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The Modern Clock
A Study of Time Keeping Mechanism;
Its Construction, Regulation
and Repair.

BY WARD L. GOODRICH

Author of the Watchmaker’s Lathe, Its Use and Abuse.

WITH NUMEROUS ILLUSTRATIONS
AND DIAGRAMS

CHICAGO
Hazlitt & Walker, Publishers
1905

Copyrighted
1905
BY HAZLITT & WALKER.

TABLE OF CONTENTS

CHAPTER I.
THE NECESSITY FOR BETTER SKILL AMONG CLOCKMAKERS.

The need for information of an exact and reliable character in regard to the hard worked and much abused clock has, we presume, been felt by every one who entered the trade. This information exists, of course, but it is scattered through such a wide range of publications and is found in them in such a fragmentary form that by the time a workman is sufficiently acquainted with the literature of the trade to know where to look for such information he no longer feels the necessity of acquiring it.

The continuous decrease in the prices of watches and the consequent rapid increase in their use has caused the neglect of the pendulum timekeepers to such an extent that good clock men are very scarce, while botches are universal. When we reflect that the average ‘life’ of a worker at the bench is rarely more than twenty years, we can readily see that information by verbal instruction is rapidly being lost, as each apprentice rushes through clock work as hastily as possible in order to do watch work and consequently each “watchmaker” knows less of clocks than his predecessor and is therefore less fitted to instruct apprentices in his turn.

The striking clock will always continue to be the timekeeper of the household and we are still dependent upon the compensating pendulum, in conjunction with the fixed stars, for the basis of our timekeeping system, upon which our commercial and legal calendars and the movements of our ships and railroad trains depend, so that an accurate knowledge of its construction and behavior forms the essential basis of the largest part of our business and social systems, while the watches for which it is slighted are themselves regulated and adjusted at the factories by the compensated pendulum.

The rapid increase in the dissemination of “standard time” and the compulsory use of watches having a maximum variation of five seconds a week by railway employees has so increased the standard of accuracy demanded by the general public that it is no longer possible to make careless work “go” with them, and, if they accept it at all, they are apt to make serious deductions from their estimate of the watchmaker’s skill and immediately transfer their custom to some one who is more thorough.

The apprentice, when he first gets an opportunity to examine a clock movement, usually considers it a very mysterious machine. Later on, if he handles many clocks of the simple order, he becomes tolerably familiar with the time train; but he seldom becomes confident of his ability regarding the striking part, the alarm and the escapement, chiefly because the employer and the older workmen get tired of telling him the same things repeatedly, or because they were similarly treated in their youth, and consider clocks a nuisance, any how, never having learned clock work thoroughly, and therefore being unable to appreciate it. In consequence of such treatment the boy makes a few spasmodic efforts to learn the portions of the business that puzzle him, and then gives it up, and thereafter does as little as possible to clocks, but begs continually to be put on watch work.

We know of a shop where two and sometimes three workmen (the best in the shop, too) are constantly employed upon clocks which country jewelers have failed to repair. If clock work is dull they will go upon watch work (and they do good work, too), but they enjoy the clocks and will do them in preference to watches, claiming that there is greater variety and more interest in the work than can be found in fitting factory made material into watches, which consist of a time train only. Two of these men have become famous, and are frequently sent for to take care of complicated clocks, with musical and mechanical figure attachments, tower, chimes, etc. The third is much younger, but is rapidly perfecting himself, and is already competent to rebuild minute repeaters and other sorts of the finer kinds of French clocks. He now totally neglects watch work, saying that the clocks give him more money and more fun.

We are confident that this would be also the case with many another American youth if he could find some one to patiently instruct him in the few indispensable facts which lie at the bottom of so much that is mysterious and from which he now turns in disgust. The object of these articles is to explain to the apprentice the mysteries of pendulums, escapements, gearing of trains, and the whole technical scheme of these measurers of time, in such a way that hereafter he may be able to answer his own questions, because he will be familiar with the facts on which they depend.

Many workmen in the trade are already incompetent to teach clockwork to anybody, owing to the slighting process above referred to; and the frequent demands for a book on clocks have therefore induced the writer to undertake its compilation. Works on the subject—nominally so, at least—are in existence, but it will generally be found on examination that they are written by outsiders, not by workmen, and that they treat the subject historically, or from the standpoint of the artistic or the curious. Any information regarding the mechanical movements is fragmentary, if found in them at all, and they are better fitted for the amusement of the general public than for the youth or man who wants to know “how and why.” These facts have impelled the writer to ignore history and art in considering the subject; to treat the clock as an existing mechanism which must be understood and made to perform its functions correctly; and to consider cases merely as housings of mechanism, regardless of how beautiful, strange or commonplace those housings may be.

We have used the word “compile” advisedly. The writer has no new ideas or theories to put forth, for the reason that the mechanism we are considering has during the last six hundred years had its mathematics reduced to an exact science; its variable factors of material and mechanical movements developed according to the laws of geometry and trigonometry; its defects observed and pointed out; its performances checked and recorded. To gather these facts, illustrate and explain them, arrange them in their proper order, and point out their relative importance in the whole sum of what we call a clock, is therefore all that will be attempted. In doing this free use has been made of the observations of Saunier, Reid, Glasgow, Ferguson, Britten, Riefler and others in Europe and of Jerome, Playtner, Finn, Learned, Ferson, Howard and various other Americans. The work is therefore presented as a compilation, which it is hoped will be of service in the trade.

In thus studying the modern American clocks, we use the word American in the sense of ownership rather than origin, the clocks which come to the American workmen to-day have been made in Germany, France, England and America.

The German clocks are generally those of the Schwartzwald (or Black Forest) district, and differ from others in their structure, chiefly in the following particulars: The movement is supported by a horizontal seatboard in the upper portion of the case. The wooden trains of many of the older type instead of being supported by plates are held in position by pillars, and these pillars are held in position by top and bottom boards. In the better class of wooden clocks the pivot holes in the pillars are bushed with brass tubing, while the movement has a brass ’scape wheel, steel wire pivots and lantern pinions of wood, with steel trundles. In all these clocks the front pillars are friction-tight, and are the ones to be removed when taking down the trains. Both these and the modern Swartzwald brass movements use a sprocket wheel and chain for the weights and have exposed pendulums and weights.

The French clocks are of two classes, pendules and carriage clocks, and both are liable to develop more hidden crankiness and apparently causeless refusals to go than ever occurred to all the English, German and American clocks ever put together. There are many causes for this, and unless a man is very new at the business he can tell stories of perversity, that would make a timid apprentice want to quit. Yet the French clocks, when they do go, are excellent timekeepers, finely finished, and so artistically designed that they make their neighbors seem very clumsy by comparison. They are found in great variety, time, half-hour and quarter-hour strike, musical and repeating clocks being a few of the general varieties. The pendulums are very short, to accommodate themselves to the artistic needs of the cases, and nearly all have the snail strike instead of the count wheel. The carriage clocks have watch escapements of cylinder or lever form, and the escapement is frequently turned at right angle by means of bevel gears, or contrate wheel and pinion, and placed on top of the movement.

The English clocks found in America are generally of the “Hall” variety, having heavy, well finished movements, with seconds pendulum and frequently with calendar and chime movements. They, like the German, are generally fitted with weights instead of springs. There are a few English carriage clocks, fitted with springs and fuzees, though most of them, like the French, have springs fitted in going barrels.

The American clocks, with which the apprentice will naturally have most to do, may be roughly divided into time, time alarm, time strike, time strike alarm, time calendar and electric winding. The American factories generally each make about forty sizes and styles of movements, and case them in many hundreds of different ways, so that the workman will frequently find the same movement in a large number of clocks, and he will soon be able to determine from the characteristics of the movement what factory made the clock, and thus be able to at once turn to the proper catalogue if the name of the maker be erased, as frequently happens.

This comparative study of the practice of different factories will prove very interesting, as the movement comes to the student after a period of prolonged and generally severe use, which is calculated to bring out any existing defects in construction or workmanship; and having all makes of clocks constantly passing through his hands, each exhibiting a characteristic defect more frequently than any other, he is in a much better position to ascertain the merits and defects of each maker than he would be in any factory.

Having thus briefly outlined the kinds of machinery used in measuring time, we will now turn our attention to the examination of the theoretical and mechanical construction of the various parts.

The man who starts out to design and build a clock will find himself limited in three particulars: It must run a specified time; the arbor carrying the minute hand must turn once in each hour; the pendulum must be short enough to go in the case. Two of these particulars are changeable according to circumstances; the length of time run may be thirty hours, eight, thirty, sixty or ninety days. The pendulum may be anywhere from four inches to fourteen feet, and the shorter it is the faster it will go. The one definite point in the time train is that the minute hand must turn once in each hour. We build or alter our train from this point both ways, back through changeable intermediate wheels and pinions to the spring or weight forming the source of power, and forward from it through another changeable series of wheels and pinions to the pendulum. Now as the pendulum governs the rate of the clock we will commence with that and consider it independently.

CHAPTER II.
THE NATURAL LAWS GOVERNING PENDULUMS.

Length of Pendulum.—A pendulum is a falling body and as such is subject to the laws which govern falling bodies. This statement may not be clear at first, as the pendulum generally moves through such a small arc that it does not appear to be falling. Yet if we take a pendulum and raise the ball by swinging it up until the ball is level with the point of suspension, as in [Fig. 1], and then let it go, we shall see it fall rapidly until it reaches its lowest point, and then rise until it exhausts the momentum it acquired in falling, when it will again fall and rise again on the other side; this process will be repeated through constantly smaller arcs until the resistance of the air and that of the pendulum spring shall overcome the other forces which operate to keep it in motion and it finally assumes a position of rest at the lowest point (nearest the earth) which the pendulum rod will allow it to assume. When it stops, it will be in line between the center of the earth (center of gravity) and the fixed point from which it is suspended. True, the pendulum bob, when it falls, falls under control of the pendulum rod and has its actions modified by the rod; but it falls just the same, no matter how small its arc of motion may be, and it is this influence of gravity—that force which makes any free body move toward the earth’s center—which keeps the pendulum constantly returning to its lowest point and which governs very largely the time taken in moving. Hence, in estimating the length of a pendulum, we must consider gravity as being the prime mover of our pendulum.

Fig. 1. Dotted lines show path of pendulum.

The next forces to consider are mass and weight, which, when put in motion, tend to continue that motion indefinitely unless brought to rest by other forces opposing it. This is known as momentum. A heavy bob will swing longer than a light one, because the momentum stored up during its fall will be greater in proportion to the resistance which it encounters from the air and the suspension spring.

As the length of the rod governs the distance through which our bob is allowed to fall, and also controls the direction of its motion, we must consider this motion. Referring again to [Fig. 1], we see that the bob moves along the circumference of a circle, with the rod acting as the radius of that circle; this opens up another series of facts. The circumference of a circle equals 3.1416 times its diameter, and the radius is half the diameter (the radius in this case being the pendulum rod). The areas of circles are proportional to the squares of their diameters and the circumferences are also proportional to their areas. Hence, the lengths of the paths of bobs moving along these circumferences are in proportion to the squares of the lengths of the pendulum rods. This is why a pendulum of half the length will oscillate four times as fast.

Now we will apply these figures to our pendulum. A body falling in vacuo, in London, moves 32.2 feet in one second. This distance has by common consent among mathematicians been designated as g. The circumference of a circle equals 3.1416 times its diameter. This is represented as π. Now, if we call the time t, we shall have the formula:

t = π √ (1/g)

Substituting the time, one second, for t, and doing the same with the others, we shall have:

(32.2 ft.)
1 = ————— = 3.2616 feet.
(3.1416)²

Turning this into its equivalent in inches by multiplying by 12, we shall have 39.1393 inches as the length of a one-second pendulum at London.

Now, as the force of gravity varies somewhat with its distance from the center of the earth, we shall find the value of g in the above formula varying slightly, and this will give us slightly different lengths of pendulum at different places. These values have been found to be as follows:

Now, taking another look at our formula, we shall see that we may get the length of any pendulum by multiplying π (which is 3.1416) by the square of the time required: To find the length of a pendulum to beat three seconds:

3² = 9.

39.1393 × 9 = 352.2537 inches = 29.3544 feet.

A pendulum beating two-thirds of a second, or 90 beats:

(⅔)² = ⁴⁄₉

39.1393 × 4
————— = 17.3952 inches.
9

A pendulum beating half-seconds or 120 beats:

(½)² = ¼

39.1393 × 1
—————— = 9.7848 inches.
4

Center of Oscillation.—Having now briefly considered the basic facts governing the time of oscillation of the pendulum, let us examine it still further. The pendulum shown in [Fig. 1] has all its weight in a mass at its end, but we cannot make a pendulum that way to run a clock, because of physical limitations. We shall have to use a rod stiff enough to transmit power from the clock movement to the pendulum bob and that rod will weigh something. If we use a compensated rod, so as to keep it the same length in varying temperature, it may weigh a good deal in proportion to the bob. How will this affect the pendulum?

If we suspend a rod from its upper end and place along-side of it our ideal pendulum, as in [Fig. 2], we shall find that they will not vibrate in equal times if they are of equal lengths. Why not? Because when the rod is swinging (being stiff) a part of its weight rests upon the fixed point of suspension and that part of the rod is consequently not entirely subject to the force of gravity. Now, as the time in which our pendulum will swing depends upon the distance of the effective center of its mass from the point of suspension, and as, owing to the difference in construction, the center of mass of one of our pendulums is at the center of its ball, while that of the other is somewhere along the rod, they will naturally swing in different times.

Fig. 2. Two pendulums of equal length but unequal vibration.
B, center of oscillation for both pendulums.

Fig. 3.

Our other pendulum (the rod) is of the same size all the way up and the center of its effective mass would be the center of its weight (gravity) if it were not for the fact which we stated a moment ago that part of the weight is upheld and rendered ineffective by the fixed support of the pendulum rod, all the while the pendulum is not in a vertical position. If we support the rod in a horizontal position, as in [Fig. 3], by holding up the lower end, the point of suspension, A, will support half the weight of the rod; if we hold it at 45 degrees the point of suspension will hold less than half the weight of the rod and more of the rod will be affected by gravity; and so on down until we reach the vertical or up and down position. Thus we see that the force of gravity pulling on our pendulum varies in its effects according to the position of the rod and consequently the effective center of its mass also varies with its position and we can only calculate what this mean (or average) position is by a long series of calculations and then taking an average of these results.

We shall find it simpler to measure the time of swing of the rod which we will do by shortening our ball and cord until it will swing in the same time as the rod. This will be at about two-thirds of the length of the rod, so that the effective length of our rod is about two-thirds of its real length. This effective length, which governs the time of vibration, is called the theoretical length of the pendulum and the point at which it is located is called its center of oscillation. The distance from the center of oscillation to the point of suspension is called the theoretical length of the pendulum and is always the distance which is given in all tables of lengths of pendulums. This length is the one given for two reasons: First, because, it is the timekeeping length, which is what we are after, and second, because, as we have just seen in [Fig. 3], the real length of the pendulum increases as more of the weight of the instrument is put into the rod. This explains why the heavy gridiron compensation pendulum beating seconds so common in regulators and which measures from 56 to 60 inches over all, beats in the same time as the wood rod and lead bob measuring 45 inches over all, while one is apparently a third longer than the other.

Table Showing the Length of a Simple Pendulum

That performs in one hour any given number of oscillations, from 1 to 20,000, and the variation in this length that will occasion a difference of 1 minute in 24 hours.

Calculated by E. Gourdin.

Table of the Length of a Simple Pendulum,
(CONTINUED.)

In the foregoing tables all dimensions are given in meters and millimeters. If it is desirable to express them in feet and inches, the necessary conversion can be at once effected in any given case by employing the following conversion table, which will prove of considerable value to the watchmaker for various purposes:

Conversion Table of Inches, Millimeters and French Lines.

Center of Gravity.—The watchmaker is concerned only with the theoretical or timekeeping lengths of pendulums, as his pendulum comes to him ready for use; but the clock maker who has to build the pendulum to fit not only the movement, but also the case, needs to know more about it, as he must so distribute the weight along its length that it may be given a length of 60 inches or of 44 inches, or anything between them, and still beat seconds, in the case of a regulator. He must also do the same thing in other clocks having pendulums which beat other numbers than 60. Therefore he must know the center of his weights; this is called the center of gravity. This center of gravity is often confused by many with the center of oscillation as its real purpose is not understood. It is simply used as a starting point in building pendulums, because there must be a starting point, and this point is chosen because it is always present in every pendulum and it is convenient to work both ways from the center of weight or gravity. In [Fig. 2] we have two pendulums, in one of which (the ball and string) the center of gravity is the center of the ball and the center of oscillation is also at the center (practically) of the ball. Such a pendulum is about as short as it can be constructed for any given number of oscillations. The other (the rod) has its center of gravity manifestly at the center of the rod, as the rod is of the same size throughout; yet we found by comparison with the other that its center of oscillation was at two-thirds the length of the rod, measured from the point of suspension, and the real length of the pendulum was consequently one-half longer than its timekeeping length, which is at the center of oscillation. This is farther apart than the center of gravity and oscillation will ever get in actual practice, the most extreme distance in practice being that of the gridiron pendulum previously mentioned. The center of gravity of a pendulum is found at that point at which the pendulum can be balanced horizontally on a knife edge and is marked to measure from when cutting off the rod.

The center of oscillation of a compound pendulum must always be below its center of gravity an amount depending upon the proportions of weight between the rod and the bob. Where the rod is kept as light as it should be in proportion to the bob this difference should come well within the limits of the adjusting screw. In an ordinary plain seconds pendulum, without compensation, with a bob of eighteen or twenty pounds and a rod of six ounces, the difference in the two points is of no practical account, and adjustments for seconds are within the screw of any ordinary pendulum, if the screw is the right length for safety, and the adjusting nut is placed in the middle of the length of the screw threads when the top of the rod is cut off, to place the suspension spring by measurement from the center of gravity as has been already described; also a zinc and iron compensation is within range of the screw if the compensating rods are not made in undue weight to the bob. The whole weight of the compensating parts of a pendulum can be safely made within one and a half pounds or lighter, and carry a bob of twenty-five pounds or over without buckling the rods, and the two points, the center of gravity and the center of oscillation, will be within the range of the screw.

There are still some other forces to be considered as affecting the performance of our pendulum. These are the resistance to its momentum offered by the air and the resistance of the suspension spring.

Barometric Error.—If we adjust a pendulum in a clock with an air-tight case so that the pendulum swings a certain number of degrees of arc, as noted on the degree plate in the case at the foot of the pendulum, and then start to pump out the air from the case while the clock is running, we shall find the pendulum swinging over longer arcs as the air becomes less until we reach as perfect a vacuum as we can produce. If we note this point and slowly admit air to the case again we shall find that the arcs of the pendulum’s swing will be slowly shortened until the pressure in the case equals that of the surrounding air, when they will be the same as when our experiment was started. If we now pump air into our clock case, the vibrations will become still shorter as the pressure of the air increases, proving conclusively that the resistance of the air has an effect on the swinging of the pendulum.

We are accustomed to measure the pressure of the air as it changes in varying weather by means of the barometer and hence we call the changes in the swing of the pendulum due to varying air pressure the “barometric error.” The barometric error of pendulums is only considered in the very finest of clocks for astronomical observatories, master clocks for watch factories, etc., but the resistance of the air is closely considered when we come to shape our bob. This is why bobs are either double-convex or cylindrical in shape, as these two forms offer the least resistance to the air and (which is more important) they offer equal resistance on both sides of the center of the bob and thus tend to keep the pendulum swinging in a straight line back and forth.

Fig. 4. A, arc of circle. B, cycloid path of pendulum, exaggerated.

The Circular Error.—As the pendulum swings over a greater arc it will occupy more time in doing it and thus the rate of the clock will be affected, if the barometric changes are very great. This is called the circular error. In ancient times, when it was customary to make pendulums vibrate at least fifteen degrees, this error was of importance and clock makers tried to make the bob take a cycloidal path, as is shown in [Fig. 4], greatly exaggerated. This was accomplished by suspending the pendulum by a cord which swung between cycloidal checks, but it created so much friction that it was abandoned in favor of the spring as used to-day. It has since been proved that the long and short arcs of the pendulum’s vibration are practically isochronous (with a spring of proper length and thickness) up to about six degrees of arc (three degrees each side of zero on the degree plate at the foot of the pendulum) and hence small variations of power in spring operated clocks and also the barometric error are taken care of, except for greatly increased variations of power, or for too great arcs of vibration. Here we see the reasons for and the amount of swing we can properly give to our pendulum.

Temperature Error.—The temperature error is the greatest which we shall have to consider. It is this which makes the compound pendulum necessary for accurate time, and we shall consequently give it a great amount of space, as the methods of overcoming it should be fully understood.

Expansion of Metals.—The materials commonly used in making pendulums are wood (deal, pine and mahogany), steel, cast iron, zinc, brass and mercury. Wood expands .0004 of its length between 32° and 212° F.; lead, .0028; steel, .0011; mercury, .0180; zinc, .0028; cast iron, .0011; brass, .0020. Now the length of a seconds pendulum, by our tables (3600 beats per hour) is 0.9939 meter; if the rod is brass it will lengthen .002 with such a range of temperature. As this is practically two-thousandths of a meter, this is a gain of two millimeters, which would produce a variation of one minute and forty seconds every twenty-four hours; consequently a brass rod would be a very bad one.

If we take two of these materials, with as wide a difference in expansion ratios as possible, and use the least variable for the rod and the other for the bob, supporting it at the bottom, we can make the expansion of the rod counterbalance the expansion of the bob and thus keep the effective length of our pendulum constant, or nearly so. This is the theory of the compensating pendulum.

CHAPTER III.
COMPENSATING PENDULUMS.

As the pendulum is the means of regulating the time consumed in unwinding the spring or weight cord by means of the escapement, passing one tooth of the escape wheel at each end of its swing, it will readily be seen that lengthening or shortening the pendulum constitutes the means of regulating the clock; this would make the whole subject a very simple affair, were it not that the reverse proposition is also true; viz.; Changing the length of the pendulum will change the rate of the clock and after a proper rate has been obtained further changes are extremely undesirable. This is what makes the temperature error spoken of in the preceding chapter so vexatious where close timing is desired and why as a rule, a well compensated pendulum costs more than the rest of the clock. The sole reason for the business existence of watch and clockmakers lies in the necessity of measuring time, and the accuracy with which it may be done decides in large measure the value of any watchmaker in his community. Hence it is of the utmost importance that he shall provide himself with an accurate means of measuring time, as all his work must be judged finally by it, not only while he is working upon time-measuring devices, but also after they have passed into the possession of the general public.

A good clock is one of the very necessary foundation elements, contributing very largely to equip the skilled mechanic and verify his work. Without some reliable means to get accurate mean time a watchmaker is always at sea—without a compass—and has to trust to his faith and a large amount of guessing, and this is always an embarrassment, no matter how skilled he may be in his craft, or adept in guessing. What I want to call particular attention to is the unreliable and worthless character of the average regulator of the present day. A good clock is not necessarily a high priced instrument and it is within the reach of most watchmakers. A thoroughly good and reliable timekeeper of American make is to be had now in the market for less than one hundred dollars, and the only serious charge that can be made against these clocks is that they cost the consumer too much money. Any of them are thirty-three and a third per cent higher than they should be. About seventy-five dollars will furnish a thoroughly good clock. The average clock to be met with in the watchmakers’ shops is the Swiss imitation gridiron pendulum, pin escapement, and these are of the low grades as a rule; the best grades of them rarely ever get into the American market. Almost without exception, the Swiss regulator, as described, is wholly worthless as a standard, as the pendulums are only an imitation of the real compensated pendulum. They are an imitation all through, the bob being hollow and filled with scrap iron, and the brass and steel rods composing the compensating element, along with the cross-pieces or binders, are all of the cheapest and poorest description. If one of these pendulums was taken away from the movement and a plain iron bob and wooden rod put to the movement, in its place, the possessor of any such clock would be surprised to find how much better average rate the clock would have the year through, although there would then be no compensating mechanism, or its semblance, in the make-up of the pendulum. In brief, the average imitation compensation pendulum of this particular variety is far poorer than the simplest plain pendulum, such as the old style, grandfather clocks were equipped with. A wood rod would be far superior to a steel one, or any metal rod, as may be seen by consulting the expansion data given in the previous chapter.

Many other pendulums that are sold as compensating are a delusion in part, as they do not thoroughly compensate, because the elements composing them are not in equilibrium or in due proportion to one another and to the general mechanism.

To all workmen who have a Swiss regulator, I would say that the movement, if put into good condition, will answer very well to maintain the motion of a good pendulum, and that it will pay to overhaul these movements and put to them good pendulums that will pretty nearly compensate. At least a well constructed pendulum will give a very useful and reliable rate with such a motor, and be a great help and satisfaction to any man repairing and rating good watches.

The facts are, that one of the good grade of American adjusted watch movements will keep a much steadier rate when maintained in one position than the average regulator. Without a reliable standard to regulate by, there is very little satisfaction in handling a good movement and then not be able to ascertain its capabilities as to rate. Very many watch carriers are better up in the capabilities of good watches than many of our American repairers are, because a large per cent of such persons have bought a watch of high grade with a published rate, and naturally when it is made to appear to entirely lack a constant rate when compared with the average regulator, they draw the conclusion that the clock is at fault, or that the cleaning and repairing are. Many a fair workman has lost his watch trade, largely on account of a lack of any kind of reliable standard of time in his establishment. There are very few things that a repairer can do in the way of advertising and holding his customers more than to keep a good clock, and furnish good watch owners a means of comparison and thus to confirm their good opinions of their watches.

We have along our railroads throughout the country a standard time system of synchronized clocks, which are an improvement over no standard of comparison; but they cannot be depended upon as a reliable standard, because they are subject to all the uncertainties that affect the telegraph lines—bad service, lack of skill, storms, etc. The clocks furnished by these systems are not reliable in themselves and they are therefore corrected once in twenty-four hours by telegraph, being automatically set to mean time by the mechanism for that purpose, which is operated by a standard or master clock at some designated point in the system.

Now all this is good in a general way; but as a means to regulate a fine watch and use as a standard from day to day, it is not adequate. A standard clock, to be thoroughly serviceable, must always, all through the twenty-four hours, have its seconds hand at the correct point at each minute and hour, or it is unreliable as a standard. The reason is that owing to train defects watches may vary back and forth and these errors cannot be detected with a standard that is right but once a day. No man can compare to a certainty unless his standard is without variation, substantially; and I do not know of any way that this can be obtained so well and satisfactorily as through the means of a thoroughly good pendulum.

Compensating seconds pendulums are, it might be said, the standard time measure. Mechanically such a pendulum is not in any way difficult of execution, yet by far the greater portion of pendulums beating seconds are not at all accurate time measures, as independently of their slight variations in length, any defects in the construction or fitting of their parts are bound to have a direct effect upon the performance of the clock. The average watchmaker as a mechanic has the ability to do the work properly, but he does not fully understand or realize what is necessary, nor appreciate the fact that little things not attended to will render useless all his efforts.

The first consideration in a compensated pendulum is to maintain the center of oscillation at a fixed distance from the point of suspension and it does not matter how this is accomplished.

So, also, the details of construction are of little consequence, so long as the main points are well looked after—the perfect solidity of all parts, with very few of them, and the free movement of all working surfaces without play, so that the compensating action may be constantly maintained at all times. Where this is not the case the sticking, rattling, binding or cramping of certain parts will give different rates at different times under the same variations of temperature, according as the parts work smoothly and evenly or move only by jerks.

The necessary and useful parts of a pendulum are all that are really admissible in thoroughly good construction. Any and all pieces attached by way of ornament merely are apt to act to the prejudice of the necessary parts and should be avoided. In this chapter we shall give measurements and details of construction for a number of compensated pendulums of various kinds, as that will be the best means of arriving at a thorough understanding of the subject, even if the reader does not desire to construct such a pendulum for his own use.

Principles of Construction.—Compensation pendulums are constructed upon two distinct principles. First, those in which the bob is supported by the bottom, resting on the adjusting screw with its entire height free to expand upward as the rod expands downward from its fixed point of suspension. In this class of pendulums the error of the bob is used to counteract that of the rod and if the bob is made of sufficiently expansible metal it only remains to make the bob of sufficient height in proportion to its expansibility for one error to offset the other. In the second class the attempt is made to leave out of consideration any errors caused by expansion of the bob, by suspending it from the center, so that its expansion downward will exactly balance its expansion upward and hence they will balance each other and may be neglected. Having eliminated the bob from consideration by this means we must necessarily confine our attempt at compensation to the rod in the second method.

The wood rod and lead bob and the mercurial pendulums are examples of the first-class and the wood rod with brass sleeve having a nut at the bottom and reaching to the center of the iron bob and the common gridiron, or compound tubular rod, or compound bar of steel and brass, or steel and zinc, are examples of the second class.

Wood Rod and Zinc Bob.—We will suppose that we have one of the Swiss imitation gridiron pendulums which we want to discard, while retaining the case and movement. As these cases are wide and generally fitted with twelve-inch dials, we shall have about twenty inches inside our case and we may therefore use a large bob, lens-shaped, made of cast zinc, polished and lacquered to look like brass.

The bobs in such imitation gridiron pendulums are generally about thirteen inches in diameter and swing about five inches (two and a half inches each side). The pendulums are generally light, convex in front and flattened at the rear, and the entire pendulum measures about 56 inches from the point of suspension to the lower end of the adjusting screw. We will also suppose that we desire to change the appearance of the clock as little as possible, while improving its rate. This will mean that we desire to retain a lens-shaped bob of about the same size as the one we are going to remove.

We shall first need to know the total length of our pendulum, so that we can calculate the expansion of the rod. A seconds pendulum measures 39.2 inches from the point in the suspension spring at the lower edge of the chops to the center of oscillation. With a lens-shaped bob the center of gravity will be practically at the center of the bob, if we use a light wooden rod and a steel adjusting screw and brass nut, as these metal parts, although short, will be heavy enough to nearly balance the suspension spring and that portion of the rod which is above the center. We shall also gain a little in balance if we leave the steel screw long enough to act as an index over the degree plate, in the case, at the bottom of the pendulum, by stripping the thread and turning the end to a taper an inch or so in length.

We shall only be able to use one-half of the expansion upwards of our bob, because the centers of gravity and oscillation will be practically together at the center of the bob. We shall find the center of gravity easily by balancing the pendulum on a knife edge and thus we will be able to make an exceedingly close guess at the center of oscillation.

Now, looking over our data, we find that we have a suspension spring of steel, then some wood and steel again at the other end. We shall need about one inch of suspension spring. The spring will, of course, be longer than one inch, but we shall hold it in iron chops and the expansion of the chops will equal that of the spring between them, so that only the free part of the spring need be considered. Now from the adjusting screw, where it leaves the last pin through the wood, to the middle position of the rating nut will be about one inch, so we shall have two inches of steel to consider in our figures of expansion.

Now to get the length of the rod. We want to keep our bob about the size of the other, so we will try 14 inches diameter, as half of this is an even number and makes easy figuring in our trials. 39.2 inches, plus 7 (half the diameter of the bob) gives us 46.2 inches; now we have an inch of adjustment in our screw, so we can discard the .2; this leaves us 46 inches of wood and steel for which we must get the expansion.

We have 7 inches as half the diameter of our bob .0198 ÷ 7 = .0028, ²⁄₇, which we find from our tables is very close to the expansion of zinc, so we will make the bob of that metal. Now let us check back; the upward expansion of 7 inches of zinc equals .0028 × 7 = .0196 inch, as against .0198 inch downward expansion of the rod. This gives us a total difference of .0002 inch between 32° and 212° or a range of 180° F. This is a difference of .0001 inch for 90° of temperature and is closer than most pendulums ever get.

The above figures are for dry, clear white pine, well baked and shellacked, with steel of average expansion, and zinc of new metal, melted and cast without the admixtures of other metals or the formation of oxide. The presence of tin, lead, antimony and other admixtures in the zinc would of course change the results secured; so also will there be a slight difference in the expansion of the rod if other woods are used. Still the jeweler can from the above get a very close approximation.

Fig. 5. Zinc bob and wood rod to replace
imitation gridiron pendulum.

Such a bob, 14 inches diameter and 1.5 inches thick, alike on both sides, with an oval hole 1 × .5 inches through its center, [see Fig. 5], would weigh about 30 to 32 pounds, and would have to be hung from a cast iron bracket, [Fig. 6], bolted through the clock case to the wall behind it, so as to get a steady rate. It would be nearly constant, as the metal is spread out so as to be quickly affected by temperature; and the shape would hold it well in its plane of oscillation, if both sides were of exactly the same curvature, while the weight would overcome minor disturbances due to vibration of the building. It would require a little heavier suspension spring, in order to be isochronous in the long and short arcs and this thickening of the spring would need the addition of from one and a half to two pounds more of driving weight.

Fig. 6. Cast iron bracket for heavy pendulums and movements.

If so heavy a pendulum is deemed undesirable, the bob would have to be made of cylindrical form, retaining the height, as necessary to compensation, and varying the diameter of the cylinder to suit the weight desired.

Fig. 7. Wood rod Fig. 8. Bob of metal casing
and lead bob.filled with shot.

Wood Rod and Lead Bob.—The wood should be clear, straight-grained and thoroughly dried, then given several coats of shellac varnish, well baked on. It may be either flat, oval or round in section, but is generally made round because the brass cap at the upper end, the lining for the crutch, and the ferrule for the adjusting screw at the lower end may then be readily made from tubing. For pendulums smaller than one second, the wood is generally hard, as it gives a firmer attachment of the metal parts.

The top of the rod should have a brass collar fixed on it by riveting through the rod and it should extend down the rod about three inches, so as to make a firm support for the slit to receive the lower clip of the suspension spring. The lower end should have a slit or a round hole drilled longitudinally three inches up the rod to receive the upper end of the adjusting screw and this should also fit snugly and be well pinned or riveted in place. [See Fig. 7]. A piece of thin brass tube about one inch in length is fitted over the rod where the crutch works.

In casting zinc and lead bobs, especially those of lens-shapes, the jeweler should not attempt to do the work himself, but should go to a pattern maker, explain carefully just what is wanted and have a pattern made, as such patterns must be larger than the casting in order to take care of the shrinkage due to cooling the molten metal. It will also be better to use an iron core, well coated with graphite when casting, as the core can be made smooth throughout and the exact shape of the pendulum rod, and there will then be no work to be done on the hole when the casting is made. The natural shrinkage of the metal on cooling will free the core, which can be easily driven out when the metal is cold and it will then leave a smooth, well shaped hole to which the rod can be fitted to work easily, but without shake. Lens-shaped bobs, particularly, should be cast flat, with register pins on the flask, so as to get both sides central with the hole, and be cast with a deep riser large enough to put considerable pressure of melted metal on the casting until it is chilled, so as to get a sound casting; it should be allowed to remain in the sand until thoroughly cold, for the same reason, as if cooled quickly the bob will have internal stresses which are liable to adjust themselves sometime after the pendulum is in the clock and thus upset the rate until such interior disturbances have ceased. Cylinders may be cast in a length of steel tubing, using a round steel core and driven out when cold.

If using oval or flat rods of wood, the adjusting screw should be flattened for about three inches at its upper end, wide enough to conform to the width of the rod; then saw a slot in the center of the rod, wide and deep enough to just fit the flattened part of the screw; heat the screw and apply shellac or lathe wax and press it firmly into the slot with the center of the screw in line with the center of the rod; after the wax is cold select a drill of the same size as the rivet wire; drill and rivet snugly through the rod, smooth everything carefully and the job is complete.

If by accident you have got the rod too small for the hole, so that there is any play, give the rod another coat of shellac varnish and after drying thoroughly, sand paper it down until it will fit properly.

Round rods may be treated in the same manner, but it is usual to drill a round hole in such a rod to just fit the wire, then insert and rivet as before after the wax is cold, finishing with a ferrule or cap of brass at the end of the rod.

The slot for the suspension spring is fitted to the upper end of the rod in the same manner.

Pendulum with Shot.—Still another method of making a compensating pendulum, which gives a lighter pendulum, is to make a case of light brass or steel tubing of about three inches diameter. [Fig. 8], with a bottom and top of equal weight, so as to keep the center of oscillation about the center of gravity, for convenience in working. The bottom may be turned to a close fit, and soldered, pinned, or riveted into the tube. It is pierced at its center and another tube of the same material as the outer tube, with an internal diameter which closely fits the pendulum rod is soldered or riveted into the center of the bottom, both bottom and top being pierced for its admission and the other parts fitted as previously described.

The length of the case or canister should be about 11.5 inches so as to give room for a column of shot of 10.5 inches (the normal compensating height for lead) and still leave room for correction. Make a tubular case for the driving weight also and then we have a flexible system. If it is necessary to add or subtract weight to obtain the proper arcs of oscillation of the pendulum, it can be readily done by adding to or taking from the shot in the weight case.

Fill the pendulum to 10.5 inches with ordinary sportsmen’s shot and try it for rate. If it gains in heat and loses in cold it is over-compensated and shot must be taken from it. If it loses in heat and gains in cold it is under-compensated and shot should be added.

The methods of calculation were given in full in describing the zinc pendulum and hence need not be repeated here, but attention should be called to the fact that there are three materials here, wood, steel or brass and lead and each should be figured separately so that the last two may just counterbalance the first. If the case is made light throughout the effect upon the center of oscillation will be inappreciable as compared with that of the lead, but if made heavier than need be, it will exert a marked influence, particularly if its highest portion (the cover) be heavy, as we then have the effect of a shifting weight high up on the pendulum rod. If made of thin steel throughout and nickel plated, we shall have a light and handsome case for our bob. If this is not practicable, or if the color of brass be preferred, it may be made of that material.

The following table of weights will be of use in making calculations for a pendulum or for clock weights.

Weight of Lead, Zinc and Cast Iron Cylinders One-Half Inch Long.

Example:—Required, the weight of a lead pendulum bob, 3 inches diameter, 9 inches long, which has a hole through it .75 inch in diameter. The weight of a lead cylinder 3 inches diameter in the table is 2.897, which multiplied by 9 (the length given) = 26.07 lbs. Then the weight in the table of a cylinder .75 inch diameter is .18 and .18 × 9 = 1.62 lbs. And 26.07 - 1.62 = 24.45, the weight required in lbs.

Auxiliary Weights.—If for any reason our pendulum does not turn out with a rating as calculated and we find after getting it to time that it is over-compensated, it is a comparatively simple matter to turn off a portion from the bottom of a solid bob. By doing this in very small portions at a time and then testing carefully for heat and cold every time any amount has been removed, we shall in the course of a few weeks arrive at a close approximation to compensation, at least as close as the ordinary standards available to the jeweler will permit. This is a matter of weeks, because if the pendulum is being rated by the standard time which is telegraphed over the country daily at noon, the jeweler, as soon as he gets his pendulum nearly right, will begin to discover variations in the noon signal of from .2 to 5 seconds on successive days. Then it becomes a matter of averages and reasoning, thus: If the pendulum beats to time on the first, second, third, fifth and seventh days, it follows that the signal was incorrect—slow or fast—on the fourth and sixth days.

If the pendulum shows a gain of one second a week on the majority of the days, the observation must be continued without changing the pendulum for another week. If the pendulum shows two seconds gain at the end of this time, we have two things to consider. Is the length right, or is the pendulum not fully compensated? We cannot answer the second query without a record of the temperature variations during the period of observations.

To get the temperature record we shall require a set of maximum and minimum thermometers in our clock case. They consist of mercurial thermometer tubes on the ordinary Fahrenheit scales, but with a marker of colored wood or metal resting on the upper end of the column of mercury in the tube. The tube is not hung vertically, but is placed in an inclined position so that the mark will stay where it is pushed by the column of mercury. Thus if the temperature rises during the day to 84 degrees the mark in the maximum thermometer will be found resting in the tube at 84° whether the mercury is there when the reading is taken or not. Similarly, if the temperature has dropped during the night to 40°, the mark in the minimum thermometer will be found at 40°, although the temperature may be 70° when the reading is taken. After reading, the thermometers are shaken to bring the marks back to the top of the column of mercury and the thermometers are then restored to their positions, ready for another reading on the following day.

These records should be set down on a sheet every day at noon in columns giving date, rate, plus or minus, maximum, minimum, average temperature and remarks as to regulation, etc., and with these data to guide us we shall be in a position to determine whether to move the rating nut or not. If the temperature has been fairly constant we can get a closer rate by moving the nut and continuing the observations. If the temperature has been increasing steadily and our pendulum has been gaining steadily it is probably over-compensated and the bob should be shortened a trifle and the observations renewed.

It is best to “make haste slowly” in such a matter. First bring the pendulum to time in a constant temperature; that will take care of its proper length. Then allow the temperature to vary naturally and note the results.

If the pendulum is under-compensated, so that the bob is too short to take care of the expansion of the rod, auxiliary weights of zinc in the shape of washers (or short cylinders) are placed between the bottom of the bob and the rating nut. This of course makes necessary a new adjustment and another course of observations all around, but it will readily be seen that it places a length of expansible metal between the nut and the center of oscillation and thus makes up for the deficiency of expansion of the bob. Zinc is generally chosen on account of its high rate of expansion, but brass, aluminum and other metals are also used. It is best to use one thick washer, rather than a number of thinner ones, as it is important to keep the construction as solid at this point as possible.

Top Weights.—After bringing the pendulum as close as possible by the compensation and the rating nuts, astronomers and others requiring exact time get a trifle closer rating by the use of top weights. These are generally U-shaped pieces of thin metal which are slipped on the rod above the bob without stopping the pendulum. They raise the center of oscillation by adding to the height of the bob when they are put on, or lower it when they are removed, but they are never resorted to until long after the pendulum is closer to time than the jeweler can get with his limited standards of comparison. They are mentioned here simply that their use may be understood when they may be encountered in cleaning siderial clocks.

Mercurial pendulums also belong to the class of compensation by expansion of the bobs, but they are so numerous and so different that they will be considered separately, later on.

Compensated Pendulum Rods.—We will now consider the second class, that in which an attempt is made to obtain a pendulum rod of unvarying length.

The oldest form of compensated rod is undoubtedly the gridiron of either nine, five or three rods. As originally made it was an accurate but expensive proposition, as the coefficients of expansion of the brass or zinc and iron or steel had all to be determined individually for each pendulum. Each rod had to be sized accurately, or if this was not done, then each rod had to be fitted carefully to each hole in the cross bars so as to move freely, without shake. The rods were spread out for two purposes, to impress the public and to secure uniform and speedy action in changes of temperature. The weight, which increased rapidly with the increase of diameter of the rod, made a long and large seconds pendulum, some of them measuring as much as sixty-two inches in length, and needing a large bob to look in proportion. Various attempts were made to ornament the great expanse of the gridiron, harps, wreaths and other forms in pierced metal being screwed to the bars. The next advance was in substituting tubes for rods in the gridiron, securing an apparently large rod that was at the same time stiff and light. Then came the era of imitation, in which the rods were made of all brass, the imitation steel portion being nickel plated. With the development of plating they were still further cheapened by being made of steel, with the supposedly brass rods plated with brass and the steel ones with nickel. Thousands of such pendulums are in use to-day; they have the rods riveted to the cross-pieces and are simply steel rods, subject to change of length with every change in temperature. It does no harm to ornament such pendulums, as the rods themselves are merely ornaments, usually all of one metal, plated to change the color.

As three rods were all that were necessary, the clockmaker who desired a pendulum that was compensated soon found his most easily made rod consisted of a zinc bar, wide, thin and flat, placed between two steel parts, like the meat and bread of a sandwich. This gives a flat and apparently solid rod of metal which if polished gives a pleasing appearance, and combines accurate performance with cheapness of construction, so that any watchmaker may make it himself, without expensive tools.

Fig. 9. Pendulum with compensated
rod of steel and zinc.

A, the lens-shaped bob; T P, the total length of the compensating part.

R, the upper round part of rod.

The side showing the heads of the screws is the face side and is finished. The screws 1, 2, 3, 4 hold the three pieces from separating, but do not confine the front and middle sections in their lengthwise expansion along the rod, but are screwed into the back iron section, while the holes in the other two sections are slotted smaller than the screw heads.

The holes at the lower extreme of combination 5, 6, 7, 8, 9 are for adjustments in effecting a compensation.

The pin at 10 is the steel adjusting pin, and is only tight in the front bar and zinc bars, being loose in the back bar.

O and P show the angles in the back rod, T shows the angle in the rod at the top, m shows the pin as placed in the iron and zinc sections where they have been soldered as described.

h shows the regulating nut carried by the tube, as described, and terminating in the nut D.

l and i show the screw of 36 threads.

The nut D is to be divided on its edge into 30 divisions.

n is the angle of the back bar to which zinc is soldered.

Flat Compensated Rod.—One of the most easily made zinc and iron compensating pendulums, shown in detail in [Fig. 9], is as follows: A lead or iron bob, lens-shaped, that is, convex equally on each side, 9 inches diameter and an inch and one-quarter thick at the center. A hole to be made straight through its diameter ½ inch. One-half through the diameter this hole is to be enlarged to ⅝ inch diameter. This will make the hole for half of its length ½ inch and the remaining half ⅝ inch diameter. The ⅝ hole must have a thin tube, just fitting it, and 5 inches long. At one end of this tube is soldered in a nut, with a hole tapped with a tap of thirty-six threads to the inch, and ¼ inch diameter, and at the other end of the tube is soldered a collar or disc one inch diameter, which is to be divided into thirty divisions, for regulating purposes, as will be described later on. The whole forms a nut into which the rod screws, and the tube allows the nut to be pushed up to the center of the diameter of the bob, through the large hole, and the nut can be operated then by means of the disc at its lower end. The rod, of flat iron, is in two sections, as follows: That section which enters the bob and terminates in the regulating screw is flat for twenty-six inches, and then rounded to ½ inch for six inches, and a screw cut on its end for two inches, to fit the thread in the nut. The upper end of this section is then to be bent at a right angle, flatwise. This angle piece will be long enough if only ³⁄₁₆ inch long, so that it covers the thickness of the zinc center rod. The zinc center rod is a bar of the metal, hammered or rolled, 25 inches long, ³frasl;₁₆ inch thick, and ¾ inch wide, and comes up against the angle piece bent on the flat part of the lower section of the rod. Now the upper section of the rod may be an exact duplicate of the lower section, with the flat part only a little longer than the zinc bar, say ½ inch, and the angle turned on the end, as previously described. The balance of the bar may be forged into a rod of ⁵⁄₁₆ inch diameter. As has been stated, the zinc bar is placed against the angle piece bent on the upper end of the lower section of the rod, P, n, [Fig. 9], and pins must be put through this angle piece into the end of the zinc bar, to hold it in close contact with the iron bar. The upper section of the rod is now to be laid on the opposite side of the zinc bar, with its angle at the other end of the zinc, but not in contact with it, say ¹⁄₁₆ inch left between the angle and the zinc bar. Now all is ready to clamp together—the two flat iron bars with the zinc between them. After clamping, taking care to have the pinned end of the zinc in contact with the angle and the free, or lower end, removed from the other angle about ¹⁄₁₆ inch, three screws should be put through all three bars, with their heads all on the side selected for the front, and one screw may be an inch from the top, another 3 inches from the bottom, and one-half way between the two first mentioned. Now the rod is complete in its composite form, and there is left only the little detail to attend to. Two flat bars, with their ends angled in one case and rounded in the other into rods of given diameter, confining between them, as described, a flat bar of wrought zinc of stated length and of the same thickness and width as the iron bars, comprises the active or compensating elements of the pendulum’s rod. The screws that are put through the three bars are each to pass through the front iron bar, without threads in the bar, and only the back iron bar is to have the holes tapped, fitting the screws. All the corresponding holes in the zinc are to be reamed a little larger than the diameter of the screws, and to be freed lengthwise of the bar, to allow of the bar’s contracting and expanding without being confined in this action by the screws. At the lower or free end of the zinc bar are to be holes carried clear through all three bars, while the combination is held firmly together by the screws. These holes are to start at ½ inch from the end of the zinc, and each carried straight through all three bars, and then broached true and a steel pin made to accurately fit them from the front side. These holes may be from three to five in number, extending up to a safe distance from the lower screw. The holes in the back bar, after boring, are to be reamed larger than those in the front bar and zinc bar. These holes and the pin serve for adjusting the compensation. The pin holds the front bar and zinc from slipping, or moving past one another at the point pinned, and also allows the back bar to be free of the pin, and not under the influence of the two front bars. The upper end of the second iron section is, as has been mentioned, forged into a round rod about ⁵⁄₁₆ inch diameter, and this rod or upper end is to receive the pendulum suspension spring, which may be one single spring, or a compound spring, as preferred.

Now that the pendulum is all ready to balance on the knife edge, proceed as in the case of the simple pendulum, and ascertain at what point up the rod the spring must be placed. In this pendulum the rod will be heavier in proportion than the wood rod was to its bob, and the center of gravity of the whole will be found higher up in the bob. However, wherever in the bob the center of gravity is found, that is the starting point to measure from to find the total length of the rod, and the point for the spring. The heavier the rod is in relation to the bob, the higher will the center of gravity of the whole rise in the bob, and the greater will be the total length of the entire pendulum.

In getting up a rod of the kind just described, the main item is to get the parts all so arranged that there will be very little settling of the joints in contact, particularly those which sustain the weight of the bob and the whole dead weight of the pendulum. The nut in the center of the pendulum holds the weight of the bob only, but it should fit against the shoulder formed for the purpose by the juncture of the two holes, and the face of the nut should be turned true and flat, so that there may not be any uneven motion, and only the one imparted by the progressive one of the threads. When this nut is put to its place for the last time, and after all is finished, there should be a little tallow put on to the face of the nut just where it comes to a seat against the shoulder of the bob, as this shoulder being not very well finished, the two surfaces coming in contact, if left dry, might cut and tear each other, and help to make the nut’s action slightly unsteady and unreliable. A finished washer can be driven into this lower hole up to the center, friction-tight, and serve as a reliable and finished seat for the nut.

In reality, the zinc at the point of contact, where pinned to the angle piece at the top of the lower section, is the point of greatest importance in the whole combination, and if the joint between the angle and the end of the zinc bar is soldered with soft solder, the result will be that of greater certainty in the maintenance of a steady rate. This joint just mentioned can be soldered as follows: File the end of the zinc and the inside surface of the angle until they fit so that no appreciable space is left between them. Then, with a soldering iron, tin the end of the zinc thoroughly and evenly, and then put into the holes already made the two steady pins. Now tin in the same manner the surface of the angle, and see that the holes are free of solder, so that the zinc bar will go to its place easily; then between the zinc and the iron, place a piece of thin writing paper, so that the flat surfaces of the zinc and iron may not become soldered. Set the iron bar upright on a piece of charcoal, and secure it in this position from any danger of falling, and then put the zinc to its place and see that the pins enter and that the paper is between the surfaces, as described. Put the screws into their places, and screw down on the zinc just enough to hold it in contact with the iron bar, but not so tight that the zinc will not readily move down and rest firmly on the angle. Put a little soldering fluid on the tinned joint, and blow with a blow pipe against the iron bar (not touching the zinc with the flame). When the solder in the joint begins to flow, press the zinc down in close contact with the angle, and then cool gradually, and if all the points described have been attended to the joint will be solidly soldered, and the two bars will be as one solid bar bent against itself. The tinning leaves surplus solder on the surfaces sufficient to make a solid joint, and to allow some to flow into the pin holes and also solder the pin to avoid any danger of getting loose in after time, and helps make a much stronger joint. At the time the solder is melted the zinc is sufficiently heated to become quite malleable, and care must be taken not to force it down against the angle in making the joint, or it may be distorted and ruined at the joint. If carefully done the result will be perfect. The paper between the surfaces burns, and is got rid of in washing to remove the soldering fluid. Soda or ammonia will help to remove all traces of the fluid. However, it is best, as a last operation, to put the joint in alcohol for a minute.

This soldering makes the lower section and the zinc practically one piece and without loose joint, and the next joint is that made by the pin pinning the outside bar and the zinc together. This is necessarily formed this way, as in this stage of the operation we do not know just what length the zinc bar will be to exactly compensate for the expansion and contraction of the balance of the pendulum. By the changing of the pin into the different holes, 5, 6, 7, 8, 9, 10, [Fig. 9], the zinc is made relatively longer or shorter, and so a compensation is arrived at in time after the clock has been running. After it is definitely settled where the pin will remain to secure the compensation of the rod, then that hole can have a screw put in to match the three upper ones. This screw must be tapped into the front bar and the zinc, and be very free in the back bar to allow of its expansion. It is supposed that in this example given of a zinc and steel compensation seconds pendulum that there has been due allowance made in the lengths of the several bars to allow for adjustment to temperature by the movements of the pin along the course of the several holes described, but the zinc is a very uncertain element, and its ultimate action is largely influenced by its treatment after being cast. Differences of working cast zinc under the hammer or rolls produce wide differences practically, and therefore materially change the results in its combination with iron in their relative expansive action. Wrought zinc can be obtained of any of the brass plate factories, of any dimensions required, and will be found to be satisfactory for the purpose in hand.

The adjusting pin should be well fitted to the holes in the front iron bar, and also fit the corresponding ones in the zinc bar closely, and if the holes are reamed smooth and true with an English clock broach, then the pin will be slightly tapering and fit the iron hole perfectly solid. After one pair of these holes have been reamed, fit the pin and drive it in place perfectly firm, and then with the broach ream all the remaining holes to just the same diameter, and then the pin will move along from one set of holes to another with mechanically accurate results. Otherwise, if poorly fitted, the full effect would not be obtained from the compensating action in making changes in the pin from one set of holes to another. This pin, if made of cast steel, hardened and drawn to a blue, will on the whole be a very good device mechanically.

Many means are used to effect the adjustments for compensation, of more or less value, but whatever the means used, it must be kept in mind that extra care must be taken to have the mechanical execution first class, as on this very much depends the steady rate of the pendulum in after time.

Tubular Compensated Rods.—There are tubular pendulums in the market which have a screw sleeve at the top of the zinc element, and by this means the adjustments are effected, and this is thought to be a very accurate mechanism. The most common form of zinc and iron compensation is where the zinc is a tube combined with one iron tube and a central rod, as shown in [Figs. 10, 11, 12]. The rod is the center piece, the zinc tube next, followed by the iron tube enveloping both. The relative lengths may be the same as those just given in the foregoing example with the compensating elements flat. The relative lengths of the several members will be virtually the same in both combinations.

Tubular Compensation with Aluminum.—The pendulum as seen by an observer appears to him as being a simple single rod pendulum. [Figs. 10] and [12] are front and side views; [Fig. 11] is an enlarged view of its parts, the upper being a sectional view. Its principal features are: The steel rod S, [Fig. 11], 4 mm. in diameter, having at its upper end a hook for fastening to the suspension spring in the usual way; the lower end has a pivot carrying the bushing, T, which solidly connects the steel rod, S, with the aluminum tube, A, the latter being 10 mm. in diameter and its sides 1.5 mm. in thickness of the wall.

The upper end of the aluminum tube is very close to the pendulum hook and is also provided with a bushing, P, [Fig. 11]. This bushing is permanently connected at the upper end of the aluminum tube with a steel tube, R, 16 mm. in diameter and 1 mm. in thickness. The outer steel tube is the only one that is visible and it supports the bob, the lower part being furnished with a fine thread on which the regulating nut, O, is movable, at the center of the bob.

For securing a central alignment of the steel rod, S, at its lowest part, where it is pivoted, a bushing, M, [Fig. 11], is screwed into the steel tube, R. The lower end of the steel tube, R, projects considerably below the lenticular bob ([compare Figs. 10 and 12]); and is also provided with a thread and regulating weight, G ([Figs. 10 and 12)], of 100 grammes in weight, which is only used in the fine regulation of small variations from correct time.

The steel tube is open at the bottom and the index at its lower end is fastened to a bridge. Furthermore all three of the bushings, P, T and M, have each three radial cuts, which will permit the surrounding air to act equally and at the same time on the steel rod, S, the aluminum tube. A, and the steel tube, R, and as the steel tube, R, is open at its lower end, and as there is also a certain amount of space between the tubes, the steel rod, and the radial openings in the bushings, there will be a draught of air passing through them, which will allow the thin-walled tubes and thin steel rod to promptly and equally adapt themselves to the temperature of the air.

Fig. 10. Fig. 11.Fig. 12.

The lenticular pendulum bob has a diameter of 24 cm., and is made of red brass. The bob is supported at its center by the regulating nut, O, [Figs. 10 and 12]. That the bob may not turn on the cylindrical pendulum rod, the latter is provided with a longitudinal groove and working therein are the ends of two shoulder screws which are placed on the back of the bob above and below the regulating nut, O; and thus properly controlling its movements.

From the foregoing description the action of the compensation is readily explained. For the purpose of illustration of its action we will accept the fact that there has been a sudden rise in temperature. The steel rod, S, and the tube, R, will lengthen in a downward direction (including the suspension spring and the pendulum hook), conversely the aluminum tube, A, which is fastened to the steel rod at one end and the steel tube at the other, will lengthen in an upward direction and thus equalize the expansion of the tube, R, and rod, S.

As the coefficients of expansion of steel and aluminum are approximately at the ratio of 1:2.0313 we find that with such a pendulum construction—accurate calculations presumed—we shall have a complete and exact coincidence in its compensation; in other words, the center of oscillation of the pendulum will be under all conditions at the same distance from the bending point of the suspension spring.

This style of pendulum is made for astronomical clocks in Europe and is furnished in two qualities. In the best quality, the tubes, steel rod, and the bob are all separately and carefully tested as to their expansion, and their coefficients of expansion fully determined in a laboratory; the bushings, P and M, are jeweled, all parts being accurately and finely finished. In the second quality the pendulum is constructed on a general calculation and finished in a more simple manner without impairing its ultimate efficiency.

At the upper part of the steel tube, R, there is a funnel-shaped piece (omitted in the drawing) in which are placed small lead and aluminum balls for the final regulation of the pendulum without stopping it.

The regulation of this pendulum is effected in three ways:

1. The preliminary or coarse regulation by turning the regulating nut, O, and so raising or lowering the bob.

2. The finer regulation by turning the 100 grammes weight, g, having the shape of a nut and turning on the threaded part of the tube, R. 3. The precision regulation is effected by placing small lead or aluminum balls in a small funnel-shaped receptacle attached to the upper part of the tube, R, or by removing them therefrom.

It will readily be seen that this form of pendulum can be used with zinc or brass instead of aluminum, by altering the lengths of the inner rod and the compensating tube to suit the expansion of the metal it is decided to use; also that alterations in length may be made by screwing the bushings in or out, provided that the tube be long enough in the first place. After securing the right position the bushings should have pins driven into them through the tube, in order to prevent further shifting.

CHAPTER IV.
THE CONSTRUCTION OF MERCURIAL PENDULUMS.

Owing to the difficulty of calculating the expansive ratios of metal which (particularly with brass and zinc) vary slightly with differences of manufacture, the manufacture of compensated pendulums from metal rods cannot be reduced to cutting up so many pieces and assembling them from calculations made previously, so that each must be separately built and tested. While this is not a great draw-back to the jeweler who wants to make himself a pendulum, it becomes a serious difficulty to a manufacturer, and hence a cheaper combination had to be devised to prevent the cost of compensated pendulums from seriously interfering with their use. The result was the pendulum composed of a steel rod and a quantity of mercury, the latter forming the principal weight for the bob and being contained in steel or glass jars, or jars of cast iron for the heavier pendulums. Other metals will not serve the purpose, as they are corroded by the mercury, become rotten and lose their contents.

Mercury has one deficiency which, however, is not serious, except for the severe conditions of astronomical observatories. It will oxidize after long exposure to the air, when it must be strained and a fresh quantity of metal added and the compensation freshly adjusted. To an astronomer this is a serious objection, as it may interfere with his work for a month, but to the jeweler this is of little moment as the rates he demands will not be seriously affected for about ten years, if the jars are tightly covered.

To construct a reliable gridiron pendulum would cost about fifty dollars while a mercurial pendulum can be well made and compensated for about twenty-five dollars, hence the popularity of the latter form.

Zinc will lengthen under severe variations of temperature as the following will show: Zinc has a decided objectionable quality in its crystalline structure that with temperature changes there is very unequal expansion and contraction, and furthermore, that these changes occur suddenly; this often results in the blending of the zinc rod, causing a binding to take place, which naturally enough prevents the correct working of the compensation.

It is probably not very well known that zinc can change its length at one and the same temperature, and that this peculiar quality must not be overlooked. The U. S. Lake Survey, which has under its charge the triangulation of the great lakes of the United States, has in its possession a steel meter measure, R, 1876; a metallic thermometer composed, of a steel and zinc rod, each being one meter in length, marked M. T., 1876s, and M. T. 1876z; and four metallic thermometers, used in connection with the base apparatus, which likewise are made of steel and zinc rods, each of these being four meters in length. All of these rods were made by Repsold, of Hamburg. Comparisons between these different rods show peculiar variations, and which point to the fact that their lengths at the same degree of temperature are not constant. For the purpose of determining these variations accurate investigations were undertaken. The metallic thermometer M. T. 1876 was removed from an observatory room having an equal temperature of about 2° C. and placed for one day in a temperature of +24° C., and also for the same period of time in one of -20° C; it was then replaced in the observatory room, where it remained for twenty-four hours, and comparisons were made during the following three days with the steel thermometer 1876, which had been left in the room. From these observations and comparisons the following results were tabulated, which give the mean lengths of the zinc rods of the metallic thermometer. The slight variations of temperature in the observatory room were also taken into consideration in the calculations:

These investigations clearly indicate, without doubt, that the zinc rod at one and the same temperature of about 2° C., is 0.018 mm. longer after having been previously heated to 24° C. than when cooled before to -20° C.

A similar but less complete examination was made with the metallic thermometer four meters in length. These trials were made by that efficient officer, General Comstock, gave the same results, and completely prove that in zinc there are considerable thermal after-effects at work.

To prove that zinc is not an efficient metal for compensation pendulums when employed for the exact measurement of time, a short calculation may be made—using the above conclusions—that a zinc rod one meter in length, after being subjected to a difference of temperature of 44° C. will alter its length 0.018 mm. after having been brought back to its initial degree. For a seconds pendulum with zinc compensation each of the zinc rods would require a length of 64.9 cm. With the above computations we get a difference in length of 0.0117 mm. at the same degree of temperature. Since a lengthening of the zinc rods without a suitable and contemporaneous expansion of the steel rods is synonymous with a shortening of the effectual pendulum length, we have, notwithstanding the compensation, a shortening of the pendulum length of 0.017 mm., which corresponds to a change in the daily rate of about 0.5 seconds.

This will sufficiently prove that zinc is unquestionably not suitable for extremely accurate compensation pendulums, and as neither is permanent under extremes of temperature the advantages of first cost and of correction of error appear to lie with the mercurial form.

The average mercurial compensation pendulums, on sale in the trade are often only partially compensated, as the mercury is nearly always deficient in quantity relatively, and not high enough in the jar to neutralize the action of the rigid metallic elements, composing the structure. The trouble generally is that the mercury forms too small a proportion of the total weight of the pendulum bob. There is a fundamental principle governing these compensating pendulums that has to be kept in mind, and that is that one of the compensating elements is expected to just undo what the other does and so establish through the medium of physical things the condition of the ideal pendulum, without weight or elements outside of the bob. As iron and mercury, for instance, have a pretty fixed relative expansive ratio, then whatever these ratios are after being found, must be maintained in the construction of the pendulum, or the results cannot be satisfactory.

First, there are 39.2 inches of rod of steel to hold the bob between the point of suspension and the center of oscillation, and it has been found that, constructively, in all the ordinary forms of these pendulums, the height of mercury in the bob cannot usually be less than 7.5 inches. Second, that in all seconds pendulums the length of the metal is fixed substantially, while the height of the mercury is a varying one, due to the differing weights of the jars, straps, etc.

Third, the mercury, at its minimum, cannot with jars of ordinary weight be less in height in the jar than 7.5 inches, to effectually counteract what the 39.2 inches of iron does in the way of expanding and contracting under the same exposure.

Whoever observes the great mass of pendulums of this description on sale and in use will find that the height of the mercury in the jar is not up to the amount given above for the least quantity that will serve under the most favorable circumstances of construction. The less weight there is in the rod, jar and frame, the less is the height of mercury which is required; but with most of the pendulums made in the present day for the market, the height given cannot be cut short without impairing the quality and efficiency of the compensation. Any amount less will have the effect of leaving the rigid metal in the ascendancy; or, in other words, the pendulum will be under compensated and leave the pendulum to feel heat and cold by raising and lowering the center of oscillation of the pendulum and hence only partly compensating. A jar with only six inches in height of mercury will in round numbers only correct the temperature error about six-sevenths.

Calculations of Weights.—As to how to calculate the amount of mercury required to compensate a seconds pendulum, the following explanation should make the matter clear to anyone having a fair knowledge of arithmetic only, though there are several points to be considered which render it a rather more complicated process than would appear at first sight.

1st. The expansion in length of steel and cast iron, as given in the tables (these tables differ somewhat in the various books), is respectively .0064 and .0066, while mercury expands .1 in bulk for the same increase of temperature. If the mercury were contained in a jar which itself had no expansion in diameter, then all its expansion would take place in height, and in round numbers it would expand sixteen times more than steel, and we should only require (neglecting at present the allowance to be explained under head 3) to make the height of the mercury—reckoned from the bottom of the jar (inside) to the middle of the column of mercury contained therein—one-sixteenth of the total length of the pendulum measured from the point of suspension to the bottom of the jar, assuming that the rod and the jar are both of steel, and that the center of oscillation is coincident with the center of the column of mercury. Practically in these pendulums, the center of oscillation is almost identical with the center of the bob.

2d. As we cannot obtain a jar having no expansion in diameter, we must allow for such expansion as follows, and as cast iron or steel jars of cylindrical shape are undoubtedly the best, we will consider that material and form only.

As above stated, cast iron expands .0066, so that if the original diameter of the jar be represented by 1, its expanded diameter will be 1.0066. Now the area of any circle varies as the square of its diameter, so that before and after its expansion the areas of the jar will be in the ratio of 1² to 1.0066²; that is, in the proportion of 1 to 1.013243; or in round numbers it will be one-seventy-sixth larger in area after expansion than before. It is evident that the mercury will then expand sideways, and that its vertical rise will be diminished to the same extent. Deduct, therefore, the one-seventy-sixth from its expansion in bulk (one-tenth) and we get one-eleventh (or more exactly .086757) remaining. This, then, is the actual vertical rise in the jar, and when compared with the expansion of steel in length it will be found to be about thirteen and a half times greater (more exactly 13.556).

The mercury, therefore (still neglecting head No. 3), must be thirteen and a half times shorter than the length of the pendulum, both being measured as explained above. The pendulum will probably be 43.5 inches long to the bottom of the jar; but as about nine inches of it is cast iron, which has a slightly greater rate of expansion than steel, we will call the length 44 inches, as the half inch added will make it about equivalent to a pendulum entirely of steel. If the height of the mercury be obtained by dividing 44 by 13.5, it will be 3.25 inches high to its center, or 6.5 inches high altogether; and were it not for the following circumstance, the pendulum would be perfectly compensated.

3d. The mercury is the only part of the bob which expands upwards; the jar does not rise, its lower end being carried downward by the expansion of the rod, which supports it. In a well-designed pendulum, the jar, straps, etc., will be from one-fourth to one-third the weight of the mercury. Assume them to be seven pounds and twenty-eight pounds respectively; therefore, the total weight of the bob is thirty-five pounds; but as it is only the mercury (four-fifths) of this total that rises with an increase of temperature, we must increase the weight of the mercury in the proportion of five to four, thus 6.5 × 5 ÷ 4 = 8⅛ inches. Or, what is the same thing, we add one-fourth to the amount of mercury, because the weight of the jar is one-fourth of that of the mercury. Eight and one-eighth inches is, therefore, the ultimate height of the mercury required to compensate the pendulum with that weight of jar. If the jar had been heavier, say one-third the weight of the mercury, then the latter would have to be nearly 8.75 inches high.

If the jar be required to be of glass, then we substitute the expansion of that material in No. 2 and its weight in No. 3.

In the above method of calculating, there are two slight elements of uncertainty: 1st. In assuming that the center of oscillation is coincident with the center of the bob; however, I should suppose that they would never be more than .25 inch apart, and generally much nearer. 2d. The weight of the jar cannot well be exactly known until after it is finished (i. e., bored smooth and parallel inside, and turned outside true with the interior), so that the exact height of the mercury cannot be easily ascertained till then.

I may explain that the reason (in Nos. 1 and 2) we measure the mercury from the bottom to the center of the column, is that it is its center which we wish to raise when an increase of temperature occurs, so that the center may always be exactly the same distance from the point of suspension; and we have seen that 3.25 inches is the necessary quantity to raise it sufficiently. Now that center could not be the center without it had as much mercury over it as it has under it; hence we double the 3.25 and get the 6.5 inches stated.

From the foregoing it will be seen that the average mercury pendulums are better than a plain rod, from the fact that the mercury is free to obey the law of expansion, and so, to a certain degree, does counteract the action of the balance of the metal of the pendulum, and this with a degree of certainty that is not found in the gridiron form, provided always that the height and amount of the mercury are correctly proportional to the total weight of the pendulum.

Compensating Mercurial Pendulums.—To compensate a pendulum of this kind takes time and study. The first thing to do is to place maximum and minimum thermometers in the clock case, so that you can tell the temperature.

Then get the rate of the clock at a given temperature. For example, say the clock gains two seconds in twenty-four hours, the temperature being at 70°. Then see how much it gains when the temperature is at 80°. We will say it gains two seconds more at 80° than it does when the temperature is at 70°.

In that case we must remove some of the mercury in order to compensate the pendulum. To do this take a syringe and soak the cotton or whatever makes the suction in the syringe with vaseline. The reason for doing this is that mercury is very heavy and the syringe must be air-tight before you can take any of the mercury up into it.

You want to remove about two pennyweights of mercury to every second the clock gains in twenty-four hours. Now, after removing the mercury the clock will lose time, because the pendulum is lighter. You must then raise the ball to bring it to time. You then repeat the same operation by getting the rate at 70° and 80° again and see if it gains. When the temperature rises, if the pendulum still gains, you must remove more mercury; but if it should lose time when the temperature rises you have taken out too much mercury and you must replace some. Continue this operation until the pendulum has the same rate, whether the temperature is high or low, raising the bob when you take out mercury to bring it to time, and lowering the bob when you put mercury in to bring it to time.

To compensate a pendulum takes time and study of the clock, but if you follow out these instructions you will succeed in getting the clock to run regularly in both summer and winter.

Besides the oxidation, which is an admitted fault, there are two theoretical questions which have to do with construction in deciding between the metallic and mercurial forms of compensation. We will present the claims of each side, therefore, with the preliminary statement that (for all except the severest conditions of accuracy) either form, if well made will answer every purpose and that therefore, except in special circumstances, these objections are more theoretical than real.

The advocates of metallic compensation claim that where there are great differences of temperature, the compensated rod, with its long bars will answer more quickly to temperature changes as follows:

The mercurial pendulum, when in an unheated room and not subjected to sudden temperature changes, gives very excellent results, but should the opposite case occur there will then be observed an irregularity in the rate of the clock. The causes which produce these effects are various. As a principal reason for such a condition it may be stated that the compensating mercury occupies only about one-fifth the pendulum length, and it inevitably follows that when the upper strata of the air is warmer than the lower, in which the mercury is placed, the steel pendulum rod will expand at a different ratio than the mercury, as the latter is influenced by a different degree of temperature than the upper part of the pendulum rod. The natural effect will be a lengthening of the pendulum rod, notwithstanding the compensation, and therefore, a loss of time by the clock.

Two thermometers, agreeing perfectly, were placed in the case of a clock, one near the point of suspension, and the other near the middle of the ball, and repeated experiments, showed a difference between these two thermometers of 7° to 10½° F., the lower one indicating less than the higher one. The thermometers were then hung in the room, one at twenty-two inches above the floor, and the other three feet higher, when they showed a difference of 7° between them. The difference of 2.5° more which was found inside the case proceeds from the heat striking the upper part of the case; and the wood, though a bad conductor, gradually increases in temperature, while, on the contrary, the cold rises from the floor and acts on the lower part of the case. The same thermometers at the same height and distance in an unused room, which was never warmed, showed no difference between them; and it would be the same, doubtless, in an observatory.

From the preceding it is very evident that the decrease of rate of the clock since December 13 proceeded from the rod of the pendulum experiencing 7° to 10.5° F. greater heat than the mercury in the bob, thus showing the impossibility of making a mercurial pendulum perfectly compensating in an artificially heated room which varies greatly in temperature. I should remark here that during the entire winter the temperature in the case is never more than 68° F., and during the summer, when the rate of the clock was regular, the thermometer in the case has often indicated 72° to 77° F.

The gridiron pendulum in this case would seem preferable, for if the temperature is higher at the top than at the lower part, the nine compensating rods are equally affected by it. But in its compensating action it is not nearly as regular, and it is very difficult to regulate it, for in any room (artificially heated) it is impossible to obtain a uniform temperature throughout its entire length, and without that all proofs are necessarily inexact.

These facts can also be applied to pendulums situated in heated rooms. In the case of a rapid change in temperature taking place in the observatory rooms, under the domes of observatories, especially during the winter months, and which are of frequent occurrence, a mercurial compensation pendulum, as generally made, is not apt to give a reliable rate. Let us accept the fact, as an example, of a considerable fall in the temperature of the surrounding air; the thin pendulum rod will quickly accept the same temperature, but with the great mass of mercury to be acted upon the responsive effects will only occur after a considerable lapse of time. The result will be a shortening of the pendulum length and a gain in the rate until the mercury has had time to respond, notwithstanding the compensation.

Others who have expressed their views in writing seem to favor the idea that this inequality in the temperature of the atmosphere is unfavorable to the accurate action of the mercurial form of compensation; and however plausible and reasonable this idea may seem at first notice, it will not take a great amount of investigation to show that, instead of being a disadvantage, its existence is beneficial, and an important element in the success of mercurial pendulums.

It appears that the majority of those who have proposed, or have tried to improve Graham’s pendulum have overlooked the fact that different substances require different quantities of heat to raise them to the same temperature. In order to warm a certain weight of water, for instance, to the same degree of heat as an equal weight of oil, or an equal weight of mercury, twice as much heat must be given to the water as to the oil, and thirty times as much as to the mercury; while in cooling down again to a given temperature, the oil will cool twice as quick as the water, and the mercury thirty times quicker than the water. This phenomenon is accounted for by the difference in the amount of latent heat that exists in various substances. On the authority of Sir Humphrey Davy, zinc is heated and cooled again ten and three-quarters times quicker than water, brass ten and a half times quicker, steel nine times, glass eight and a half times, and mercury is heated and cooled again thirty times quicker than water.

From the above it will be noticed that the difference in the time steel and mercury takes to rise and fall to a given temperature is as nine to thirty, and also that the difference in the quantity of heat that it takes to raise steel and mercury to a given temperature is in the ratio of nine to thirty.

Now, without entering into minute details on the properties which different substances possess for absorbing or reflecting heat, it is plain that mercury should move in a proportionally different atmosphere from steel in order to be expanded or contracted a given distance in the same length of time; and to obtain this result the amount of difference in the temperature of the atmosphere at the opposite ends of the pendulum must vary a little more or less according to the nature of the material the mercury jars are constructed from.

Differences in the temperature of the atmosphere of a room will generally vary according to its size, the height of the ceiling, and the ventilation of the apartment; and if the difference must continue to exist, it is of importance that the difference should be uniformly regular. We must not lose sight of the fact, however, that clocks having these pendulums, and placed in apartments every way favorable to an equal temperature, and in some instances, the clocks and their pendulums encased in double casing in order to more effectually obtain this result, still the rates of the clock show the same eccentricities as those placed in less favorable position. This clearly shows that many changes in the rates of fine clocks are due to other causes than a change in the temperature of the surrounding atmosphere. Still it must be admitted that any change in the condition of the atmosphere that surrounds a pendulum is a most formidable obstacle to be overcome by those who seek to improve compensated pendulums, and it would be of service to them to know all that can possibly be known on the subject.

The differences spoken of above have resulted in some practical improvements, which are: 1st, the division of the mercury into two, three or four jars in order to expose as much surface as possible to the action of the air, so that the expansion of the mercury should not lag behind that of the rod, which it will do if too large amounts of it are kept in one jar. 2nd, the use of very thin steel jars made from tubing, so that the transmission of heat from the air to the mercury may be hastened as much as possible. 3rd, the increase in the number of jars makes a thinner bob than a single jar of the same total weight and hence gives an advantage in decreasing the resistant effect of air friction in dense air, thereby decreasing somewhat the barometric error of the pendulum.

The original form of mercurial pendulums, as made by Graham, and still used in tower and other clocks where extraordinary accuracy is not required, was a single jar which formed the bob and had the pendulum rod extending into the mercury to assist in conducting heat to the variable element of the pendulum. It is shown in section in [Fig. 13], which is taken from a working drawing for a tower clock.

The pendulum, [Fig. 13], is suspended from the head or cock shown in the figure, and supported by the clock frame itself, instead of being hung on a wall, since the intention is to set the clock in the center of the clockroom, and also because the weight, forty pounds, is not too much for the clock frame to carry. The head, A, forms a revolving thumb-nut, which is divided into sixty parts around the circumference of its lower edge, and the regulating screw, B, is threaded ten to the inch. A very fine adjustment is thus obtained for regulating the time of the pendulum. The lower end of the regulating screw, B, holds the end of the pendulum spring, E, which is riveted between two pieces of steel, C, and a pin, C′, is put through them and the end of the regulating screw, by which to suspend the pendulum.

The cheeks or chops are the pieces D, the lower edges of which form the theoretical point of suspension of the pendulum. These pieces must be perfectly square at their lower edges, otherwise the center of gravity would describe a cylindrical curve. The chops are clamped tightly in place by the setscrews, D′, after the pendulum has been hung.

The lower end of the regulating screw is squared to fit the ways and slotted on one side, sliding on a pin to prevent its turning and therefore twisting the suspension spring when it is raised or lowered.

The spring is three inches long between its points of suspension, one and three-eighths inches wide, and one-sixtieth of an inch thick. Its lower end is riveted between two small blocks of steel, F, and suspended from a pin, F′, in the upper end of the cap, G, of the pendulum rod.

The tubular steel portion of the pendulum rod is seven-eighths of an inch in diameter and one-thirty-second of an inch thickness of the wall. It is enclosed at each end by the solid ends, G and L, and is made as nearly air-tight as possible.

Fig. 13.

The compensation is by mercury inclosed in a cast iron bob. The mercury, the bob and the rod together weigh forty pounds. The bob of the pendulum is a cast iron jar, K, three inches in diameter inside, one-quarter inch thick at the sides, and five-sixteenths thick at the bottom, with the cap, J, screwed into its upper end. The cap, J, forms also the socket for the lower end of the pendulum rod, H. The rod, L, one-quarter inch in diameter, screws into the cap, J, and its large end at the same time forms a plug for the lower end of the pendulum tube, H. The pin, J′, holds all these parts together. The rod, L, extends nearly to the bottom of the jar, and forms a medium for the transmission of the changes in temperature from the pendulum tube to the mercury. The screw in the cap, J, is for filling or emptying the jar. The jar is finished as smoothly as possible, outside and inside, and should be coated with at least three coats of shellac inside. Of course if one was building an astronomical clock, it would be necessary to boil the mercury in the jar in order to drive off the layer of air between the mercury and the walls of the jar, but with the smooth finish the shellac will give, in addition to the good work of the machinist, the amount of air held by the jar can be ignored.

The cast iron jar was decided upon because it was safer to handle, can be attached more firmly to the rod with less multiplication of parts, and also on account of the weight as compared with glass, which is the only other thing that should be used, the glass requiring a greater height of jar for equal weight. In making cast iron jars, they should always be carefully turned inside and out in order that the walls of the jar may be of equal thickness throughout; then they will not throw the pendulum out of balance when they are screwed up or down on the pendulum rod in making the coarse regulation before timing by the upper screw. The thread on the rod should have the cover of the jar at about the center of the thread when nearly to time and that portion which extends into the jar should be short enough to permit this.

Ignoring the rod and its parts for the present, and calling the jar one-third of the weight of the mercury, we shall find that thirty pounds of mercury, at .49 pounds per cubic inch, will fill a cylinder which is three inches inside diameter to a height of 8.816 inches, after deducting for the mass of the rod L, when the temperature of the mercury is 60 degrees F. Mercury expands one-tenth in bulk, while cast iron expands .0066 in diameter: so the sectional area increases as 1.0066² or 1.0132 to 1, therefore the mercury will rise .1-.013243, or .086757; then the mercury in our jar will rise .767 of an inch in the ordinary changes of temperature, making a total height of 9.58 inches to provide for; so the jar was made ten inches long.

Pendulums of this pattern as used in the high grade English clocks, are substantially as follows: Rod of steel ⁵⁄₁₆inch diameter jar about 2.1 inches diameter inside and 8¾ inches deep inside. The jar may be wrought or cast iron and about ⅜ of an inch thick with the cover to screw on with fine thread, making a tight joint. The cover of the jar is to act as a nut to turn on the rod for regulation. The thread cut on the rod should be thirty-six to the inch, and fit into the jar cover easily, so that it may turn without binding. With a thirty-six thread one turn of the jar on the rod changes the rate thirty seconds per day and by laying off on the edge of the cover 30 divisions, a scale is made by which movements for one second per day are obtained.

We will now describe ([Fig. 14]) the method of making a mercurial pendulum to replace an imitation gridiron pendulum for a Swiss, pin escapement regulator, such as is commonly found in the jewelry stores of the United States, that is, a clock in which the pendulum is supported by the plates of the movement and swings between the front plate and the dial of the movement. In thus changing our pendulum, we shall desire to retain the upper portion of the old rod, as the fittings are already in place and we shall save considerable time and labor by this course. As the pendulum is suspended from the movement, it must be lighter in weight than if it were independently supported by a cast iron bracket, as shown in [Fig. 6], so we will make the weight about that of the one we have removed, or about twelve pounds. If it is desired to make the pendulum heavier, four jars of the dimensions given would make it weigh about twenty pounds, or four jars of one inch diameter would make a thinner bob and one weighing about fourteen pounds. As the substitution of a different number or different sizes of jars merely involves changing the lengths of the upper and lower bars of the frame, further drawings will be unnecessary, the jeweler having sufficient mechanical capacity to be able to make them for himself. I might add, however, that the late Edward Howard, in building his astronomical clocks, used four jars containing twenty-eight pounds of mercury for such movements, and the perfection of his trains was such that a seven-ounce driving weight was sufficient to propel the thirty pound pendulum.

The two jars are filled with mercury to a height of 7⅝ inches, are 1⅜ inches in diameter outside and 8⅜ inches in height outside. The caps and foot pieces are screwed on and when the foot pieces are screwed on for the last time the screw threads should be covered with a thick shellac varnish which, when dry, makes the joint perfectly air-tight. The jars are best made of the fine, thin tubing, used in bicycles, which can be purchased from any factory, of various sizes and thickness. In the pendulum shown in the illustration, the jar stock is close to 14 wire gauge, or about 2 mm. in thickness. In cutting the threads at the ends of the jars they should be about 36 threads to the inch, the same number as the threads on the lower end of the rod used to carry the regulating nut. A fine thread makes the best job and the tightest joints. The caps to the jars are turned up from cold rolled shafting, it being generally good stock and finishes well. The threads need not be over ³⁄₁₆ inch, which is ample. Cut the square shoulder so the caps and foot pieces come full up and do not show any thread when screwed home. These jars will hold ten pounds of mercury and this weight is about right for this particular style of pendulum. The jars complete will weigh about seven ounces each.

Fig. 14.

The frame is also made of steel and square finished stock is used as far as possible and of the quality used in the caps. The lower bar of the frame is six inches long and ⅝ inch square at the center and tapered, as shown in the illustration. It is made light by being planed away on the under side, an end view being shown at 3. The top bar of the frame, shown at 4, is planed away also and is one-half inch square the whole length and is six inches long. The two side rods are to bind the two bars together, and with the four thumb nuts at the top and bottom make a strong light frame.

The pendulum described is nickel plated and polished, except the jars, which are left half dead; that is, they are frosted with a sand blast and scratch brushed a little. The effect is good and makes a good contrast to the polished parts. The side rods are five inches apart, which leaves one-half inch at the ends outside.

The rod is ⁵⁄₁₆ of an inch in diameter and 33 inches long from the bottom of the frame at a point where the regulating nut rests against it to the lower end of the piece of the usual gridiron pendulum shown in [Fig. 14] at 10. This piece shown is the usual style and size of those in the majority of these clocks and is the standard adopted by the makers. This piece is 11⅛ inches long from the upper leaf of the suspension spring, which is shown at 12, to the lower end marked 10. By cutting out the lower end of this piece, as shown at 10, and squaring the upper end of the rod, pinning it into the piece as shown, the union can be made easily and any little adjustments for length can be made by drilling another set of holes in the rod and raising the pendulum by so doing to the correct point. A rod whose total length is 37 inches will leave 2 inches for the prolongation below the frame carrying the regulating nut, 9, and for the portion squared at the top, and will then be so long that the rate of the clock will be slow and leave a surplus to be cut off either at the top or bottom, as may seem best.

The screw at the lower end carrying the nut should have 36 threads to the inch and the nut graduated to 30 divisions, each of which is equal in turning the nut to one minute in 24 hours, fast or slow, as the case may be.

The rod should pass through the frame bars snugly and not rattle or bind. It also should have a slot cut so that a pin can be put through the upper bar of the frame to keep the frame from turning on the rod and yet allow it to move up and down about an inch. The thread at the lower end of the rod should be cut about two inches in length and when cutting off the rod for a final length, put the nut in the middle of the run of the thread and shorten the rod at the top. This will be found the most satisfactory method, for when all is adjusted the nut will stand in the middle of its scope and have an equal run for fast or slow adjustment. With the rod of the full length as given, this pendulum had to be cut at the top about one inch to bring to a minute or two in twenty-four hours, and this left all other points below corrected. The pin in the rod should be adjusted the last thing, as this allows the rod to slide on the pin equal distances each way. One inch in the raising or lowering of the frame on the rod will alter the rate for twenty-four hours about eighteen minutes.

Many attempts have been made to combine the good qualities of the various forms of pendulums and thus produce an instrument which would do better work under the severe exactions of astronomical observatories and master clocks controlling large systems. The reader should understand that, just as in watch work, the difficulties increase enormously the nearer we get towards absolute accuracy, and while anybody can make a pendulum which will stay within a minute a month, it takes a very good one to stay within five seconds per month, under the conditions usually found in a store, and such a performance makes it totally unfit for astronomical work, where variations of not over five-thousandths of a second per day are demanded. In order to secure such accuracy every possible aid is given to the pendulum. Barometric errors are avoided by enclosing it in an air-tight case, provided with an air pump; the temperature is carefully maintained as nearly constant as possible and its performance is carefully checked against the revolutions of the fixed stars, while various astronomers check their observations against each other by correspondence, so that each can get the rate of his clock by calculations of observations and the law of averages, eliminating personal errors.

One of the successful attempts at such a combination of mercury and metallic pendulums is that of Riefler, as shown in [Fig. 15], which illustrates a seconds pendulum one-thirtieth of the actual size.

It consists of a Mannesmann steel tube (rod), bore 16 mm., thickness of metal 1 mm., filled with mercury to about two-thirds of its length, the expansion of the mercury in the tube changing the center of weight an amount sufficient to compensate for the lengthening of the tube by heat, or vice versa. The pendulum, has further, a metal bob weighing several kilograms, and shaped to cut the air. Below the bob are disc shaped weights, attached by screw threads, for correcting the compensation, the number of which may be increased or diminished as appears necessary.

Whereas in the Graham pendulum regulation for temperature is effected by altering the height of the column of mercury, in this pendulum it is effected by changing the position of the center of weight of the pendulum by moving the regulating weights referred to, and thus the height of the column of mercury always remains the same, except as it is influenced by the temperature.

Fig. 15.

A correction of the compensation should be effected, however, only in case the pendulum is to show sidereal time, instead of mean solar time, for which latter it is calculated. In this case a weight of 110 to 120 grams should be screwed on to correct the compensation.

In order to calculate the effect of the compensation, it is necessary to know precisely the coefficients of the expansion by heat of the steel rod, the mercury, and the material of which the bob is made.

The last two of these coefficients of expansion are of subordinate importance, the two adjusting screws for shifting the bob up and down being fixed in the middle of the latter. A slight deviation is, therefore, of no consequence. In the calculation for all these pendulums the co-efficient for the bob is, therefore, fixed at 0.000018, and for the mercury at 0.00018136, being the closest approximation hitherto found for chemically pure mercury, such as that used in these pendulums.

The co-efficient of the expansion of the steel rod is, however, of greater importance. It is therefore, ascertained for every pendulum constructed in Mr. Riefler’s factory, by the physikalisch-technische Reichsanstalt at Charlottenburg, examinations showing, in the case of a large number of similar steel rods, that the co-efficient of expansion lies between 0.00001034 and 0.00001162.

The precision with which the measurements are carried out is so great that the error in compensation resulting from a possible deviation from the true value of the co-efficient of expansion, as ascertained by the Reichsanstalt, does not amount to over ± 0.0017; and, as the precision with which the compensation for each pendulum may be calculated absolutely precludes any error of consequence, Mr. Riefler is in a position to guarantee that the probable error of compensation in these pendulums will not exceed ± 0.005 seconds per diem and ± 1° variation in temperature.

A subsequent correction of the compensation is, therefore, superfluous, whereas, with all other pendulums it is necessary, partly because the coefficients of expansion of the materials used are arbitrarily assumed; and partly because none of the formulæ hitherto employed for calculating the compensation can yield an exact result, for the reason that they neglect to notice certain important influences, in particular that of the weight of the several parts of the pendulum. Such formulæ are based on the assumption that this problem can be solved by simple geometrical calculation, whereas, its exact solution can be arrived at only with the aid of physics.

This is hardly the proper place for details concerning the lengthy and rather complicated calculations required by the method employed. It is intended to publish them later, either in some mathematical journal or in a separate pamphlet. Here I will only say that the object of the whole calculation is to find the allowable or requisite weight of the bob, i. e., the weight proportionate to the coefficients of expansion of the steel rod, dimensions and weight of the rod and the column of mercury being given in each separate case. To this end the relations of all the parts of the pendulum, both in regard to statics and inertia, have to be ascertained, and for various temperatures.

A considerable number of these pendulums have already been constructed, and are now running in astronomical observatories. One of them is in the observatory of the University of Chicago, and others are in Europe. The precision of this compensation which was discovered by purely theoretical computations, has been thoroughly established by the ascertained records of their running at different temperatures.

The adjustment of the pendulums, which is, of course, almost wholly without influence on the compensation, can be effected in three different ways;

(1.) The rough adjustment, by screwing the bob up or down.

(2.) A finer adjustment, by screwing the correction discs up or down.

(3.) The finest adjustment, by putting on additional weights.

These weights are to be placed on a cup attached to a special part of the rod of the pendulum. Their shape and size is such that they can be readily put on or taken off while the pendulum is swinging. Their weight bears a fixed proportion to the static momentum of the pendulum, so that each additional weight imparts to the pendulum, for twenty-four hours, an acceleration expressed in even seconds and parts of seconds, and marked on each weight.

Each pendulum is accompanied with additional weights of German silver, for a daily acceleration of 1 second each, and ditto of aluminum for an acceleration of 0.5 and 0.1 second respectively.

A metal clasp attached on the rear side of the clock case, may be pushed up to hold the pendulum in such a way that it can receive no twisting motion during adjustment.

Further, a pointer is attached to the lower end of the pendulum, for reading off the arc of oscillation.

The essential advantages of this pendulum over the mercurial compensation pendulums are the following:

(1.) It follows the changes of temperature more rapidly, because a small amount of mercury is divided over a greater length of pendulum, whereas, in the older ones the entire (and decidedly larger) mass of mercury is situated in a vessel at the lower end of the pendulum rod.

(2.) For this reason differences in the temperature of the air at different levels have no such disturbing influence on this pendulum as on the others.

(3.) This pendulum is not so strongly influenced as the others by changes in the atmospheric pressure, because the principal mass of the pendulum has the shape of a lens, and therefore cuts the air easily.

CHAPTER V.
REGULATIONS, SUSPENSIONS, CRUTCHES
AND MINOR POINTS.

Regulation.—The reader will have noticed that in describing the various forms of seconds pendulums we have specified either eighteen or thirty-six threads to the inch; this is because a revolution of the nut with such a thread gives us a definite proportion of the length of the rod, so that it means an even number of seconds in twenty-four hours.

Moving the bob up or down ¹⁄₁₈ inch makes the clock having a seconds pendulum gain or lose in twenty-four hours one minute, hence the selecting definite numbers of threads has for its reason a philosophical standpoint, and is not a matter of convenience and chance, as seems to be the practice with many clockmakers. With a screw of eighteen threads, we shall get one minute change of the clock’s rate in twenty-four hours for every turn of the nut, and if the nut is divided into sixty parts at its edge, each of these divisions will make a change of the clock’s rate of one second in twenty-four hours. Thus by using a thread having a definite relation to the length of the rod regulating is made comparatively easy, and a clock can be brought to time without delay. Suppose, after comparing your clock for three or four days with some standard, you find it gains twelve seconds per day, then, turning the nut down twelve divisions will bring the rate down to within one second a day in one operation, if the screw is eighteen threads. With the screw thirty-six threads the nut will require moving just the same number of divisions, only the divisions are twice as long as those with the screw of eighteen threads.

The next thing is the size and weight of the nut. If it is to be placed in the middle of the bob as in [Figs. 10, 12] and [15], it should project slightly beyond the surface and its diameter will be governed by the thickness of the bob. If it is an internal nut, worked by means of a sleeve and disc, as in [Fig. 9], the disc should be of sufficient diameter to make the divisions long enough to be easily read. If the nut is of the class shown in Fig. [5], [6], [7], a nut is most convenient, 1 inch in diameter, and cut on its edge into thirty equal divisions, each of which is equal to one second in change of rate in twenty-four hours, if the screw has thirty-six threads to the inch. This gives 3.1416 inches of circumference for the thirty divisions, which makes them long enough to be subdivided if we choose, each division being a little over one-tenth of an inch in length, so that quarter-seconds may be measured or estimated.