I. • My Ancestors •   [1]
• II. • Childhood •   [7]
• III. • Boyhood •  [17]
• IV. • Cambridge •  [25]
• V. • Difference Engine No. 1 •  [41]
• VI. • Statement relative to the Difference Engine, drawn up by the late Sir H. Nicolas from the Author’s Papers •  [68]
• VII. • Difference Engine No. 2 •  [97]
• VIII. • Of the Analytical Engine • [112]
• IX. • Of the Mechanical Notation • [142]
• X. • The Exhibition of 1862 • [147]
• XI. • The late Prince Consort • [168]
• XII. • Recollections of the Duke of Wellington • [173]
• XIII. • Recollections of Wollaston, Davy, and Rogers • [186]
• XIV. • Recollections of Laplace, Biot, and Humboldt • [195]
• XV. • Experience by Water • [205]
• XVI. • Experience by Fire • [213]
• XVII. • Experience amongst Workmen • [228]
• XVIII. • Picking Locks and Deciphering • [233]
• XIX. • Experience in St. Giles’s • [242]
• XX. • Theatrical Experience • [251]
• XXI. • Electioneering Experience • [259]
• XXII. • Scene from a New After-Piece • [276]
• XXIII. • Experience at Courts • [292]
• XXIV. • Experience at Courts • [298]
• XXV. • Railways • [313]
• XXVI. • Street Nuisances • [337]
• XXVII. • Wit • [363]
• XXVIII. • Hints for Travellers • [371]
• XXIX. • Miracles • [387]
• XXX. • Religion • [396]
• XXXI. • A Vision • [406]
• XXXII. • Various Reminiscences • [421]
• XXXIII. • The Author’s Cont­ri­bu­tions to Human Knowledge • [430]
• XXXIV. • The Author’s further Cont­ri­bu­tions to Human Knowledge • [441]
• XXXV. • Results of Science • [473]
• XXXVI. • Agreeable Recollections • [482]
• Appendix • [487]

PASSAGES FROM THE LIFE OF A PHILOSOPHER.

CHAPTER I. MY ANCESTORS.

Traced his descent, through ages dark,

From cats that caterwauled in Noah’s ark.

SALMAGUNDI, 4to, 1793.

Value of a celebrated Name — My Ancestors — Their Ante-Mosaic origin — Flint-workers — Tool-makers — Not descended from Cain — Ought a Phi­los­o­pher to avow it if he were? — Probability of Descent from Tubal Cain — Argument in favour, he worked in Iron — On the other side, he invented Organs — Possible origin of my Name — Family History in very recent times.

WHAT is there in a name? It is merely an empty basket, until you put something into it. My earliest visit to the Continent taught me the value of such a basket, filled with the name of my venerable friend the first Herschel, ere yet my younger friend his son, had adorned his distinguished patronymic with the additional laurels of his own well-earned fame.

The inheritance of a celebrated name is not, however, without its disadvantages. This truth I never found more fully appreciated, nor more admirably expressed, than in a conversation with the son of Filangieri, the author of the {2} celebrated Treatise on Legislation, with whom I became acquainted at Naples, and in whose company I visited several of the most interesting institutions of that capital.

In the course of one of our drives, I alluded to the advantages of inheriting a distinguished name, as in the case of the second Herschel. His remark was, “For my own part, I think it a great disadvantage. Such a man must feel in the position of one inheriting a vast estate, so deeply mortgaged that he can never hope, by any efforts of his own, to redeem it.”

Without reverting to the philosophic, but unromantic, views of our origin taken by Darwin, I shall pass over the long history of our progress from a monad up to man, and commence tracing my ancestry as the world generally do: namely, as soon as there is the slightest ground for conjecture. Although I have contended for the Mosaic date of the creation of man as long as I decently could, and have even endeavoured to explain away[1] some of the facts relied upon to prove man’s long anterior origin; yet I must admit that the continual accumulation of evidence probably will, at last, compel me to acknowledge that, in this single instance, the writings of Moses may have been misapprehended.

[1] On the remains of human art, mixed with the bones of extinct races of animals. Proceedings of the Royal Society, 26th May, 1859.

〈DESCENT FROM FLINT-WORKERS.〉

Let us, therefore, take for granted that man and certain extinct races of animals lived together, thousands of years before Adam. We find, at that period, a race who formed knives, and hammers, and arrow-heads out of flint. Now, considering my own inveterate habit of contriving tools, it is more probable that I should derive my passion by hereditary transmission from these original tool-makers, than from any other inferior race existing at that period. {3}

Many years ago I met a very agreeable party at Mr. Rogers’ table. Somebody introduced the subject of ancestry. I remarked that most people are reluctant to acknowledge as their father or grandfather, any person who had committed a dishonest action or a crime. But that no one ever scrupled to be proud of a remote ancestor, even though he might have been a thief or a murderer. Various remarks were made, and reasons assigned, for this tendency of the educated mind. I then turned to my next neighbour, Sir Robert H. Inglis, and asked him what he would do, supposing he possessed undoubted documents, that he was lineally descended from Cain.

Sir Robert said he was at that moment proposing to himself the very same question. After some consideration, he said he should burn them; and then inquired what I should do in the same circumstances. My reply was, that I should preserve them: but simply because I thought the preservation of any fact might ultimately be useful.

〈NOT THROUGH CAIN.〉

I possess no evidence that I am descended from Cain. If any herald suppose that there may be such a presumption, I think it must arise from his confounding Cain with Tubal Cain, who was a great worker in iron. Still, however he might argue that, the probabilities are in favour of his opinion: for I, too, work in iron. But a friend of mine, to whose kind criticisms I am much indebted, suggests that as Tubal Cain invented the Organ, this probability is opposed to the former one.

The next step in my pedigree is to determine whence the origin of my modern family name.

Some have supposed it to be derived from the cry of sheep. If so, that would point to a descent from the Shepherd Kings. Others have supposed it is derived from the name of a place called Bab or Babb, as we have, in the West of England, Bab {4} Tor, Babbacombe, &c. But this is evidently erroneous; for, when a people took possession of a desert country, its various localities could possess no names; consequently, the colonists could not take names from the country to which they migrated, but would very naturally give their own names to the several lands they appropriated: “mais revenons à nos moutons.”

How my blood was trans­mit­ted to me through more modern races, is quite immaterial, seeing the admitted antiquity of the flint-workers.

〈SAD OMISSION.〉

In recent times, that is, since the Conquest, my knowledge of the history of my family is limited by the unfortunate omission of my name from the roll of William’s followers. Those who are curious about the subject, and are idlers, may, if they think it worth while, search all the parish registers in the West of England and elsewhere.

The light I can throw upon it is not great, and rests on a few documents, and on family tradition. During the past four generations I have no surviving collateral relatives of my own name.

The name of Babbage is not uncommon in the West of England. One day during my boyhood, I observed it over a small grocer’s shop, whilst riding through the town of Chudley. I dismounted, went into the shop, purchased some figs, and found a very old man of whom I made inquiry as to his family. He had not a good memory himself, but his wife told me that his name was Babb when she married him, and that it was only during the last twenty years he had adopted the name of Babbage, which, the old man thought, sounded better. Of course I told his wife that I entirely agreed with her husband, and thought him a very sensible fellow.

The craft most frequently practised by my ancestors seems {5} to have been that of a goldsmith, although several are believed to have practised less dignified trades.

In the time of Henry the Eighth one of my ancestors, together with a hundred men, were taken prisoners at the siege of Calais.

When William the Third landed in Torbay, another ancestor of mine, a yeoman possessing some small estate, undertook to distribute his proclamations. For this bit of high treason he was rewarded with a silver medal, which I well remember seeing, when I was a boy. It had descended to a very venerable and truthful old lady, an unmarried aunt, the historian of our family, on whose authority the identity of the medal I saw with that given by King William must rest.

Another ancestor married one of two daughters, the only children of a wealthy physician, Dr. Burthogge, an intimate friend and cor­res­pon­dent of John Locke.

〈A WILD ANCESTOR.〉

Somewhere about 1700 a member of my family, one Richard Babbage, who appears to have been a very wild fellow, having tried his hand at various trades, and given them all up, offended a wealthy relative.

To punish this idleness, his relative entailed all his large estates upon eleven different people, after whom he gave it to this Richard Babbage, who, had there been no entail, would have taken them as heir-at-law.

Ten of these lives had dropped, and the eleventh was in a consumption, when Richard Babbage took it into his head to go off to America with Bamfylde Moore Carew, the King of the Beggars.

The last only of the eleven lives existed when he embarked, and that life expired within twelve months after Richard Babbage sailed. The estates remained in possession of the rep­re­sen­ta­tives of the eleventh in the entail. {6}

If it could have been proved that Richard Babbage had survived twelve months after his voyage to America, these estates would have remained in my own branch of the family.

I possess a letter from Richard Babbage, dated on board the ship in which he sailed for America.

〈ACT OF PARLIAMENT.〉

In the year 1773 it became necessary to sell a portion of this property, for the purpose of building a church at Ashbrenton. A private Act of Parliament was passed for that purpose, in which the rights of the true heir were reserved.

CHAPTER II. CHILDHOOD.

“The Prince of Darkness is a gentleman.”—Hamlet.

Early Passion for inquiry and inquisition into Toys — Lost on London Bridge — Supposed value of the young Phi­los­o­pher — Found again — Strange Coincidence in after-years — Poisoned — Frightened a Schoolfellow by a Ghost — Frightened himself by trying to raise the Devil — Effect of Want of Occupation for the Mind — Treasure-trove — Death and Non-appearance of a Schoolfellow.

FROM my earliest years I had a great desire to inquire into the causes of all those little things and events which astonish the childish mind. At a later period I commenced the still more important inquiry into those laws of thought and those aids which assist the human mind in passing from received knowledge to that other knowledge then unknown to our race. I now think it fit to record some of those views to which, at various periods of my life, my reasoning has led me. Truth only has been the object of my search, and I am not conscious of ever having turned aside in my inquiries from any fear of the conclusions to which they might lead.

As it may be interesting to some of those who will hereafter read these lines, I shall briefly mention a few events of my earliest, and even of my childish years. My parents being born at a certain period of history, and in a certain latitude and longitude, of course followed the religion {8} of their country. They brought me up in the Protestant form of the Christian faith. My excellent mother taught me the usual forms of my daily and nightly prayer; and neither in my father nor my mother was there any mixture of bigotry and intolerance on the one hand, nor on the other of that unbecoming and familiar mode of addressing the Almighty which afterwards so much disgusted me in my youthful years.

My invariable question on receiving any new toy, was “Mamma, what is inside of it?” Until this information was obtained those around me had no repose, and the toy itself, I have been told, was generally broken open if the answer did not satisfy my own little ideas of the “fitness of things.”

Earliest Recollections.

Two events which impressed themselves forcibly on my memory happened, I think, previously to my eighth year.

〈THE YOUNG PHI­LOS­O­PHER LOST.〉

When about five years old, I was walking with my nurse, who had in her arms an infant brother of mine, across London Bridge, holding, as I thought, by her apron. I was looking at the ships in the river. On turning round to speak to her, I found that my nurse was not there, and that I was alone upon London Bridge. My mother had always impressed upon me the necessity of great caution in passing any street-crossing: I went on, therefore, quietly until I reached Tooley Street, where I remained watching the passing vehicles, in order to find a safe opportunity of crossing that very busy street.

〈THE CRI­ER OF­FERS A RE­WARD.〉

In the mean time the nurse, having lost one of her charges, had gone to the crier, who proceeded immediately to call, by the ringing of his bell, the attention of the public to the fact that a young phi­los­o­pher was lost, and to the still more important fact that five shillings would be the reward of his fortunate discoverer. I well remember sitting on the steps of {9} the door of the linendraper’s shop on the opposite corner of Tooley Street, when the gold-laced crier was making proclamation of my loss; but I was too much occupied with eating some pears to attend to what he was saying.

The fact was, that one of the men in the linendraper’s shop, observing a little child by itself, went over to it, and asked what it wanted. Finding that it had lost its nurse, he brought it across the street, gave it some pears, and placed it on the steps at the door: having asked my name, the shopkeeper found it to be that of one of his own customers. He accordingly sent off a messenger, who announced to my mother the finding of young Pickle before she was aware of his loss.

Those who delight in observing coincidences may perhaps account for the following singular one. Several years ago when the houses in Tooley Street were being pulled down, I believe to make room for the new railway terminus, I happened to pass along the very spot on which I had been lost in my infancy. A slate of the largest size, called a Duchess,[2] was thrown from the roof of one of the houses, and penetrated into the earth close to my feet.

[2] There exists an aristocracy even amongst slates, perhaps from their occupying the most elevated position in every house. Small ones are called Ladies, a larger size Countesses, and the biggest of all are Duchesses.

The other event, which I believe happened some time after the one just related, is as follows. I give it from memory, as I have always repeated it.

〈YOUNG PHI­LOS­O­PHER POISONED.〉

I was walking with my nurse and my brother in a public garden, called Mont­pel­ier Gar­dens, in Wal­worth. On returning through the private road leading to the gardens, I gathered and swallowed some dark berries very like black currants:—these were poisonous. {10}

On my return home, I recollect being placed between my father’s knees, and his giving me a glass of castor oil, which I took from his hand.

My father at that time possessed a collection of pictures. He sat on a chair on the right hand side of the chimney-piece in the breakfast room, under a fine picture of our Saviour taken down from the cross. On the opposite wall was a still-celebrated “Interior of Antwerp Cathedral.”

In after-life I several times mentioned the subject both to my father and to my mother; but neither of them had the slightest recollection of the matter.

Having suffered in health at the age of five years, and again at that of ten by violent fevers, from which I was with difficulty saved, I was sent into Devonshire and placed under the care of a clergyman (who kept a school at Alphington, near Exeter), with in­struc­tions to attend to my health; but, not to press too much knowledge upon me: a mission which he faithfully accomplished. Perhaps great idleness may have led to some of my childish reasonings.

Relations of ghost stories often circulate amongst children, and also of visitations from the devil in a personal form. Of course I shared the belief of my comrades, but still had some doubts of the existence of these personages, although I greatly feared their appearance. Once, in conjunction with a companion, I frightened another boy, bigger than myself, with some pretended ghost; how prepared or how represented by natural objects I do not now remember: I believe it was by the accidental passing shadows of some external objects upon the walls of our common bedroom.

〈DELUDES A BOY WITH A GHOST.〉

The effect of this on my playfellow was painful; he was much frightened for several days; and it naturally occurred to me, after some time, that as I had deluded him with ghosts, {11} I might myself have been deluded by older persons, and that, after all, it might be a doubtful point whether ghost or devil ever really existed. I gathered all the information I could on the subject from the other boys, and was soon informed that there was a peculiar process by which the devil might be raised and become personally visible. I carefully collected from the traditions of different boys the visible forms in which the Prince of Darkness had been recorded to have appeared. Amongst them were—

• A rabbit,
• An owl,
• A black cat, very frequently,
• A raven,
• A man with a cloven foot, also frequent.

After long thinking over the subject, although checked by a belief that the inquiry was wicked, my curiosity at length over-balanced my fears, and I resolved to attempt to raise the devil. Naughty people, I was told, had made written compacts with the devil, and had signed them with their names written in their own blood. These had become very rich and great men during their life, a fact which might be well known. But, after death, they were described as having suffered and continuing to suffer physical torments throughout eternity, another fact which, to my uninstructed mind, it seemed difficult to prove.

As I only desired an interview with the gentleman in black simply to convince my senses of his existence, I declined adopting the legal forms of a bond, and preferred one more resembling that of leaving a visiting card, when, if not at home, I might expect the sat­is­fac­tion of a return of the visit by the devil in person. {12}

〈TRIES TO RAISE THE DEVIL.〉

Accordingly, having selected a promising locality, I went one evening towards dusk up into a deserted garret. Having closed the door, and I believe opened the window, I proceeded to cut my finger and draw a circle on the floor with the blood which flowed from the incision.

I then placed myself in the centre of the circle, and either said or read the Lord’s Prayer backwards. This I accomplished at first with some trepidation and in great fear towards the close of the scene. I then stood still in the centre of that magic and superstitious circle, looking with intense anxiety in all directions, especially at the window and at the chimney. Fortunately for myself, and for the reader also, if he is interested in this narrative, no owl or black cat or unlucky raven came into the room.

In either case my then weakened frame might have expiated this foolish experiment by its own extinction, or by the alienation of that too curious spirit which controlled its feeble powers.

〈EXPERIMENTAL RELIGION.〉

After waiting some time for my expected but dreaded visitor, I, in some degree, recovered my self-possession, and leaving the circle of my incantation, I gradually opened the door and gently closing it, descended the stairs, at first slowly, and by degrees much more quickly. I then rejoined my companions, but said nothing whatever of my recent attempt. After supper the boys retired to bed. When we were in bed and the candle removed, I proceeded as usual to repeat my prayers silently to myself. After the few first sentences of the Lord’s Prayer, I found that I had forgotten a sentence, and could not go on to the conclusion. This alarmed me very much, and having repeated another prayer or hymn, I remained long awake, and very unhappy. I thought that this forgetfulness was a punishment inflicted {13} upon me by the Almighty, and that I was a wicked little boy for having attempted to satisfy myself about the existence of a devil. The next night my memory was more faithful, and my prayers went on as usual. Still, however, I was unhappy, and continued to brood over the inquiry. My uninstructed faculties led me from doubts of the existence of a devil to doubts of the book and the religion which asserted him to be a living being. My sense of justice (whether it be innate or acquired) led me to believe that it was impossible that an almighty and all-merciful God could punish me, a poor little boy, with eternal torments because I had anxiously taken the only means I knew of to verify the truth or falsehood of the religion I had been taught. I thought over these things for a long time, and, in my own childish mind, wished and prayed that God would tell me what was true. After long meditation, I resolved to make an experiment to settle the question. I thought, if it was really of such immense importance to me here and hereafter to believe rightly, that the Almighty would not consign me to eternal misery because, after trying all means that I could devise, I was unable to know the truth. I took an odd mode of making the experiment; I resolved that at a certain hour of a certain day I would go to a certain room in the house, and that if I found the door open, I would believe the Bible; but that if it were closed, I should conclude that it was not true. I remember well that the ob­ser­va­tion was made, but I have no recollection as to the state of the door. I presume it was found open from the circumstance that, for many years after, I was no longer troubled by doubts, and indeed went through the usual religious forms with very little thought about their origin.

〈DISCOVERY OF GOLD.〉

At length, as time went on, my bodily health was restored {14} by my native air: my mind, however, receiving but little in­struc­tion, began, I imagine, to prey upon itself—such at least I infer to have been the case from the following circumstance. One day, when uninterested in the sports of my little companions, I had retired into the shrubbery and was leaning my head, supported by my left arm, upon the lower branch of a thorn-tree. Listless and unoccupied, I imagined I had a head-ache. After a time I perceived, lying on the ground just under me, a small bright bit of metal. I instantly seized the precious discovery, and turning it over, examined both sides. I immediately concluded that I had discovered some valuable treasure, and running away to my deserted companions, showed them my golden coin. The little company became greatly excited, and declared that it must be gold, and that it was a piece of money of great value. We ran off to get the opinion of the usher; but whether he partook of the delusion, or we acquired our knowledge from the higher authority of the master, I know not. I only recollect the entire dissipation of my head-ache, and then my ultimate great disappointment when it was pronounced, upon the undoubted authority of the village doctor, that the square piece of brass I had found was a half-dram weight which had escaped from the box of a pair of medical scales. This little incident had an important effect upon my after-life. I reflected upon the extraordinary fact, that my head-ache had been entirely cured by the discovery of the piece of brass. Although I may not have put into words the principle, that occupation of the mind is such a source of pleasure that it can relieve even the pain of a head-ache; yet I am sure it practically gave an additional stimulus to me in many a difficult inquiry. Some few years after, when suffering under a form of tooth-ache, not acute though tediously {15} wearing, I often had recourse to a volume of Don Quixote, and still more frequently to one of Robinson Crusoe. Although at first it required a painful effort of attention, yet it almost always happened, after a time, that I had forgotten the moderate pain in the overpowering interest of the novel.

〈COMPACT TO APPEAR AFTER DEATH.〉

My most intimate companion and friend was a boy named Dacres, the son of Admiral Richard Dacres. We had often talked over such questions as those I have mentioned in this chapter, and we had made an agreement that whichever died first should, if possible, appear to the other after death, in order to satisfy the survivor about their solution.

After a year or two my young friend entered the navy, but we kept up our friendship, and when he was ashore I saw him frequently. He was in a ship of eighty guns at the passage of the Dardanelles, under the command of Sir Thomas Duckworth. Ultimately he was sent home in charge of a prize-ship, in which he suffered the severest hardships during a long and tempestuous voyage, and then died of consumption.

I saw him a few days before his death, at the age of about eighteen. We talked of former times, but neither of us mentioned the compact. I believe it occurred to his mind: it was certainly strongly present to my own.

〈DID NOT APPEAR.〉

He died a few days after. On the evening of that day I retired to my own room, which was partially detached from the house by an intervening conservatory. I sat up until after midnight, endeavouring to read, but found it impossible to fix my attention on any subject, except the overpowering feeling of curiosity, which absorbed my mind. I then undressed and went into bed; but sleep was entirely banished. I had previously carefully examined whether any cat, bird, or living animal might be accidentally concealed in my room, {16} and I had studied the forms of the furniture lest they should in the darkness mislead me.

I passed a night of perfect sleeplessness. The distant clock and a faithful dog, just outside my own door, produced the only sounds which disturbed the intense silence of that anxious night.

CHAPTER III. BOYHOOD.

Taken to an Exhibition of Mechanism — Silver Ladies — School near London — Unjustly punished — Injurious Effect — Ward’s Young Mathematician’s Guide — Got up in the Night to Study — Frederick Marryat interrupts — Treaty of Peace — Found out — Strange Effect of Treacle and Cognac on Boys — Taught to write Sermons under the Rev. Charles Simeon.

DURING my boyhood my mother took me to several exhibitions of machinery. I well remember one of them in Hanover Square, by a man who called himself Merlin. I was so greatly interested in it, that the Exhibitor remarked the circumstance, and after explaining some of the objects to which the public had access, proposed to my mother to take me up to his workshop, where I should see still more wonderful automata. We accordingly ascended to the attic. There were two uncovered female figures of silver, about twelve inches high.

One of these walked or rather glided along a space of about four feet, when she turned round and went back to her original place. She used an eye-glass oc­ca­sion­al­ly, and bowed frequently, as if recognizing her acquaintances. The motions of her limbs were singularly graceful.

The other silver figure was an admirable danseuse, with a bird on the fore finger of her right hand, which wagged its tail, flapped its wings, and opened its beak. This lady attitudinized in a most fascinating manner. Her eyes were full of imagination, and irresistible. {18}

These silver figures were the chef-d’œuvres of the artist: they had cost him years of unwearied labour, and were not even then finished.

After I left Devonshire I was placed at a school in the neighbourhood of London, in which there were about thirty boys.

〈UNJUST PUNISHMENT.〉

My first experience was unfortunate, and prob­a­bly gave an un­fa­vour­a­ble turn to my whole career during my residence of three years.

After I had been at school a few weeks, I went with one of my companions into the play-ground in the dusk of the evening. We heard a noise, as of people talking in an orchard at some distance, which belonged to our master. As the orchard had recently been robbed, we thought that thieves were again at work. We accordingly climbed over the boundary wall, ran across the field, and saw in the orchard beyond a couple of fellows evidently running away. We pursued as fast as our legs could carry us, and just got up to the supposed thieves at the ditch on the opposite side of the orchard.

A roar of laughter then greeted us from two of our own companions, who had entered the orchard for the purpose of getting some manure for their flowers out of a rotten mulberry-tree. These boys were aware of our mistake, and had humoured it.

We now returned all together towards the play-ground, when we met our master, who immediately pronounced that we were each fined one shilling for being out of bounds. We two boys who had gone out of bounds to protect our master’s property, and who if thieves had really been there would probably have been half-killed by them, attempted to remonstrate and explain the case; but all {19} remonstrance was vain, and we were accordingly fined. I never forgot that injustice.

The school-room adjoined the house, but was not directly connected with it. It contained a library of about three hundred volumes on various subjects, generally very well selected; it also contained one or two works on subjects which do not usually attract at that period of life. I derived much advantage from this library; and I now mention it because I think it of great importance that a library should exist in every school-room.

〈NIGHT WORK.〉

Amongst the books was a treatise on Algebra, called “Ward’s Young Mathematician’s Guide.” I was always partial to my arithmetical lessons, but this book attracted my particular attention. After I had been at this school for about a twelvemonth, I proposed to one of my school-fellows, who was of a studious habit, that we should get up every morning at three o’clock, light a fire in the school-room, and work until five or half-past five. We accomplished this pretty regularly for several months. Our plan had, however, become partially known to a few of our companions. One of these, a tall boy, bigger than ourselves, having heard of it, asked me to allow him to get up with us, urging that his sole object was to study, and that it would be of great importance to him in after-life. I had the cruelty to refuse this very reasonable request. The subject has often recurred to my memory, but never without regret.

〈RIVAL COMPETITORS.〉

Another of my young companions, Frederick Marryat,[3] made the same request, but not with the same motive. I told him we got up in order to work; that he would only play, and that we should then be found out. After some time, having exhausted all his arguments, Marryat told me he was {20} determined to get up, and would do it whether I liked it or not.

[3] Afterwards Captain Marryat.

Marryat slept in the same room as myself: it contained five beds. Our room opened upon a landing, and its door was exactly opposite that of the master. A flight of stairs led up to a passage just over the room in which the master and mistress slept. Passing along this passage, another flight of stairs led down, on the other side of the master’s bed-room, to another landing, from which another flight of stairs led down to the external door of the house, leading by a long passage to the school-room.

Through this devious course I had cautiously threaded my way, calling up my companion in his room at the top of the last flight of stairs, almost every night for several months.

One night on trying to open the door of my own bed-room, I found Marryat’s bed projecting a little before the door, so that I could not open it. I perceived that this was done purposely, in order that I might awaken him. I therefore cautiously, and by degrees, pushed his bed back without awaking him, and went as usual to my work. This occurred two or three nights successively.

One night, however, I found a piece of pack-thread tied to the door lock, which I traced to Marryat’s bed, and concluded it was tied to his arm or hand. I merely untied the cord from the lock, and passed on.

A few nights after I found it impossible to untie the cord, so I cut it with my pocket-knife. The cord then became thicker and thicker for several nights, but still my pen-knife did its work.

〈VARIOUS STRATAGEMS.〉

One night I found a small chain fixed to the lock, and passing thence into Marryat’s bed. This defeated my efforts for that night, and I retired to my own bed. The next night {21} I was provided with a pair of plyers, and unbent one of the links, leaving the two portions attached to Marryat’s arm and to the lock of the door. This occurred several times, varying by stouter chains, and by having a padlock which I could not pick in the dark.

At last one morning I found a chain too strong for the tools I possessed; so I retired to my own bed, defeated. The next night, however, I provided myself with a ball of packthread. As soon as I heard by his breathing that Marryat was asleep, I crept over to the door, drew one end of my ball of packthread through a link of the too-powerful chain, and bringing it back with me to bed, gave it a sudden jerk by pulling both ends of the packthread passing through the link of the chain.

Marryat jumped up, put out his hand to the door, found his chain all right, and then lay down. As soon as he was asleep again, I repeated the operation. Having awakened him for the third time, I let go one end of the string, and drew it back by the other, so that he was unable at daylight to detect the cause.

At last, however, I found it expedient to enter into a treaty of peace, the basis of which was that I should allow Marryat to join the night party; but that nobody else should be admitted. This continued for a short time; but, one by one, three or four other boys, friends of Marryat, joined our party, and, as I had anticipated, no work was done. We all got to play; we let off fire-works in the play-ground, and were of course discovered.

〈FOUND OUT.〉

Our master read us a very grave lecture at breakfast upon the impropriety of this irregular system of turning night into day, and pointed out its injurious effects upon the health. This, he said, was so remarkable that he could distinguish by {22} their pallid countenances those who had taken part in it. Now he certainly did point out every boy who had been up on the night we were detected. But it appeared to me very odd that the same means of judging had not enabled him long before to discover the two boys who had for several months habitually practised this system of turning night into day.

Another of our pranks never received its solution in our master’s mind; indeed I myself scarcely knew its early history. Somehow or other, a Russian young gentleman, who was a parlour-boarder, had I believe, expatiated to Marryat on the virtues of Cognac.

One evening my friend came to me with a quart bottle of what he called excellent stuff. A council was held amongst a few of us boys to decide how we should dispose of this treasure. I did not myself much admire the liquid, but suggested that it might be very good when mixed up with a lot of treacle. This thought was unanimously adopted, and a subscription made to purchase the treacle. Having no vessel sufficiently large to hold the intended mixture, I proposed to take one of our garden-pots, stopping up the hole in its bottom with a cork.

A good big earthen vessel, thus extemporised, was then filled with this wonderful mixture. A spoon or two, an oyster-shell, and various other contrivances delivered it to its numerous consumers, and all the boys got a greater or less share, according to their taste for this extraordinary liqueur.

The feast was over, the garden-pot was restored to its owner, and the treacled lips of the boys had been wiped with their handkerchiefs or on their coat-sleeves, when the bell announced that it was prayer-time. We all knelt in silence at our respective desks. As soon as the prayers were over, one of the oddest scenes occurred. {23}

〈EFFECT OF COGNAC.〉

Many boys rose up from their knees—but some fell down again. Some turned round several times, and then fell. Some turned round so often that they resembled spinning dervishes. Others were only more stupid than usual; some complained of being sick; many were very sleepy; others were sound asleep, and had to be carried to bed; some talked fast and heroically, two attempted psalmody, but none listened.

All investigation at the time was useless: we were sent off to bed as quickly as possible. It was only known that Count Cognac had married the sweet Miss Treacle, whom all the boys knew and loved, and who lodged at the grocer’s, in the neighbouring village. But I believe neither the pedigree of the bridegroom nor his domicile were ever discovered. It is probable that he was of French origin, and dwelt in a cellar.

After I left this school I was for a few years under the care of an excellent clergyman in the neighbourhood of Cambridge. There were only six boys; but I fear I did not derive from it all the advantage that I might have done. I came into frequent contact with the Rev. Charles Simeon, and with many of his enthusiastic disciples. Every Sunday I had to write from memory an abstract of the sermon he preached in our village. Even at that period of my life I had a taste for generalization. Accordingly, having generalized some of Mr. Simeon’s sermons up to a kind of skeleton form, I tried, by way of experiment, to fill up such a form in a sermon of my own composing from the text of “Alexander the coppersmith hath done us much harm.” As well as I remember, there were in my sermon some queer deductions from this text; but then they fulfilled all the usual conditions of our sermons: so thought also two of my companions to whom I communicated in confidence this new man­u­fac­ture. {24}

〈COMPOSES SERMONS.〉

By some unexplained circumstance my sermon relating to copper being isomorphous with Simeon’s own productions, got by substitution into the hands of our master as the recollections of one of the other boys. Thereupon arose an awful explosion which I decline to paint.

I did, however, learn something at this school, for I observed a striking illustration of the Economy of Man­u­fac­tures. Mr. Simeon had the cure of a very wicked parish in Cambridge, whilst my instructor held that of a tolerably decent country village. If each minister had stuck to the in­struc­tion of his own parish, it would have necessitated the man­u­fac­ture of four sermons per week, whilst, by this beneficial interchange of duties, only two were required.

Each congregation enjoyed also another advantage from this arrangement—the advantage of variety, which, when moderately indulged in, excites the appetite.

CHAPTER IV. CAMBRIDGE.

Universal Language — Purchase Lacroix’s Quarto Work on the Integral Calculus — Disappointment on getting no explanation of my Math­e­mat­i­cal Difficulties — Origin of the Analytical Society — The Ghost Club — Chess — Sixpenny Whist and Guinea Whist — Boating — Chemistry — Elected Lucasian Professor of Mathematics in 1828.

MY father, with a view of acquiring some information which might be of use to me at Cambridge, had consulted a tutor of one of the colleges, who was passing his long vacation at the neighbouring watering-place, Teignmouth. He dined with us frequently. The advice of the Rev. Doctor was quite sound, but very limited. It might be summed up in one short sentence: “Advise your son not to purchase his wine in Cambridge.”

Previously to my entrance at Trinity College, Cambridge, I resided for a time at Totnes, under the guidance of an Oxford tutor, who undertook to superintend my classical studies only.

During my residence at this place I accidentally heard, for the first time, of an idea of forming a universal language. I was much fascinated by it, and, soon after, proceeded to write a kind of grammar, and then to devise a dictionary. Some trace of the former, I think, I still possess: but I was stopped in my idea of making a universal dictionary by the apparent impossibility of arranging signs in any consecutive {26} order, so as to find, as in a dictionary, the meaning of each when wanted. It was only after I had been some time at Cambridge that I became acquainted with the work of “Bishop Wilkins on Universal Language.”

Being passionately fond of algebra, I had instructed myself by means of Ward’s “Young Mathematician’s Guide,” which had casually fallen into my hands at school. I now employed all my leisure in studying such math­e­mat­i­cal works as accident brought to my knowledge. Amongst these were Humphrey Ditton’s “Fluxions,” of which I could make nothing; Madame Agnesi’s “Analytical Institutions,” from which I acquired some knowledge; Woodhouse’s “Principles of Analytical Calculation,” from which I learned the notation of Leibnitz; and Lagrange’s “Théorie des Fonctions.” I possessed also the Fluxions of Maclaurin and of Simpson.

Thus it happened that when I went to Cambridge I could work out such questions as the very moderate amount of mathematics which I then possessed admitted, with equal facility, in the dots of Newton, the d’s of Leibnitz, or the dashes of Lagrange. I had, however, met with many difficulties, and looked forward with intense delight to the certainty of having them all removed on my arrival at Cambridge. I had in my imagination formed a plan for the institution amongst my future friends of a chess club, and also of another club for the discussion of math­e­mat­i­cal subjects.

〈PURCHASE THE WORK OF LACROIX.〉

In 1811, during the war, it was very difficult to procure foreign books. I had heard of the great work of Lacroix, on the “Differential and Integral Calculus,” which I longed to possess, and being misinformed that its price was two guineas, I resolved to purchase it in London on my passage to Cambridge. As soon as I arrived I went to the French {27} bookseller, Dulau, and to my great surprise found that the price of the book was seven guineas. After much thought I made the costly purchase, went on immediately to Cambridge, saw my tutor, Hudson, got lodgings, and then spent the greater part of the night in turning over the pages of my newly-acquired purchase. After a few days, I went to my public tutor Hudson, to ask the explanation of one of my math­e­mat­i­cal difficulties. He listened to my question, said it would not be asked in the Senate House, and was of no sort of consequence, and advised me to get up the earlier subjects of the university studies.

〈DIFFICULTIES NOT ANSWERED.〉

After some little while I went to ask the explanation of another difficulty from one of the lecturers. He treated the question just in the same way. I made a third effort to be enlightened about what was really a doubtful question, and felt satisfied that the person I addressed knew nothing of the matter, although he took some pains to disguise his ignorance.

I thus acquired a distaste for the routine of the studies of the place, and devoured the papers of Euler and other mathematicians, scattered through innumerable volumes of the academies of Petersburgh, Berlin, and Paris, which the libraries I had recourse to contained.

Under these circumstances it was not surprising that I should perceive and be penetrated with the superior power of the notation of Leibnitz.

At an early period, probably at the commencement of the second year of my residence at Cambridge, a friend of mine, Michael Slegg, of Trinity, was taking wine with me, discussing math­e­mat­i­cal subjects, to which he also was enthusiastically attached. Hearing the chapel bell ring, he took leave of me, promising to return for a cup of coffee. {28}

〈RESULT OF BIBLE SOCIETY.〉

At this period Cambridge was agitated by a fierce controversy. Societies had been formed for printing and circulating the Bible. One party proposed to circulate it with notes, in order to make it intelligible; whilst the other scornfully rejected all explanations of the word of God as profane attempts to mend that which was perfect.

The walls of the town were placarded with broadsides, and posters were sent from house to house. One of the latter form of advertisement was lying upon my table when Slegg left me. Taking up the paper, and looking through it, I thought it, from its exaggerated tone, a good subject for a parody.

I then drew up the sketch of a society to be instituted for translating the small work of Lacroix on the Differential and Integral Lacroix. It proposed that we should have periodical meetings for the propagation of d’s; and consigned to perdition all who supported the heresy of dots. It maintained that the work of Lacroix was so perfect that any comment was unnecessary.

On Slegg’s return from chapel I put the parody into his hands. My friend enjoyed the joke heartily, and at parting asked my permission to show the parody to a math­e­mat­i­cal friend of his, Mr. Bromhead.[4]

The next day Slegg called on me, and said that he had put the joke into the hand of his friend, who, after laughing heartily, remarked that it was too good a joke to be lost, and proposed seriously that we should form a society for the cultivation of mathematics.

〈ANALYTICAL SOCIETY.〉

The next day Bromhead called on me. We talked the subject over, and agreed to hold a meeting at his lodgings {29} for the purpose of forming a society for the promotion of analysis.

At that meeting, besides the projectors, there were present Herschel, Peacock, D’Arblay,[5] Ryan,[6] Robinson,[7] Frederick Maule,[8] and several others. We constituted ourselves “The Analytical Society;” hired a meeting-room, open daily; held meetings, read papers, and discussed them. Of course we were much ridiculed by the Dons; and, not being put down, it was darkly hinted that we were young infidels, and that no good would come of us.

In the meantime we quietly pursued our course, and at last resolved to publish a volume of our Transactions. Owing to the illness of one of the number, and to various other circumstances, the volume which was published was entirely contributed by Herschel and myself.

At last our work was printed, and it became necessary to decide upon a title. Recalling the slight imputation which had been made upon our faith, I suggested that the most appropriate title would be—

The Principles of pure D-ism in opposition to the Dot-age of the University.[9]

[4] Afterwards Sir Edward Ffrench Bromhead, Bart., the author of an interesting paper in the Transactions of the Royal Society.

[5] The only son of Madame D’Arblay.

[6] Now the Right Honourable Sir Edward Ryan.

[7] The Rev. Dr. Robinson, Master of the Temple.

[8] A younger brother of the late Mr. Justice Maule.

[9] Leibnitz indicated fluxions by a d, Newton by a dot.

〈ELECTED LUCASIAN PROFESSOR.〉

In thus reviving this wicked pun, I ought at the same time to record an instance of forgiveness unparalleled in history. Fourteen years after, being then at Rome, I accidentally read in Galignani’s newspaper the following paragraph, dated Cambridge:—“Yesterday the bells of St. Mary rang on the election of Mr. Babbage as Lucasian Professor of Mathematics.” {30}

If this event had happened during the lifetime of my father, it would have been most gratifying to myself, because, whilst it would have given him much pleasure, it would then also have afforded intense delight to my mother.

I concluded that the next post would bring me the official confirmation of this report, and after some consideration I sketched the draft of a letter, in which I proposed to thank the University sincerely for the honour they had done me, but to decline it.

This sketch of a letter was hardly dry when two of my intimate friends, the Rev. Mr. Lunn and Mr. Beilby Thompson,[10] who resided close to me in the Piazza del Populo, came over to congratulate me on the appointment. I showed them my proposed reply, against which they earnestly protested. Their first, and as they believed their strongest, reason was that it would give so much pleasure to my mother. To this I answered that my mother’s opinion of her son had been confirmed by the reception he had met with in every foreign country he had visited, and that this, in her estimation, would add but little to it. To their next argument I had no sat­is­fac­tory answer. It was that this election could not have occurred unless some friends of mine in England had taken active measures to promote it; that some of these might have been personal friends, but that many others might have exerted themselves entirely upon principle, and that it would be harsh to disappoint such friends, and reject such a compliment.

[10] Afterwards Lord Wenlock.

My own feelings were of a mixed nature. I saw the vast field that the Difference Engine had opened out; for, before I left England in the previous year, I had extended its mechanism to the tabulation of functions having no constant {31} difference, and more par­tic­u­lar­ly I had arrived at the knowledge of the entire command it would have over the computation of the most important classes of tables, those of astronomy and of navigation. I was also most anxious to give my whole time to the completion of the mechanism of the Difference Engine No. 1 which I had then in hand. Small as the admitted duties of the Lucasian Chair were, I felt that they would absorb time which I thought better devoted to the completion of the Difference Engine. If I had then been aware that the lapse of a few years would have thrown upon me the enormous labour which the Analytical Engine absorbed, no motive short of absolute necessity would have induced me to accept any office which might, in the slightest degree, withdraw my attention from its contrivance.

The result of this consultation with my two friends was, that I determined to accept the Chair of Newton, and to hold it for a few years. In 1839 the demands of the Analytical Engine upon my attention had become so incessant and so exhausting, that even the few duties of the Lucasian Chair had a sensible effect in impairing my bodily strength. I therefore sent in my resignation.

〈FIRST EXAMINATION.〉

In January, 1829, I visited Cambridge, to fulfil one of the first duties of my new office, the examination for Dr. Smith’s prizes.

These two prizes, of twenty-five pounds each, exercise a very curious and important influence. Usually three or four hundred young men are examined previously to taking their degree. The University officers examine and place them in the order of their math­e­mat­i­cal merit. The class called Wranglers is the highest; of these the first is called the senior wrangler, the others the second and third, &c., wranglers. {32}

All the young men who have just taken their degree, whether with or without honours, are qualified to compete for the Smith’s prizes by sending in notice to the electors, who consist of the three Professors of Geometry, Astronomy, and Physics, assisted oc­ca­sion­al­ly by two official electors, the Vice-Chancellor and the Master of Trinity College. However, in point of fact, generally three, and rarely above six young men compete.

〈COURT OF APPEAL.〉

It is manifest that the University officers, who examine several hundred young men, cannot bestow the same minute attention upon each as those who, at the utmost, only examine six. Nor is this of any importance, except to the few first wranglers, who usually are candidates for these prizes. The consequence is that the examiners of the Smith’s prizes constitute, as it were, a court of appeal from the decision of the University officers. The decision of the latter is thus therefore, necessarily appealed against upon every occasion. Perhaps in one out of five or six cases the second or third wrangler obtains the first Smith’s prize. I may add that in the few cases known to me previously to my becoming an examiner, the public opinion of the University always approved those decisions, without implying any censure on the officers of the University.

In forming my set of questions, I consulted the late Dean of Ely and another friend, in order that I might not suddenly deviate too much from the usual style of examinations.

After having examined the young men, I sat up the whole night, carefully weighing the relative merits of their answers. I found, with some mortification, that, according to my marks, the second wrangler ought to have the first prize. I therefore put aside the papers until the day before the decision. I then took an unmarked copy of my questions, and put new {33} numbers for their respective values. After very carefully going over the whole of the examination-papers again, I arrived almost exactly at my former conclusion.

〈REMARKABLE AGREEMENT.〉

On our meeting at the Vice-Chancellor’s, that functionary asked me, as the senior professor, what was my decision as to the two prizes. I stated that the result of my examination obliged me to award the first prize to the second wrangler. Professor Airy was then asked the same question. He made the same reply. Professor Lax being then asked, said he had arrived at the same conclusion as his two colleagues.

The Vice-Chancellor remarked that when we altered the arrangement of the University Examiners, it was very sat­is­fac­tory that we should be unanimous. Professor Airy observed that this sat­is­fac­tion was enhanced by the fact of the remarkable difference in the tastes of the three examiners.

The Vice-Chancellor, turning to me, asked whether it might be permitted to inquire the numbers we had respectively assigned to each candidate.

I and my colleagues immediately mentioned our numbers, which Professor Airy at once reduced to a common scale. On this it appeared that the number of marks assigned to each by Professor Airy and myself very nearly agreed, whilst that of Professor Lax differed but little.

On this occasion the first Smith’s prize was assigned to the second wrangler, Mr. Cavendish, now Duke of Devonshire, the present Chancellor of the University.

The result of the whole of my after-experience showed that amongst the highest men the peculiar tastes of the examiners had no effect in disturbing the proper decision.

I held the Chair of Newton for some few years, and still feel deeply grateful for the honour the University conferred {34} upon me—the only honour I ever received in my own country.[11]

[11] This professorship is not in the gift of the Government. The electors are the masters of the various colleges. It was founded in 1663 by Henry Lucas, M.P. for the University, and was endowed by him with a small estate in Bedfordshire. During my tenure of that office my net receipts were between 80 l. and 90 l. a year. I am glad to find that the estate is now improved, and that the University have added an annual salary to the Chair of Newton.

I must now return to my pursuits during my residence at Cambridge, the account of which has been partially interrupted by the history of my appointment to the Chair of Newton.

Whilst I was an undergraduate, I lived probably in a greater variety of sets than any of my young companions. But my chief and choicest consisted of some ten or a dozen friends who usually breakfasted with me every Sunday after chapel; arriving at about nine, and remaining to between twelve and one o’clock. We discussed all knowable and many unknowable things.

〈GHOST CLUB—EXTRACTORS.〉

At one time we resolved ourselves into a Ghost Club, and proceeded to collect evidence, and entered into a considerable correspondence upon the subject. Some of this was both interesting and instructive.

At another time we resolved ourselves into a Club which we called The Extractors. Its rules were as follows,—

• 1st. Every member shall communicate his address to the Secretary once in six months.
• 2nd. If this communication is delayed beyond twelve months, it shall be taken for granted that his relatives had shut him up as insane.
• 3rd. Every effort legal and illegal shall be made to get him out of the madhouse. Hence the name of the club—The Extractors. {35}
• 4th. Every candidate for admission as a member shall produce six certificates. Three that he is sane and three others that he is insane.

It has often occurred to me to inquire of my legal friends whether, if the sanity of any member of the club had been questioned in after-life, he would have adduced the fact of membership of the Club of Extractors as an indication of sanity or of insanity.

〈SHYNESS—CHESS.〉

During the first part of my residence at Cambridge, I played at chess very frequently, often with D’Arblay and with several other good players. There was at that period a fellow-commoner at Trinity named Brande, who devoted almost his whole time to the study of chess. I was invited to meet him one evening at the rooms of a common friend for the purpose of trying our strength.

On arriving at my friend’s rooms, I found a note informing me that he had gone to Newmarket, and had left coffee and the chessmen for us. I was myself tormented by great shyness, and my yet unseen adversary was, I understood, equally diffident. I was sitting before the chess-board when Brande entered. I rose, he advanced, sat down, and took a white and a black pawn from the board, which he held, one in either hand. I pointed with my finger to the left hand and won the move.

The game then commenced; it was rather a long one, and I won it: but not a word was exchanged until the end: when Brande uttered the first word. “Another?” To this I nodded assent.

How that game was decided I do not now remember; but the first sentence pronounced by either of us, was a remark by Brande, that he had lost the first game by a certain move of his white bishop. To this I replied, that I thought he was {36} mistaken, and that the real cause of his losing the game arose from the use I had made of my knight two moves previously to his white bishop’s move.

We then immediately began to replace the men on the board in the positions they occupied at that particular point of the game when the white bishop’s move was made. Each took up any piece indiscriminately, and placed it without hesitation on the exact square on which it had stood. It then became apparent that the effective move to which I had referred was that of my knight.

Brande, during his residence at Cambridge, studied chess regularly several hours each day, and read almost every treatise on the subject. After he left college he travelled abroad, took lessons from every celebrated teacher, and played with all the most eminent players on the Continent.

At intervals of three or four years I oc­ca­sion­al­ly met him in London. After the usual greeting he always proposed that we should play a game of chess.

I found on these occasions, that if I played any of the ordinary openings, such as are found in the books, I was sure to be beaten. The only way in which I had a chance of winning, was by making early in the game a move so bad that it had not been mentioned in any treatise. Brande possessed, and had read, almost every book upon the subject.

〈SIXPENNY WHIST.〉

Another set which I frequently joined were addicted to sixpenny whist. It consisted of Higman, afterwards Tutor of Trinity; Follet, afterwards Attorney-General; of a learned and accomplished Dean still living, and I have no doubt still playing an excellent rubber, and myself. We not unfrequently sat from chapel-time in the evening until the sound {37} of the morning chapel bell again called us to our religious duties.

I mixed oc­ca­sion­al­ly with a different set of whist players at Jesus College. They played high: guinea points, and five guineas on the rubber. I was always a most welcome visitor, not from my skill at the game; but because I never played more than shilling points and five shillings on the rubber. Consequently my partner had what they considered an advantage: namely, that of playing guinea points with one of our adversaries and pound points with the other.

〈EXPEDITIONS TO THE FENS.〉

Totally different in character was another set in which I mixed. I was very fond of boating, not of the manual labour of rowing, but the more in­tel­lec­tual art of sailing. I kept a beautiful light, London-built boat, and oc­ca­sion­al­ly took long voyages down the river, beyond Ely into the fens. To accomplish these trips, it was necessary to have two or three strong fellows to row when the wind failed or was contrary. These were useful friends upon my aquatic expeditions, but not being of exactly the same calibre as my friends of the Ghost Club, were very cruelly and disrespectfully called by them “my Tom fools.”

The plan of our voyage was thus:—I sent my servant to the apothecary for a thing called an ægrotat, which I understood, for I never saw one, meant a certificate that I was indisposed, and that it would be injurious to my health to attend chapel, or hall, or lectures. This was forwarded to the college authorities.

I also directed my servant to order the cook to send me a large well-seasoned meat pie, a couple of fowls, &c. These were packed in a hamper with three or four bottles of wine and one of noyeau. We sailed when the wind was fair, and rowed when there was none. Whittlesea Mere was a very {38} favourite resort for sailing, fishing, and shooting. Sometimes we reached Lynn. After various adventures and five or six days of hard exercise in the open air, we returned with our health more renovated than if the best physician had prescribed for us.

〈CHEMISTRY.〉

During my residence at Cambridge, Smithson Tennant was the Professor of Chemistry, and I attended his lectures. Having a spare room, I turned it into a kind of laboratory, in which Herschel worked with me, until he set up a rival one of his own. We both oc­ca­sion­al­ly assisted the Professor in preparing his experiments. The science of chemistry had not then assumed the vast development it has now attained. I gave up its practical pursuit soon after I resided in London, but I have never regretted the time I bestowed upon it at the commencement of my career. I had hoped to have long continued to enjoy the friendship of my entertaining and valued instructor, and to have profited by his introducing me to the science of the metropolis, but his tragical fate deprived me of that advantage. Whilst riding with General Bulow across a drawbridge at Boulogne, the bolt having been displaced, Smithson Tennant was precipitated to the bottom, and killed on the spot. The General, having an earlier warning, set spurs to his horse, and just escaped a similar fate.

〈TRANSLATION OF LACROIX.〉

My views respecting the notation of Leibnitz now (1812) received confirmation from an extensive course of reading. I became convinced that the notation of fluxions must ultimately prove a strong impediment to the progress of English science. But I knew, also, that it was hopeless for any young and unknown author to attempt to introduce the notation of Leibnitz into an elementary work. This opinion naturally {39} suggested to me the idea of translating the smaller work of Lacroix. It is possible, although I have no recollection of it, that the same idea may have occurred to several of my colleagues of the Analytical Society, but most of them were so occupied, first with their degree, and then with their examination for fellowships, that no steps were at that time taken by any of them on that subject.

Unencumbered by these distractions, I commenced the task, but at what period of time I do not exactly recollect. I had finished a portion of the translation, and laid it aside, when, some years afterwards, Peacock called on me in Devonshire Street, and stated that both Herschel and himself were convinced that the change from the dots to the d’s would not be accomplished until some foreign work of eminence should be translated into English. Peacock then proposed that I should either finish the translation which I had commenced, or that Herschel and himself should complete the remainder of my translation. I suggested that we should toss up which alternative to take. It was determined by lot that we should make a joint translation. Some months after, the translation of the small work of Lacroix was published.

For several years after, the progress of the notation of Leibnitz at Cambridge was slow. It is true that the tutors of the two largest colleges had adopted it, but it was taught at none of the other colleges.

〈COLLECTION OF EXAMPLES.〉

It is always difficult to think and reason in a new language, and this difficulty discouraged all but men of energetic minds. I saw, however, that, by making it their interest to do so, the change might be accomplished. I therefore proposed to make a large collection of examples of the differential and integral calculus, consisting merely of the statement of each problem and its final solution. I foresaw that if such a {40} publication existed, all those tutors who did not approve of the change of the Newtonian notation would yet, in order to save their own time and trouble, go to this collection of examples to find problems to set to their pupils. After a short time the use of the new signs would become familiar, and I anticipated their general adoption at Cambridge as a matter of course.

I commenced by copying out a large portion of the work of Hirsch. I then communicated to Peacock and Herschel my view, and proposed that they should each contribute a portion.

Peacock considerably modified my plan by giving the process of solution to a large number of the questions. Herschel prepared the questions in finite differences, and I supplied the examples to the calculus of functions. In a very few years the change was completely established; and thus at last the English cultivators of math­e­mat­i­cal science, untrammelled by a limited and imperfect system of signs, entered on equal terms into competition with their continental rivals.

CHAPTER V. DIFFERENCE ENGINE NO. 1.

“Oh no! we never mention it,

Its name is never heard.”

Difference Engine No. 1 — First Idea at Cambridge, 1812 — Plan for Dividing Astronomical Instruments — Idea of a Machine to calculate Tables by Differences — Illustrations by Piles of Cannon-balls.

CALCULATING MACHINES comprise various pieces of mechanism for assisting the human mind in executing the operations of arithmetic. Some few of these perform the whole operation without any mental attention when once the given numbers have been put into the machine.

Others require a moderate portion of mental attention: these latter are generally of much simpler construction than the former, and it may also be added, are less useful.

The simplest way of deciding to which of these two classes any calculating machine belongs is to ask its maker—Whether, when the numbers on which it is to operate are placed in the instrument, it is capable of arriving at its result by the mere motion of a spring, a descending weight, or any other constant force? If the answer be in the affirmative, the machine is really automatic; if otherwise, it is not self-acting.

Of the various machines I have had occasion to examine, many of those for Addition and Subtraction have been found {42} to be automatic. Of machines for Multiplication and Division, which have fully come under my examination, I cannot at present recall one to my memory as absolutely fulfilling this condition.

〈ORIGIN OF DIFFERENCE ENGINE.〉

The earliest idea that I can trace in my own mind of calculating arithmetical Tables by machinery arose in this manner:—

One evening I was sitting in the rooms of the Analytical Society, at Cambridge, my head leaning forward on the Table in a kind of dreamy mood, with a Table of logarithms lying open before me. Another member, coming into the room, and seeing me half asleep, called out, “Well, Babbage, what are you dreaming about?” to which I replied, “I am thinking that all these Tables (pointing to the logarithms) might be calculated by machinery.”

I am indebted to my friend, the Rev. Dr. Robinson, the Master of the Temple, for this anecdote. The event must have happened either in 1812 or 1813.

About 1819 I was occupied with devising means for accurately dividing astronomical instruments, and had arrived at a plan which I thought was likely to succeed perfectly. I had also at that time been speculating about making machinery to compute arithmetical Tables.

One morning I called upon the late Dr. Wollaston, to consult him about my plan for dividing instruments. On talking over the matter, it turned out that my system was exactly that which had been described by the Duke de Chaulnes, in the Memoirs of the French Academy of Sciences, about fifty or sixty years before. I then mentioned my other idea of computing Tables by machinery, which Dr. Wollaston thought a more promising subject.

I considered that a machine to execute the mere isolated {43} operations of arithmetic, would be comparatively of little value, unless it were very easily set to do its work, and unless it executed not only accurately, but with great rapidity, whatever it was required to do.

〈ADDITION AND CARRIAGE.〉

On the other hand, the method of differences supplied a general principle by which all Tables might be computed through limited intervals, by one uniform process. Again, the method of differences required the use of mechanism for Addition only. In order, however, to insure accuracy in the printed Tables, it was necessary that the machine which computed Tables should also set them up in type, or else supply a mould in which stereotype plates of those Tables could be cast.

I now began to sketch out arrangements for accomplishing the several partial processes which were required. The arithmetical part must consist of two distinct processes—the power of adding one digit to another, and also of carrying the tens to the next digit, if it should be necessary.

The first idea was, naturally, to add each digit successively. This, however, would occupy much time if the numbers added together consisted of many places of figures.

The next step was to add all the digits of the two numbers each to each at the same instant, but reserving a certain mechanical memorandum, wherever a carriage became due. These carriages were then to be executed successively.

Having made various drawings, I now began to make models of some portions of the machine, to see how they would act. Each number was to be expressed upon wheels placed upon an axis; there being one wheel for each figure in the number operated upon.

Having arrived at a certain point in my progress, it became necessary to have teeth of a peculiar form cut upon these {44} wheels. As my own lathe was not fit for this job, I took the wheels to a wheel-cutter at Lambeth, to whom I carefully conveyed my in­struc­tions, leaving with him a drawing as his guide.

〈UNEXPECTED DIFFICULTY EXPLAINED.〉

These wheels arrived late one night, and the next morning I began putting them in action with my other mechanism, when, to my utter astonishment, I found they were quite unfit for their task. I examined the shape of their teeth, compared them with those in the drawings, and found they agreed perfectly; yet they could not perform their intended work. I had been so certain of the truth of my previous reasoning, that I now began to be somewhat uneasy. I reflected that, if the reasoning about which I had been so certain should prove to have been really fallacious, I could then no longer trust the power of my own reason. I therefore went over with my wheels to the artist who had formed the teeth, in order that I might arrive at some explanation of this extraordinary contradiction.

On conferring with him, it turned out that, when he had understood fully the peculiar form of the teeth of wheels, he discovered that his wheel-cutting engine had not got amongst its divisions that precise number which I had required. He therefore had asked me whether another number, which his machine possessed, would not equally answer my object. I had inadvertently replied in the affirmative. He then made arrangements for the precise number of teeth I required; and the new wheels performed their expected duty perfectly.

The next step was to devise means for printing the tables to be computed by this machine. My first plan was to make it put together moveable type. I proposed to make metal boxes, each containing 3,000 types of one of the ten digits. These types were to be made to pass out one by one from the {45} bottom of their boxes, when required by the computing part of the machine.

〈VERIFICATION OF TYPE.〉

But here a new difficulty arose. The attendant who put the types into the boxes might, by mistake, put a wrong type in one or more of them. This cause of error I removed in the following manner:—There are usually certain notches in the side of the type. I caused these notches to be so placed that all the types of any given digit possessed the same char­ac­ter­is­tic notches, which no other type had. Thus, when the boxes were filled, by passing a small wire down these peculiar notches, it would be impeded in its passage, if there were included in the row a single wrong figure. Also, if any digit were accidentally turned upside down, it would be indicated by the stoppage of the testing wire.

One notch was reserved as common to every species of type. The object of this was that, before the types which the Difference Engine had used for its computation were removed from the iron platform on which they were placed, a steel wire should be passed through this common notch, and remain there. The tables, composed of moveable types, thus interlocked, could never have any of their figures drawn out by adhesion to the inking-roller, and then by possibility be restored in an inverted order. A small block of such figures tied together by a bit of string, remained unbroken for several years, although it was rather roughly used as a plaything by my children. One such box was finished, and delivered its type satisfactorily.

Another plan for printing the tables, was to place the ordinary printing type round the edges of wheels. Then, as each successive number was produced by the arithmetical part, the type-wheels would move down upon a plate of soft composition, upon which the tabular number would be {46} impressed. This mould was formed of a mixture of plaster-of-Paris with other materials, so as to become hard in the course of a few hours.

〈MOULDS AND COPPER-PLATE.〉

The first difficulty arose from the impression of one tabular number on the mould being distorted by the succeeding one.

I was not then aware that a very slight depth of impression from the type would be quite sufficient. I surmounted the difficulty by previously passing a roller, having longitudinal wedge-shaped projections, over the plastic material. This formed a series of small depressions in the matrix between each line. Thus the expansion arising from the impression of one line partially filled up the small depression or ditch which occurred between each successive line.

The various minute difficulties of this kind were successively overcome; but subsequent experience has proved that the depth necessary for stereotype moulds is very small, and that even thick paper, prepared in a peculiar manner, is quite sufficient for the purpose.

Another series of experiments were, however, made for the purpose of punching the computed numbers upon copper plate. A special machine was contrived and constructed, which might be called a co-ordinate machine, because it moved the copper plate and steel punches in the direction of three rectangular co-ordinates. This machine was afterwards found very useful for many other purposes. It was, in fact, a general shaping machine, upon which many parts of the Difference Engine were formed.

Several specimens of surface and copper-plate printing, as well as of the copper plates, produced by these means, were exhibited at the Exhibition of 1862.

I have proposed and drawn various machines for the purpose of calculating a series of numbers forming Tables {47} by means of a certain system called “The Method of Differences,” which it is the object of this sketch to explain.

The first Difference Engine with which I am acquainted comprised a few figures, and was made by myself, between 1820 and June 1822. It consisted of from six to eight figures. A much larger and more perfect engine was sub­se­quent­ly commenced in 1823 for the Government.

It was proposed that this latter Difference Engine should have six orders of differences, each consisting of about twenty places of figures, and also that it should print the Tables it computed.

The small portion of it which was placed in the International Exhibition of 1862 was put together nearly thirty years ago. It was accompanied by various parts intended to enable it to print the results it calculated, either as a single copy on paper—or by putting together moveable types—or by stereotype plates taken from moulds punched by the machine—or from copper plates impressed by it. The parts necessary for the execution of each of these processes were made, but these were not at that time attached to the calculating part of the machine.

A considerable number of the parts by which the printing was to be accomplished, as also several specimens of portions of tables punched on copper, and of stereotype moulds, were exhibited in a glass case adjacent to the Engine.

〈‘EDINBURGH REVIEW.’〉

In 1834 Dr. Lardner published, in the ‘Edinburgh Review,’[12] a very elaborate description of this portion of the machine, in which he explained clearly the method of Differences.

[12] ‘Edinburgh Review,’ No. cxx., July, 1834.

It is very singular that two persons, one resident in London, the other in Sweden, should both have been struck, on reading this review, with the simplicity of the math­e­mat­i­cal principle {48} of differences as applied to the calculation of Tables, and should have been so fascinated with it as to have undertaken to construct a machine of the kind.

〈MR. DEACON—MR. SCHEUTZ.〉

Mr. Deacon, of Beaufort House, Strand, whose mechanical skill is well known, made, for his own sat­is­fac­tion, a small model of the calculating part of such a machine, which was shown only to a few friends, and of the existence of which I was not aware until after the Swedish machine was brought to London.

Mr. Scheutz, an eminent printer at Stockholm, had far greater difficulties to encounter. The construction of mechanism, as well as the math­e­mat­i­cal part of the question, was entirely new to him. He, however, undertook to make a machine having four differences, and fourteen places of figures, and capable of printing its own Tables.

After many years’ indefatigable labour, and an almost ruinous expense, aided by grants from his Government, by the constant assistance of his son, and by the support of many enlightened members of the Swedish Academy, he completed his Difference Engine. It was brought to London, and some time afterwards exhibited at the great Exhibition at Paris. It was then purchased for the Dudley Observatory at Albany by an enlightened and public-spirited merchant of that city, John F. Rathbone, Esq.

An exact copy of this machine was made by Messrs. Donkin and Co., for the English Government, and is now in use in the Registrar-General’s Department at Somerset House. It is very much to be regretted that this specimen of English workmanship was not exhibited in the International Exhibition.

{49}

Explanation of the Difference Engine.

Those who are only familiar with ordinary arithmetic may, by following out with the pen some of the examples which will be given, easily make themselves acquainted with the simple principles on which the Difference Engine acts.

〈ARITHMETICAL TABLES.〉

It is necessary to state distinctly at the outset, that the Difference Engine is not intended to answer special questions. Its object is to calculate and print a series of results formed according to given laws. These are called Tables—many such are in use in various trades. For example—there are collections of Tables of the amount of any number of pounds from 1 to 100 lbs. of butchers’ meat at various prices per lb. Let us examine one of these Tables: viz.—the price of meat 5 d. per lb., we find

There are two ways of computing this Table:—

• 1st. We might have multiplied the number of lbs. in each line by 5, the price per lb., and have put down the result in l. s. d., as in the 2nd column: or,
• 2nd. We might have put down the price of 1 lb., which is 5 d., and have added five pence for each succeeding lb.

Let us now examine the relative advantages of each plan. We shall find that if we had multiplied each number of lbs. in {50} the Table by 5, and put down the resulting amount, then every number in the Table would have been computed independently. If, therefore, an error had been committed, it would not have affected any but the single tabular number at which it had been made. On the other hand, if a single error had occurred in the system of computing by adding five at each step, any such error would have rendered the whole of the rest of the Table untrue.

〈DIFFERENCES.〉

Thus the system of calculating by differences, which is the easiest, is much more liable to error. It has, on the other hand, this great advantage: viz., that when the Table has been so computed, if we calculate its last term directly, and if it agree with the last term found by the continual addition of 5, we shall then be quite certain that every term throughout is correct. In the system of computing each term directly, we possess no such check upon our accuracy.

Now the Table we have been considering is, in fact, merely a Table whose first difference is constant and equal to five. If we express it in pence it becomes—

Any machine, therefore, which could add one number to another, and at the same time retain the original number called the first difference for the next operation, would be able to compute all such Tables.

〈GROUPS OF MARBLES.〉

Let us now consider another form of Table which might readily occur to a boy playing with his marbles, or to a young lady with the balls of her solitaire board. {51}

The boy may place a row of his marbles on the sand, at equal distances from each other, thus—

He might then, beginning with the second, place two other marbles under each, thus—

He might then, beginning with the third, place three other marbles under each group, and so on; commencing always one group later, and making the addition one marble more each time. The several groups would stand thus arranged—

He will not fail to observe that he has thus formed a series of triangular groups, every group having an equal number of marbles in each of its three sides. Also that the side of each successive group contains one more marble than that of its preceding group.

Now an inquisitive boy would naturally count the numbers in each group and he would find them thus—

1 3 6 10 15 21

He might also want to know how many marbles the thirtieth or any other distant group might contain. Perhaps he might go to papa to obtain this information; but I much fear papa would snub him, and would tell him that it was nonsense—that it was useless—that nobody knew the number, and so forth. If the boy is told by papa, that he is not able to answer the question, then I recommend him to pay careful attention to whatever that father may at any time say, for he has overcome two of the greatest obstacles to the acquisition {52} of knowledge—inasmuch as he possesses the consciousness that he does not know—and he has the moral courage to avow it.[13]

[13] The most remarkable instance I ever met with of the distinctness with which any individual perceived the exact boundary of his own knowledge, was that of the late Dr. Wollaston.

If papa fail to inform him, let him go to mamma, who will not fail to find means to satisfy her darling’s curiosity. In the meantime the author of this sketch will endeavour to lead his young friend to make use of his own common sense for the purpose of becoming better acquainted with the triangular figures he has formed with his marbles.

〈SECOND DIFFERENCE CONSTANT.〉

In the case of the Table of the price of butchers’ meat, it was obvious that it could be formed by adding the same constant difference continually to the first term. Now suppose we place the numbers of our groups of marbles in a column, as we did our prices of various weights of meat. Instead of adding a certain difference, as we did in the former case, let us subtract the figures representing each group of marbles from the figures of the succeeding group in the Table. The process will stand thus:—

It is usual to call the third column thus formed the column of {53} first dif­fer­ences. It is evident in the present instance that that column represents the natural numbers. But we already know that the first difference of the natural numbers is constant and equal to unity. It appears, therefore, that a Table of these numbers, representing the group of marbles, might be constructed to any extent by mere addition—using the number 1 as the first number of the Table, the number 1 as the first Difference, and also the number 1 as the second Difference, which last always remains constant.

Now as we could find the value of any given number of pounds of meat directly, without going through all the previous part of the Table, so by a somewhat different rule we can find at once the value of any group whose number is given.

Thus, if we require the number of marbles in the fifth group, proceed thus:—

If the reader will take the trouble to calculate with his pencil the five groups given above, he will soon perceive the general truth of this rule.

We have now arrived at the fact that this Table—like that of the price of butchers’ meat—can be calculated by two different methods. By the first, each number of the Table is calculated independently: by the second, the truth of each number depends upon the truth of all the previous numbers.

〈TRIANGULAR NUMBERS.〉

Perhaps my young friend may now ask me, What is the use of such Tables? Until he has advanced further in his {54} arithmetical studies, he must take for granted that they are of some use. The very Table about which he has been reasoning possesses a special name—it is called a Table of Triangular Numbers. Almost every general collection of Tables hitherto published contains portions of it of more or less extent.

Above a century ago, a volume in small quarto, containing the first 20,000 triangular numbers, was published at the Hague by E. De Joncourt, A.M., and Professor of Philosophy.[14] I cannot resist quoting the author’s enthusiastic expression of the happiness he enjoyed in composing his celebrated work:

“The Trigonals here to be found, and nowhere else, are exactly elaborate. Let the candid reader make the best of these numbers, and feel (if possible) in perusing my work the pleasure I had in composing it.

“That sweet joy may arise from such contemplations cannot be denied. Numbers and lines have many charms, unseen by vulgar eyes, and only discovered to the unwearied and respectful sons of Art. In features the serpentine line (who starts not at the name) produces beauty and love; and in numbers, high powers, and humble roots, give soft delight.

“Lo! the raptured arithmetician! Easily satisfied, he asks no Brussels lace, nor a coach and six. To calculate, contents his liveliest desires, and obedient numbers are within his reach.”

[14] ‘On the Nature and Notable Use of the most Simple Trigonal Numbers.’ By E. De Joncourt, at the Hague. 1762.

〈SQUARE NUMBERS.〉

I hope my young friend is acquainted with the fact—that the product of any number multiplied by itself is called the square of that number. Thus 36 is the product of 6 multiplied by 6, and 36 is called the square of 6. I would now recommend him to examine the series of square numbers

1, 4, 9, 16, 25, 36, 49, 64, &c.,

{55} and to make, for his own in­struc­tion, the series of their first and second differences, and then to apply to it the same reasoning which has been already applied to the Table of Triangular Numbers.

〈CANNON BALLS.〉

When he feels that he has mastered that Table, I shall be happy to accompany mamma’s darling to Woolwich or to Portsmouth, where he will find some practical illustrations of the use of his newly-acquired numbers. He will find scattered about in the Arsenal various heaps of cannon balls, some of them triangular, others square or oblong pyramids.

Looking on the simplest form—the triangular pyramid—he will observe that it exactly represents his own heaps of marbles placed each successively above one another until the top of the pyramid contains only a single ball.

The new series thus formed by the addition of his own triangular numbers is—

He will at once perceive that this Table of the number of cannon balls contained in a triangular pyramid can be carried to any extent by simply adding successive differences, the third of which is constant.

The next step will naturally be to inquire how any number in this Table can be calculated by itself. A little consideration will lead him to a fair guess; a little industry will enable him to confirm his conjecture.

〈NUMBER IN EACH PILE.〉

It will be observed at p. 49 that in order to find {56} independently any number of the Table of the price of butchers’ meat, the following rule was observed:—

Take the number whose tabular number is required.

Multiply it by the first difference.

This product is equal to the required tabular number.

Again, at p. 53, the rule for finding any triangular number was:—

This is the number of marbles in the 5th group.

Now let us make a bold conjecture respecting the Table of cannon balls, and try this rule:—

The real number in the 5th pyramid is 35. But the number 105 at which we have arrived is exactly three times as great. If, therefore, instead of dividing by 2 we had divided by 2 and also by 3, we should have arrived at a true result in this instance.

The amended rule is therefore— {57}

This rule will, upon trial, be found to give correctly every tabular number.

By similar reasoning we might arrive at the knowledge of the number of cannon balls in square and rectangular pyramids. But it is presumed that enough has been stated to enable the reader to form some general notion of the method of calculating arithmetical Tables by differences which are constant.

〈ASTRONOMICAL TABLES.〉

It may now be stated that mathematicians have discovered that all the Tables most important for practical purposes, such as those relating to Astronomy and Navigation, can, although they may not possess any constant differences, still be calculated in detached portions by that method.

Hence the importance of having machinery to calculate by differences, which, if well made, cannot err; and which, if carelessly set, presents in the last term it calculates the power of verification of every antecedent term.

Of the Mechanical Arrangements necessary for computing Tables by the Method of Differences.

From the preceding explanation it appears that all Tables may be calculated, to a greater or less extent, by the method of Differences. That method requires, for its successful {58} execution, little beyond mechanical means of performing the arithmetical operation of Addition. Subtraction can, by the aid of a well-known artifice, be converted into Addition.

〈ADDITION.〉

The process of Addition includes two distinct parts—1st. The first consists of the addition of any one digit to another digit; 2nd. The second consists in carrying the tens to the next digit above.

Let us take the case of the addition of the two following numbers, in which no carriages occur:—

• 6023
• 1970
• 7993

It will be observed that, in making this addition, the mind acts by successive steps. The person adding says to himself—

• 0 and 3 make three,
• 7 and 2 make nine,
• 9 and 0 make nine,
• 1 and 6 make seven.

〈CARRIAGE.〉

In the following addition there are several carriages:—

• 2648
• 4564
• 7212

The person adding says to himself—

4 and 8 make 12: put down 2 and carry one.

1 and 6 are 7 and 4 make 11: put down 1 and carry one.

1 and 5 are 6 and 6 make 12: put down 2 and carry one.

1 and 4 are 5 and 2 make  7: put down 7. and carry non

Now, the length of time required for adding one number to another is mainly dependent upon the number of figures to {59} be added. If we could tell the average time required by the mind to add two figures together, the time required for adding any given number of figures to another equal number would be found by multiplying that average time by the number of digits in either number.

When we attempt to perform such additions by machinery we might follow exactly the usual process of the human mind. In that case we might take a series of wheels, each having marked on its edges the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. These wheels might be placed above each other upon an axis. The lowest would indicate the units’ figure, the next above the tens, and so on, as in the Difference Engine at the Exhibition, a woodcut of which faces the title-page.

Several such axes, with their figure wheels, might be placed around a system of central wheels, with which the wheels of any one or more axes might at times be made to gear. Thus the figures on any one axis might, by means of those central wheels, be added to the figure wheels of any other axis.

But it may fairly be expected, and it is indeed of great importance that calculations made by machinery should not merely be exact, but that they should be done in a much shorter time than those performed by the human mind. Suppose there were no tens to carry, as in the first of the two cases; then, if we possessed mechanism capable of adding any one digit to any other in the units’ place of figures, a similar mechanism might be placed above it to add the tens’ figures, and so on for as many figures as might be required.

But in this case, since there are no carriages, each digit might be added to its corresponding digit at the same time. Thus, the time of adding by means of mechanism, any two numbers, however many figures they might consist of, would {60} not exceed that of adding a single digit to another digit. If this could be accomplished it would render additions and subtractions with numbers having ten, twenty, fifty, or any number of figures, as rapid as those operations are with single figures.

〈SUCCESSIVE CARRIAGE.〉

Let us now examine the case in which there were several carriages. Its successive stages may be better explained, thus—

Now if, as in this case, all the carriages were known, it would then be possible to make all the additions of digits at the same time, provided we could also record each carriage as it became due. We might then complete the addition by adding, at the same instant, each carriage in its proper place. The process would then stand thus:— {61}

Now, whatever mechanism is contrived for adding any one digit to any other must, of course, be able to add the largest digit, nine, to that other digit. Supposing, therefore, one unit of number to be passed over in one second of time, it is evident that any number of pairs of digits may be added together in nine seconds, and that, when all the consequent carriages are known, as in the above case, it will cost one second more to make those carriages. Thus, addition and carriage would be completed in ten seconds, even though the numbers consisted each of a hundred figures.

But, unfortunately, there are multitudes of cases in which the carriages that become due are only known in successive periods of time. As an example, add together the two following numbers:—

{62}

In this case the carriages only become known successively, and they amount to the number of figures to be added; consequently, the mere addition of two numbers, each of fifty places of figures, would require only nine seconds of time, whilst the possible carriages would consume fifty seconds.

The mechanical means I employed to make these carriages bears some slight analogy to the operation of the faculty of memory. A toothed wheel had the ten digits marked upon its edge; between the nine and the zero a projecting tooth was placed. Whenever any wheel, in receiving addition, passed from nine to zero, the projecting tooth pushed over a certain lever. Thus, as soon as the nine seconds of time required for addition were ended, every carriage which had become due was indicated by the altered position of its lever. An arm now went round, which was so contrived that the act of replacing that lever caused the carriage which its position indicated to be made to the next figure above. But this figure might be a nine, in which case, in passing to zero, it would put over its lever, and so on. By placing the arms spirally round an axis, these successive carriages were accomplished.

Multitudes of contrivances were designed, and almost endless drawings made, for the purpose of economizing the time and simplifying the mechanism of carriage. In that portion of the Difference Engine in the Exhibition of 1862 the time of carriage has been reduced to about one-fourth part of what was at first required.

〈ANTICIPATING CARRIAGE.〉

At last having exhausted, during years of labour, the principle of successive carriages, it occurred to me that it might be possible to teach mechanism to accomplish another mental process, namely—to foresee. This idea occurred to me in October, 1834. It cost me much thought, but the {63} principle was arrived at in a short time. As soon as that was attained, the next step was to teach the mechanism which could foresee to act upon that foresight. This was not so difficult: certain mechanical means were soon devised which, although very far from simple, were yet sufficient to dem­on­strate the possibility of constructing such machinery.

The process of simplifying this form of carriage occupied me, at intervals, during a long series of years. The demands of the Analytical Engine, for the mechanical execution of arithmetical operations, were of the most extensive kind. The multitude of similar parts required by the Analytical Engine, amounting in some instances to upwards of fifty thousand, rendered any, even the simplest, improvement of each part a matter of the highest importance, more especially as regarded the diminished amount of expenditure for its construction.

Description of the existing portion of Difference Engine No. 1.

That portion of Difference Engine, No. 1, which during the last twenty years has been in the museum of King’s College, at Somerset House, is represented in the woodcut opposite the title page.

It consists of three columns; each column contains six cages; each cage contains one figure-wheel.

The column on the right hand has its lowest figure-wheel covered by a shade which is never removed, and to which the reader’s attention need not be directed.

The figure-wheel next above may be placed by hand at any one of the ten digits. In the woodcut it stands at zero.

The third, fourth, and fifth cages are exactly the same as the second.

The sixth cage contains exactly the same as the four just {64} described. It also contains two other figure-wheels, which with a similar one above the frame, may also be dismissed from the reader’s attention. Those wheels are entirely unconnected with the moving part of the engine, and are only used for memoranda.

It appears, therefore, that there are in the first column on the right hand five figure-wheels, each of which may be set by hand to any of the figures 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

The lowest of these figure-wheels represents the unit’s figure of any number; the next above the ten’s figure, and so on. The highest figure-wheel will therefore represent tens of thousands.

Now, as each of these figure-wheels may be set by hand to any digit, it is possible to place on the first column any number up to 99999. It is on these wheels that the Table to be calculated by the engine is expressed. This column is called the Table column, and the axis of the wheels the Table axis.

The second or middle column has also six cages, in each of which a figure-wheel is placed. It will be observed that in the lowest cage, the figure on the wheel is concealed by a shade. It may therefore be dismissed from the attention. The five other figure-wheels are exactly like the figure-wheels on the Table axis, and can also represent any number up to 99999.

This column is called the First Difference column, and the axis is called the First Difference axis.

The third column, which is that on the left hand, has also six cages, in each of which is a figure-wheel capable of being set by hand to any digit.

The mechanism is so contrived that whatever may be the numbers placed respectively on the figure-wheels of each of {65} the three columns, the following succession of operations will take place as long as the handle is moved:—

• 1st. Whatever number is found upon the column of first differences will be added to the number found upon the Table column.
• 2nd. The same first difference remaining upon its own column, the number found upon the column of second differences will be added to that first difference.

It appears, therefore, that with this small portion of the Engine any Table may be computed by the method of differences, provided neither the Table itself, nor its first and second differences, exceed five places of figures.

If the whole Engine had been completed it would have had six orders of differences, each of twenty places of figures, whilst the three first columns would each have had half a dozen additional figures.

This is the simplest explanation of that portion of the Difference Engine No. 1, at the Exhibition of 1862. There are, however, certain modifications in this fragment which render its exhibition more instructive, and which even give a mechanical insight into those higher powers with which I had endowed it in its complete state.

As a matter of convenience in exhibiting it, there is an arrangement by which the three upper figures of the second difference are transformed into a small engine which counts the natural numbers.

By this means it can be set to compute any Table whose second difference is constant and less than 1000, whilst at the same time it thus shows the position in the Table of each tabular number.

In the existing portion there are three bells; they can be respectively ordered to ring when the Table, its first difference {66} and its second difference, pass from positive to negative. Several weeks after the machine had been placed in my drawing-room, a friend came by appointment to test its power of calculating Tables. After the Engine had computed several Tables, I remarked that it was evidently finding the root of a quadratic equation; I therefore set the bells to watch it. After some time the proper bell sounded twice, indicating, and giving the two positive roots to be 28 and 30. The Table thus calculated related to the barometer and really involved a quadratic equation, although its maker had not previously observed it. I afterwards set the Engine to tabulate a formula containing impossible roots, and of course the other bell warned me when it had attained those roots. I had never before used these bells, simply because I did not think the power it thus possessed to be of any practical utility.

Again, the lowest cages of the Table, and of the first difference, have been made use of for the purpose of illustrating three important faculties of the finished engine.

• 1st. The portion exhibited can calculate any Table whose third difference is constant and less than 10.
• 2nd. It can be used to show how much more rapidly astronomical Tables can be calculated in an engine in which there is no constant difference.
• 3rd. It can be employed to illustrate those singular laws which might continue to be produced through ages, and yet after an enormous interval of time change into other different laws; each again to exist for ages, and then to be superseded by new laws. These views were first proposed in the “Ninth Bridgewater Treatise.”

〈CURIOUS QUESTIONS.〉

Amongst the various questions which have been asked respecting the Difference Engine, I will mention a few of the most remarkable:—One gentleman addressed me thus: {67} “Pray, Mr. Babbage, can you explain to me in two words what is the principle of this machine?” Had the querist possessed a moderate acquaintance with mathematics I might in four words have conveyed to him the required information by answering, “The method of differences.” The question might indeed have been answered with six characters thus—

Δ⁷ u_x = 0.

but such information would have been unintelligible to such inquirers.

On two occasions I have been asked,—“Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?” In one case a member of the Upper, and in the other a member of the Lower, House put this question. I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question. I did, however, explain the following property, which might in some measure approach towards an answer to it.

It is possible to construct the Analytical Engine in such a manner that after the question is once communicated to the engine, it may be stopped at any turn of the handle and set on again as often as may be desired. At each stoppage every figure-wheel throughout the Engine, which is capable of being moved without breaking, may be moved on to any other digit. Yet after each of these apparent falsifications the engine will be found to make the next calculation with perfect truth.

The explanation is very simple, and the property itself useless. The whole of the mechanism ought of course to be enclosed in glass, and kept under lock and key, in which case the mechanism necessary to give it the property alluded to would be useless.

CHAPTER VI.

Statement relative to the Difference Engine, drawn up by the late Sir H. Nicolas from the Author’s Papers.

THE following statement was drawn up by the late Sir Harris Nicolas, G.S.M. & G., from papers and documents in my possession relating to the Difference Engine. I believe every paper I possessed at all bearing on the subject was in his hands for several months.

For some time previous to 1822, Mr. Babbage had been engaged in contriving machinery for the execution of extensive arithmetical operations, and in devising mechanism by which the machine that made the calculations might also print the results.

On the 3rd of July, 1822, he published a letter to Sir Humphry Davy, President of the Royal Society, containing a statement of his views on that subject; and more par­tic­u­lar­ly describing an Engine for calculating astronomical, nautical, and other Tables, by means of the “method of differences.” In that letter it is stated that a small Model, consisting of six figures, and capable of working two orders of differences, had been constructed; and that it performed its work in a sat­is­fac­tory manner.

The concluding paragraph of that letter is as follows:—

“Whether I shall construct a larger Engine of this kind, and bring to {69} perfection the others I have described, will, in a great measure, depend on the nature of the encouragement I may receive.

“Induced, by a conviction of the great utility of such Engines, to withdraw, for some time, my attention from a subject on which it has been engaged during several years, and which possesses charms of a higher order, I have now arrived at a point where success is no longer doubtful. It must, however, be attained at a very considerable expense, which would not probably be replaced, by the works it might produce, for a long period of time; and which is an undertaking I should feel unwilling to commence, as altogether foreign to my habits and pursuits.”

The Model alluded to had been shown to a large number of Mr. Babbage’s acquaintances, and to many other persons; and copies of his letter having been given to several of his friends, it is probable that one of the copies was sent to the Treasury.

On the 1st of April, 1823, the Lords of the Treasury referred that Letter to the Royal Society, requesting—

“The opinion of the Royal Society on the merits and utility of this invention.”

On the 1st of May the Royal Society reported to the Treasury, that—

“Mr. Babbage has displayed great talent and ingenuity in the construction of his Machine for Computation, which the Committee think fully adequate to the attainment of the objects proposed by the inventor; and they consider Mr. Babbage as highly deserving of public encouragement, in the prosecution of his arduous undertaking.”[15]

On the 21st of May these papers were ordered to be printed by the House of Commons.

In July, 1823, Mr. Babbage had an interview with the Chancellor of the Exchequer (Mr. Robinson[16] ), to ascertain if it was the wish of the Government that he should construct a large Engine of the kind, which would also print the results it calculated. {70}

[15] Parliamentary Paper, No. 370, printed 22nd May, 1823.

[16] Afterwards Lord Goderich, now Earl of Ripon.

From the conversation which took place on that occasion, Mr. Babbage apprehended that such was the wish of the Government. The Chancellor of the Exchequer remarked that the Government were in general unwilling to make grants of money for any inventions, however meritorious; because, if they really possessed the merit claimed for them, the sale of the article produced would be the best, as well as largest reward of the inventor: but that the present case was an exception; it being apparent that the construction of such a Machine could not be undertaken with a view to profit from the sale of its produce; and that, as math­e­mat­i­cal Tables were peculiarly valuable for nautical purposes, it was deemed a fit object of encouragement by the Government.

The Chancellor of the Exchequer mentioned two modes of advancing money for the construction:—either through the recommendation of a Committee of the House of Commons, or by taking a sum from the Civil Contingencies: and he observed that, as the Session of Parliament was near its termination, the latter course might, perhaps, be the most convenient.

Mr. Babbage thinks the Chancellor of the Exchequer also made some ob­ser­va­tion, indicating that the amount of money taken from the Civil Contingencies would be smaller than that which might be had by means of a Committee of the House of Commons: and he then proposed to take 1,000 l. as a commencement from the Civil Contingencies Fund. To this Mr. Babbage replied, in words which he distinctly remembers, “Would it be too much, in the first instance, to take 1,500 l.?” The Chancellor of the Exchequer immediately answered, that 1,500 l. should be advanced.

Mr. Babbage’s opinion at that time was, that the Engine would be completed in two, or at the most in three years; and that by having 1,500 l. in the first instance, he would be {71} enabled to advance, from his own private funds, the residue of the 3,000 l., or even 5,000 l., which he then imagined the Engine might possibly cost; so that he would not again have occasion to apply to Government until it was completed. Some ob­ser­va­tions were made by the Chancellor of the Exchequer about the mode of accounting for the money received, as well as about its expenditure; but it seemed to be admitted that it was not possible to prescribe any very definite system, and that much must be left to Mr. Babbage’s own judgment.

Very unfortunately, no Minute of that conversation was made at the time, nor was any sufficiently distinct understanding between the parties arrived at. Mr. Babbage’s conviction was, that whatever might be the labour and difficulty of the undertaking, the Engine itself would, of course, become the property of the Government, which had paid for its construction.

Soon after this interview with the Chancellor of the Exchequer, a letter was sent from the Treasury to the Royal Society, informing that body that the Lords of the Treasury

“Had directed the issue of 1,500 l. to Mr. Babbage, to enable him to bring his invention to perfection, in the manner recommended.”

These latter words, “in the manner recommended,” can only refer to the previous recommendation of the Royal Society; but it does not appear, from the Report of the Royal Society, that any plan, terms, or conditions had been pointed out by that body.

Towards the end of July, 1823, Mr. Babbage took measures for the construction of the present Difference Engine,* and it was regularly proceeded with for four years. {72}

* NOTE.—It will be convenient to distinguish between—

• 1. The small Model of the original or Difference Engine.
• 2. The Difference Engine itself, belonging to the Government, a part only of which has been put together.
• 3. The designs for another Engine, which in this Statement is called the Analytical Engine.

In October, 1827, the expense incurred had amounted to 3,475 l.; and Mr. Babbage having suffered severe domestic affliction, and being in a very ill state of health, was recommended by his medical advisers to travel on the Continent. He left, however, sufficient drawings to enable the work to be continued, and gave an order to his own banker to advance 1,000 l. during his absence: he also received, from time to time, drawings and inquiries relating to the mechanism, and returned in­struc­tions to the engineer who was constructing it.

As it now appeared probable that the expense would much exceed what Mr. Babbage had originally anticipated, he thought it desirable to inform the Government of that fact, and to procure a further grant. As a preliminary step, he wrote from Italy to his brother-in-law, Mr. Wolryche Whitmore, to request that he would see Lord Goderich upon the subject of the interview in July, 1823; but it is probable that he did not sufficiently inform Mr. Whitmore of all the circumstances of the case.

Mr. Whitmore, having had some conversation with Lord Goderich on the subject, addressed a letter, dated on the 29th of February, 1828, to Mr. Babbage, who was then at Rome, stating that

“That interview was unsat­is­fac­tory; that Lord Goderich did not like to admit that there was any understanding, at the time the 1,500 l. was advanced, that more would be given by Government.”

On Mr. Babbage’s return to England, towards the end of {73} 1828, he waited in person upon Lord Goderich, who admitted that the understanding of 1823 was not very definite. He then addressed a statement to the Duke of Wellington, as the head of the Government, explaining the previous steps in the affair; stating the reasons for his inferences from what took place at the interview with the Chancellor of the Exchequer in July, 1823; and referring his Grace for further information to Lord Goderich, to whom also he sent a copy of that statement.

The Duke of Wellington, in consequence of this application, requested the Royal Society to inquire—

“Whether the progress of the Machine confirms them in their former opinion, that it will ultimately prove adequate to the important object it was intended to attain.”

The Royal Society reported, in February, 1829, that—

“They had not the slightest hesitation in pronouncing their decided opinion in the affirmative.”

The Royal Society also expressed their hope that—

“Whilst Mr. Babbage’s mind is intensely occupied in an undertaking likely to do so much honour to his country, he may be relieved, as much as possible, from all other sources of anxiety.”

On the 28th of April, 1829, a Treasury Minute directed a further payment to Mr. Babbage of

“1,500 l. to enable him to complete the Machine by which such important benefit to Science might be expected.”

At that time the sum expended on the Engine amounted to 6,697 l. 12 s., of which 3,000 l. had been received from the Treasury; so that Mr. Babbage had provided 3,697 l. 12 s. from his own private funds.

Under these circumstances, by the advice of Mr. Wolryche Whitmore, a meeting of Mr. Babbage’s personal friends was held on the 12th of May, 1829. It consisted of— {74}

• THE DUKE OF SOMERSET,
• LORD ASHLEY,
• SIR JOHN FRANKLIN,
• MR. WOLRYCHE WHITMORE,
• DR. FITTON,
• MR. FRANCIS BAILY,
• MR. (now SIR JOHN) HERSCHEL.

Being satisfied, upon inquiry, of the following facts, they came to the annexed resolutions:—

“1st. That Mr. Babbage was originally induced to take up the work, on its present extensive scale, by an understanding on his part that it was the wish of Government that he should do so, and by an advance of 1,500 l., at the outset; with a full impression on his mind, that such further advances would be made as the work might require.

“2nd. That Mr. Babbage’s expenditure had amounted to nearly 7,000 l., while the whole sum advanced by Government was 3,000 l.

“3rd. That Mr. Babbage had devoted the most assiduous and anxious attention to the progress of the Engine, to the injury of his health, and the neglect and refusal of other profitable occupations.

“4th. That a very large expense remained to be incurred; and that his private fortune was not such as would justify his completing the Engine, without further and effectual assistance from Government.

“5th. That a personal application upon the subject should be made to the Duke of Wellington.

“6th. That if such application should be unsuccessful in procuring effectual and adequate assistance, they must regard Mr. Babbage (considering the great pecuniary and personal sacrifices he will then have made; the entire expenditure of all he had received from the public on the subject of its destination; and the moral certainty of completing it, to which it was, by his exertions, reduced) as no longer called on to proceed with an undertaking which might destroy his health, and injure, if not ruin, his fortune.

“7th. That Mr. Wolryche Whitmore and Mr. Herschel should request an interview with the Duke of Wellington, to state to his Grace these opinions on the subject.”

Mr. Whitmore and Mr. Herschel accordingly had an interview with the Duke of Wellington; and some time after they were informed by the Chancellor of the Exchequer, to whom they had applied for his Grace’s answer, that the Duke of {75} Wellington intended to see the portion of the Engine which had been then made.

In November, 1829, the Duke of Wellington, accompanied by the Chancellor of the Exchequer (Mr. Goulburn) and Lord Ashley, saw the Model of the Engine, the drawings, and the parts in progress. On the 23rd of that month Mr. Babbage received a note from Mr. Goulburn, dated on the 20th, informing him that the Duke of Wellington and himself had recommended the Treasury to make a further payment towards the completion of the Machine; and that their Lordships had in consequence directed a payment of 3,000 l. to be made to him. This letter also contained a suggestion about separating the Calculating from the Printing part of the Machine, which was repeated in the letter from the Treasury of the 3rd of December, 1829, communicating officially the information contained in Mr. Goulburn’s private note, and stating that directions had been given—

“To pay to you the further sum of 3,000 l., to enable you to complete the Machine which you have invented for the calculation of various tables; but I have to intimate to you that, in making this additional payment, my Lords think it extremely desirable that the Machine should be so constructed, that, if any failure should take place in the attempt to print by it, the calculating part of the Machine may nevertheless be perfect and available for that object.”

Mr. Babbage inferred from this further grant, that Government had adopted his view of the arrangement entered into with the Chancellor of the Exchequer in July, 1823; but, to prevent the recurrence of difficulty from any remaining indistinctness, he wrote to Mr. Goulburn, stating that, before he received the 3,000 l., he wished to propose some general arrangements for expediting the completion of the Engine, further notes of which he would shortly submit to him. On the 25th of November, 1829, he addressed a letter to Lord {76} Ashley, to be communicated to the Chancellor of the Exchequer, stating the grounds on which he thought the following arrangements desirable:—

• 1st. That the Engine should be considered as the property of Government.
• 2nd. That pro­fes­sion­al engineers should be appointed by Government to examine the charges made for the work already executed, as well as for its future progress; and that such charges should be defrayed by Government.
• 3rd. That under this arrangement he himself should continue to direct the construction of the Engine, as he had hitherto done.

Mr. Babbage also stated that he had been obliged to suspend the work for nearly nine months; and that such delay risked the final completion of the Engine.

In reply to these suggestions, Mr. Goulburn wrote to Lord Ashley, stating—

“That we (the Government) could not adopt the course which Mr. Babbage had pointed out, consistently with the principle on which we have rendered him assistance in the construction of his Machine, and without considerable inconvenience. The view of the Government was, to assist an able and ingenious man of science, whose zeal had induced him to exceed the limits of prudence, in the construction of a work which would, if successful, redound to his honour, and be of great public advantage. We feel ourselves, therefore, under the necessity of adhering to our original intention, as expressed in the Minute of the Treasury, which granted Mr. Babbage the last 3,000 l., and in the letter in which I informed him of that grant.”

Mr. Goulburn’s letter was enclosed by Lord Ashley to Mr. Babbage, with a note, in which his Lordship observed, with reference to Mr. Goulburn’s opinion, that it was

“A wrong view of the position in which Mr. Babbage was placed, after his conference with Lord Goderich—which must be explained to him (Mr. Goulburn).” {77}

“The original intention” of the Government is here stated to have been communicated to Mr. Babbage, both in the letter from the Treasury of the 3rd of December, 1829, granting the 3,000 l., and also in Mr. Goulburn’s private letter of the 20th of November, 1829. These letters have been just given; and it certainly does not appear from either of them, that the “original intention” was then in any degree more apparent than it was at the commencement of the undertaking in July, 1823.

On the 16th of December, 1829, Mr. Babbage wrote to Lord Ashley, observing, that Mr. Goulburn seemed to think that he [Mr. Babbage] had commenced the machine on his own account; and that, pursuing it zealously, he had expended more than was prudent, and had then applied to Government for aid. He remarked, that a reference to papers and dates would confirm his own positive declaration, that this was never for one moment, in his apprehension, the ground on which the matter rested; and that the following facts would prove that it was absolutely impossible it could have been so:—

• 1stly. Mr. Babbage referred to the passage[17] (already quoted) in his letter to Sir Humphry Davy, in which he had expressed his opinion as decidedly adverse to the plan of making a larger Machine, on his own account.
• 2ndly. Mr. Babbage stated that the small Model of the Machine seen by the Duke of Wellington and Mr. Goulburn, was completed before his interview with Lord Goderich in July, 1823; for it was alluded to in the Report of the Royal Society, of the 1st of May, 1823.
• 3rdly. That the interview with Lord Goderich having taken place in July, 1823; the present Machine (i.e. the Difference {78} Engine) was commenced in consequence of that interview; and after Mr. Babbage had received the first grant of 1,500 l. on the 7th of August, 1823.

[17] See page [69].

Having thus shown that the light in which Mr. Goulburn viewed these transactions was founded on a misconception, Mr. Babbage requested Lord Ashley to inquire whether the facts to which he had called Mr. Goulburn’s attention might not induce him to reconsider the subject. And in case Mr. Goulburn should decline revising his opinion, then he wished Lord Ashley to ascertain the opinion of Government, upon the contingent questions which he enclosed; viz.—

1. Supposing Mr. Babbage received the 3,000 l. now directed to be issued, what are the claims which Government will have on the Engine, or on himself?

2. Would Mr. Babbage owe the 6,000 l., or any part of that sum to the Government?

If this question be answered in the negative,

3. Is the portion of the Engine now made, as completely Mr. Babbage’s property as if it had been entirely paid for with his own money?

4. Is it expected by Government that Mr. Babbage should continue to construct the Engine at his own private expense; and, if so, to what extent in money?

5. Supposing Mr. Babbage should decline resuming the construction of the Engine, to whom do the drawings and parts already made belong?

The following statement was also enclosed:—

[*] The difference between this sum and 6,697 l. 12 s. mentioned in page [73], seems to have arisen from the fact of the former sum having included the estimated amount of a bill which, when received, was found to be less than had been anticipated.

In January, 1830, Mr. Babbage wrote to Lord Goderich, {79} stating that the Chancellor of the Exchequer (Mr. Goulburn) would probably apply to his Lordship respecting the interview in July, 1823. He therefore recalled some of the circumstances attending it to Lord Goderich, and concluded thus:—

“The matter was, as you have justly observed on another occasion, left, in a certain measure, indefinite; and I have never contended that any promise was made to me. My subsequent conduct was founded upon the impression left on my mind by that interview. I always considered that, whatever difficulties I might encounter, it could never happen that I should ultimately suffer any pecuniary loss.

“I understand that Mr. Goulburn wishes to ascertain from your Lordship whether, from the nature of that interview, it was reasonable that I should have such expectation.”

In the mean time Mr. Babbage had encountered difficulties of another kind. The Engineer who had been constructing the Engine under Mr. Babbage’s direction had delivered his bills in such a state that it was impossible to judge how far the charges were just and reasonable; and although Mr. Babbage had paid several thousand pounds, yet there remained a considerable balance, which he was quite prepared and willing to pay, as soon as the accounts should be examined, and the charges approved of by pro­fes­sion­al engineers.

The delay in deciding whether the Engine was the property of Government, added greatly to this embarrassment. Mr. Babbage, therefore, wrote to Lord Ashley on the 8th of February, to mention these difficulties; and to point out the serious inconvenience which would arise, in the future progress of the Engine, from any dispute between the Engineer and himself relative to payments.

On the 24th of February, 1830, Mr. Babbage called on Lord Ashley, to request he would represent to the Duke of Wellington the facts of the case, and point out to his Grace {80} the importance of a decision. In the afternoon of the same day, he again saw Lord Ashley, who communicated to him the decision of the Government; to the following effect:—

• 1 st. Although the Government would not pledge themselves to COMPLETE the Machine, they were willing to declare it their property.
• 2 nd. That pro­fes­sion­al Engineers should be appointed to examine the bills.
• 3 rd. That the Government were willing to advance 3,000 l. more than the sum (6,000 l.) already granted.
• 4 th. That, when the Machine was completed, the Government would be willing to attend to any claim of Mr. Babbage to remuneration, either by bringing it before the Treasury, or the House of Commons.

Thus, after considerable discussion, the doubts arising from the indefiniteness of the understanding with the Chancellor of the Exchequer, in July, 1823, were at length removed. Mr. Babbage’s impression of the original arrangement entered into between Lord Goderich and himself was thus formally adopted in the first three propositions: and the Government voluntarily added the expression of their disposition to attend to any claim of his for remuneration when the Engine should be completed.

When the arrangements consequent upon this decision were made, the work of the Engine was resumed, and continued to advance.

After some time, the increasing amount of costly drawings, and of parts of the Engine already executed, remaining exposed to destruction from fire and from other casualties became a source of some anxiety.

These facts having been represented to Lord Althorp (then Chancellor of the Exchequer), an experienced surveyor {81} was directed to find a site adapted for a building for the reception of the Engine in the neighbourhood of Mr. Babbage’s residence.

On the 19th of January the Surveyor’s reports were forwarded to Lord Althorp (the Chancellor of the Exchequer), who referred the case to a committee of practical Engineers for their opinion. This committee reported strongly in favour of the removal, on the grounds of security, and of economy in completing the Engine; and also recommended the site which had been previously selected by the Surveyor. The Royal Society, also, to whom Lord Althorp had applied, examined the question, and likewise reported strongly to the same effect.

A lease of some property, adjacent to Mr. Babbage’s residence, was therefore sub­se­quent­ly granted by him to the Government; and a fire-proof building, capable of containing the Engine, with its drawings, and workshops necessary for its completion, were erected.

With respect to the expenses of constructing the Engine, the following plan was agreed upon and carried out:—The great bulk of the work was executed by the Engineer under the direction of Mr. Babbage. When the bills were sent in, they were immediately forwarded by him to two eminent Engineers, Messrs. Donkin and Field, who, at the request of Government, had undertaken to examine their accuracy. On these gentlemen certifying those bills to be correct, Mr. Babbage trans­mit­ted them to the Treasury; and after the usual forms, a warrant was issued directing the payment of the respective sums to Mr. Babbage. This course, however, required considerable time; and the Engineer having represented that he was unable to pay his workmen without more immediate advances, Mr. Babbage, to prevent delay in {82} completing the Engine, did himself, from time to time, advance from his own funds several sums of money; so that he was, in fact, usually in advance from 500 l. to 1,000 l. Those sums were, of course, repaid when the Treasury warrants were issued.

Early in the year 1833, an event of great importance in the history of the Engine occurred. Mr. Babbage had directed a portion of it, consisting of sixteen figures, to be put together. It was capable of calculating Tables having two or three orders of differences; and, to some extent, of forming other Tables. The action of this portion completely justified the expectations raised, and gave a most sat­is­fac­tory assurance of its final success.

The fire-proof building and workshops having been completed, arrangements were made for the removal of the Engine. Mr. Babbage finding it no longer convenient to make payments in advance, informed the Engineer that he should in future not pay him until the money was received from the Treasury. Upon receiving this intimation, the Engineer immediately discontinued the construction of the Engine, and dismissed the workmen employed on it; which fact Mr. Babbage immediately communicated to the Treasury.

In this state of affairs it appeared, both to the Treasury and to Mr. Babbage, that it would be better to complete the removal of the drawings, and all the parts of the Engine to the fire-proof building; and then make such arrangements between the Treasury and the Engineer, respecting the future payments, as might prevent further discussion on that subject.

After much delay and difficulty the whole of the drawings, and parts of the Engine, were at length removed to the fire-proof building in East-street, Manchester-square. Mr. Babbage wrote, on the 16th of July, 1834, to the Treasury, {83} informing their Lordships of the fact;—adding that no advance had been made in its construction for above a year and a quarter; and requesting further in­struc­tions on the subject.

Mr. Babbage received a letter from the Treasury, expressing their Lordships’ sat­is­fac­tion at learning that the drawings, and parts of the Calculating Engine were removed to the fire-proof building, and stating that as soon as Mr. Clement’s Accounts should be received and examined, they would

“Take into consideration what further proceedings may be requisite with a view to its completion.”

A few weeks afterwards Mr. Babbage received a letter from the Treasury, conveying their Lordships’ authority to proceed with the construction of the Engine.

During the time which had elapsed since the Engineer had ceased to proceed with the construction of the Engine, Mr. Babbage had been deprived of the use of his own drawings. Having, in the meanwhile, naturally speculated upon the general principles on which machinery for calculation might be constructed, a principle of an entirely new kind occurred to him, the power of which over the most complicated arithmetical operations seemed nearly unbounded. On re-examining his drawings when returned to him by the Engineer, the new principle appeared to be limited only by the extent of the mechanism it might require. The invention of simpler mechanical means for executing the elementary operations of the Engine now derived a far greater importance than it had hitherto possessed; and should such simp­li­fi­ca­tions be discovered, it seemed difficult to anticipate, or even to over-estimate, the vast results which might be attained. In the Engine for calculating by differences, such simp­li­fi­ca­tions affected only about a hundred and twenty {84} similar parts, whilst in the new or Analytical Engine, they would affect a great many thousand. The Difference Engine might be constructed with more or less advantage by employing various mechanical modes for the operation of addition: the Analytical Engine could not exist without inventing for it a method of mechanical addition possessed of the utmost simplicity. In fact, it was not until upwards of twenty different mechanical modes for performing the operation of addition had been designed and drawn, that the necessary degree of simplicity required for the Analytical Engine was ultimately attained. Hence, therefore, the powerful motive for simp­li­fi­ca­tion.

These new views acquired additional importance, from their bearings upon the Engine already partly executed for the Government. For, if such simp­li­fi­ca­tions should be discovered, it might happen that the Analytical Engine would execute more rapidly the calculations for which the Difference Engine was intended; or, that the Difference Engine would itself be superseded by a far simpler mode of construction. Though these views might, perhaps, at that period have appeared visionary, both have sub­se­quent­ly been completely realized.

To withhold those new views from the Government, and under such circumstances to have allowed the construction of the Engine to be resumed, would have been improper; yet the state of uncertainty in which those views were then necessarily involved rendered any written communication respecting their probable bearing on the Difference Engine a matter of very great difficulty. It appeared to Mr. Babbage that the most straightforward course was to ask for an interview on the subject with the Head of the Government, and to communicate to him the exact state of the case. {85}

Had that interview taken place, the First Lord of the Treasury might have ascertained from his inquiries, in a manner quite impracticable by any written communications, the degree of importance which Mr. Babbage attached to his new inventions, and his own opinion of their probable effect, in superseding the whole or any part of the original, or Difference, Engine. The First Lord of the Treasury would then have been in a position to decide, either on the immediate continuation and completion of the original design, or on its temporary suspension, until the character of the new views should be more fully developed by further drawings and examination.

There was another, although a far less material point, on which also it was desirable to obtain the opinion of the Government: the serious impediments to the progress of the Engine, arising from the Engineer’s conduct, as well as the consequent great expense, had induced Mr. Babbage to consider, whether it might not be possible to employ some other person as his agent for constructing it. His mind had gradually become convinced of the practicability of that measure; but he was also aware that however advantageous it might prove to the Government, from its greater economy, yet that it would add greatly to his own personal labour, responsibility, and anxiety.

On the 26th of September, 1834, Mr. Babbage therefore requested an interview with Lord Melbourne, for the purpose of placing before him these views. Lord Melbourne acceded to the proposed interview, but it was then postponed; and soon after, the Administration of which his Lordship was the Head went out of Office, without the interview having taken place.

For the same purpose, Mr. Babbage applied in December, {86} 1834, for an interview with the Duke of Wellington, who, in reply, expressed his wish to receive a written communication on the subject. He accordingly addressed a statement to his Grace, pointing out the only plans which, in his opinion, could be pursued for terminating the questions relative to the Difference Engine; namely,

• 1st. The Government might desire Mr. Babbage to continue the construction of the Engine, in the hands of the person who has hitherto been employed in making it.
• 2ndly. The Government might wish to know whether any other person could be substituted for the Engineer at present employed to continue the construction;—a course which was possible.
• 3rdly. The Government might (although he did not presume that they would) substitute some person to superintend the completion of the Engine instead of Mr. Babbage himself.
• 4thly. The Government might be disposed to give up the undertaking entirely.

He also stated to the Duke of Wellington, the circumstances which had led him to the invention of a new Engine, of far more extensive powers of calculation; which he then observed did not supersede the former one, but added greatly to its utility.

At this period, the impediments relating to the Difference Engine had been partially and temporarily removed. The chief difficulty would have been either the formation of new arrangements with the Engineer, or the appointment of some other person to supply his place. This latter alternative, which was of great importance for economy as well as for its speedy completion, Mr. Babbage had carefully examined, and was then prepared to point out means for its accomplishment. {87}

The duration of the Duke of Wellington’s Administration was short; and no decision on the subject of the Difference Engine was obtained.

On the 15th of May the Difference Engine was alluded to in the House of Commons; when the Chancellor of the Exchequer did Mr. Babbage the justice to state distinctly, that the whole of the money voted had been expended in paying the workmen and for the materials employed in constructing it, and that not one shilling of it had ever gone into his own pocket.

About this time several communications took place between the Chancellor of the Exchequer and Mr. Babbage, respecting a reference to the Royal Society for an opinion on the subject of the Engine.

A new and serious impediment to the possibility of executing one of the plans which had been suggested to the Duke of Wellington for completing the Difference Engine arose from these delays. The draftsman whom Mr. Babbage had, at his own expense, employed, both on the Difference and on the Analytical Engine, received an offer of a very liberal salary, if he would enter into an engagement abroad, which would occupy many years. His assistance was indispensable, and his services were retained only by Mr. Babbage considerably increasing his salary.

On the 14th of January, 1836, Mr. Babbage received a communication from the Chancellor of the Exchequer (Mr. Spring Rice[19] ), expressing his desire to come to some definite result on the subject of the Calculating Engine, in which he remarked, that the conclusion to be drawn from Mr. Babbage’s statement to the Duke of Wellington was, that he {88} (Mr. Babbage) having invented a new machine, of far greater powers than the former one, wished to be informed if the Government would undertake to defray the expense of this new Engine.

The Chancellor of the Exchequer then pointed out reasons why he should feel himself bound to look to the completion of the first machine, before he could propose to Parliament to enter on the consideration of the second: and he proposed to refer to the Royal Society for their opinion, authorizing them, if they thought fit, to employ any practical mechanist or engineer to assist them in their inquiries. The Chancellor of the Exchequer concluded with expressing his readiness to communicate with Mr. Babbage respecting the best mode of attaining that result.

From these statements it is evident that Mr. Babbage had failed in making his own views distinctly understood by the Chancellor of the Exchequer. His first anxiety, when applying to Lord Melbourne, had been respecting the question, whether the Discoveries with which he was then advancing might not ultimately supersede the work already executed. His second object had been to point out a possible arrangement, by which great expense might be saved in the mechanical construction of the Difference Engine.

So far was Mr. Babbage from having proposed to the Government to defray the expenses of the new or Analytical Engine, that though he expressly pointed out in the statement to the Duke of Wellington[20] four courses which it was possible for the Government to take,—yet in no one of them was the construction of the new Engine alluded to.

[19] The present Lord Monteagle.

[20] See page [86].

Those views of improved machinery for making calculations {89} which had appeared in but faint perspective in 1834, as likely to lead to important consequences, had, by this time, assumed a form and distinctness which fully justified the anticipations then made. By patient inquiry, aided by extensive drawings and notations, the projected Analytical Engine had acquired such powers, that it became necessary, for its further advancement, to simplify the elements of which it was composed. In the progress of this inquiry, Mr. Babbage had gradually arrived at simpler mechanical modes of performing those arithmetical operations on which the action of the Difference Engine depended; and he felt it necessary to communicate these new circumstances, as well as their consequences, to the Chancellor of the Exchequer.

On the 20th of January, 1836, Mr. Babbage wrote, in answer to the communication from the Chancellor of the Exchequer, that he did not, on re-examining the statement addressed to the Duke of Wellington, perceive that it contained any application to take up the new or Analytical Engine; and he accompanied this reply by a statement relative to the progress of the Analytical Engine, and its bearing upon the Difference Engine belonging to the Government. The former, it was said,

“Is not only capable of accomplishing all those other complicated calculations which I had intended, but it also performs all calculations which were peculiar to the Difference Engine, both in less time, and to a greater extent: in fact, it completely supersedes the Difference Engine.”

The Reply then referred to the statement laid before the Duke of Wellington in July, 1834, in which it was said,

“That all the elements of the Analytical were essentially different from those of the Difference Engine;”

and that the mechanical simplicity to which its elements had now been reduced was such, that it would probably cost more {90} to finish the old Difference Engine on its original plan than to construct a new Difference Engine with the simplified elements devised for the Analytical Engine.

It then proceeded to state that—

“The fact of a new superseding an old machine, in a very few years, is one of constant occurrence in our manufactories; and instances might be pointed out in which the advance of invention has been so rapid, and the demand for machinery so great, that half-finished machines have been thrown aside as useless before their completion.

“It is now nearly fourteen years since I undertook for the Government to superintend the making of the Difference Engine. During nearly four years its construction has been absolutely stopped, and, instead of being employed in overcoming the physical impediments, I have been harassed by what may be called the moral difficulties of the question. It is painful to reflect that, in the time so employed, the first Difference Engine might, under more favourable circumstances, have been completed.

“In making this Report, I wish distinctly to state, that I do not entertain the slightest doubt of the success of the Difference Engine; nor do I intend it as any application to finish the one or to construct the other; but I make it from a conviction that the information it contains ought to be communicated to those who must decide the question relative to the Difference Engine.”

The reference to the Royal Society, proposed by the Chancellor of the Exchequer, in his letter of the 14th of January, 1836,[21] did not take place; and during more than a year and a half no further measures appear to have been adopted by the Government respecting the Engine.

[21] See page [88].

It was obviously of the greatest importance to Mr. Babbage that a final decision should be made by the Government. When he undertook to superintend the construction of the Difference Engine for the Government, it was, of course, understood that he would not leave it unfinished. He had now been engaged fourteen years upon an object which he {91} had anticipated would not require more than two or three; and there seemed no limit to the time his engagement with the Government might thus be supposed to endure, unless some steps were taken to terminate it. Without such a decision Mr. Babbage felt that he should be impeded in any plans he might form, and liable to the most serious in­ter­rup­tion, if he should venture to enter upon the execution of them. He therefore most earnestly pressed, both by his personal applications and by those of his friends, for the settlement of the question. Mr. Wolryche Whitmore, in particular, repeatedly urged upon the Chancellor of the Exchequer, personally, as well as by letter, the injustice of keeping Mr. Babbage so very long in a state of suspense.

Time, however, passed on, and during nearly two years the question remained in the same state. Mr. Babbage, wearied with this delay, determined upon making a last effort to obtain a decision. He wrote to the First Lord of the Treasury (Lord Melbourne) on the 26th of July, 1838, recalling to his Lordship’s attention the frequency of his applications on this subject, and urging the necessity of a final decision upon it. He observed, that if the question had become more difficult, because he had invented superior mechanism, which had superseded that which was already partly executed, this consequence had arisen from the very delay against which he had so repeatedly remonstrated. He then asked, for the last time, not for any favour, but for that which it was an injustice to withhold—a decision.

On the 16th of August Mr. Spring Rice (the Chancellor of the Exchequer) addressed a note to Mr. Babbage, in reference to his application to Lord Melbourne. After recapitulating his former statement of the subject, which had been shown to be founded on a misapprehension, viz., that Mr. Babbage {92} had made an application to the Government to construct for them the Analytical Engine, the Chancellor of the Exchequer inquired whether he was solicitous that steps should be taken for the completion of the old, or for the commencement of a new machine,—and what he considered would be the cost of the one proceeding, and of the other?

Being absent on a distant journey, Mr. Babbage could not reply to this note until the 21st of October. He then reminded the Chancellor of the Exchequer of his previous communication of the 20th of January, 1836 (see p. 89), in which it was expressly stated that he did not intend to make any application to construct a new machine; but that the communication to the Duke of Wellington and the one to himself were made, simply because he thought it would be unfair to conceal such important facts from those who were called upon to decide on the continuance or discontinuance of the construction of the Difference Engine.

With respect to the expense of either of the courses pointed out by the Chancellor of the Exchequer, Mr. Babbage observed that, not being a pro­fes­sion­al Engineer, and his past experience having taught him not to rely upon his own judgment on matters of that nature, he should be very reluctant to offer any opinion upon the subject.

In conclusion, Mr. Babbage stated that the question he wished to have settled was—

Whether the Government required him to superintend the completion of the Difference Engine, which had been suspended during the last five years, according to the original plan and principles; or whether they intended to discontinue it altogether ?

In November, 1841, Mr. Babbage, on his return from the Continent, finding that Sir Robert Peel had become First {93} Lord of the Treasury, determined upon renewing his application for a decision of the question. With this view the previous pages of this Statement were drawn up, and a copy of it was forwarded to him, accompanied by a letter from Mr. Babbage, in which he observed—

“Of course, when I undertook to give the invention of the Calculating Engine to the Government, and to superintend its construction, there must have been an implied understanding that I should carry it on to its termination. I entered upon that understanding, believing that two or at the utmost that three years would complete it. The better part of my life has now been spent on that machine, and no progress whatever having been made since 1834, that understanding may possibly be considered by the Government as still subsisting: I am therefore naturally very anxious that this state of uncertainty should be put an end to as soon as possible.”

Mr. Babbage, in reply, received a note from Sir George Clerk (Secretary to the Treasury), stating that Sir Robert Peel feared that it would not be in his power to turn his attention to the subject for some days, but that he hoped, as soon as the great pressure of business previous to the opening of the session of Parliament was over, he might be able to determine on the best course to be pursued.

The session of Parliament closed in August, and Mr. Babbage had received no further communication on the subject. Having availed himself of several private channels for recalling the question to Sir Robert Peel’s attention without effect, Mr. Babbage, on the 8th of October, 1842, again wrote to him, requesting an early decision.

On the 4th of November, 1842, a note from Sir Robert Peel explained to Mr. Babbage that some delay had arisen, from his wish to communicate personally with the Chancellor of the Exchequer, who would shortly announce to him their joint conclusion on the subject.

On the same day Mr. Babbage received a letter from Mr. {94} Goulburn (the Chancellor of the Exchequer), who stated that he had communicated with Sir Robert Peel, and that they both regretted the necessity of abandoning the completion of a machine, on which so much scientific labour had been bestowed. He observed, that the expense necessary for rendering it either sat­is­fac­tory to Mr. Babbage or generally useful appeared, on the lowest calculation, so far to exceed what they should be justified in incurring, that they considered themselves as having no other alternative.

Mr. Goulburn concluded by expressing their hope, that by the Government withdrawing all claim to the machine as already constructed, and placing it entirely at Mr. Babbage’s disposal, they might in some degree assist him in his future exertions in the cause of Science.

On the 6th of November, 1842, Mr. Babbage wrote to Sir Robert Peel and the Chancellor of the Exchequer, acknowledging the receipt of their decision, thanking them for the offer of the machine as already constructed, but, under all the circumstances, declining to accept it.[22]

[22] The part of the Difference Engine already constructed, together with all the Drawings relating to the whole machine, were, in January, 1843 (by the direction of the Government), deposited in the Museum of King’s College, London.

On the 11th of November Mr. Babbage obtained an interview with Sir Robert Peel, and stated, that having given the original Invention to the Government—having superintended for them its construction—having dem­on­strated the possibility of the undertaking by the completion of an important portion of it—and that the non-completion of the design arose neither from his fault nor his desire, but was the act of the Government itself, he felt that he had some claims on their consideration.

He rested those claims upon the sacrifices he had made, {95} both personal and pecuniary, in the advancement of the Mechanical Arts and of Science—on the anxiety and the injury he had experienced by the delay of eight years in the decision of the Government on the subject, and on the great annoyance he had constantly been exposed to by the prevailing belief in the public mind that he had been amply remunerated by large grants of public money. Nothing, he observed, but some public act of the Government could ever fully refute that opinion, or repair the injustice with which he had been treated.

The result of this interview was entirely unsat­is­fac­tory. Mr. Babbage went to it prepared, had his statement produced any effect, to have pointed out two courses, by either of which it was probable that not only a Difference Engine, but even the Analytical Engine, might in a few years have been completed. The state of Sir Robert Peel’s information on the subject, and the views he took of Mr. Babbage’s services and position, prevented Mr. Babbage from making any allusion to either of those plans.

Thus finally terminated an engagement, which had existed upwards of twenty years. During no part of the last eight of those years does there appear to have been any reason why the same decision should not have been arrived at by the Government as was at last actually pronounced.

It was during this last period that all the great principles on which the Analytical Engine rests were discovered, and that the mechanical contrivances in which they might be embodied were invented. The establishment which Mr. Babbage had long maintained in his own house, and at his own expense, was now directed with increased energy to the new inquiries required for its perfection.

In this Statement the heavy sacrifices, both pecuniary and {96} personal, which the invention of these machines has entailed upon their author, have been alluded to as slightly as possible. Few can imagine, and none will ever know their full extent. Some idea of those sacrifices must nevertheless have occurred to every one who has read this Statement. During upwards of twenty years Mr. Babbage has employed, in his own house, and at his own expense, workmen of various kinds, to assist him in making experiments necessary for attaining a knowledge of every art which could possibly tend to the perfection of those Engines; and with that object he has frequently visited the manufactories of the Continent, as well as our own.

Since the discontinuance of the Difference Engine belonging to the Government, Mr. Babbage has himself maintained an establishment for making drawings and descriptions dem­on­strat­ing the nature and power of the Analytical Engine, and for its construction at some future period, when its value may be appreciated.

To these remarks it will only be added, that at an early stage of the construction of the Difference Engine he refused more than one highly desirable and profitable situation, in order that he might give his whole time and thoughts to the fulfilment of the engagement which he considered himself to have entered into with the Government.

August, 1843.

CHAPTER VII. DIFFERENCE ENGINE NO. II.

Difference Engine No. 2 — The Earl of Rosse, President of the Royal Society, proposed to the Government a Plan by which the Difference Engine No. 2 might have been executed — It was addressed to the Earl of Derby, and rejected by his Chancellor of the Exchequer.

IT was not until 1848, when I had mastered the subject of the Analytical Engine, that I resolved on making a complete set of drawings of the Difference Engine No. 2. In this I proposed to take advantage of all the improvements and simp­li­fi­ca­tions which years of unwearied study had produced for the Analytical Engine.

In 1852, the Earl of Rosse, who, from its commencement, had looked forward with the greatest interest to the application of mechanism to purposes of calculation, and who was well acquainted with the drawings and notations of the Difference Engine No. 2, inquired of me whether I was willing to give them to the Government, provided they would have the Engine constructed. My feeling was, after the sad experience of the past, that I ought not to think of sacrificing any further portion of my life upon the subject. If, however, they chose to have the Difference Engine made, I was ready to give them the whole of the drawings, and also the notations by which it was dem­on­strated that such a machine could be constructed, and that when made it would necessarily do the work prescribed for it. {98}

My much-valued friend, the late Sir Benjamin Hawes, had also been consulted, and it was agreed that the draft of a letter to Lord Derby, who was then prime minister, should be prepared; in which I should make this offer. Lord Rosse proposed to place my letter in Lord Derby’s hands, with his own statement of a plan by which the whole question might be determined.

Lord Rosse’s suggestion was, that the Government should apply to the President of the Institution of Civil Engineers to ascertain,

• 1st. Whether it was possible, from the drawings and notations, to make an estimate of the cost of constructing the machine?
• 2ndly. In case this question was answered in the affirmative—then, could a Mechanical Engineer be found who would undertake to construct it, and at what expense?

The Institution of Civil Engineers was undoubtedly the highest authority upon the first question. That being decided in the affirmative, no other body had equal power to find out those mechanical engineers who might be willing to undertake the contract.

Supposing both these questions, or even the latter only, answered in the negative, the proposition, of course, fell to the ground. But if they were both answered in the affirmative, then there would have arisen a further question for the consideration of the Government: namely, Whether the object to be obtained was worthy of the expenditure?

〈LORD ROSSE’S ADDRESS TO THE ROYAL SOCIETY.〉

The final result of this eminently practical plan was communicated to the Royal Society by their President, in his address at their anniversary on the 30th November, 1854. The following is an extract:— {99}

“The progress of the work was suspended: there was a change of Government. Science was weighed against gold by a new standard, and it was resolved to proceed no further. No enterprise could have had its beginning under more auspicious circumstances: the Government had taken the initiative—they had called for advice, and the adviser was the highest scientific authority in this country;—your Council; guided by such men as Davy, Wollaston, and Herschel. By your Council the undertaking was inaugurated,—by your Council it was watched over in its progress. That the first great effort to employ the powers of calculating mechanism, in aid of the human intellect, should have been suffered in this great country to expire fruitless, because there was no tangible evidence of immediate profit, as a British subject I deeply regret, and as a Fellow my regret is accompanied with feelings of bitter disappointment. Where a question has once been disposed of, succeeding Governments rarely reopen it, still I thought I should not be doing my duty if I did not take some opportunity of bringing the facts once more before Government. Circumstances had changed, mechanical engineering had made much progress; the tools required and trained workmen were to be found in the workshops of the leading mechanists, the founder’s art was so advanced that casting had been substituted for cutting, in making the change wheels, even of screw-cutting engines, and therefore it was very probable that persons would be found willing to undertake to complete the Difference Engine for a specific sum.

“That finished, the question would then have arisen, how far it was advisable to endeavour, by the same means, to turn to account the great labour which had been expended under the guidance of inventive powers the most original, {100} controlled by mathematics of a very high order; and which had been wholly devoted for so many years to the great task of carrying the powers of calculating machinery to its utmost limits. Before I took any step I wrote to several very eminent men of science, inquiring whether, in their opinion, any great scientific object would be gained if Mr. Babbage’s views, as explained in Ménabrèa’s little essay, were completely realized. The answers I received were strongly in the affirmative. As it was necessary the subject should be laid before Government in a form as practical as possible, I wrote to one of our most eminent mechanical engineers to inquire whether I should be safe in stating to Government that the expense of the Calculating Engine had been more than repaid in the improvements in mechanism directly referable to it; he replied,—unquestionably. Fortified by these opinions, I submitted this proposition to Government:—that they should call upon the President of the Society of Civil Engineers to report whether it would be practicable to make a contract for the completion of Mr. Babbage’s Difference Engine, and if so, for what sum. This was in 1852, during the short administration of Lord Derby, and it led to no result. The time was unfortunate; a great political contest was impending, and before there was a lull in politics, so that the voice of Science could be heard, Lord Derby’s government was at an end.”

〈MR. BABBAGE’S LETTER TO THE EARL OF DERBY.〉

The following letter was then drawn up, and placed in Lord Derby’s hands by Lord Rosse:—

June 8, 1852. MY LORD,

I TAKE the liberty of drawing your Lordship’s attention to the subject of the construction of a Difference Engine, for {101} calculating and printing Astronomical and Nautical Tables, which was brought under the notice of the Government so far back as the year 1823, and upon which the Government of that day desired the opinion of the Royal Society.

I annex a copy of the correspondence which took place at that time, and which your Lordship will observe was laid before Parliament.

The Committee of the Royal Society, to which the subject was referred, reported generally that the invention was one “fully adequate to the attainment of the objects proposed by the inventor, and that they considered Mr. Babbage as highly deserving of public encouragement in the prosecution of his arduous undertaking.”—Report of Royal Society, 1 st May, 1823. Parliamentary Paper, 370, 22 nd May, 1823.

And in a subsequent and more detailed Report, which I annex also, they state:—

“The Committee have no intention of entering into any consideration of the abstract math­e­mat­i­cal principle on which the practicability of such a machine as Mr. Babbage’s relies, nor of its public utility when completed. They consider the former as not only sufficiently clear in itself, but as already admitted and acted on by the Council in their former proceedings. The latter they regard as obvious to every one who considers the immense advantage of accurate numerical Tables in all matters of calculation, especially in those which relate to Astronomy and Navigation, and the great variety and extent of those which it is the object and within the compass of Mr. Babbage’s Engine to calculate and print with perfect accuracy.”—Report of Committee of Royal Society, 12th Feb., 1829.

Upon the first of these Reports, the Government determined to construct the machine, under my personal {102} superintendence and direction. The Engine was accordingly commenced and partially completed. Tables of figures were calculated, limited in extent only by the number of wheels put together.

Delays, from various causes arose in the progress of the work, and great expenses were incurred. The machine was altogether new in design and construction, and required the utmost mechanical skill which could be obtained for its execution. “It involved,” to quote again from the Report of the Committee of the Royal Society, “the necessity of constructing, and in many instances inventing, tools and machinery of great expense and complexity (and in many instances of ingenious contrivances likely to prove useful for other purposes hereafter), for forming with the requisite precision parts of the apparatus dissimilar to any used in ordinary mechanical works; that of making many previous trials to ascertain the validity of proposed movements; and that of altering, improving, and simplifying those already contrived and reduced to drawings. Your Committee are so far from being surprised at the time it has occupied to bring it to its present state, that they feel more disposed to wonder it has been possible to accomplish so much.” The true explanation both of the slow progress and of the cost of the work is clearly stated in this passage; and I may remark in passing, that the tools which were invented for the construction of the machine were afterwards found of utility, and that this anticipation of the Committee has been realized, as some of our most eminent mechanical engineers will readily testify.

Similar circumstances will, I apprehend, always attend and prolong the period of bringing to perfection inventions which have no parallel in the previous history of mechanical {103} construction. The necessary science and skill specially acquired in executing such works must also, as experience is gained, suggest deviations from, and improvements in, the original plan of those works; and the adoption or rejection of such changes, especially under circumstances similar to those in which I was placed, often involves questions of the greatest difficulty and anxiety.

From whatever cause, however, the delays and expenses arose, the result was that the Government was discouraged, and declined to proceed further with the work.

Mr. Goulburn’s letter, intimating this decision to me, in 1842, will be found in the accompanying printed Statement. And that the impediments to the completion of the engine, described by the Royal Society, were those which influenced the Government in the determination they came to, I infer from the reason assigned by Mr. Goulburn for its discontinuance, viz., “the expense which would be necessary in order to render it either sat­is­fac­tory to yourself or generally useful.” I readily admit that the work could not have been rendered sat­is­fac­tory to myself unless I was free to introduce every improvement which experience and thought could suggest. But that even with this additional source of expense its general usefulness would have been impaired, I cannot assent to, for I believe, in the words of the Report I have already quoted, the “immense advantage of accurate Numerical Tables in all matters of calculation, especially in those which relate to Astronomy and Navigation, cannot, within any reasonable limits, be over-estimated.” As to the expense actually incurred upon the first Difference Engine, that of the Government was about 17,000 l. On my own part, and out of my own private resources, I have sacrificed upon this and other works of science upwards of 20,000 l. {104}

From the date of Mr. Goulburn’s letter, nothing has been done towards the further completion of the Difference Engine by the Government or myself. So much of it as was completed was deposited in the Museum of King’s College, where it now remains.

Three consequences have, however, resulted from my subsequent labours, to which I attach great importance.

First, I have been led to conceive the most important elements of another Engine upon a new principle (the details of which are reduced accurately to paper), the power of which over the most complicated analytical operations appears nearly unlimited; but no portion of which is yet commenced. I have called this engine, in contradistinction to the other, the Analytical Engine.

Secondly, I have invented and brought to maturity a system of signs for the explanation of machinery, which I have called Mechanical Notation, by means of which the drawings, the times of action, and the trains for the transmission of force, are expressed in a language at once simple and concise. Without the aid of this language I could not have invented the Analytical Engine; nor do I believe that any machinery of equal complexity can ever be contrived without the assistance of that or of some other equivalent language. The Difference Engine No. 2, to which I shall presently refer, is entirely described by its aid.

Thirdly, in labouring to perfect this Analytical Machine of greater power and wider range of computation, I have discovered the means of simplifying and expediting the mechanical processes of the first or Difference Engine.

After what has passed, I cannot expect the Government to undertake the construction of the Analytical Engine, and I do not offer it for that purpose. It is not so matured as to {105} enable any other person, without long previous training and application, even to attempt its execution; and on my own part, to superintend its construction would demand an amount of labour, anxiety, and time which could not, after the treatment I have received, be expected from me. I therefore make no such offer.

But that I may fulfil to the utmost of my power the original expectation that I should be able to complete, for the Government, an Engine capable of calculating astronomical and nautical Tables with perfect accuracy, such as that which is described in the Reports of the Royal Society, I am willing to place at the disposal of Government (if they will undertake to execute a new Difference Engine) all those improvements which I have invented and have applied to the Analytical Engine. These comprise a complete series of drawings and explanatory notations, finished in 1849, of the Difference Engine No. 2,—an instrument of greater power as well as of greater simplicity than that formerly commenced, and now in the possession of the Government.

I have sacrificed time, health, and fortune, in the desire to complete these Calculating Engines. I have also declined several offers of great personal advantage to myself. But, not­with­stand­ing the sacrifice of these advantages for the purpose of maturing an engine of almost in­tel­lec­tual power, and after expending from my own private fortune a larger sum than the Government of England has spent on that machine, the execution of which it only commenced, I have received neither an acknowledgment of my labours, nor even the offer of those honours or rewards which are allowed to fall within the reach of men who devote themselves to purely scientific investigations. I might, perhaps, advance some claims to consideration, founded on my works and {106} cont­ri­bu­tions in aid of various departments of industrial and physical science,—but it is for others to estimate those services.

I now, however, simply ask your Lordship to do me the honour to consider this statement and the offer I make. I prefer no claim to the distinctions or the advantages which it is in the power of the Crown or the Government to bestow. I desire only to discharge whatever imagined obligation may be supposed to rest upon me, in connexion with the original undertaking of the Difference Engine; though I cannot but feel that whilst the public has already derived advantage from my labours, I have myself experienced only loss and neglect.

If the work upon which I have bestowed so much time and thought were a mere triumph over mechanical difficulties, or simply curious, or if the execution of such engines were of doubtful practicability or utility, some justification might be found for the course which has been taken; but I venture to assert that no mathematician who has a reputation to lose will ever publicly express an opinion that such a machine would be useless if made, and that no man distinguished as a Civil Engineer will venture to declare the construction of such machinery impracticable. The names appended to the Report of the Committee of the Royal Society fully justify my expressing this opinion, which I apprehend will not be disputed.

And at a period when the progress of physical science is obstructed by that exhausting in­tel­lec­tual and manual labour, indispensable for its advancement, which it is the object of the Analytical Engine to relieve, I think the application of machinery in aid of the most complicated and abstruse calculations can no longer be deemed unworthy of the attention of the country. In fact, there is no reason why mental as {107} well as bodily labour should not be economized by the aid of machinery.

With these views I have addressed your Lordship, as the head of the Government; and whatever may be my sense of the injustice that has hitherto been done me, I feel, in laying this rep­re­sen­ta­tion before your Lordship, and in making the offer I now make, that I have discharged to the utmost limit every implied obligation I originally contracted with the country.

I have the honour to be,

&c., &c., &c.,

CHARLES BABBAGE.

Dorset Street, Manchester Square.

June 8, 1852.

As this question was one of finance and of calculation, the sagacious Premier adroitly turned it over to his Chancellor of the Exchequer—that official being, from his office, supposed to be well versed in both subjects.

The opinion pronounced by the novelist and financier was, “That Mr. Babbage’s projects appear to be so indefinitely expensive, the ultimate success so problematical, and the expenditure certainly so large and so utterly incapable of being calculated, that the Government would not be justified in taking upon itself any further liability.”—Extract from the Reply of Earl Derby to the application of the Earl of Rosse, K.P., President of the Royal Society.

〈REFERRED TO THE CHANCELLOR OF THE EXCHEQUER.〉

The answer of Lord Derby to Lord Rosse was in substance—

That he had consulted the Chancellor of the Exchequer, who pronounced Mr. Babbage’s project as— {108}

• 1. “Indefinitely expensive.”
• 2. “The ultimate success problematical.”
• 3. “The expenditure utterly incapable of being calculated.”

1. With regard to the “indefinite expense.” Lord Rosse had proposed to refer this question to the President of the Institution of Civil Engineers, who would have given his opinion after a careful examination of the drawings and notations. These had not been seen by the Chancellor of the Exchequer; and, if seen by him, would not have been comprehended.

The objection that its success was “problematical” may refer either to its mechanical construction or to its math­e­mat­i­cal principles.

Who, possessing one grain of common sense, could look upon the unrivalled workmanship of the then existing portion of the Difference Engine No. 1, and doubt whether a simplified form of the same engine could be executed?

As to any doubt of its math­e­mat­i­cal principles, this was excusable in the Chancellor of the Exchequer, who was himself too practically acquainted with the fallibility of his own figures, over which the severe duties of his office had stultified his brilliant imagination. Far other figures are dear to him—those of speech, in which it cannot be denied he is indeed pre-eminent.

Any junior clerk in his office might, however, have told him that the power of computing Tables by differences merely required a knowledge of simple addition.

As to the impossibility of ascertaining the expenditure, this merges into the first objection; but a poetical brain must be pardoned when it repeats or amplifies. I will recall to the ex-Chancellor of the Exchequer what Lord Rosse really {109} proposed, namely, that the Government should take the opinion of the President of the Institution of Civil Engineers upon the question, whether a contract could be made for constructing the Difference Engine, and if so, for what sum.

But the very plan proposed by Lord Rosse and refused by Lord Derby, for the construction of the English Difference Engine, was adopted some few years after by another administration for the Swedish Difference Engine. Messrs. Donkin, the eminent Engineers, made an estimate, and a contract was in consequence executed to construct for Government a fac-simile of the Swedish Difference Engine, which is now in use in the department of the Registrar-General, at Somerset House. There were far greater mechanical difficulties in the production of that machine than in the one the drawings of which I had offered to the Government.

From my own experience of the cost of executing such works, I have no doubt, although it was highly creditable to the skill of the able firm who constructed it, but that it must have been commercially unprofitable. Under such circumstances, surely it was harsh on the part of the Government to refuse Messrs. Donkin permission to exhibit it as a specimen of English workmanship at the Exhibition of 1862.

〈HIS OPINION WORTHLESS.〉

But the machine upon which everybody could calculate, had little chance of fair play from the man on whom nobody could calculate.

If the Chancellor of the Exchequer had read my letter to Lord Derby, he would have found the opinion of the Committee of the Royal Society expressed in these words:—

“They consider the former [the abstract math­e­mat­i­cal principle] as not only sufficiently clear in itself, but as already admitted and acted on by the Council in their former proceedings. {110}

“The latter [its public utility] they consider as obvious to every one who considers the immense advantage of accurate numerical tables in all matters of calculation, especially in those which relate to astronomy and navigation.”—Report of the Royal Society, 12th Feb., 1829.

Thus it appears:—

• 1st. That the Chancellor of the Exchequer presumed to set up his own idea of the utility of the Difference Engine in direct opposition to that of the Royal Society.
• 2nd. That he refused to take the opinion of the highest mechanical authority in the country on its probable cost, and even to be informed whether a contract for its construction at a definite sum might not be attainable: he then boldly pronounced the expense to be “utterly incapable of being calculated.”

〈DIFFERENCE ENGINE No. 2. FEELS FOR THE CHANCELLOR OF THE EXCHEQUER.〉

This much-abused Difference Engine is, however, like its prouder relative the Analytical, a being of sensibility, of impulse, and of power.

It can not only calculate the millions the ex-Chancellor of the Exchequer squandered, but it can deal with the smallest quantities; nay, it feels even for zeros.[23] It is as conscious as Lord Derby himself is of the presence of a negative quantity, and it is not beyond the ken of either of them to foresee the existence of impossible ones.[24]

[23] It discovers the roots of equations by feeling whether all the figures in a certain column are zeros.

[24] It may be necessary to explain to the unmath­e­mat­i­cal reader and to the ex-Chancellor of the Exchequer that impossible quantities in algebra are something like mare’s-nests in ordinary life.

Yet should any unexpected course of events ever raise the {111} ex-Chancellor of the Exchequer to his former dignity, I am sure he will be its friend as soon as he is convinced that it can be made useful to him.

It may possibly enable him to un-muddle even his own financial accounts, and to ———

But as I have no wish to crucify him, I will leave his name in obscurity.

The Herostratus of Science, if he escape oblivion, will be linked with the destroyer of the Ephesian Temple.

CHAPTER VIII. OF THE ANALYTICAL ENGINE.

Man wrongs, and Time avenges.

BYRON.—The Prophecy of Dante.

Built Workshops for constructing the Analytical Engine — Difficulties about carrying the Tens — Unexpectedly solved — Application of the Jacquard Principle — Treatment of Tables — Probable Time required for Arithmetical Operations — Conditions it must fulfil — Unlimited in Number of Figures, or in extent of Analytical Operations — The Author invited to Turin in 1840 — Meetings for Discussion — Plana, Menabrea, MacCullagh, Mosotti — Difficulty proposed by the latter — Ob­ser­va­tions on the Errata of Astronomical Tables — Suggestions for a Reform of Analytical Signs.

THE circular arrangement of the axes of the Difference Engine round large central wheels led to the most extended prospects. The whole of arithmetic now appeared within the grasp of mechanism. A vague glimpse even of an Analytical Engine at length opened out, and I pursued with enthusiasm the shadowy vision. The drawings and the experiments were of the most costly kind. Draftsmen of the highest order were necessary to economize the labour of my own head; whilst skilled workmen were required to execute the experimental machinery to which I was obliged constantly to have recourse.

In order to carry out my pursuits successfully, I had purchased a house with above a quarter of an acre of ground in a {113} very quiet locality. My coach-house was now converted into a forge and a foundry, whilst my stables were transformed into a workshop. I built other extensive workshops myself, and had a fire-proof building for my drawings and draftsmen. Having myself worked with a variety of tools, and having studied the art of constructing each of them, I at length laid it down as a principle—that, except in rare cases, I would never do anything myself if I could afford to hire another person who could do it for me.

〈THE MECHANICAL NOTATION.〉

The complicated relations which then arose amongst the various parts of the machinery would have baffled the most tenacious memory. I overcame that difficulty by improving and extending a language of signs, the Mechanical Notation, which in 1826 I had explained in a paper printed in the “Phil. Trans.” By such means I succeeded in mastering trains of investigation so vast in extent that no length of years ever allotted to one individual could otherwise have enabled me to control. By the aid of the Mechanical Notation, the Analytical Engine became a reality: for it became susceptible of demonstration.

Such works could not be carried on without great expenditure. The fluctuations in the demand and supply of skilled labour were considerable. The railroad mania withdrew from other pursuits the most in­tel­lec­tual and skilful draftsmen. One who had for some years been my chief assistant was tempted by an offer so advantageous that in justice to his own family he could scarcely have declined it. Under these circumstances I took into consideration the plan of advancing his salary to one guinea per day. Whilst this was in abeyance, I consulted my venerable surviving parent. When I had fully explained the circumstances, my excellent mother replied: “My dear son, you have advanced {114} far in the accomplishment of a great object, which is worthy of your ambition. You are capable of completing it. My advice is—pursue it, even if it should oblige you to live on bread and cheese.”

This advice entirely accorded with my own feelings. I therefore retained my chief assistant at his advanced salary.

〈CARRYING THE TENS BY ANTICIPATION.〉

The most important part of the Analytical Engine was undoubtedly the mechanical method of carrying the tens. On this I laboured incessantly, each succeeding improvement advancing me a step or two. The difficulty did not consist so much in the more or less complexity of the contrivance as in the reduction of the time required to effect the carriage. Twenty or thirty different plans and modifications had been drawn. At last I came to the conclusion that I had exhausted the principle of successive carriage. I concluded also that nothing but teaching the Engine to foresee and then to act upon that foresight could ever lead me to the object I desired, namely, to make the whole of any unlimited number of carriages in one unit of time. One morning, after I had spent many hours in the drawing-office in endeavouring to improve the system of successive carriages, I mentioned these views to my chief assistant, and added that I should retire to my library, and endeavour to work out the new principle. He gently expressed a doubt whether the plan was possible, to which I replied that, not being able to prove its impossibility, I should follow out a slight glimmering of light which I thought I perceived.

After about three hours’ examination, I returned to the drawing-office with much more definite ideas upon the subject. I had discovered a principle that proved the possibility, and I had contrived mechanism which, I thought, would accomplish my object. {115}

I now commenced the explanation of my views, which I soon found were but little understood by my assistant; nor was this surprising, since in the course of my own attempt at explanation, I found several defects in my plan, and was also led by his questions to perceive others. All these I removed one after another, and ultimately terminated at a late hour my morning’s work with the conviction that anticipating carriage was not only within my power, but that I had devised one mechanism at least by which it might be accomplished.

Many years after, my assistant, on his return from a long residence abroad, called upon me, and we talked over the progress of the Analytical Engine. I referred back to the day on which I had made that most important step, and asked him if he recollected it. His reply was that he perfectly remembered the circumstance; for that on retiring to my library, he seriously thought that my intellect was beginning to become deranged. The reader may perhaps be curious to know how I spent the rest of that remarkable day.

After working, as I constantly did, for ten or eleven hours a day, I had arrived at this sat­is­fac­tory conclusion, and was revising the rough sketches of the new contrivance, when my servant entered the drawing-office, and announced that it was seven o’clock—that I dined in Park Lane—and that it was time to dress. I usually arrived at the house of my friend about a quarter of an hour before the appointed time, in order that we might have a short conversation on subjects on which we were both much interested. Having mentioned my recent success, in which my host thoroughly sympathized, I remarked that it had produced an exhilaration of the spirits which not even his excellent champagne could rival. Having enjoyed the society of Hallam, of Rogers, and of some few {116} others of that delightful circle, I retired, and joined one or perhaps two much more extensive reunions. Having thus forgotten science, and enjoyed society for four or five hours, I returned home. About one o’clock I was asleep in my bed, and thus continued for the next five hours.

This new and rapid system of carrying the tens when two numbers are added together, reduced the actual time of the addition of any number of digits, however large, to nine units of time for the addition, and one unit for the carriage. Thus in ten’s units of time, any two numbers, however large, might be added together. A few more units of time, perhaps five or six, were required for making the requisite previous arrangements.

Having thus advanced as nearly as seemed possible to the minimum of time requisite for arithmetical operations, I felt renewed power and increased energy to pursue the far higher object I had in view.

To describe the successive improvements of the Analytical Engine would require many volumes. I only propose here to indicate a few of its more important functions, and to give to those whose minds are duly prepared for it some information which will remove those vague notions of wonder, and even of its impossibility, with which it is surrounded in the minds of some of the most enlightened.

〈JACQUARD LOOM.〉

To those who are acquainted with the principles of the Jacquard loom, and who are also familiar with analytical formulæ, a general idea of the means by which the Engine executes its operations may be obtained without much difficulty. In the Exhibition of 1862 there were many splendid examples of such looms.

It is known as a fact that the Jacquard loom is capable of {117} weaving any design which the imagination of man may conceive. It is also the constant practice for skilled artists to be employed by man­u­fac­turers in designing patterns. These patterns are then sent to a peculiar artist, who, by means of a certain machine, punches holes in a set of pasteboard cards in such a manner that when those cards are placed in a Jacquard loom, it will then weave upon its produce the exact pattern designed by the artist.

〈WEAVING FORMULÆ.〉

Now the man­u­fac­turer may use, for the warp and weft of his work, threads which are all of the same colour; let us suppose them to be unbleached or white threads. In this case the cloth will be woven all of one colour; but there will be a damask pattern upon it such as the artist designed.

But the man­u­fac­turer might use the same cards, and put into the warp threads of any other colour. Every thread might even be of a different colour, or of a different shade of colour; but in all these cases the form of the pattern will be precisely the same—the colours only will differ.

The analogy of the Analytical Engine with this well-known process is nearly perfect.

The Analytical Engine consists of two parts:—

• 1st. The store in which all the variables to be operated upon, as well as all those quantities which have arisen from the result of other operations, are placed.
• 2nd. The mill into which the quantities about to be operated upon are always brought.

Every formula which the Analytical Engine can be required to compute consists of certain algebraical operations to be performed upon given letters, and of certain other modifications depending on the numerical value assigned to those letters.

There are therefore two sets of cards, the first to direct the {118} nature of the operations to be performed—these are called operation cards: the other to direct the particular variables on which those cards are required to operate—these latter are called variable cards. Now the symbol of each variable or constant, is placed at the top of a column capable of containing any required number of digits.

Under this arrangement, when any formula is required to be computed, a set of operation cards must be strung together, which contain the series of operations in the order in which they occur. Another set of cards must then be strung together, to call in the variables into the mill, the order in which they are required to be acted upon. Each operation card will require three other cards, two to represent the variables and constants and their numerical values upon which the previous operation card is to act, and one to indicate the variable on which the arithmetical result of this operation is to be placed.

But each variable has below it, on the same axis, a certain number of figure-wheels marked on their edges with the ten digits: upon these any number the machine is capable of holding can be placed. Whenever variables are ordered into the mill, these figures will be brought in, and the operation indicated by the preceding card will be performed upon them. The result of this operation will then be replaced in the store.

〈LAW OF DEVELOPMENT.〉

The Analytical Engine is therefore a machine of the most general nature. Whatever formula it is required to develop, the law of its development must be communicated to it by two sets of cards. When these have been placed, the engine is special for that particular formula. The numerical value of its constants must then be put on the columns of wheels below them, and on setting the Engine in motion it will calculate and print the numerical results of that formula. {119}

Every set of cards made for any formula will at any future time recalculate that formula with whatever constants may be required.

Thus the Analytical Engine will possess a library of its own. Every set of cards once made will at any future time reproduce the calculations for which it was first arranged. The numerical value of its constants may then be inserted.

It is perhaps difficult to apprehend these descriptions without a familiarity both with analytical forms and mechanical structures. I will now, therefore, confine myself to the math­e­mat­i­cal view of the Analytical Engine, and illustrate by example some of its supposed difficulties.

An excellent friend of mine, the late Professor MacCullagh, of Dublin, was discussing with me, at breakfast, the various powers of the Analytical Engine. After a long conversation on the subject, he inquired what the machine could do if, in the midst of algebraic operations, it was required to perform logarithmic or trigonometric operations.

〈ITS USE OF TABLES.〉

My answer was, that whenever the Analytical Engine should exist, all the developments of formula would be directed by this condition—that the machine should be able to compute their numerical value in the shortest possible time. I then added that if this answer were not sat­is­fac­tory, I had provided means by which, with equal accuracy, it might compute by logarithmic or other Tables.

〈DISCOVERS A MISTAKE.〉

I explained that the Tables to be used must, of course, be computed and punched on cards by the machine, in which case they would undoubtedly be correct. I then added that when the machine wanted a tabular number, say the logarithm of a given number, that it would ring a bell and then stop itself. On this, the attendant would look at a certain part of the machine, and find that it wanted the logarithm of a given {120} number, say of 2303. The attendant would then go to the drawer containing the pasteboard cards representing its table of logarithms. From amongst these he would take the required logarithmic card, and place it in the machine. Upon this the engine would first ascertain whether the assistant had or had not given him the correct logarithm of the number; if so, it would use it and continue its work. But if the engine found the attendant had given him a wrong logarithm, it would then ring a louder bell, and stop itself. On the attendant again examining the engine, he would observe the words, “Wrong tabular number,” and then discover that he really had given the wrong logarithm, and of course he would have to replace it by the right one.

Upon this, Professor MacCullagh naturally asked why, if the machine could tell whether the logarithm was the right one, it should have asked the attendant at all? I told him that the means employed were so ridiculously simple that I would not at that moment explain them; but that if he would come again in the course of a few days, I should be ready to explain it. Three or four days after, Bessel and Jacobi, who had just arrived in England, were sitting with me, inquiring about the Analytical Engine, when fortunately my friend MacCullagh was announced. The meeting was equally agreeable to us all, and we continued our conversation. After some time Bessel put to me the very same question which MacCullagh had previously asked. On this Jacobi remarked that he, too, was about to make the same inquiry when Bessel had asked the question. I then explained to them the following very simple means by which that verification was accomplished.

〈KNOWS WHAT IT WANTS.〉

Besides the sets of cards which direct the nature of the operations to be performed, and the variables or constants {121} which are to be operated upon, there is another class of cards called number cards. These are much less general in their uses than the others, although they are necessarily of much larger size.

Any number which the Analytical Engine is capable of using or of producing can, if required, be expressed by a card with certain holes in it; thus—

The above card contains eleven vertical rows for holes, each row having nine or any less number of holes. In this example the tabular number is 3 6 2 2 9 3 9, whilst its number in the order of the table is 2 3 0 3. In fact, the former number is the logarithm of the latter.

The Analytical Engine will contain,

• 1st. Apparatus for printing on paper, one, or, if required, two copies of its results.
• 2nd. Means for producing a stereotype mould of the tables or results it computes.
• 3rd. Mechanism for punching on blank pasteboard cards or metal plates the numerical results of any of its computations.

〈STOPS AND RINGS A BELL.〉

Of course the Engine will compute all the Tables which {122} it may itself be required to use. These cards will therefore be entirely free from error. Now when the Engine requires a tabular number, it will stop, ring a bell, and ask for such number. In the case we have assumed, it asks for the logarithm of 2 3 0 3.

When the attendant has placed a tabular card in the Engine, the first step taken by it will be to verify the number of the card given it by subtracting its number from 2 3 0 3, the number whose logarithm it asked for. If the remainder is zero, then the engine is certain that the logarithm must be the right one, since it was computed and punched by itself.

Thus the Analytical Engine first computes and punches on cards its own tabular numbers. These are brought to it by its attendant when demanded. But the engine itself takes care that the right card is brought to it by verifying the number of that card by the number of the card which it demanded. The Engine will always reject a wrong card by continually ringing a loud bell and stopping itself until supplied with the precise in­tel­lec­tual food it demands.

It will be an interesting question, which time only can solve, to know whether such tables of cards will ever be required for the Engine. Tables are used for saving the time of continually computing individual numbers. But the computations to be made by the Engine are so rapid that it seems most probable that it will make shorter work by computing directly from proper formulæ than by having recourse even to its own Tables.

The Analytical Engine I propose will have the power of expressing every number it uses to fifty places of figures. It will multiply any two such numbers together, and then, if required, will divide the product of one hundred figures by number of fifty places of figures. {123}

〈ARITHMETICAL DIFFICULTIES.〉

Supposing the velocity of the moving parts of the Engine to be not greater than forty feet per minute, I have no doubt that

• Sixty additions or subtractions may be completed and printed in one minute.
• One multiplication of two numbers, each of fifty figures, in one minute.
• One division of a number having 100 places of figures by another of 50 in one minute.

In the various sets of drawings of the modifications of the mechanical structure of the Analytical Engines, already numbering upwards of thirty, two great principles were embodied to an unlimited extent.

• 1st. The entire control over arithmetical operations, however large, and whatever might be the number of their digits.
• 2nd. The entire control over the combinations of algebraic symbols, however lengthened those processes may be required. The possibility of fulfilling these two conditions might reasonably be doubted by the most accomplished mathematician as well as by the most ingenious mechanician.

The difficulties which naturally occur to those capable of examining the question, as far as they relate to arithmetic, are these,—

• (a). The number of digits in each constant inserted in the Engine must be without limit.
• (b). The number of constants to be inserted in the Engine must also be without limit.
• (c). The number of operations necessary for arithmetic is only four, but these four may be repeated an unlimited number of times.
• (d). These operations may occur in any order, or follow an unlimited number of laws. {124}

〈ALGEBRAICAL DIFFICULTIES.〉

The following conditions relate to the algebraic portion of the Analytical Engine:—

• (e). The number of litteral constants must be unlimited.
• (f). The number of variables must be without limit.
• (g). The combinations of the algebraic signs must be unlimited.
• (h). The number of functions to be employed must be without limit.

This enumeration includes eight conditions, each of which is absolutely unlimited as to the number of its combinations.

Now it is obvious that no finite machine can include infinity. It is also certain that no question necessarily involving infinity can ever be converted into any other in which the idea of infinity under some shape or other does not enter.

It is impossible to construct machinery occupying unlimited space; but it is possible to construct finite machinery, and to use it through unlimited time. It is this substitution of the infinity of time for the infinity of space which I have made use of, to limit the size of the engine and yet to retain its unlimited power.

(a). I shall now proceed briefly to point out the means by which I have effected this change.

〈LARGER NUMBERS TREATED.〉

Since every calculating machine must be constructed for the calculation of a definite number of figures, the first datum must be to fix upon that number. In order to be somewhat in advance of the greatest number that may ever be required, I chose fifty places of figures as the standard for the Analytical Engine. The intention being that in such a machine two numbers, each of fifty places of figures, might be multiplied together and the resultant product of one hundred places might then be divided by another number of fifty {125} places. It seems to me probable that a long period must elapse before the demands of science will exceed this limit. To this it may be added that the addition and subtraction of numbers in an engine constructed for n places of figures would be equally rapid whether n were equal to five or five thousand digits. With respect to multiplication and division, the time required is greater:—

Thus if a . 10⁵⁰ + b and a′ . 10⁵⁰ + b′ are two numbers each of less than a hundred places of figures, then each can be expressed upon two columns of fifty figures, and a, b, a′, b′ are each less than fifty places of figures: they can therefore be added and subtracted upon any column holding fifty places of figures.

The product of two such numbers is—

a a′ 10¹⁰⁰ + (a b′ + a′ b) 10⁵⁰ + b b′.

This expression contains four pair of factors, a a′, a b′, a′ b, b b′, each factor of which has less than fifty places of figures. Each multiplication can therefore be executed in the Engine. The time, however, of multiplying two numbers, each consisting of any number of digits between fifty and one hundred, will be nearly four times as long as that of two such numbers of less than fifty places of figures.

The same reasoning will show that if the numbers of digits of each factor are between one hundred and one hundred and fifty, then the time required for the operation will be nearly nine times that of a pair of factors having only fifty digits.

Thus it appears that whatever may be the number of digits the Analytical Engine is capable of holding, if it is required to make all the computations with k times that number of digits, then it can be executed by the same Engine, but in an amount of time equal to k² times the former. Hence the {126} condition (a), or the unlimited number of digits contained in each constant employed, is fulfilled.

It must, however, be admitted that this advantage is gained at the expense of diminishing the number of the constants the Engine can hold. An engine of fifty digits, when used as one of a hundred digits, can only contain half the number of variables. An engine containing m columns, each holding n digits, if used for computations requiring k n digits, can only hold m / k constants or variables.

〈OF PUNCHING CARDS.〉

(b). The next step is therefore to prove (b), viz.: to show that a finite engine can be used as if it contained an unlimited number of constants. The method of punching cards for tabular numbers has already been alluded to. Each Analytical Engine will contain one or more apparatus for printing any numbers put into it, and also an apparatus for punching on pasteboard cards the holes corresponding to those numbers. At another part of the machine a series of number cards, resembling those of Jacquard, but delivered to and computed by the machine itself, can be placed. These can be called for by the Engine itself in any order in which they may be placed, or according to any law the Engine may be directed to use. Hence the condition (b) is fulfilled, namely: an unlimited number of constants can be inserted in the machine in an unlimited time.

I propose in the Engine I am constructing to have places for only a thousand constants, because I think it will be more than sufficient. But if it were required to have ten, or even a hundred times that number, it would be quite possible to make it, such is the simplicity of its structure of that portion of the Engine.

〈A THOUSAND VARIABLES.〉

(c). The next stage in the arithmetic is the number of times {127} the four processes of addition, subtraction, multiplication, and division can be repeated. It is obvious that four different cards thus punched

would give the orders for the four rules of arithmetic.

Now there is no limit to the number of such cards which may be strung together according to the nature of the operations required. Consequently the condition (c) is fulfilled.

(d). The fourth arithmetical condition (d), that the order of succession in which these operations can be varied, is itself unlimited, follows as a matter of course.

The four remaining conditions which must be fulfilled, in order to render the Analytical Engine as general as the science of which it is the powerful executive, relate to algebraic quantities with which it operates.

The thousand columns, each capable of holding any number of less than fifty-one places of figures, may each represent a constant or a variable quantity. These quantities I have called by the comprehensive title of variables, and have denoted them by V_n, with an index below. In the machine I have designed, n may vary from 0 to 999. But after any one or more columns have been used for variables, if those variables are not required afterwards, they may be printed upon paper, and the columns themselves again used for other variables. In such cases the variables must have a new index; thus, ^mVⁿ. I propose to make n vary from 0 to 99. If more variables are required, these may be supplied by Variable Cards, which may follow each other in unlimited succession. Each card will cause its symbol to be printed with its proper indices. {128}

For the sake of uniformity, I have used V with as many indices as may be required throughout the Engine. This, however, does not prevent the printed result of a development from being represented by any letters which may be thought to be more convenient. In that part in which the results are printed, type of any form may be used, according to the taste of the proposer of the question.

It thus appears that the two conditions, (e) and (f), which require that the number of constants and of variables should be unlimited, are both fulfilled.

The condition (g) requiring that the number of combinations of the four algebraic signs shall be unlimited, is easily fulfilled by placing them on cards in any order of succession the problem may require.

The last condition (h), namely, that the number of functions to be employed must be without limit, might seem at first sight to be difficult to fulfil. But when it is considered that any function of any number of operations performed upon any variables is but a combination of the four simple signs of operation with various quantities, it becomes apparent that any function whatever may be represented by two groups of cards, the first being signs of operation, placed in the order in which they succeed each other, and the second group of cards representing the variables and constants placed in the order of succession in which they are acted upon by the former.

〈A FINITE MACHINE MAY MAKE UNLIMITED CALCULATION.〉

Thus it appears that the whole of the conditions which enable a finite machine to make calculations of unlimited extent are fulfilled in the Analytical Engine. The means I have adopted are uniform. I have converted the infinity of space, which was required by the conditions of the problem, into the infinity of time. The means I have employed are in {129} daily use in the art of weaving patterns. It is accomplished by systems of cards punched with various holes strung together to any extent which may be demanded. Two large boxes, the one empty and the other filled with perforated cards, are placed before and behind a polygonal prism, which revolves at intervals upon its axis, and advances through a short space, after which it immediately returns.

A card passes over the prism just before each stroke of the shuttle; the cards that have passed hang down until they reach the empty box placed to receive them, into which they arrange themselves one over the other. When the box is full, another empty box is placed to receive the coming cards, and a new full box on the opposite side replaces the one just emptied. As the suspended cards on the entering side are exactly equal to those on the side at which the others are delivered, they are perfectly balanced, so that whether the formulæ to be computed be excessively complicated or very simple, the force to be exerted always remains nearly the same.

〈DISCUSSIONS AT TURIN.〉

In 1840 I received from my friend M. Plana a letter pressing me strongly to visit Turin at the then approaching meeting of Italian phi­los­o­phers. In that letter M. Plana stated that he had inquired anxiously of many of my countrymen about the power and mechanism of the Analytical Engine. He remarked that from all the information he could collect the case seemed to stand thus:—

“Hitherto the legislative department of our analysis has been all powerful—the executive all feeble.

“Your engine seems to give us the same control over the executive which we have hitherto only possessed over the legislative department.”

Considering the exceedingly limited information which {130} could have reached my friend respecting the Analytical Engine, I was equally surprised and delighted at his exact prevision of its powers. Even at the present moment I could not express more clearly, and in fewer terms, its real object. I collected together such of my models, drawings, and notations as I conceived to be best adapted to give an insight into the principles and mode of operating of the Analytical Engine. On mentioning my intention to my excellent friend the late Professor MacCullagh, he resolved to give up a trip to the Tyrol, and join me at Turin.

We met at Turin at the appointed time, and as soon as the first bustle of the meeting had a little abated, I had the great pleasure of receiving at my own apartments, for several mornings, Messrs. Plana, Menabrea, Mossotti, MacCullagh, Plantamour, and others of the most eminent geometers and engineers of Italy.

Around the room were hung the formula, the drawings, notations, and other illustrations which I had brought with me. I began on the first day to give a short outline of the idea. My friends asked from time to time further explanations of parts I had not made sufficiently clear. M. Plana had at first proposed to make notes, in order to write an outline of the principles of the engine. But his own laborious pursuits induced him to give up this plan, and to transfer the task to a younger friend of his, M. Menabrea, who had already established his reputation as a profound analyst.

These discussions were of great value to me in several ways. I was thus obliged to put into language the various views I had taken, and I observed the effect of my explanations on different minds. My own ideas became clearer, and I profited by many of the remarks made by my highly-gifted friends. {131}

〈MOSOTTI’S DIFFICULTY.〉

One day Mosotti, who had been unavoidably absent from the previous meeting, when a question of great importance had been discussed, again joined the party. Well aware of the acuteness and rapidity of my friend’s intellect, I asked my other friends to allow me five minutes to convey to Professor Mosotti the substance of the preceding sitting. After putting a few questions to Mosotti himself, he placed before me distinctly his greatest difficulty.

He remarked that he was now quite ready to admit the power of mechanism over numerical, and even over algebraical relations, to any extent. But he added that he had no conception how the machine could perform the act of judgment sometimes required during an analytical inquiry, when two or more different courses presented themselves, especially as the proper course to be adopted could not be known in many cases until all the previous portion had been gone through.

〈SOLUTION OF EQUATIONS.〉

I then inquired whether the solution of a numerical equation of any degree by the usual, but very tedious proceeding of approximation would be a type of the difficulty to be explained. He at once admitted that it would be a very eminent one.

For the sake of perspicuity and brevity I shall confine my present explanation to possible roots.

I then mentioned the successive stages:—

• Number of
  Operation
  Cards used.
• 1 a. Ascertain the number of possible roots by applying Sturm’s theorem to the coefficients.
• 2 b. Find a number greater than the greatest root.
• 3 c. Substitute the powers of ten (commencing with that next greater than the greatest root, and {132} diminishing the powers by unity at each step) for the value of x in the given equation.
• Continue this until the sign of the resulting number changes from positive to negative.
• The index of the last power of ten (call it n), which is positive, expresses the number of digits in that part of the root which consists of whole numbers. Call this index n + 1.
• 4 d. Substitute successively for x in the original equation 0 × 10ⁿ, 1 × 10ⁿ, 2 × 10ⁿ, 3 × 10ⁿ, . . . . 9 × 10ⁿ, until a change of sign occurs in the result. The digit previously substituted will be the first figure of the root sought.
• 5 e. Transform the original equation into another whose roots are less by the number thus found.
• The transformed equation will have a real root, the digit, less than 10ⁿ.
• 6 f. Substitute 1 × 10ⁿ⁻¹, 2 × 10ⁿ⁻¹, 3 × 10ⁿ⁻¹, &c., successively for the root of this equation, until a change of sign occurs in the result, as in process 4.
• This will give the second figure of the root.
• This process of alternately finding a new figure in the root, and then transforming the equation into another (as in process 4 and 5), must be carried on until as many figures as are required, whether whole numbers or decimals, are arrived at.
• 7 g. The root thus found must now be used to reduce the original equation to one dimension lower. {133}
• 8 h. This new equation of one dimension lower must now be treated by sections 3, 4, 5, 6, and 7, until the new root is found.
• 9 i. The repetition of sections 7 and 8 must go on until all the roots have been found.

Now it will be observed that Professor Mosotti was quite ready to admit at once that each of these different processes could be performed by the Analytical Machine through the medium of properly-arranged sets of Jacquard cards.

His real difficulty consisted in teaching the engine to know when to change from one set of cards to another, and back again repeatedly, at intervals not known to the person who gave the orders.

The dimensions of the algebraic equation being known, the number of arithmetical processes necessary for Sturm’s theorem is consequently known. A set of operation cards can therefore be prepared. These must be accompanied by a corresponding set of variable cards, which will represent the columns in the store, on which the several coefficients of the given equation, and the various combinations required amongst them, are to be placed.

The next stage is to find a number greater than the greatest root of the given equation. There are various courses for arriving at such a number. Any one of these being selected, another set of operation and variable cards can be prepared to execute this operation.

Now, as this second process invariably follows the first, the second set of cards may be attached to the first set, and the engine will pass on from the first to the second process, and again from the second to the third process. {134}

But here a difficulty arises: successive powers of ten are to be substituted for x in the equation, until a certain event happens. A set of cards may be provided to make the substitution of the highest power of ten, and similarly for the others; but on the occurrence of a certain event, namely, the change of a sign from + to −, this stage of the calculation is to terminate.

Now at a very early period of the inquiry I had found it necessary to teach the engine to know when any numbers it might be computing passed through zero or infinity.

The passage through zero can be easily ascertained, thus: Let the continually-decreasing number which is being computed be placed upon a column of wheels in connection with a carrying apparatus. After each process this number will be diminished, until at last a number is subtracted from it which is greater than the number expressed on those wheels.

Now in every case of a carriage becoming due, a certain lever is transferred from one position to another in the cage next above it.

Consequently in the highest cage of all (say the fiftieth in the Analytical Engine), an arm will be moved or not moved accordingly as the carriages do or do not run up beyond the highest wheel.

This arm can, of course, make any change which has previously been decided upon. In the instance we have been considering it would order the cards to be turned on to the next set.

If we wish to find when any number, which is increasing, {135} exceeds in the number of its digits the number of wheels on the columns of the machine, the same carrying arm can be employed. Hence any directions may be given which the circumstances require.

It will be remarked that this does not actually prove, even in the Analytical Engine of fifty figures, that the number computed has passed through infinity; but only that it has become greater than any number of fifty places of figures.

There are, however, methods by which any machine made for a given number of figures may be made to compute the same formulæ with double or any multiple of its original number. But the nature of this work prevents me from explaining that method.

It may here be remarked that in the process, the cards employed to make the substitutions of the powers of ten are operation cards. They are, therefore, quite independent of the numerical values substituted. Hence the same set of operation cards which order the substitutions 1 × 10ⁿ will, if backed, order the substitution of 2 × 10ⁿ, &c. We may, therefore, avail ourselves of mechanism for backing these cards, and call it into action whenever the circumstances themselves require it.

The explanation of M. Mosotti’s difficulty is this:—Mechanical means have been provided for backing or advancing the operation cards to any extent. There exist means of expressing the conditions under which these various processes are required to be called into play. It is not even necessary that two courses only should be possible. Any number of courses may be possible at the same time; and the choice of each may depend upon any number of conditions.

〈GENERAL MENABREA’S DESCRIPTION.〉

It was during these meetings that my highly valued friend, M. Menabrea, collected the materials for that lucid and {136} admirable description which he sub­se­quent­ly published in the Bibli. Univ. de Genève, t. xli. Oct. 1842.

The elementary principles on which the Analytical Engine rests were thus in the first instance brought before the public by General Menabrea.

〈THE COUNTESS OF LOVELACE’S NOTES.〉

Some time after the appearance of his memoir on the subject in the “Bibliothèque Universelle de Genève,” the late Countess of Lovelace[25] informed me that she had translated the memoir of Menabrea. I asked why she had not herself written an original paper on a subject with which she was so intimately acquainted? To this Lady Lovelace replied that the thought had not occurred to her. I then suggested that she should add some notes to Menabrea’s memoir; an idea which was immediately adopted.

[25] Ada Augusta, Countess of Lovelace, only child of the Poet Byron.

We discussed together the various illustrations that might be introduced: I suggested several, but the selection was entirely her own. So also was the algebraic working out of the different problems, except, indeed, that relating to the numbers of Bernouilli, which I had offered to do to save Lady Lovelace the trouble. This she sent back to me for an amendment, having detected a grave mistake which I had made in the process.

The notes of the Countess of Lovelace extend to about three times the length of the original memoir. Their author has entered fully into almost all the very difficult and abstract questions connected with the subject.

These two memoirs taken together furnish, to those who are capable of understanding the reasoning, a complete demonstration—That the whole of the developments and operations of analysis are now capable of being executed by machinery.

〈VARIOUS APPLICATIONS.〉

There are various methods by which these developments {137} are arrived at:—1. By the aid of the Differential and Integral Calculus. 2. By the Combinatorial Analysis of Hindenburg. 3. By the Calculus of Derivations of Arbogast.

Each of these systems professes to expand any function according to any laws. Theoretically each method may be admitted to be perfect; but practically the time and attention required are, in the greater number of cases, more than the human mind is able to bestow. Consequently, upon several highly interesting questions relative to the Lunar theory, some of the ablest and most indefatigable of existing analysts are at variance.

The Analytical Engine is capable of executing the laws prescribed by each of these methods. At one period I examined the Combinatorial Analysis, and also took some pains to ascertain from several of my German friends, who had had far more experience of it than myself, whether it could be used with greater facility than the Differential system. They seemed to think that it was more readily applicable to all the usual wants of analysis.

I have myself worked with the system of Arbogast, and if I were to decide from my own limited use of the three methods, I should, for the purposes of the Analytical Engine, prefer the Calcul des Derivations.

As soon as an Analytical Engine exists, it will necessarily guide the future course of the science. Whenever any result is sought by its aid, the question will then arise—By what course of calculation can these results be arrived at by the machine in the shortest time?

In the drawings I have prepared I proposed to have a thousand variables, upon each of which any number not having more than fifty figures can be placed. This machine would multiply 50 figures by other 50, and print the product {138} of 100 figures. Or it would divide any number having 100 figures by any other of 50 figures, and print the quotient of 50 figures. Allowing but a moderate velocity for the machine, the time occupied by either of these operations would be about one minute.

The whole of the numerical constants throughout the works of Laplace, Plana, Le Verrier, Hansen, and other eminent men whose indefatigable labours have brought astronomy to its present advanced state, might easily be recomputed. They are but the numerical coefficients of the various terms of functions developed according to certain series. In all cases in which these numerical constants can be calculated by more than one method, it might be desirable to compute them by several processes until frequent practice shall have confirmed our belief in the infallibility of mechanism.

〈ERRORS OF TABLES.〉

The great importance of having accurate Tables is admitted by all who understand their uses; but the multitude of errors really occurring is comparatively little known. Dr. Lardner, in the “Edinburgh Review,” has made some very instructive remarks on this subject.

I shall mention two within my own experience: these are selected because they occurred in works where neither care nor expense were spared on the part of the Government to insure perfect accuracy. It is, however, but just to the eminent men who presided over the preparation of these works for the press to observe, that the real fault lay not in them but in the nature of things.

In 1828 I lent the Government an original MS. of the table of Logarithmic Sines, Cosines, &c., computed to every second of the quadrant, in order that they might have it compared with Taylor’s Logarithms, 4to., 1792, of which they possessed a considerable number of copies. Nineteen {139} errors were thus detected, and a list of these errata was published in the Nautical Almanac for 1832: these may be called

Nineteen errata of the first order . . 1832.

An error being detected in one of these errata, in the following Nautical Almanac we find an

Erratum of the errata in N. Alm. 1832 . . 1833.

But in this very erratum of the second order a new mistake was introduced larger than any of the original mistakes. In the year next following there ought to have been found

Erratum in the erratum of the errata in N. Alm. 1832 . . 1834.

In the “Tables de la Lune,” by M. P. A. Hansen, 4to, 1857, published at the expense of the English Government, under the direction of the Astronomer Royal, is to be found a list of errata amounting to 155. In the 21st of these original errata there have been found three mistakes. These are duly noted in a newly-printed list of errata discovered during computations made with them in the “Nautical Almanac;” so that we now have the errata of an erratum of the original work.

This list of errata from the office of the “Nautical Almanac” is larger than the original list. The total number of errors at present (1862) discovered in Hansen’s “Tables of the Moon” amounts to above three hundred and fifty. In making these remarks I have no intention of imputing the slightest blame to the Astronomer Royal, who, like other men, cannot avoid submitting to inevitable fate. The only circumstance which is really extraordinary is that, when it was dem­on­strated that all tables are capable of being computed by machinery, and even when a machine existed which {140} computed certain tables, that the Astronomer Royal did not become the most enthusiastic supporter of an instrument which could render such invaluable service to his own science.

In the Supplementary Notices of the Astronomical Society, No. 9, vol. xxiii., p. 259, 1863, there occurs a Paper by M. G. de Ponteculant, in which forty-nine numerical coefficients relative to the Longitude, Latitude, and Radius vector of the Moon are given as computed by Plana, Delaunay, and Ponteculant. The computations of Plana and Ponteculant agree in thirteen cases; those of Delaunay and Ponteculant in two; and in the remaining thirty-four cases they all three differ.

〈REMARKS ON ANALYSIS.〉

I am unwilling to terminate this chapter without reference to another difficulty now arising, which is calculated to impede the progress of Analytical Science. The extension of analysis is so rapid, its domain so unlimited, and so many inquirers are entering into its fields, that a variety of new symbols have been introduced, formed on no common principles. Many of these are merely new ways of expressing well-known functions. Unless some philosophical principles are generally admitted as the basis of all notation, there appears a great probability of introducing the confusion of Babel into the most accurate of all languages.

A few months ago I turned back to a paper in the Philosophical Transactions, 1844, to examine some analytical investigations of great interest by an author who has thought deeply on the subject. It related to the separation of symbols of operation from those of quantity, a question peculiarly interesting to me, since the Analytical Engine contains the embodiment of that method. There was no ready, sufficient, and simple mode of distinguishing letters which represented quantity from those which indicated operation. To {141} understand the results the author had arrived at, it became necessary to read the whole Memoir.

Although deeply interested in the subject, I was obliged, with great regret, to give up the attempt; for it not only occupied much time, but placed too great a strain on the memory.

Whenever I am thus perplexed it has often occurred to me that the very simple plan I have adopted in my Mechanical Notation for lettering drawings might be adopted in analysis.

On the geometrical drawings of machinery every piece of matter which represents framework is invariably denoted by an upright letter; whilst all letters indicating moveable parts are marked by inclined letters.

The analogous rule would be—

Let all letters indicating operations or modifications be expressed by upright letters;

Whilst all letters representing quantity should be represented by inclined letters.

The subject of the principles and laws of notation is so important that it is desireable, before it is too late, that the scientific academies of the world should each contribute the results of their own examination and conclusions, and that some congress should assemble to discuss them. Perhaps it might be still better if each academy would draw up its own views, illustrated by examples, and have a sufficient number printed to send to all other academies.

CHAPTER IX. OF THE MECHANICAL NOTATION.

Art of Lettering Drawings — Of expressing the Time and Duration of Action of every Part — A New Demonstrative Science — Royal Medals of 1826.

SOON after I had commenced the Difference Engine, my attention was strongly directed to the imperfection of all known modes of explaining and dem­on­strat­ing the construction of machinery. It soon became apparent that my progress would be seriously impeded unless I could devise more rapid means of understanding and recalling the interpretation of my own drawings.

By a new system of very simple signs I ultimately succeeded in rendering the most complicated machine capable of explanation almost without the aid of words.

In order thoroughly to understand the action of any machine, we must have full information upon the following subjects, and it is of the greatest importance that this information should be acquired in the shortest possible time.

I. The actual shape and relative position of every piece of matter of which the machine is composed.

This can be accomplished by the ordinary mechanical drawings. Such drawings usually have letters upon them for the sake of reference in the description of the machine. Hitherto such letters were chosen without any principle, {143} and in fact gave no indication of anything except the mere spot upon the paper on which they were written.

〈RULES FOR LETTERING.〉

I then laid down rules for the selection of letters. I shall only mention one or two of them:—

• 1. All upright letters, as a, c, d, e, A, B, represent framing.
• 2. All inclined letters, as a, c, d, e, A, B, represent moveable parts.
• 3. All small letters represent working points. One of the most obvious advantages of these rules is that they enable the attention to be more easily confined to the immediate object sought.

By other rules it is rendered possible, when looking at a plan of any complicated machine, to perceive the relative order of super-position of any number of wheels, arms, &c., without referring to the elevation or end view.

II. The actual time and duration of every motion throughout the action of any machine can be ascertained almost instantly by a system of signs called the Notations of Periods.

It possesses equal facilities for ascertaining every contemporaneous as well as for every successive system of movements.

III. The actual connection of each moveable piece of the machine with every other on which it acts. Thus, taking from any special part of the drawing the indicating letter, and looking for it on a certain diagram, called the trains, the whole course of its movements may be traced, up to the prime mover, or down to the final result.

I have called this system of signs the Mechanical Notation. By its application to geometrical drawing it has given us a new demonstrative science, namely, that of proving that any given machine can or cannot exist; and if it can exist, that it will accomplish its desired object. {144}

It is singular that this addition to human knowledge should have been made just about the period when it was beginning to be felt by those most eminently skilled in analysis that the time has arrived when many of its conclusions rested only on probable evidence. This state of things arose chiefly from the enormous extent to which the developments were necessarily carried in the lunar and planetary theories.

〈ASTRONOMICAL MEDAL.〉

After employing this language for several years, it was announced, in December 1825, that King William IV. had founded two medals of fifty guineas each, to be given annually by the Royal Society according to rules to be laid down by the Council.

On the 26th January 1826, it was resolved,

“That it is the opinion of the Council that the medals be awarded for the most important discoveries or series of investigations, completed and made known to the Royal Society in the year preceding the day of the award.”

This rule reduced the number of competitors to a very few. Although I had had some experience as to the mode in which medals were awarded, and therefore valued them accordingly, I was simple enough to expect that the Council of the Royal Society would not venture upon a fraud on the very first occasion of exercising the royal liberality. I had also another motive for taking a ticket in this philosophical lottery of medals.

〈ROYAL SOCIETY MEDAL.〉

In 1824, the Astronomical Society did me the honour to award to me the first gold medal they ever bestowed. It was rendered still more grateful by the address of that eminent man, the late Henry Thomas Colebrooke, the President, who in a spirit of prophecy anticipated the results of years, at that period, long future. {145}

“It may not, therefore, be deemed too sanguine an anticipation, when I express the hope that an instrument which in its simpler form attains to the extraction of the roots of numbers, and approximates to the roots of equations, may, in a more advanced state of improvement, rise to the approximate solutions of algebraic equations of elevated degrees. I refer to solutions of such equations proposed by Lagrange, and more recently by other analysts, which involve operations too tedious and intricate for use, and which must remain without efficacy, unless some mode be devised of abridging the labour or facilitating the means of performance.”[26]

[26] ‘Discourse of the President on delivering the first Gold Medal of the Astronomical Society to Charles Babbage, Esq.’ ‘Memoirs of the Astronomical Society,’ vol. i. p. 509.

I felt, therefore, that the first Royal Medal might fairly become an object of ambition, whatever might be the worth of subsequent ones.

In order to qualify myself for this chance, I carefully drew up a paper, “On a Method of expressing by Signs the Action of Machinery,” which I otherwise should not have published at that time.

This Memoir was read at the Royal Society on the 16th March, 1826. To the system of signs which it first expounded I afterwards gave the name of “Mechanical Notation.” It had been used in England and in Ireland, although not taught in its schools. It applies to the description of a combat by sea or by land. It can assist in representing the functions of animal life; and I have had both from the Continent and from the United States, specimens of such applications. Finally, to whatever degree of simplicity I may at last have reduced the Analytical Engine, the course {146} through which I arrived at it was the most entangled and perplexed which probably ever occupied the human mind. Through the aid of the Mechanical Notation I examined numberless plans and systems of computing, and I am sure, from the nature of its self-necessary verifications that it is impossible I can have been deceived.

On the 16th November, 1826, that very Council of the Royal Society which had made the law took the earliest opportunity to violate it by awarding the two Royal Medals, the first to Dalton, whose great discovery had been made nearly twenty years before, and the other to Ivory, for a paper published in their “Transactions” three years before. The history of their proceedings will be found in the “Decline of Science in England,” p. 115, 1830.

CHAPTER X. THE EXHIBITION OF 1862.

“En administration, toutes les sottises sont mères.”—Maximes, par M. G. De Levis.

“An abject worship of princes and an unaccountable appetite for knighthood are probably unavoidable results of placing second-rate men in prominent positions.”—Saturday Review, January 16, 1864.

“Whose fault is this? But tallow, toys, and sweetmeats evidently stand high in the estimation of Her Majesty’s Com­mis­sion­ers.”—The Times, August 13, 1862.

Mr. Gravatt suggests to King’s College the exhibition of the Dif­fer­ence Engine No. 1, and offers to superintend its Trans­mis­sion and Return — Place allotted to it most unfit — Not Exhibited in 1851 — Its Loan refused to New York — Refused to the Dublin Exhibition in 1847 — Not sent to the great French Exhibition in 1855 — Its Exhibition in 1862 entirely due to Mr. Gravatt — Space for its Drawings refused — The Payment of Six Shillings a Day for a compe­tent person to explain it refused by the Com­mis­sioners — Copy of Swedish Dif­fer­ence Engine made by English Workmen not exhibited — Loan of various other Cal­cu­la­ting Machines offered — Anecdote of Count Strzelecki’s — The Royal Com­mis­sion­ers’ elaborate taste for Children’s Toys — A plan for making such Exhibitions prof­i­table — Extrav­a­gance of the Com­mis­sioners to their favourite — Contrast between his Treat­ment and that of Indust­rious Workmen — The Inventor of the Dif­fer­ence Engine publicly insulted by his Country­men in the Exhibition of 1862.

Circumstances connected with the Exhibition of the Difference Engine No. 1 in the International Exhibition of 1862.

WHEN the construction of the Difference Engine No. 1 was abandoned by the Government in 1842, I was consulted respecting the place in which it should be deposited. Well aware of the unrivalled perfection of its workmanship, and {148} conscious that it formed the first great step towards reducing the whole science of number to the absolute control of mechanism, I wished it to be placed wherever the greatest number of persons could see it daily.

〈ENGINE No. 1 IN KING’S COLLEGE.〉

With this view, I advised that it should be placed in one of the much-frequented rooms of the British Museum. Another locality was, however, assigned to it, and it was confided by the Government to the care of King’s College, Somerset House. It remained in safe custody within its glass case in the Museum of that body for twenty years. It is remarkable that during that long period no person should have studied its structure, and, by explaining its nature and use, have acquired an amount of celebrity which the singularity of that knowledge would undoubtedly have produced.

The College authorities did justice to their charge. They put it in the place of honour, in the centre of their Museum, and would, no doubt have given facilities to any of their members or to other persons who might have wished to study it.

〈THE GOVERNMENT IGNORE IT.〉

But the system quietly pursued by the Government, of ignoring the existence of the Difference Engine and its inventor doubtlessly exercised its deadening influence[27] on those who were inclined, by taste or acquirements, to take such a course. {149}

[27] An illustration fell under my notice a few days after this paragraph was printed. A new work on Geometrical Drawing, commissioned by the Committee of Council on Education, was published by Professor Bradley. I have not been able to find in it a single word concerning “Mechanical Notation,” not even the very simplest portion of that science, namely, the Art of Lettering Drawings. It would seem impossible that any Professor of so limited a subject could be ignorant of the existence of such an important addition to its powers.

I shall enumerate a few instances.

1. In 1850, the Government appointed a Commission to organize the Exhibition of 1851.

The name of the author of the Economy of Man­u­fac­tures was not thought worthy by the Government to be placed on that Commission.

2. In 1851, the Com­mis­sion­ers of the International Exhibition did not think proper to exhibit the Difference Engine, although it was the property of the nation. They were as insensible to the greatest mechanical as to, what has been regarded by some, the greatest in­tel­lec­tual triumph of their country.

3. When it was decided by the people of the United States to have an Exhibition at New York, they sent a Com­mis­sion­er to Europe to make arrangement for its success. He was authorized to apply for the loan of the Difference Engine for a few months, and was empowered to give any pecuniary guarantee which might be required for its safe return.

That Com­mis­sion­er, on his arrival, applied to me on the subject. I explained to him the state of the case, and advised him to apply to the Government, whose property it was. I added that, if his application was successful, I would at my own expense put the machine in good working order, and give him every information requisite for its safe conveyance and use. His application was, however, unsuccessful.

4. In 1847, Mr. Dargan nobly undertook at a vast expense to make an Exhibition in Dublin to aid in the relief of his starving countrymen. It was thought that the exhibition of the Difference Engine would be a great attraction. I was informed at the time that an application was made to the Government for its loan, and that it was also unsuccessful. {150}

5. In 1855 the great French Exhibition occurred. Previously to its opening, our Government sent Com­mis­sion­ers to arrange and superintend the English department.

These Com­mis­sion­ers reported that the English cont­ri­bu­tion was remarkably deficient in what in France are termed “instruments de précision,” a term which includes a variety of instruments for scientific purposes. They recommended that “a Committee should be appointed who could represent to the producers of Philosophical Instruments how necessary it was that they should, upon an occasion of this kind, maintain their credit in the eyes of Europe.” The Government also applied to the Royal Society for advice; but neither did the Royal Society advise, nor the Government propose, to exhibit the Difference Engine.

6. The French Exhibition of 1855 was remarkable beyond all former ones for the number and ingenuity of the machines which performed arithmetical operations.

Pre-eminently above all others stood the Swedish Machine for calculating and printing math­e­mat­i­cal Tables. It is honourable to France that its highest reward was deservedly given to the inventor of that machine; whilst it is somewhat remarkable that the English Com­mis­sion­ers appointed to report upon the French Exhibition omitted all notice of these Calculating Machines.

〈MR. GRAVATT SUCCEEDS IN EXHIBITING IT IN 1862.〉

The appearance of the finished portion of the unfinished Difference Engine No. 1 at the Exhibition of 1862 is entirely due to Mr. Gravatt. That gentleman had a few years before paid great attention to the Swedish Calculating Engine of M. Scheutz, and was the main cause of its success in this country.

Being satisfied that it was possible to calculate and print all Tables by machinery, Mr. Gravatt became convinced that {151} the time must arrive when no Tables would ever be calculated or printed except by machines. He felt that it was of great importance to accelerate the arrival of that period, more especially as numerical Tables, which are at present the most expensive kind of printing, would then become the cheapest.

In furtherance of this idea, Mr. Gravatt wrote to Dr. Jelf, the Principal of King’s College, Somerset House, to suggest that the Difference Engine of Mr. Babbage, which had for so many years occupied a prominent place in the museum, should be exhibited in the International Exhibition of 1862. He at the same time offered his assistance in the removal and reinstatement of that instrument.

The authorities of the College readily acceded to this plan. On further inquiry, it appeared that the Difference Engine belonged to the Government, and was only deposited with the College. It was then found necessary to make an application to the Treasury for permission to exhibit it, which was accordingly done by the proper authorities.

The Government granted the permission, and referred it to the Board of Works to superintend its placement in the building.

The Board of Works sent to me a copy of the correspondence relative to this matter, asking my opinion whether any danger might be apprehended for the safety of the machine during its transport, and also inquiring whether I had any other suggestion to make upon the subject.

Knowing the great strength of the work, I immediately answered that I did not anticipate the slightest injury from its transport, and that, under the superintendence of Mr. Gravatt, I considered it might be removed with perfect safety. The only suggestion I ventured to offer was, that as the Government possessed in the department of the {152} Registrar-General a copy, made by English workmen, of the Swedish Difference Engine, that it should be exhibited by the side of mine: and that both the Engines should be kept constantly working with a very slow motion.

〈SWEDISH ENGINE NOT EXHIBITED.〉

By a subsequent communication I was informed that the Swedish Machine could not be exhibited, because it was then in constant use, computing certain Tables relating to the values of lives. I regretted this very much. I had intended to alter the handle of my own Engine in order to make it moveable circularly by the same catgut which I had hoped might have driven both. The Tables which the Swedish Machine was employed in printing were not of any pressing necessity, and their execution could, upon such an occasion, have been postponed for a few months without loss or inconvenience.

Besides, if the Swedish Engine had, as I proposed, been placed at work, its superintendent might have continued his table-making with but little delay, and the public would have been highly gratified by the sight.

He could also have given information to the public by occasional explanations of its principles; thus might Her Majesty’s Com­mis­sion­ers have gratified thousands of her subjects who came, with intense curiosity, prepared to be pleased and instructed, and whom they sent away amazed and disappointed.

From the experience I had during the first week of the Exhibition, I am convinced that if a fit place had been provided for the two Calculating Machines, so that the public might have seen them both in constant but slow motion, and if the superintendent had oc­ca­sion­al­ly given a short explanation of the principles on which they acted, they would have been one of the greatest attractions within the building. {153}

On Mr. Gravatt applying to the Com­mis­sion­ers for space, it was stated that the Engine must be placed amongst philosophical instruments, Class XIII.

〈ENGLISH ENGINE POKED INTO A HOLE.〉

The only place offered for its reception was a small hole, 4 feet 4 inches in front by 5 feet deep. On one side of this was the only passage to the office of the superintendent of the class. The opposite side was occupied by a glass case in which I placed specimens of the separate parts of the unfinished engine. These, although executed by English workmen above thirty years ago, were yet, in the opinion of the most eminent engineers, unsurpassed by any work the building of 1862 contained. The back of this recess was closed in and dark, and only allowed a space on the wall of about five feet by four, on which to place the whole of the drawings and illustrations of the Difference Engine. Close above the top of the machine was a flat roof, which deprived the drawings and the work itself of much light.

The public at first flocked to it: but it was so placed that only three persons could conveniently see it at the same time. When Mr. Gravatt kindly explained and set it in motion, he was continually interrupted by the necessity of moving away in order to allow access to the numerous persons whose business called them to the superintendent’s office. At a very early period various rep­re­sen­ta­tions were made to the Com­mis­sion­ers by the Jury, the superintendent, and very strongly by the press, of the necessity of having some qualified person to explain the machine to the public. I was continually informed by the attendants that hundreds of persons had, during my absence asked, when they could get an opportunity of seeing the machine in motion.

Admiring the earnestness of purpose and the sagacity with which Mr. Gravatt had steadily followed out the convictions of {154} his own mind relative to the abolition of all tables except those made and stereotyped by machinery, I offered all the assistance in my power to accelerate the accomplishment of his task.

I lent him for exhibition numerous specimens of the unfinished portions of the Difference Engine No. 1. These I had purchased on the determination of the Government to abandon its construction in 1842.

I proposed also to lend him the Mechanical Notations of the Difference Engine, which had been made at my own expense, and were finished by myself and my eldest son, Mr. B. Herschel Babbage.

I had had several applications from foreigners[28] for some account of my system of Mechanical Notation, and great desire was frequently expressed to see the illustrations of the method itself, and of its various applications.

[28] One object of the mission of Professor Bolzani was, to take back with him to Russia such an account of the Mechanical Notation as might facilitate its teaching in the Russian Universities. I regret that it was entirely out of my power to assist him.

These, however, were so extensive that it was impossible, without very great inconvenience, to exhibit them even in my own house.

〈THE LOAN OF OTHER CALCULATING MACHINES OFFERED.〉

I therefore wrote to Mr. Gravatt to offer him the loan of the following property for the Exhibition:—

• 1. A small Calculating Machine of the simplest order for adding together any number of separate sums of money, provided the total was under 100,000 l., by Sir Samuel Morland. 1666.
• 2. A very complete and well-executed Machine for answering all questions in plane trigonometry, by Sir Samuel Morland. 1663. {155}
• 3. An original set of Napier’s bones.
• 4. A small Arithmetical Machine, by Viscount Mahon, afterwards Earl Stanhope. Without date.
• 5. A larger Machine, to add, subtract, multiply, and divide, by Viscount Mahon. 1775.
• 6. Another similar Machine, of a somewhat different construction, for the same operations, by Viscount Mahon. 1777.
• 7. A small Difference Engine, made in London, in consequence of its author having read Dr. Lardner’s article in the “Edinburgh Review” of July, 1834, No. CXX.

List of Mechanical Notations proposed to be Lent for the Exhibition.

• 1. All the drawings explaining the principles of the Mechanical Notation.
• 2. The complete Mechanical Notations of the Swedish Calculating Engine of M. Scheutz.
• These latter drawings had been made and used by my youngest son, Major Henry P. Babbage, now resident in India, in explaining the principles of the Mechanical Notation at the meeting of the British Association at Glasgow, and afterwards in London, at a meeting of the Institution of Civil Engineers.[29]
• 3. The Mechanical Notations of the Difference Engine No. 1. {156}
• These had been made at my own expense, and were finished by myself and my eldest son, Mr. B. Herschel Babbage, now resident in South Australia.
• 4. A complete set of the drawings of the Difference Engine No. 2, for calculating and printing tables, with seven orders of differences, and thirty places of figures. Finished in 1849.
• 5. A complete set of the Notations necessary for the explanation and demonstration of Difference Engine No. 2, finished in 1849.

[29] See Proceedings of British Association at Glasgow, 1855, p. 203; also Minutes of Proceedings of the Institution of Civil Engineers, vol. xv., 1856.

These drawings and notations would have required for their exhibition about seven or eight hundred square feet of wall. My letter to Mr. Gravatt was forwarded to the Com­mis­sion­ers with his own application for space to exhibit them. The Com­mis­sion­ers declined this offer; yet during the first six weeks of the Exhibition there was at a short distance from the Difference Engine an empty space of wall large enough for the greater part of these instructive diagrams. This portion of wall was afterwards filled up by a vast oil-cloth. Other large portions of wall, to the amount of thousands of square feet, were given up to other oil-cloths, and to numberless carpets. It is evident the Royal Com­mis­sion­ers were much better qualified to judge of furniture for the feet than of furniture for the head.

I was myself frequently asked why I did not employ a person to explain the Difference Engine. In reply to some of my friends, I inquired whether, when they purchased a carriage, they expected the builder to pay the wages of their coachman.

〈FOREIGN VISITORS PUZZLED.〉

But my greatest difficulty was with foreigners; no explanation I could devise, and I tried many, appeared at all {157} to satisfy their minds. The thing seemed to them entirely in­com­pre­hen­sible.

That the nation possessing the greatest military and commercial marine in the world—the nation which had spent so much in endeavouring to render perfect the means of finding the longitude—which had recently caused to be computed and published at considerable expense an entirely new set of lunar Tables should not have availed itself at any cost of mechanical means of computing and stereotyping such Tables, seemed entirely beyond their comprehension.

At last they asked me whether the Com­mis­sion­ers were bêtes. I assured them that the only one with whom I was personally acquainted certainly was not.

When hard pressed by difficult questions, I thought it my duty as an Englishman to save my country’s character, even at the expense of my own. So on one occasion I suggested to my unsatisfied friends that Com­mis­sion­ers were usually selected from the highest class of society, and that possibly four out of five had never heard of my name.

But here again my generous efforts to save the character of my country and its Com­mis­sion­ers entirely failed. Several of my foreign friends had known me in their own homes, and had seen the estimation in which I was held by their own countrymen and by their own sovereign. These were still more astonished.

〈CHINESE INQUIRE ABOUT IT.〉

On another occasion an anecdote was quoted against me to prove that my name was well known even in China. It may, perhaps, amuse the reader. A short time after the arrival of Count Strzelecki in England, I had the pleasure of meeting him at the table of a common friend. Many inquiries were made relative to his residence in China. Much interest was expressed by several of the party to learn on {158} what subject the Chinese were most anxious to have information. Count Strzelecki told them that the subject of most frequent inquiry was Babbage’s Calculating Machine. On being further asked as to the nature of the inquiries, he said they were most anxious to know whether it would go into the pocket. Our host now introduced me to Count Strzelecki, opposite to whom I was then sitting. After expressing my pleasure at the introduction, I told the Count that he might safely assure his friends in the Celestial Empire that it was in every sense of the word an out-of-pocket machine.

At last the Com­mis­sion­ers were moved, not to supply the deficiency themselves, but to address the Government, to whom the Difference Engine belonged, to send somebody to explain it. I received a communication from the Board of Works, inquiring whether I could make any suggestions for getting over this difficulty. I immediately made inquiries, and found a person who formerly had been my amanuensis, and had, under my direction, worked out many most intricate problems. He possessed very considerable knowledge of mathematics, and was willing, for the moderate remuneration of six shillings a day, to be present daily during nine hours to explain the Difference Engine.

I immediately sent this information to the Board of Works, with the name and address of the person I recommended. This, I have little doubt, was directly communicated to the Com­mis­sion­ers; but they did not avail themselves of his services.

〈COMMISSIONERS INEXPLICABLE.〉

It is difficult, upon any principle, to explain the conduct of the Royal Com­mis­sion­ers of the Exhibition of 1862. They were appointed by the Government, yet when the Government itself became an exhibitor, and sent for exhibition a {159} Difference Engine, the property of the nation, these Com­mis­sion­ers placed it in a small hole in a dark corner, where it could, with some difficulty, be seen by six people at the same time.

No remonstrance was of the slightest avail; it was “Hobson’s choice,” that or none. It was represented that all other space was occupied.

A trophy of children’s toys, whose merits, it is true, the Com­mis­sion­ers were somewhat more competent to appreciate, filled one of the most prominent positions in the building. On the other hand, a trophy of the workmanship of English engineers, executed by machine tools thirty years before, and admitted by the best judges to be unsurpassed by any rival, was placed in a position not very inappropriate for the authorities themselves who condemned it to that locality.

But no hired aristocratic[30] agent was employed to excite the slumbering perceptions of the Com­mis­sion­ers, who might have secured a favourable position for the Difference Engine, by practising on their good nature, or by imposing upon their imbecility.

[30] See “The Times,” 19 Jan., 1863, and elsewhere.

It has been urged, in extenuation of the con­duct of these Com­mis­sion­ers, that their duty as guardians of the funds intrusted to them, and of the interests of the Guarantors, compelled them to practise a rigid economy.

Rigid economy is to be respected only when it is under the control of judgment, not of favouritism. If the machinery for making arithmetical calculations which was placed at the disposal of the Com­mis­sion­ers had been properly arranged, it might have been made at once a source of high gratification to the public and even of profit to the Exhibition. {160}

〈A COURT FOR CALCULATING MACHINES.〉

Such a group of Calculating Machines might have been placed by themselves in a small court capable of holding a limited number of persons. Round the walls of this court might have been hung the drawings I had offered to lend, containing the whole of those necessary for the Difference Engine No. 2, as well as a large number of illustrations for the explanation of the Mechanical Notation. The Swedish Difference Engine and my own might have been slowly making calculations during the whole day.

This court should have been open to the public generally, except at two or three periods of half an hour each, during which it should have been accessible only to those who had previously secured tickets at a shilling apiece.

During each half hour the person whom I had recommended to the Com­mis­sion­ers might have given a short popular explanation of the subject.

This attraction might have been still further increased, and additional profit made, if a single sheet of paper had been printed containing a woodcut of the Swedish Machine, an impression from a page of the Tables computed and stereotyped by it at Somerset House, and also an impression from a stereotype plate of the Difference Engine exhibited by the Government.

A plate of the Swedish Machine is in existence in London. I am confident that, for such a purpose, I could have procured the loan of it for the Com­mis­sion­ers, and I would willingly have supplied them with the stereotype plate from which the frontispage of the present volume was printed, together with from ten to twenty lines of necessary explanation.

These illustrations of machinery used for computing and printing Tables might have been put up into packets of dozens and half dozens, and also have been sold in single {161} sheets at the rate of one penny each copy. There can be no doubt the sale of them would have been very considerable. As it was, I found the woodcut representing the Difference Engine No. 1 in great request, and during the exhibition I had numberless applications for it; having given away my whole stock of about 800 copies.

〈AN ASSISTANT EXPLAINING.〉

The calculating court might have held comfortably from sixty to eighty seats. Each lecture would have produced say 3 l. This being repeated three times each day, together with the sale of the woodcuts, would have produced about 10 l. per day, out of which the Com­mis­sion­ers would have had six shillings per day to pay the assistant who gave the required explanations.

If the dignity of the Com­mis­sion­ers would not permit them to make money by such means, they might have announced that the proceeds of the tickets would be given to the distressed population of the Manchester district, and there would then have been crowds of visitors.

But the rigid economy of the Com­mis­sion­ers, who refused to expend six shillings a day for an attendant, although it would most probably have produced a return of several hundred pounds, was entirely laid aside when their patronage was to be extended to a brother official.

Captain Fowke, an officer of engineers, whose high order of architectural talent became afterwards so well known to the public, and whose whole time and services were retained and paid for by the country, was employed to make a design for the Exhibition Building.

〈THE COMMISSIONERS DO A JOB.〉

The Com­mis­sion­ers approved of this design, which comprised two lofty domes, uniting in themselves the threefold inconvenience of being ugly, useless, and expensive. They then proceeded to pay him five thousand pounds for the job. {162} This system of awarding large sums of money to certain favoured public officers who are already paid for their services by liberal salaries seems to be a growing evil. At the period of the Irish famine the under-secretary of the Treasury condescended to accept 2,500 l. out of the fund raised to save a famished nation. Some inquiries, even recently, were oc­ca­sion­al­ly made whether any similar deduction will be allowed from the liberal cont­ri­bu­tions to the sufferers by the cotton famine.

The question was raised and the practice reprobated in the House of Commons by men of opposite party politics. Mr. Gladstone remarked:—

“If there was one rule connected with the public service which more than any other ought to be scrupulously observed, it was this, that the salary of a public officer, more especially if he were of high rank, ought to cover all the services he might be called upon to render. Any departure from this rule must be dangerous.” Hansard, vol. 101, p. 138, 1848. Supply, 14 Aug. 1848. See also “The Exposition of 1851,” 8vo., p. 217.

〈THE ADMIRALTY REFUSE.〉

The following paragraph appeared in “The Times”[31] a short time since, under the head Naval Intelligence:—

“A reply has been received to the memorial trans­mit­ted to the Admiralty some few days since from the inspectors employed on the iron frigate ‘Achilles,’ building at Chatham dockyard, requesting that they may be placed on the same footing as regards increased pay as the junior officers and mechanics working on the iron frigate for the additional number of hours they are employed in the dockyard. The Lords of the Admiralty intimate that they cannot accede to the wishes of the memorialists, who are reminded that, as {163} salaried officers of the establishment, the whole of their time is at the disposal of the Admiralty. This decision has caused considerable dissat­is­fac­tion.”

[31] About the 20th of May, 1863.

It appears that the Admiralty wisely adopted the principle enunciated by Mr. Gladstone.

It may, however, not unreasonably have caused dis­sat­is­fac­tion to those who had no interest to back them on finding that such large sums are pocketed by those who are blessed with influential friends in high quarters.

If the Com­mis­sion­ers had really wished to have obtained a suitable building at a fair price their course was simple and obvious. They need only have stated the nature and amount of accommodation required, and then have selected half a dozen of the most eminent firms amongst our great contractors, who would each have given them an estimate of the plans they respectively suggested.

The Com­mis­sion­ers might have made it one of the conditions that they should not be absolutely bound to give the contract to the author of the plan accepted. But in case of not employing him a sum previously stipulated should have been assigned for the use of the design.

By such means they would have had a choice of various plans, and if those plans had, previously to the decision of the Com­mis­sion­ers, been publicly exhibited for a few weeks, they might have been enlightened by public criticism. Such a course would have prevented the gigantic job they afterwards perpetrated. It could therefore find no support from the Com­mis­sion­ers.

The present Com­mis­sion­ers, however, are fit successors to those who in 1851 ignored the existence of the author of the “Economy of Man­u­fac­tures” and his inventions. They seem to have been deluded into the belief that they possessed {164} the strength, as well as the desire, quietly to strangle the Difference Engine.

It would be idle to break such butterflies upon its matchless wheels, or to give permanence to such names by reflecting them from its diamond-graven plates.[32] Though the steam-hammer can crack the coating without injuring the kernel of the filbert it drops upon—the admirable precision of its gigantic power could never be dem­on­strated by exhausting its energy upon an empty nut-shell.

[32] For the purpose of testing the steadiness and truth of the tools employed in forming the gun-metal plates, I had some dozen of them turned with a diamond point. The perfect equality of its cut caused the reflected light to be resolved into those beautiful images pointed out by Frauenhofer, and also so much admired in the celebrated gold buttons produced by the late Mr. Barton, the Comptroller of the Mint.

Peace, then, to their memory, aptly enshrined in unknown characters within the penetralia of the temple of oblivion.

〈CONSOLATION FOR THE COMMISSIONERS.〉

These celebrities may there at last console themselves in the enjoyment of one enviable privilege denied to them during their earthly career—exemption from the daily consciousness of being “found out.”

It is, however, not quite impossible, although deciphering is a brilliant art, that one or other of them may have heard of the dread power of the decipherer. Having myself had some slight acquaintance with that fascinating pursuit, it gives me real pleasure to relieve them from this very natural fear by assuring them that not even the most juvenile decipherer could be so stupid as to apply himself to the interpretation of—characters known to be meaningless.

Yet there is one name amongst, but not of them—a fellow-worshipper with myself at far other fanes, whose hands, like mine, have wielded the hammer, and whose pen, like mine, has endeavoured to communicate faithfully to his fellow-men {165} the measure of those truths he has himself laboriously extracted from the material world. With such endowments, it is impossible that he could have had any cognizance of this part of the proceedings of his colleagues.[33]

[33] I have since learnt, with real sat­is­fac­tion, that my friend, Mr. Fairbairn, was not a member of that incompetent Commission.

〈MR. GRAVATT EXPLAINS THE ENGINE.〉

At the commencement of the Exhibition, Mr. Gravatt was constantly present, and was so kind as to explain to many anxious inquirers the nature and uses of the Difference Engine. This, however, interfered so much with his pro­fes­sion­al engagements as a Civil Engineer, that it would have been unreasonable to have expected its continuance. In fact, as not above half a dozen spectators could see the machine at once, it was a great sacrifice of valuable time for a very small result.

During the early part of my own examination of the Exhibition I had many opportunities of conversing with experienced workmen, well qualified to appreciate the workmanship of the Difference Engine; these I frequently accompanied to its narrow cell, and pointed out to them its use, as well as the means by which its various parts had received their destined form.

Oc­ca­sion­al­ly also I explained it to some few of my personal friends. When Mr. Gravatt or myself were thus engaged, a considerable crowd was often collected, who were anxious to hear about, although they could not see, the Engine itself.

Upon one of these occasions I was insulted by impertinent questions conveyed in a loud voice from a person at a distance in the crowd. My taste for music, and especially for organs, was questioned. I was charitable enough to suppose that this was an exceptional case; but in less than a week another instance {166} occurred. After this experience, of course, I seldom went near the Difference Engine. Mr. Gravatt who had generously sacrificed a considerable portion of his valuable time for the information and in­struc­tion of the public was now imperatively called away by pro­fes­sion­al engagements, and the public had no information whatever upon a subject on which it was really very anxious to be instructed.

〈MR. WILMOT BUXTON EXPLAINS THE DIFFERENCE ENGINE.〉

Fortunately, however, the Exhibition took place during the long vacation; and a friend of mine, Mr. Wilmot Buxton, of the Chancery Bar, very frequently accompanied me in my visits. Possessing a profound knowledge of the math­e­mat­i­cal principles embodied in the mechanism, I had frequently pointed out to him its nature and relations. These I soon found he so well apprehended that I felt justified in intrusting him with one of my keys of the machine, in order that he might have access to it without the necessity of my presence.

Whenever he opened it for his own sat­is­fac­tion or for the in­struc­tion of his friends, he was speedily surrounded by a far larger portion of the public than could possibly see it, but who were still attracted by his lucid oral explanation.

It was fortunate for many of the visitors to the Exhibition that this occurred, for the demands on his time, when present, were incessant, and hundreds thus acquired from his explanations a popular view of the subject.

After the close of the Exhibition, Mr. Gravatt and myself attended to prepare the Difference Engine for its return to the Museum of King’s College. To our great astonishment, we found that it had already been removed to the Museum at South Kensington. Not only the Difference Engine itself, but also the illustrations and all the unfinished portions of exquisite workmanship which I had lent to the Exhibition for its explanation, were gone. {167}

On Mr. Gravatt applying to the Board of Works, it was stated that the Difference Engine itself had been placed in the Kensington Museum because the authorities of King’s College had declined receiving it, and immediate in­struc­tions were of course given for the restoration of my own property.

CHAPTER XI. THE LATE PRINCE CONSORT.

“Suum cuique.”