PRINCIPLES OF MINING

PRINCIPLES OF MINING

VALUATION, ORGANIZATION AND ADMINISTRATION

COPPER, GOLD, LEAD, SILVER, TIN AND ZINC

BY
HERBERT C. HOOVER

Member American Institute of Mining Engineers, Mining and Metallurgical Society of America, Société des Ingénieurs Civils de France, Fellow Royal Geographical Society, etc.

First Edition
FOURTH THOUSAND

McGRAW-HILL BOOK COMPANY
239 WEST 39TH STREET, NEW YORK
BOUVERIE STREET, LONDON, E.C.
1909

PREFACE.

This volume is a condensation of a series of lectures delivered in part at Stanford and in part at Columbia Universities. It is intended neither for those wholly ignorant of mining, nor for those long experienced in the profession.

The bulk of the material presented is the common heritage of the profession, and if any one may think there is insufficient reference to previous writers, let him endeavor to find to whom the origin of our methods should be credited. The science has grown by small contributions of experience since, or before, those unnamed Egyptian engineers, whose works prove their knowledge of many fundamentals of mine engineering six thousand eight hundred years ago. If I have contributed one sentence to the accumulated knowledge of a thousand generations of engineers, or have thrown one new ray of light on the work, I shall have done my share.

I therefore must acknowledge my obligations to all those who have gone before, to all that has been written that I have read, to those engineers with whom I have been associated for many years, and in particular to many friends for kindly reply to inquiry upon points herein discussed.

CONTENTS.

PRINCIPLES OF MINING.

CHAPTER I.

Valuation of Copper, Gold, Lead, Silver, Tin, and Zinc Lode Mines.

The following discussion is limited to in situ deposits of copper, gold, lead, silver, tin, and zinc. The valuation of alluvial deposits, iron, coal, and other mines is each a special science to itself and cannot be adequately discussed in common with the type of deposits mentioned above.

The value of a metal mine of the order under discussion depends upon:—

1. The profit that may be won from ore exposed;
2. The prospective profit to be derived from extension of the ore beyond exposures;
3. The effect of a higher or lower price of metal (except in gold mines);
4. The efficiency of the management during realization.

The first may be termed the positive value, and can be approximately determined by sampling or test-treatment runs. The second and the third may be termed the speculative values, and are largely a matter of judgment based on geological evidence and the industrial outlook. The fourth is a question of development, equipment, and engineering method adapted to the prospects of the enterprise, together with capable executive control of these works.

It should be stated at the outset that it is utterly impossible to accurately value any mine, owing to the many speculative factors involved. The best that can be done is to state that the value lies between certain limits, and that various stages above the minimum given represent various degrees of risk. Further, it would be but stating truisms to those engaged in valuing mines to repeat that, because of the limited life of every mine, valuation of such investments cannot be based upon the principle of simple interest; nor that any investment is justified without a consideration of the management to ensue. Yet the ignorance of these essentials is so prevalent among the public that they warrant repetition on every available occasion.

To such an extent is the realization of profits indicated from the other factors dependent upon the subsequent management of the enterprise that the author considers a review of underground engineering and administration from an economic point of view an essential to any essay upon the subject. While the metallurgical treatment of ores is an essential factor in mine economics, it is considered that a detailed discussion of the myriad of processes under hypothetic conditions would lead too far afield. Therefore the discussion is largely limited to underground and administrative matters.

The valuation of mines arises not only from their change of ownership, but from the necessity in sound administration for a knowledge of some of the fundamentals of valuation, such as ore reserves and average values, that managerial and financial policy may be guided aright. Also with the growth of corporate ownership there is a demand from owners and stockholders for periodic information as to the intrinsic condition of their properties.

The growth of a body of speculators and investors in mining stocks and securities who desire professional guidance which cannot be based upon first-hand data is creating further demand on the engineer. Opinions in these cases must be formed on casual visits or second-hand information, and a knowledge of men and things generally. Despite the feeling of some engineers that the latter employment is not properly based professionally, it is an expanding phase of engineers' work, and must be taken seriously. Although it lacks satisfactory foundation for accurate judgment, yet the engineer can, and should, give his experience to it when the call comes, out of interest to the industry as a whole. Not only can he in a measure protect the lamb, by insistence on no investment without the provision of properly organized data and sound administration for his client, but he can do much to direct the industry from gambling into industrial lines.

An examination of the factors which arise on the valuation of mines involves a wide range of subjects. For purposes of this discussion they may be divided into the following heads:—

1. Determination of Average Metal Contents of the Ore.
2. Determination of Quantities of Ore.
3. Prospective Value.
4. Recoverable Percentage of Gross Value.
5. Price of Metals.
6. Cost of Production.
7. Redemption or Amortization of Capital and Interest.
8. Valuation of Mines without Ore in Sight.
9. General Conduct of Examination and Reports.

DETERMINATION OF AVERAGE METAL CONTENTS OF THE ORE.

Three means of determination of the average metal content of standing ore are in use—Previous Yield, Test-treatment Runs, and Sampling.

Previous Yield.—There are certain types of ore where the previous yield from known space becomes the essential basis of determination of quantity and metal contents of ore standing and of the future probabilities. Where metals occur like plums in a pudding, sampling becomes difficult and unreliable, and where experience has proved a sort of regularity of recurrence of these plums, dependence must necessarily be placed on past records, for if their reliability is to be questioned, resort must be had to extensive test-treatment runs. The Lake Superior copper mines and the Missouri lead and zinc mines are of this type of deposit. On the other sorts of deposits the previous yield is often put forward as of important bearing on the value of the ore standing, but such yield, unless it can be authentically connected with blocks of ore remaining, is not necessarily a criterion of their contents. Except in the cases mentioned, and as a check on other methods of determination, it has little place in final conclusions.

Test Parcels.—Treatment on a considerable scale of sufficiently regulated parcels, although theoretically the ideal method, is, however, not often within the realm of things practical. In examination on behalf of intending purchasers, the time, expense, or opportunity to fraud are usually prohibitive, even where the plant and facilities for such work exist. Even in cases where the engineer in management of producing mines is desirous of determining the value of standing ore, with the exception of deposits of the type mentioned above, it is ordinarily done by actual sampling, because separate mining and treatment of test lots is generally inconvenient and expensive. As a result, the determination of the value of standing ore is, in the great majority of cases, done by sampling and assaying.

Sampling.—The whole theory of sampling is based on the distribution of metals through the ore-body with more or less regularity, so that if small portions, that is samples, be taken from a sufficient number of points, their average will represent fairly closely the unit value of the ore. If the ore is of the extreme type of irregular metal distribution mentioned under "previous yield," then sampling has no place.

How frequently samples must be taken, the manner of taking them, and the quantity that constitutes a fair sample, are matters that vary with each mine. So much depends upon the proper performance of this task that it is in fact the most critical feature of mine examination. Ten samples properly taken are more valuable than five hundred slovenly ones, like grab samples, for such a number of bad ones would of a surety lead to wholly wrong conclusions. Given a good sampling and a proper assay plan, the valuation of a mine is two-thirds accomplished. It should be an inflexible principle in examinations for purchase that every sample must be taken under the personal supervision of the examining engineer or his trusted assistants. Aside from throwing open the doors to fraud, the average workman will not carry out the work in a proper manner, unless under constant supervision, because of his lack of appreciation of the issues involved. Sampling is hard, uncongenial, manual labor. It requires a deal of conscientiousness to take enough samples and to take them thoroughly. The engineer does not exist who, upon completion of this task, considers that he has got too many, and most wish that they had taken more.

The accuracy of sampling as a method of determining the value of standing ore is a factor of the number of samples taken. The average, for example, of separate samples from each square inch would be more accurate than those from each alternate square inch. However, the accumulated knowledge and experience as to the distribution of metals through ore has determined approximately the manner of taking such samples, and the least number which will still by the law of averages secure a degree of accuracy commensurate with the other factors of estimation.

As metals are distributed through ore-bodies of fissure origin with most regularity on lines parallel to the strike and dip, an equal portion of ore from every point along cross-sections at right angles to the strike will represent fairly well the average values for a certain distance along the strike either side of these cross-sections. In massive deposits, sample sections are taken in all directions. The intervals at which sample sections must be cut is obviously dependent upon the general character of the deposit. If the values are well distributed, a longer interval may be employed than in one subject to marked fluctuations. As a general rule, five feet is the distance most accepted. This, in cases of regular distribution of values, may be stretched to ten feet, or in reverse may be diminished to two or three feet.

The width of ore which may be included for one sample is dependent not only upon the width of the deposit, but also upon its character. Where the ore is wider than the necessary stoping width, the sample should be regulated so as to show the possible locus of values. The metal contents may be, and often are, particularly in deposits of the impregnation or replacement type, greater along some streak in the ore-body, and this difference may be such as to make it desirable to stope only a portion of the total thickness. For deposits narrower than the necessary stoping width the full breadth of ore should be included in one sample, because usually the whole of the deposit will require to be broken.

In order that a payable section may not possibly be diluted with material unnecessary to mine, if the deposit is over four feet and under eight feet, the distance across the vein or lode is usually divided into two samples. If still wider, each is confined to a span of about four feet, not only for the reason given above, but because the more numerous the samples, the greater the accuracy. Thus, in a deposit twenty feet wide it may be taken as a good guide that a test section across the ore-body should be divided into five parts.

As to the physical details of sample taking, every engineer has his own methods and safeguards against fraud and error. In a large organization of which the writer had for some years the direction, and where sampling of mines was constantly in progress on an extensive scale, not only in contemplation of purchase, but where it was also systematically conducted in operating mines for working data, he adopted the above general lines and required the following details.

A fresh face of ore is first broken and then a trench cut about five inches wide and two inches deep. This trench is cut with a hammer and moil, or, where compressed air is available and the rock hard, a small air-drill of the hammer type is used. The spoil from the trench forms the sample, and it is broken down upon a large canvas cloth. Afterwards it is crushed so that all pieces will pass a half-inch screen, mixed and quartered, thus reducing the weight to half. Whether it is again crushed and quartered depends upon what the conditions are as to assaying. If convenient to assay office, as on a going mine, the whole of the crushing and quartering work can be done at that office, where there are usually suitable mechanical appliances. If the samples must be taken a long distance, the bulk for transport can be reduced by finer breaking and repeated quartering, until there remain only a few ounces.

Precautions against Fraud.—Much has been written about the precautions to be taken against fraud in cases of valuations for purchase. The best safeguards are an alert eye and a strong right arm. However, certain small details help. A large leather bag, arranged to lock after the order of a mail sack, into which samples can be put underground and which is never unfastened except by responsible men, not only aids security but relieves the mind. A few samples of country rock form a good check, and notes as to the probable value of the ore, from inspection when sampling, are useful. A great help in examination is to have the assays or analyses done coincidentally with the sampling. A doubt can then always be settled by resampling at once, and much knowledge can be gained which may relieve so exhaustive a program as might be necessary were results not known until after leaving the mine.

Assay of Samples.—Two assays, or as the case may be, analyses, are usually made of every sample and their average taken. In the case of erratic differences a third determination is necessary.

Assay Plans.—An assay plan is a plan of the workings, with the location, assay value, and width of the sample entered upon it. In a mine with a narrow vein or ore-body, a longitudinal section is sufficient base for such entries, but with a greater width than one sample span it is desirable to make preliminary plans of separate levels, winzes, etc., and to average the value of the whole payable widths on such plans before entry upon a longitudinal section. Such a longitudinal section will, through the indicated distribution of values, show the shape of the ore-body—a step necessary in estimating quantities and of the most fundamental importance in estimating the probabilities of ore extension beyond the range of the openings. The final assay plan should show the average value of the several blocks of ore, and it is from these averages that estimates of quantities must be made up.

Calculations of Averages.—The first step in arriving at average values is to reduce erratic high assays to the general tenor of other adjacent samples. This point has been disputed at some length, more often by promoters than by engineers, but the custom is very generally and rightly adopted. Erratically high samples may indicate presence of undue metal in the assay attributable to unconscious salting, for if the value be confined to a few large particles they may find their way through all the quartering into the assay. Or the sample may actually indicate rich spots of ore; but in any event experience teaches that no dependence can be put upon regular recurrence of such abnormally rich spots. As will be discussed under percentage of error in sampling, samples usually indicate higher than the true value, even where erratic assays have been eliminated. There are cases of profitable mines where the values were all in spots, and an assay plan would show 80% of the assays nil, yet these pockets were so rich as to give value to the whole. Pocket mines, as stated before, are beyond valuation by sampling, and aside from the previous yield recourse must be had to actual treatment runs on every block of ore separately.

After reduction of erratic assays, a preliminary study of the runs of value or shapes of the ore-bodies is necessary before any calculation of averages. A preliminary delineation of the boundaries of the payable areas on the assay plan will indicate the sections of the mine which are unpayable, and from which therefore samples can be rightly excluded in arriving at an average of the payable ore (Fig. 1). In a general way, only the ore which must be mined need be included in averaging.

The calculation of the average assay value of standing ore from samples is one which seems to require some statement of elementals. Although it may seem primitive, it can do no harm to recall that if a dump of two tons of ore assaying twenty ounces per ton be added to a dump of five tons averaging one ounce per ton, the result has not an average assay of twenty-one ounces divided by the number of dumps. Likewise one sample over a width of two feet, assaying twenty ounces per ton, if averaged with another sample over a width of five feet, assaying one ounce, is no more twenty-one ounces divided by two samples than in the case of the two dumps. If common sense were not sufficient demonstration of this, it can be shown algebraically. Were samples equidistant from each other, and were they of equal width, the average value would be the simple arithmetical mean of the assays. But this is seldom the case. The number of instances, not only in practice but also in technical literature, where the fundamental distinction between an arithmetical and a geometrical mean is lost sight of is amazing.

To arrive at the average value of samples, it is necessary, in effect, to reduce them to the actual quantity of the metal and volume of ore represented by each. The method of calculation therefore is one which gives every sample an importance depending upon the metal content of the volume of ore it represents.

The volume of ore appertaining to any given sample can be considered as a prismoid, the dimensions of which may be stated as follows:—

[Footnote *: Strictly, the prismoidal formula should be used, but it complicates the study unduly, and for practical purposes the above may be taken as the volume.]

The average value of a number of samples is the total metal contents of their respective prismoids, divided by the total tonnage of these prismoids. If we let W, W₁, V, V₁ etc., represent different samples, we have:—

This may be reduced to:—

As a matter of fact, samples actually represent the value of the outer shell of the block of ore only, and the continuity of the same values through the block is a geological assumption. From the outer shell, all the values can be taken to penetrate equal distances into the block, and therefore D, D₁, D₂ may be considered as equal and the equation becomes:—

The length of the prismoid base L for any given sample will be a distance equal to one-half the sum of the distances to the two adjacent samples. As a matter of practice, samples are usually taken at regular intervals, and the lengths L, L₁, L₂ becoming thus equal can in such case be eliminated, and the equation becomes:—

The name "assay foot" or "foot value" has been given to the relation VW, that is, the assay value multiplied by the width sampled.[*] It is by this method that all samples must be averaged. The same relation obviously can be evolved by using an inch instead of a foot, and in narrow veins the assay inch is generally used.

[Footnote *: An error will be found in this method unless the two end samples be halved, but in a long run of samples this may be disregarded.]

Where the payable cross-section is divided into more than one sample, the different samples in the section must be averaged by the above formula, before being combined with the adjacent section. Where the width sampled is narrower than the necessary stoping width, and where the waste cannot be broken separately, the sample value must be diluted to a stoping width. To dilute narrow samples to a stoping width, a blank value over the extra width which it is necessary to include must be averaged with the sample from the ore on the above formula. Cases arise where, although a certain width of waste must be broken with the ore, it subsequently can be partially sorted out. Practically nothing but experience on the deposit itself will determine how far this will restore the value of the ore to the average of the payable seam. In any event, no sorting can eliminate all such waste; and it is necessary to calculate the value on the breaking width, and then deduct from the gross tonnage to be broken a percentage from sorting. There is always an allowance to be made in sorting for a loss of good ore with the discards.

Percentage of Error in Estimates from Sampling.—It must be remembered that the whole theory of estimation by sampling is founded upon certain assumptions as to evenness of continuity and transition in value and volume. It is but a basis for an estimate, and an estimate is not a statement of fact. It cannot therefore be too forcibly repeated that an estimate is inherently but an approximation, take what care one may in its founding. While it is possible to refine mathematical calculation of averages to almost any nicety, beyond certain essentials it adds nothing to accuracy and is often misleading.

It is desirable to consider where errors are most likely to creep in, assuming that all fundamental data are both accurately taken and considered. Sampling of ore in situ in general has a tendency to give higher average value than the actual reduction of the ore will show. On three West Australian gold mines, in records covering a period of over two years, where sampling was most exhaustive as a daily régime of the mines, the values indicated by sampling were 12% higher than the mill yield plus the contents of the residues. On the Witwatersrand gold mines, the actual extractable value is generally considered to be about 78 to 80% of the average shown by sampling, while the mill extractions are on average about 90 to 92% of the head value coming to the mill. In other words, there is a constant discrepancy of about 10 to 12% between the estimated value as indicated by mine samples, and the actual value as shown by yield plus the residues. At Broken Hill, on three lead mines, the yield is about 12% less than sampling would indicate. This constancy of error in one direction has not been so generally acknowledged as would be desirable, and it must be allowed for in calculating final results. The causes of the exaggeration seem to be:—

First, inability to stope a mine to such fine limitations of width, or exclusion of unpayable patches, as would appear practicable when sampling, that is by the inclusion when mining of a certain amount of barren rock. Even in deposits of about normal stoping width, it is impossible to prevent the breaking of a certain amount of waste, even if the ore occurrence is regularly confined by walls.

If the mine be of the impregnation type, such as those at Goldfield, or Kalgoorlie, with values like plums in a pudding, and the stopes themselves directed more by assays than by any physical differences in the ore, the discrepancy becomes very much increased. In mines where the range of values is narrower than the normal stoping width, some wall rock must be broken. Although it is customary to allow for this in calculating the average value from samples, the allowance seldom seems enough. In mines where the ore is broken on to the top of stopes filled with waste, there is some loss underground through mixture with the filling.

Second, the metal content of ores, especially when in the form of sulphides, is usually more friable than the matrix, and in actual breaking of samples an undue proportion of friable material usually creeps in. This is true more in lead, copper, and zinc, than in gold ores. On several gold mines, however, tests on accumulated samples for their sulphide percentage showed a distinctly greater ratio than the tenor of the ore itself in the mill. As the gold is usually associated with the sulphides, the samples showed higher values than the mill.

In general, some considerable factor of safety must be allowed after arriving at calculated average of samples,—how much it is difficult to say, but, in any event, not less than 10%.

CHAPTER II.

Mine Valuation (Continued).

As mines are opened by levels, rises, etc., through the ore, an extension of these workings has the effect of dividing it into "blocks." The obvious procedure in determining tonnages is to calculate the volume and value of each block separately. Under the law of averages, the multiplicity of these blocks tends in proportion to their number to compensate the percentage of error which might arise in the sampling or estimating of any particular one. The shapes of these blocks, on longitudinal section, are often not regular geometrical figures. As a matter of practice, however, they can be subdivided into such figures that the total will approximate the whole with sufficient closeness for calculations of their areas.

The average width of the ore in any particular block is the arithmetical mean of the width of the sample sections in it,[*] if the samples be an equal distance apart. If they are not equidistant, the average width is the sum of the areas between samples, divided by the total length sampled. The cubic foot contents of a particular block is obviously the width multiplied by the area of its longitudinal section.

[Footnote *: This is not strictly true unless the sum of the widths of the two end-sections be divided by two and the result incorporated in calculating the means. In a long series that error is of little importance.]

The ratio of cubic feet to tons depends on the specific gravity of the ore, its porosity, and moisture. The variability of ores throughout the mine in all these particulars renders any method of calculation simply an approximation in the end. The factors which must remain unknown necessarily lead the engineer to the provision of a margin of safety, which makes mathematical refinement and algebraic formulæ ridiculous.

There are in general three methods of determination of the specific volume of ores:—

First, by finding the true specific gravity of a sufficient number of representative specimens; this, however, would not account for the larger voids in the ore-body and in any event, to be anything like accurate, would be as expensive as sampling and is therefore of little more than academic interest.

Second, by determining the weight of quantities broken from measured spaces. This also would require several tests from different portions of the mine, and, in examinations, is usually inconvenient and difficult. Yet it is necessary in cases of unusual materials, such as leached gossans, and it is desirable to have it done sooner or later in going mines, as a check.

Third, by an approximation based upon a calculation from the specific gravities of the predominant minerals in the ore. Ores are a mixture of many minerals; the proportions vary through the same ore-body. Despite this, a few partial analyses, which are usually available from assays of samples and metallurgical tests, and a general inspection as to the compactness of the ore, give a fairly reliable basis for approximation, especially if a reasonable discount be allowed for safety. In such discount must be reflected regard for the porosity of the ore, and the margin of safety necessary may vary from 10 to 25%. If the ore is of unusual character, as in leached deposits, as said before, resort must be had to the second method.

The following table of the weights per cubic foot and the number of cubic feet per ton of some of the principal ore-forming minerals and gangue rocks will be useful for approximating the weight of a cubic foot of ore by the third method. Weights are in pounds avoirdupois, and two thousand pounds are reckoned to the ton.

The specific gravity of any particular mineral has a considerable range, and a medium has been taken. The possible error is inconsequential for the purpose of these calculations.

For example, a representative gold ore may contain in the main 96% quartz, and 4% iron pyrite, and the weight of the ore may be deduced as follows:—

Most engineers, to compensate porosity, would allow twelve to thirteen cubic feet per ton.

CLASSIFICATION OF ORE IN SIGHT.

The risk in estimates of the average value of standing ore is dependent largely upon how far values disclosed by sampling are assumed to penetrate beyond the tested face, and this depends upon the geological character of the deposit. From theoretical grounds and experience, it is known that such values will have some extension, and the assumption of any given distance is a calculation of risk. The multiplication of development openings results in an increase of sampling points available and lessens the hazards. The frequency of such openings varies in different portions of every mine, and thus there are inequalities of risk. It is therefore customary in giving estimates of standing ore to classify the ore according to the degree of risk assumed, either by stating the number of sides exposed or by other phrases. Much discussion and ink have been devoted to trying to define what risk may be taken in such matters, that is in reality how far values may be assumed to penetrate into the unbroken ore. Still more has been consumed in attempts to coin terms and make classifications which will indicate what ratio of hazard has been taken in stating quantities and values.

The old terms "ore in sight" and "profit in sight" have been of late years subject to much malediction on the part of engineers because these expressions have been so badly abused by the charlatans of mining in attempts to cover the flights of their imaginations. A large part of Volume X of the "Institution of Mining and Metallurgy" has been devoted to heaping infamy on these terms, yet not only have they preserved their places in professional nomenclature, but nothing has been found to supersede them.

Some general term is required in daily practice to cover the whole field of visible ore, and if the phrase "ore in sight" be defined, it will be easier to teach the laymen its proper use than to abolish it. In fact, the substitutes are becoming abused as much as the originals ever were. All convincing expressions will be misused by somebody.

The legitimate direction of reform has been to divide the general term of "ore in sight" into classes, and give them names which will indicate the variable amount of risk of continuity in different parts of the mine. As the frequency of sample points, and consequently the risk of continuity, will depend upon the detail with which the mine is cut into blocks by the development openings, and upon the number of sides of such blocks which are accessible, most classifications of the degree of risk of continuity have been defined in terms of the number of sides exposed in the blocks. Many phrases have been coined to express such classifications; those most currently used are the following:—

No two of these parallel expressions mean quite the same thing; each more or less overlies into another class, and in fact none of them is based upon a logical footing for such a classification. For example, values can be assumed to penetrate some distance from every sampled face, even if it be only ten feet, so that ore exposed on one side will show some "positive" or "developed" ore which, on the lines laid down above, might be "probable" or even "possible" ore. Likewise, ore may be "fully developed" or "blocked out" so far as it is necessary for stoping purposes with modern wide intervals between levels, and still be in blocks too large to warrant an assumption of continuity of values to their centers (Fig. 1). As to the third class of "possible" ore, it conveys an impression of tangibility to a nebulous hazard, and should never be used in connection with positive tonnages. This part of the mine's value comes under extension of the deposit a long distance beyond openings, which is a speculation and cannot be defined in absolute tons without exhaustive explanation of the risks attached, in which case any phrase intended to shorten description is likely to be misleading.

Therefore empirical expressions in terms of development openings cannot be made to cover a geologic factor such as the distribution of metals through a rock mass. The only logical basis of ore classification for estimation purposes is one which is founded on the chances of the values penetrating from the surface of the exposures for each particular mine. Ore that may be calculated upon to a certainty is that which, taking into consideration the character of the deposit, can be said to be so sufficiently surrounded by sampled faces that the distance into the mass to which values are assumed to extend is reduced to a minimum risk. Ore so far removed from the sampled face as to leave some doubt, yet affording great reason for expectation of continuity, is "probable" ore. The third class of ore mentioned, which is that depending upon extension of the deposit and in which, as said above, there is great risk, should be treated separately as the speculative value of the mine. Some expressions are desirable for these classifications, and the writer's own preference is for the following, with a definition based upon the controlling factor itself.

They are:—

What extent of openings, and therefore of sample faces, is required for the ore to be called "proved" varies naturally with the type of deposit,—in fact with each mine. In a general way, a fair rule in gold quartz veins below influence of secondary alteration is that no point in the block shall be over fifty feet from the points sampled. In limestone or andesite replacements, as by gold or lead or copper, the radius must be less. In defined lead and copper lodes, or in large lenticular bodies such as the Tennessee copper mines, the radius may often be considerably greater,—say one hundred feet. In gold deposits of such extraordinary regularity of values as the Witwatersrand bankets, it can well be two hundred or two hundred and fifty feet.

"Probable ore" should be ore which entails continuity of values through a greater distance than the above, and such distance must depend upon the collateral evidence from the character of the deposit, the position of openings, etc.

Ore beyond the range of the "probable" zone is dependent upon the extension of the deposit beyond the realm of development and will be discussed separately.

Although the expression "ore in sight" may be deprecated, owing to its abuse, some general term to cover both "positive" and "probable" ore is desirable; and where a general term is required, it is the intention herein to hold to the phrase "ore in sight" under the limitations specified.

CHAPTER III.

Mine Valuation (Continued).

[Footnote *: The term "extension in depth" is preferred by many to the phrase "prospective value." The former is not entirely satisfactory, as it has a more specific than general application. It is, however, a current miner's phrase, and is more expressive. In this discussion "extension in depth" is used synonymously, and it may be taken to include not alone the downward prolongation of the ore below workings, but also the occasional cases of lateral extension beyond the range of development work. The commonest instance is continuance below the bottom level. In any event, to the majority of cases of different extension the same reasoning applies.]

It is a knotty problem to value the extension of a deposit beyond a short distance from the last opening. A short distance beyond it is "proved ore," and for a further short distance is "probable ore." Mines are very seldom priced at a sum so moderate as that represented by the profit to be won from the ore in sight, and what value should be assigned to this unknown portion of the deposit admits of no certainty. No engineer can approach the prospective value of a mine with optimism, yet the mining industry would be non-existent to-day were it approached with pessimism. Any value assessed must be a matter of judgment, and this judgment based on geological evidence. Geology is not a mathematical science, and to attach a money equivalence to forecasts based on such evidence is the most difficult task set for the mining engineer. It is here that his view of geology must differ from that of his financially more irresponsible brother in the science. The geologist, contributing to human knowledge in general, finds his most valuable field in the examination of mines largely exhausted. The engineer's most valuable work arises from his ability to anticipate in the youth of the mine the symptoms of its old age. The work of our geologic friends is, however, the very foundation on which we lay our forecasts.

Geologists have, as the result of long observation, propounded for us certain hypotheses which, while still hypotheses, have proved to account so widely for our underground experience that no engineer can afford to lose sight of them. Although there is a lack of safety in fixed theories as to ore deposition, and although such conclusions cannot be translated into feet and metal value, they are nevertheless useful weights on the scale where probabilities are to be weighed.

A method in vogue with many engineers is, where the bottom level is good, to assume the value of the extension in depth as a sum proportioned to the profit in sight, and thus evade the use of geological evidence. The addition of various percentages to the profit in sight has been used by engineers, and proposed in technical publications, as varying from 25 to 50%. That is, they roughly assess the extension in depth to be worth one-fifth to one-third of the whole value of an equipped mine. While experience may have sometimes demonstrated this to be a practical method, it certainly has little foundation in either science or logic, and the writer's experience is that such estimates are untrue in practice. The quantity of ore which may be in sight is largely the result of managerial policy. A small mill on a large mine, under rapid development, will result in extensive ore-reserves, while a large mill eating away rapidly on the same mine under the same scale of development would leave small reserves. On the above scheme of valuation the extension in depth would be worth very different sums, even when the deepest level might be at the same horizon in both cases. Moreover, no mine starts at the surface with a large amount of ore in sight. Yet as a general rule this is the period when its extension is most valuable, for when the deposit is exhausted to 2000 feet, it is not likely to have such extension in depth as when opened one hundred feet, no matter what the ore-reserves may be. Further, such bases of valuation fail to take into account the widely varying geologic character of different mines, and they disregard any collateral evidence either of continuity from neighboring development, or from experience in the district. Logically, the prospective value can be simply a factor of how far the ore in the individual mine may be expected to extend, and not a factor of the remnant of ore that may still be unworked above the lowest level.

An estimation of the chances of this extension should be based solely on the local factors which bear on such extension, and these are almost wholly dependent upon the character of the deposit. These various geological factors from a mining engineer's point of view are:—

1. The origin and structural character of the ore-deposit.
2. The position of openings in relation to secondary alteration.
3. The size of the deposit.
4. The depth to which the mine has already been exhausted.
5. The general experience of the district for continuity and the development of adjoining mines.

The Origin and Structural Character of the Deposit.—In a general way, the ore-deposits of the order under discussion originate primarily through the deposition of metals from gases or solutions circulating along avenues in the earth's crust.[*] The original source of metals is a matter of great disagreement, and does not much concern the miner. To him, however, the origin and character of the avenue of circulation, the enclosing rock, the influence of the rocks on the solution, and of the solutions on the rocks, have a great bearing on the probable continuity of the volume and value of the ore.

[Footnote *: The class of magmatic segregations is omitted, as not being of sufficiently frequent occurrence in payable mines to warrant troubling with it here.]

All ore-deposits vary in value and, in the miner's view, only those portions above the pay limit are ore-bodies, or ore-shoots. The localization of values into such pay areas in an ore-deposit are apparently influenced by:

1. The distribution of the open spaces created by structural movement, fissuring, or folding as at Bendigo.
2. The intersection of other fractures which, by mingling of solutions from different sources, provided precipitating conditions, as shown by enrichments at cross-veins.
3. The influence of the enclosing rocks by:—
   1. Their solubility, and therefore susceptibility to replacement.
   2. Their influence as a precipitating agent on solutions.
   3. Their influence as a source of metal itself.
   4. Their texture, in its influence on the character of the fracture. In homogeneous rocks the tendency is to open clean-cut fissures; in friable rocks, zones of brecciation; in slates or schistose rocks, linked lenticular open spaces;—these influences exhibiting themselves in miner's terms respectively in "well-defined fissure veins," "lodes," and "lenses."
   5. The physical character of the rock mass and the dynamic forces brought to bear upon it. This is a difficult study into the physics of stress in cases of fracturing, but its local application has not been without results of an important order.
4. Secondary alteration near the surface, more fully discussed later.

It is evident enough that the whole structure of the deposit is a necessary study, and even a digest of the subject is not to be compressed into a few paragraphs.

From the point of view of continuity of values, ore-deposits may be roughly divided into three classes. They are:—

1. Deposits of the infiltration type in porous beds, such as Lake Superior copper conglomerates and African gold bankets.
2. Deposits of the fissure vein type, such as California quartz veins.
3. Replacement or impregnation deposits on the lines of fissuring or otherwise.

In a general way, the uniformity of conditions of deposition in the first class has resulted in the most satisfactory continuity of ore and of its metal contents. In the second, depending much upon the profundity of the earth movements involved, there is laterally and vertically a reasonable basis for expectation of continuity but through much less distance than in the first class.

The third class of deposits exhibits widely different phenomena as to continuity and no generalization is of any value. In gold deposits of this type in West Australia, Colorado, and Nevada, continuity far beyond a sampled face must be received with the greatest skepticism. Much the same may be said of most copper replacements in limestone. On the other hand the most phenomenal regularity of values have been shown in certain Utah and Arizona copper mines, the result of secondary infiltration in porphyritic gangues. The Mississippi Valley lead and zinc deposits, while irregular in detail, show remarkable continuity by way of reoccurrence over wide areas. The estimation of the prospective value of mines where continuity of production is dependent on reoccurrence of ore-bodies somewhat proportional to the area, such as these Mississippi deposits or to some extent as in Cobalt silver veins, is an interesting study, but one that offers little field for generalization.

The Position of the Openings in Relation to Secondary Alteration.—The profound alteration of the upper section of ore-deposits by oxidation due to the action of descending surface waters, and their associated chemical agencies, has been generally recognized for a great many years. Only recently, however, has it been appreciated that this secondary alteration extends into the sulphide zone as well. The bearing of the secondary alteration, both in the oxidized and upper sulphide zones, is of the most sweeping economic character. In considering extension of values in depth, it demands the most rigorous investigation. Not only does the metallurgical character of the ores change with oxidation, but the complex reactions due to descending surface waters cause leaching and a migration of metals from one horizon to another lower down, and also in many cases a redistribution of their sequence in the upper zones of the deposit.

The effect of these agencies has been so great in many cases as to entirely alter the character of the mine and extension in depth has necessitated a complete reëquipment. For instance, the Mt. Morgan gold mine, Queensland, has now become a copper mine; the copper mines at Butte were formerly silver mines; Leadville has become largely a zinc producer instead of lead.

From this alteration aspect ore-deposits may be considered to have four horizons:—

1. The zone near the outcrop, where the dominating feature is oxidation and leaching of the soluble minerals.
2. A lower horizon, still in the zone of oxidation, where the predominant feature is the deposition of metals as native, oxides, and carbonates.
3. The upper horizon of the sulphide zone, where the special feature is the enrichment due to secondary deposition as sulphides.
4. The region below these zones of secondary alteration, where the deposit is in its primary state.

These zones are seldom sharply defined, nor are they always all in evidence. How far they are in evidence will depend, among other things, upon the amount and rapidity of erosion, the structure and mineralogical character of the deposit, and upon the enclosing rock.

If erosion is extremely rapid, as in cold, wet climates, and rough topography, or as in the case of glaciation of the Lake copper deposits, denudation follows close on the heels of alteration, and the surface is so rapidly removed that we may have the primary ore practically at the surface. Flat, arid regions present the other extreme, for denudation is much slower, and conditions are most perfect for deep penetration of oxidizing agencies, and the consequent alteration and concentration of the metals.

The migration of metals from the top of the oxidized zone leaves but a barren cap for erosion. The consequent effect of denudation that lags behind alteration is to raise slowly the concentrated metals toward the surface, and thus subject them to renewed attack and repeated migration. In this manner we can account for the enormous concentration of values in the lower oxidized and upper sulphide zones overlying very lean sulphides in depth.

Some minerals are more freely soluble and more readily precipitated than others. From this cause there is in complex metal deposits a rearrangement of horizontal sequence, in addition to enrichment at certain horizons and impoverishment at others. The whole subject is one of too great complexity for adequate consideration in this discussion. No engineer is properly equipped to give judgment on extension in depth without a thorough grasp of the great principles laid down by Van Hise, Emmons, Lindgren, Weed, and others. We may, however, briefly examine some of the theoretical effects of such alteration.

Zinc, iron, and lead sulphides are a common primary combination. These metals are rendered soluble from their usual primary forms by oxidizing agencies, in the order given. They reprecipitate as sulphides in the reverse sequence. The result is the leaching of zinc and iron readily in the oxidized zone, thus differentially enriching the lead which lags behind, and a further extension of the lead horizon is provided by the early precipitation of such lead as does migrate. Therefore, the lead often predominates in the second and the upper portion of the third zone, with the zinc and iron below. Although the action of all surface waters is toward oxidation and carbonation of these metals, the carbonate development of oxidized zones is more marked when the enclosing rocks are calcareous.

In copper-iron deposits, the comparatively easy decomposition and solubility and precipitation of the copper and some iron salts generally result in more extensive impoverishment of these metals near the surface, and more predominant enrichment at a lower horizon than is the case with any other metals. The barren "iron hat" at the first zone, the carbonates and oxides at the second, the enrichment with secondary copper sulphides at the top of the third, and the occurrence of secondary copper-iron sulphides below, are often most clearly defined. In the easy recognition of the secondary copper sulphides, chalcocite, bornite, etc., the engineer finds a finger-post on the road to extension in depth; and the directions upon this post are not to be disregarded. The number of copper deposits enriched from unpayability in the first zone to a profitable character in the next two, and unpayability again in the fourth, is legion.

Silver occurs most abundantly in combination with either lead, copper, iron, or gold. As it resists oxidation and solution more strenuously than copper and iron, its tendency when in combination with them is to lag behind in migration. There is thus a differential enrichment of silver in the upper two zones, due to the reduction in specific gravity of the ore by the removal of associated metals. Silver does migrate somewhat, however, and as it precipitates more readily than copper, lead, zinc, or iron, its tendency when in combination with them is towards enrichment above the horizons of enrichment of these metals. When it is in combination with lead and zinc, its very ready precipitation from solution by the galena leaves it in combination more predominantly with the lead. The secondary enrichment of silver deposits at the top of the sulphide zone is sometimes a most pronounced feature, and it seems to be the explanation of the origin of many "bonanzas."

In gold deposits, the greater resistance to solubility of this metal than most of the others, renders the phenomena of migration to depth less marked. Further than this, migration is often interfered with by the more impervious quartz matrix of many gold deposits. Where gold is associated with large quantities of base metals, however, the leaching of the latter in the oxidized zone leaves the ore differentially richer, and as gold is also slightly soluble, in such cases the migration of the base metals does carry some of the gold. In the instance especially of impregnation or replacement deposits, where the matrix is easily permeable, the upper sulphide zone is distinctly richer than lower down, and this enrichment is accompanied by a considerable increase in sulphides and tellurides. The predominant characteristic of alteration in gold deposits is, however, enrichment in the oxidized zone with the maximum values near the surface. The reasons for this appear to be that gold in its resistance to oxidation and wholesale migration gives opportunities to a sort of combined mechanical and chemical enrichment.

In dry climates, especially, the gentleness of erosion allows of more thorough decomposition of the outcroppings, and a mechanical separation of the gold from the detritus. It remains on or near the deposit, ready to be carried below, mechanically or otherwise. In wet climates this is less pronounced, for erosion bears away the croppings before such an extensive decomposition and freeing of the gold particles. The West Australian gold fields present an especially prominent example of this type of superficial enrichment. During the last fifteen years nearly eight hundred companies have been formed for working mines in this region. Although from four hundred of these high-grade ore has been produced, some thirty-three only have ever paid dividends. The great majority have been unpayable below oxidation,—a distance of one or two hundred feet. The writer's unvarying experience with gold is that it is richer in the oxidized zone than at any point below. While cases do occur of gold deposits richer in the upper sulphide zone than below, even the upper sulphides are usually poorer than the oxidized region. In quartz veins preëminently, evidence of enrichment in the third zone is likely to be practically absent.

Tin ores present an anomaly among the base metals under discussion, in that the primary form of this metal in most workable deposits is an oxide. Tin in this form is most difficult of solution from ground agencies, as witness the great alluvial deposits, often of considerable geologic age. In consequence the phenomena of migration and enrichment are almost wholly absent, except such as are due to mechanical penetration of tin from surface decomposition of the matrix akin to that described in gold deposits.

In general, three or four essential facts from secondary alteration must be kept in view when prognosticating extensions.

Oxidation usually alters treatment problems, and oxidized ore of the same grade as sulphides can often be treated more cheaply. This is not universal. Low-grade ores of lead, copper, and zinc may be treatable by concentration when in the form of sulphides, and may be valueless when oxidized, even though of the same grade.

Copper ores generally show violent enrichment at the base of the oxidized, and at the top of the sulphide zone.

Lead-zinc ores show lead enrichment and zinc impoverishment in the oxidized zone but have usually less pronounced enrichment below water level than copper. The rearrangement of the metals by the deeper migration of the zinc, also renders them metallurgically of less value with depth.

Silver deposits are often differentially enriched in the oxidized zone, and at times tend to concentrate in the upper sulphide zone.

Gold deposits usually decrease in value from the surface through the whole of the three alteration zones.

Size of Deposits.—The proverb of a relation between extension in depth and size of ore-bodies expresses one of the oldest of miners' beliefs. It has some basis in experience, especially in fissure veins, but has little foundation in theory and is applicable over but limited areas and under limited conditions.

From a structural view, the depth of fissuring is likely to be more or less in proportion to its length and breadth and therefore the volume of vein filling with depth is likely to be proportional to length and width of the fissure. As to the distribution of values, if we eliminate the influence of changing wall rocks, or other precipitating agencies which often cause the values to arrange themselves in "floors," and of secondary alteration, there may be some reason to assume distribution of values of an extent equal vertically to that displayed horizontally. There is, as said, more reason in experience for this assumption than in theory. A study of the shape of a great many ore-shoots in mines of fissure type indicates that when the ore-shoots or ore-bodies are approaching vertical exhaustion they do not end abruptly, but gradually shorten and decrease in value, their bottom boundaries being more often wedge-shaped than even lenticular. If this could be taken as the usual occurrence, it would be possible (eliminating the evident exceptions mentioned above) to state roughly that the minimum extension of an ore-body or ore-shoot in depth below any given horizon would be a distance represented by a radius equal to one-half its length. By length is not meant necessarily the length of a horizontal section, but of one at right angles to the downward axis.

On these grounds, which have been reënforced by much experience among miners, the probabilities of extension are somewhat in proportion to the length and width of each ore-body. For instance, in the A mine, with an ore-shoot 1000 feet long and 10 feet wide, on its bottom level, the minimum extension under this hypothesis would be a wedge-shaped ore-body with its deepest point 500 feet below the lowest level, or a minimum of say 200,000 tons. Similarly, the B mine with five ore-bodies, each 300 hundred feet long and 10 feet wide, exposed on its lowest level, would have a minimum of five wedges 100 feet deep at their deepest points, or say 50,000 tons. This is not proposed as a formula giving the total amount of extension in depth, but as a sort of yardstick which has experience behind it. This experience applies in a much less degree to deposits originating from impregnation along lines of fissuring and not at all to replacements.

Development in Neighboring Mines.—Mines of a district are usually found under the same geological conditions, and show somewhat the same habits as to extension in depth or laterally, and especially similar conduct of ore-bodies and ore-shoots. As a practical criterion, one of the most intimate guides is the actual development in adjoining mines. For instance, in Kalgoorlie, the Great Boulder mine is (March, 1908) working the extension of Ivanhoe lodes at points 500 feet below the lowest level in the Ivanhoe; likewise, the Block 10 lead mine at Broken Hill is working the Central ore-body on the Central boundary some 350 feet below the Central workings. Such facts as these must have a bearing on assessing the downward extension.

Depth of Exhaustion.—All mines become completely exhausted at some point in depth. Therefore the actual distance to which ore can be expected to extend below the lowest level grows less with every deeper working horizon. The really superficial character of ore-deposits, even outside of the region of secondary enrichment is becoming every year better recognized. The prospector's idea that "she gets richer deeper down," may have some basis near the surface in some metals, but it is not an idea which prevails in the minds of engineers who have to work in depth. The writer, with some others, prepared a list of several hundred dividend-paying metal mines of all sorts, extending over North and South America, Australasia, England, and Africa. Notes were made as far as possible of the depths at which values gave out, and also at which dividends ceased. Although by no means a complete census, the list indicated that not 6% of mines (outside banket) that have yielded profits, ever made them from ore won below 2000 feet. Of mines that paid dividends, 80% did not show profitable value below 1500 feet, and a sad majority died above 500. Failures at short depths may be blamed upon secondary enrichment, but the majority that reached below this influence also gave out. The geological reason for such general unseemly conduct is not so evident.

Conclusion.—As a practical problem, the assessment of prospective value is usually a case of "cut and try." The portion of the capital to be invested, which depends upon extension, will require so many tons of ore of the same value as that indicated by the standing ore, in order to justify the price. To produce this tonnage at the continued average size of the ore-bodies will require their extension in depth so many feet—or the discovery of new ore-bodies of a certain size. The five geological weights mentioned above may then be put into the scale and a basis of judgment reached.

CHAPTER IV.

Mine Valuation (Continued).

The method of treatment for the ore must be known before a mine can be valued, because a knowledge of the recoverable percentage is as important as that of the gross value of the ore itself. The recoverable percentage is usually a factor of working costs. Practically every ore can be treated and all the metal contents recovered, but the real problem is to know the method and percentage of recovery which will yield the most remunerative result, if any. This limit to profitable recovery regulates the amount of metal which should be lost, and the amount of metal which consequently must be deducted from the gross value before the real net value of the ore can be calculated. Here, as everywhere else in mining, a compromise has to be made with nature, and we take what we can get—profitably. For instance, a copper ore may be smelted and a 99% recovery obtained. Under certain conditions this might be done at a loss, while the same ore might be concentrated before smelting and yield a profit with a 70% recovery. An additional 20% might be obtained by roasting and leaching the residues from concentration, but this would probably result in an expenditure far greater than the value of the 20% recovered. If the ore is not already under treatment on the mine, or exactly similar ore is not under treatment elsewhere, with known results, the method must be determined experimentally, either by the examining engineer or by a special metallurgist.

Where partially treated products, such as concentrates, are to be sold, not only will there be further losses, but deductions will be made by the smelter for deleterious metals and other charges. All of these factors must be found out,—and a few sample smelting returns from a similar ore are useful.

To cover the whole field of metallurgy and discuss what might apply, and how it might apply, under a hundred supposititious conditions would be too great a digression from the subject in hand. It is enough to call attention here to the fact that the residues from every treatment carry some metal, and that this loss has to be deducted from the gross value of the ore in any calculations of net values.

PRICE OF METALS.

Unfortunately for the mining engineer, not only has he to weigh the amount of risk inherent in calculations involved in the mine itself, but also that due to fluctuations in the value of metals. If the ore is shipped to custom works, he has to contemplate also variations in freights and smelting charges. Gold from the mine valuer's point of view has no fluctuations. It alone among the earth's products gives no concern as to the market price. The price to be taken for all other metals has to be decided before the mine can be valued. This introduces a further speculation and, as in all calculations of probabilities, amounts to an estimate of the amount of risk. In a free market the law of supply and demand governs the value of metals as it does that of all other commodities. So far, except for tariff walls and smelting rings, there is a free market in the metals under discussion.

The demand for metals varies with the unequal fluctuations of the industrial tides. The sea of commercial activity is subject to heavy storms, and the mine valuer is compelled to serve as weather prophet on this ocean of trouble. High prices, which are the result of industrial booms, bring about overproduction, and the collapse of these begets a shrinkage of demand, wherein consequently the tide of price turns back. In mining for metals each pound is produced actually at a different cost. In case of an oversupply of base metals the price will fall until it has reached a point where a portion of the production is no longer profitable, and the equilibrium is established through decline in output. However, in the backward swing, due to lingering overproduction, prices usually fall lower than the cost of producing even a much-diminished supply. There is at this point what we may call the "basic" price, that at which production is insufficient and the price rises again. The basic price which is due to this undue backward swing is no more the real price of the metal to be contemplated over so long a term of years than is the highest price. At how much above the basic price of depressed times the product can be safely expected to find a market is the real question. Few mines can be bought or valued at this basic price. An indication of what this is can be gained from a study of fluctuations over a long term of years.

It is common to hear the average price over an extended period considered the "normal" price, but this basis for value is one which must be used with discretion, for it is not the whole question when mining. The "normal" price is the average price over a long term. The lives of mines, and especially ore in sight, may not necessarily enjoy the period of this "normal" price. The engineer must balance his judgments by the immediate outlook of the industrial weather. When lead was falling steadily in December, 1907, no engineer would accept the price of that date, although it was then below "normal"; his product might go to market even lower yet.

It is desirable to ascertain what the basic and normal prices are, for between them lies safety. Since 1884 there have been three cycles of commercial expansion and contraction. If the average prices are taken for these three cycles separately (1885-95), 1895-1902, 1902-08) it will be seen that there has been a steady advance in prices. For the succeeding cycles lead on the London Exchange,[*] the freest of the world's markets was £12 12s. 4d., £13 3s. 7d., and £17 7s. 0d. respectively; zinc, £17 14s. 10d., £19 3s. 8d., and £23 3s. 0d.; and standard copper, £48 16s. 0d., £59 10s. 0d., and £65 7s. 0d. It seems, therefore, that a higher standard of prices can be assumed as the basic and normal than would be indicated if the general average of, say, twenty years were taken. During this period, the world's gold output has nearly quadrupled, and, whether the quantitative theory of gold be accepted or not, it cannot be denied that there has been a steady increase in the price of commodities. In all base-metal mining it is well to remember that the production of these metals is liable to great stimulus at times from the discovery of new deposits or new processes of recovery from hitherto unprofitable ores. It is therefore for this reason hazardous in the extreme to prophesy what prices will be far in the future, even when the industrial weather is clear. But some basis must be arrived at, and from the available outlook it would seem that the following metal prices are justifiable for some time to come, provided the present tariff schedules are maintained in the United States:

[Footnote *: All London prices are based on the long ton of 2,240 lbs. Much confusion exists in the copper trade as to the classification of the metal. New York prices are quoted in electrolytic and "Lake"; London's in "Standard." "Standard" has now become practically an arbitrary term peculiar to London, for the great bulk of copper dealt in is "electrolytic" valued considerably over "Standard.">[

In these figures the writer has not followed strict averages, but has taken the general outlook combined with the previous records. The likelihood of higher prices for lead is more encouraging than for any other metal, as no new deposits of importance have come forward for years, and the old mines are reaching considerable depths. Nor does the frenzied prospecting of the world's surface during the past ten years appear to forecast any very disturbing developments. The zinc future is not so bright, for metallurgy has done wonders in providing methods of saving the zinc formerly discarded from lead ores, and enormous supplies will come forward when required. The tin outlook is encouraging, for the supply from a mining point of view seems unlikely to more than keep pace with the world's needs. In copper the demand is growing prodigiously, but the supplies of copper ores and the number of copper mines that are ready to produce whenever normal prices recur was never so great as to-day. One very hopeful fact can be deduced for the comfort of the base metal mining industry as a whole. If the growth of demand continues through the next thirty years in the ratio of the past three decades, the annual demand for copper will be over 3,000,000 tons, of lead over 1,800,000 tons, of spelter 2,800,000 tons, of tin 250,000 tons. Where such stupendous amounts of these metals are to come from at the present range of prices, and even with reduced costs of production, is far beyond any apparent source of supply. The outlook for silver prices is in the long run not bright. As the major portion of the silver produced is a bye product from base metals, any increase in the latter will increase the silver production despite very much lower prices for the precious metal. In the meantime the gradual conversion of all nations to the gold standard seems a matter of certainty. Further, silver may yet be abandoned as a subsidiary coinage inasmuch as it has now but a token value in gold standard countries if denuded of sentiment.

COST OF PRODUCTION.

It is hardly necessary to argue the relative importance of the determination of the cost of production and the determination of the recoverable contents of the ore. Obviously, the aim of mine valuation is to know the profits to be won, and the profit is the value of the metal won, less the cost of production.

The cost of production embraces development, mining, treatment, management. Further than this, it is often contended that, as the capital expended in purchase and equipment must be redeemed within the life of the mine, this item should also be included in production costs. It is true that mills, smelters, shafts, and all the paraphernalia of a mine are of virtually negligible value when it is exhausted; and that all mines are exhausted sometime and every ton taken out contributes to that exhaustion; and that every ton of ore must bear its contribution to the return of the investment, as well as profit upon it. Therefore it may well be said that the redemption of the capital and its interest should be considered in costs per ton. The difficulty in dealing with the subject from the point of view of production cost arises from the fact that, except possibly in the case of banket gold and some conglomerate copper mines, the life of a metal mine is unknown beyond the time required to exhaust the ore reserves. The visible life at the time of purchase or equipment may be only three or four years, yet the average equipment has a longer life than this, and the anticipation for every mine is also for longer duration than the bare ore in sight. For clarity of conclusions in mine valuation the most advisable course is to determine the profit in sight irrespective of capital redemption in the first instance. The questions of capital redemption, purchase price, or equipment cost can then be weighed against the margin of profit. One phase of redemption will be further discussed under "Amortization of Capital" and "Ratio of Output to the Mine."

The cost of production depends upon many things, such as the cost of labor, supplies, the size of the ore-body, the treatment necessary, the volume of output, etc.; and to discuss them all would lead into a wilderness of supposititious cases. If the mine is a going concern, from which reliable data can be obtained, the problem is much simplified. If it is virgin, the experience of other mines in the same region is the next resource; where no such data can be had, the engineer must fall back upon the experience with mines still farther afield. Use is sometimes made of the "comparison ton" in calculating costs upon mines where data of actual experience are not available. As costs will depend in the main upon items mentioned above, if the known costs of a going mine elsewhere be taken as a basis, and subtractions and additions made for more unfavorable or favorable effect of the differences in the above items, a fairly close result can be approximated.

Mine examinations are very often inspired by the belief that extended operations or new metallurgical applications to the mine will expand the profits. In such cases the paramount questions are the reduction of costs by better plant, larger outputs, new processes, or alteration of metallurgical basis and better methods. If every item of previous expenditure be gone over and considered, together with the equipment, and method by which it was obtained, the possible savings can be fairly well deduced, and justification for any particular line of action determined. One view of this subject will be further discussed under "Ratio of Output to the Mine." The conditions which govern the working costs are on every mine so special to itself, that no amount of advice is very useful. Volumes of advice have been published on the subject, but in the main their burden is not to underestimate.

In considering the working costs of base-metal mines, much depends upon the opportunity for treatment in customs works, smelters, etc. Such treatment means a saving of a large portion of equipment cost, and therefore of the capital to be invested and subsequently recovered. The economics of home treatment must be weighed against the sum which would need to be set aside for redemption of the plant, and unless there is a very distinct advantage to be had by the former, no risks should be taken. More engineers go wrong by the erection of treatment works where other treatment facilities are available, than do so by continued shipping. There are many mines where the cost of equipment could never be returned, and which would be valueless unless the ore could be shipped. Another phase of foreign treatment arises from the necessity or advantage of a mixture of ores,—the opportunity of such mixtures often gives the public smelter an advantage in treatment with which treatment on the mine could never compete.

Fluctuation in the price of base metals is a factor so much to be taken into consideration, that it is desirable in estimating mine values to reduce the working costs to a basis of a "per unit" of finished metal. This method has the great advantage of indicating so simply the involved risks of changing prices that whoso runs may read. Where one metal predominates over the other to such an extent as to form the "backbone" of the value of the mine, the value of the subsidiary metals is often deducted from the cost of the principal metal, in order to indicate more plainly the varying value of the mine with the fluctuating prices of the predominant metal. For example, it is usual to state that the cost of copper production from a given ore will be so many cents per pound, or so many pounds sterling per ton. Knowing the total metal extractable from the ore in sight, the profits at given prices of metal can be readily deduced. The point at which such calculation departs from the "per-ton-of-ore" unto the per-unit-cost-of-metal basis, usually lies at the point in ore dressing where it is ready for the smelter. To take a simple case of a lead ore averaging 20%: this is to be first concentrated and the lead reduced to a concentrate averaging 70% and showing a recovery of 75% of the total metal content. The cost per ton of development, mining, concentration, management, is to this point say $4 per ton of original crude ore. The smelter buys the concentrate for 95% of the value of the metal, less the smelting charge of $15 per ton, or there is a working cost of a similar sum by home equipment. In this case 4.66 tons of ore are required to produce one ton of concentrates, and therefore each ton of concentrates costs $18.64. This amount, added to the smelting charge, gives a total of $33.64 for the creation of 70% of one ton of finished lead, or equal to 2.40 cents per pound which can be compared with the market price less 5%. If the ore were to contain 20 ounces of silver per ton, of which 15 ounces were recovered into the leady concentrates, and the smelter price for the silver were 50 cents per ounce, then the $7.50 thus recovered would be subtracted from $33.64, making the apparent cost of the lead 1.86 cents per pound.

CHAPTER V.

Mine Valuation (Continued).

It is desirable to state in some detail the theory of amortization before consideration of its application in mine valuation.

As every mine has a limited life, the capital invested in it must be redeemed during the life of the mine. It is not sufficient that there be a bare profit over working costs. In this particular, mines differ wholly from many other types of investment, such as railways. In the latter, if proper appropriation is made for maintenance, the total income to the investor can be considered as interest or profit; but in mines, a portion of the annual income must be considered as a return of capital. Therefore, before the yield on a mine investment can be determined, a portion of the annual earnings must be set aside in such a manner that when the mine is exhausted the original investment will have been restored. If we consider the date due for the return of the capital as the time when the mine is exhausted, we may consider the annual instalments as payments before the due date, and they can be put out at compound interest until the time for restoration arrives. If they be invested in safe securities at the usual rate of about 4%, the addition of this amount of compound interest will assist in the repayment of the capital at the due date, so that the annual contributions to a sinking fund need not themselves aggregate the total capital to be restored, but may be smaller by the deficiency which will be made up by their interest earnings. Such a system of redemption of capital is called "Amortization."

Obviously it is not sufficient for the mine investor that his capital shall have been restored, but there is required an excess earning over and above the necessities of this annual funding of capital. What rate of excess return the mine must yield is a matter of the risks in the venture and the demands of the investor. Mining business is one where 7% above provision for capital return is an absolute minimum demanded by the risks inherent in mines, even where the profit in sight gives warranty to the return of capital. Where the profit in sight (which is the only real guarantee in mine investment) is below the price of the investment, the annual return should increase in proportion. There are thus two distinct directions in which interest must be computed,—first, the internal influence of interest in the amortization of the capital, and second, the percentage return upon the whole investment after providing for capital return.

There are many limitations to the introduction of such refinements as interest calculations in mine valuation. It is a subject not easy to discuss with finality, for not only is the term of years unknown, but, of more importance, there are many factors of a highly speculative order to be considered in valuing. It may be said that a certain life is known in any case from the profit in sight, and that in calculating this profit a deduction should be made from the gross profit for loss of interest on it pending recovery. This is true, but as mines are seldom dealt with on the basis of profit in sight alone, and as the purchase price includes usually some proportion for extension in depth, an unknown factor is introduced which outweighs the known quantities. Therefore the application of the culminative effect of interest accumulations is much dependent upon the sort of mine under consideration. In most cases of uncertain continuity in depth it introduces a mathematical refinement not warranted by the speculative elements. For instance, in a mine where the whole value is dependent upon extension of the deposit beyond openings, and where an expected return of at least 50% per annum is required to warrant the risk, such refinement would be absurd. On the other hand, in a Witwatersrand gold mine, in gold and tin gravels, or in massive copper mines such as Bingham and Lake Superior, where at least some sort of life can be approximated, it becomes a most vital element in valuation.

In general it may be said that the lower the total annual return expected upon the capital invested, the greater does the amount demanded for amortization become in proportion to this total income, and therefore the greater need of its introduction in calculations. Especially is this so where the cost of equipment is large proportionately to the annual return. Further, it may be said that such calculations are of decreasing use with increasing proportion of speculative elements in the price of the mine. The risk of extension in depth, of the price of metal, etc., may so outweigh the comparatively minor factors here introduced as to render them useless of attention.

In the practical conduct of mines or mining companies, sinking funds for amortization of capital are never established. In the vast majority of mines of the class under discussion, the ultimate duration of life is unknown, and therefore there is no basis upon which to formulate such a definite financial policy even were it desired. Were it possible to arrive at the annual sum to be set aside, the stockholders of the mining type would prefer to do their own reinvestment. The purpose of these calculations does not lie in the application of amortization to administrative finance. It is nevertheless one of the touchstones in the valuation of certain mines or mining investments. That is, by a sort of inversion such calculations can be made to serve as a means to expose the amount of risk,—to furnish a yardstick for measuring the amount of risk in the very speculations of extension in depth and price of metals which attach to a mine. Given the annual income being received, or expected, the problem can be formulated into the determination of how many years it must be continued in order to amortize the investment and pay a given rate of profit. A certain length of life is evident from the ore in sight, which may be called the life in sight. If the term of years required to redeem the capital and pay an interest upon it is greater than the life in sight, then this extended life must come from extension in depth, or ore from other direction, or increased price of metals. If we then take the volume and profit on the ore as disclosed we can calculate the number of feet the deposit must extend in depth, or additional tonnage that must be obtained of the same grade, or the different prices of metal that must be secured, in order to satisfy the demanded term of years. These demands in actual measure of ore or feet or higher price can then be weighed against the geological and industrial probabilities.

The following tables and examples may be of assistance in these calculations.

Table 1. To apply this table, the amount of annual income or dividend and the term of years it will last must be known or estimated factors. It is then possible to determine the present value of this annual income after providing for amortization and interest on the investment at various rates given, by multiplying the annual income by the factor set out.

A simple illustration would be that of a mine earning a profit of $200,000 annually, and having a total of 1,000,000 tons in sight, yielding a profit of $2 a ton, or a total profit in sight of $2,000,000, thus recoverable in ten years. On a basis of a 7% return on the investment and amortization of capital (Table I), the factor is 6.52 x $200,000 = $1,304,000 as the present value of the gross profits exposed. That is, this sum of $1,304,000, if paid for the mine, would be repaid out of the profit in sight, together with 7% interest if the annual payments into sinking fund earn 4%.

TABLE I.

Present Value of an Annual Dividend Over — Years at —% and Replacing Capital by Reinvestment of an Annual Sum at 4%.

Table II is practically a compound discount table. That is, by it can be determined the present value of a fixed sum payable at the end of a given term of years, interest being discounted at various given rates. Its use may be illustrated by continuing the example preceding.

TABLE II.

Present Value of $1, or £1, payable in — Years, Interest taken at —%.

If such a mine is not equipped, and it is assumed that $200,000 are required to equip the mine, and that two years are required for this equipment, the value of the ore in sight is still less, because of the further loss of interest in delay and the cost of equipment. In this case the present value of $1,304,000 in two years, interest at 7%, the factor is .87 X 1,304,000 = $1,134,480. From this comes off the cost of equipment, or $200,000, leaving $934,480 as the present value of the profit in sight. A further refinement could be added by calculating the interest chargeable against the $200,000 equipment cost up to the time of production.

TABLE III.

Table III. This table is calculated by inversion of the factors in Table I, and is the most useful of all such tables, as it is a direct calculation of the number of years that a given rate of income on the investment must continue in order to amortize the capital (the annual sinking fund being placed at compound interest at 4%) and to repay various rates of interest on the investment. The application of this method in testing the value of dividend-paying shares is very helpful, especially in weighing the risks involved in the portion of the purchase or investment unsecured by the profit in sight. Given the annual percentage income on the investment from the dividends of the mine (or on a non-producing mine assuming a given rate of production and profit from the factors exposed), by reference to the table the number of years can be seen in which this percentage must continue in order to amortize the investment and pay various rates of interest on it. As said before, the ore in sight at a given rate of exhaustion can be reduced to terms of life in sight. This certain period deducted from the total term of years required gives the life which must be provided by further discovery of ore, and this can be reduced to tons or feet of extension of given ore-bodies and a tangible position arrived at. The test can be applied in this manner to the various prices which must be realized from the base metal in sight to warrant the price.

Taking the last example and assuming that the mine is equipped, and that the price is $2,000,000, the yearly return on the price is 10%. If it is desired besides amortizing or redeeming the capital to secure a return of 7% on the investment, it will be seen by reference to the table that there will be required a life of 21.6 years. As the life visible in the ore in sight is ten years, then the extensions in depth must produce ore for 11.6 years longer—1,160,000 tons. If the ore-body is 1,000 feet long and 13 feet wide, it will furnish of gold ore 1,000 tons per foot of depth; hence the ore-body must extend 1,160 feet deeper to justify the price. Mines are seldom so simple a proposition as this example. There are usually probabilities of other ore; and in the case of base metal, then variability of price and other elements must be counted. However, once the extension in depth which is necessary is determined for various assumptions of metal value, there is something tangible to consider and to weigh with the five geological weights set out in Chapter III.

The example given can be expanded to indicate not only the importance of interest and redemption in the long extension in depth required, but a matter discussed from another point of view under "Ratio of Output." If the plant on this mine were doubled and the earnings increased to 20% ($400,000 per annum) (disregarding the reduction in working expenses that must follow expansion of equipment), it will be found that the life required to repay the purchase money,—$2,000,000,—and 7% interest upon it, is about 6.8 years.

As at this increased rate of production there is in the ore in sight a life of five years, the extension in depth must be depended upon for 1.8 years, or only 360,000 tons,—that is, 360 feet of extension. Similarly, the present value of the ore in sight is $268,000 greater if the mine be given double the equipment, for thus the idle money locked in the ore is brought into the interest market at an earlier date. Against this increased profit must be weighed the increased cost of equipment. The value of low grade mines, especially, is very much a factor of the volume of output contemplated.

CHAPTER VI.

Mine Valuation (Concluded).

A large number of examinations arise upon prospecting ventures or partially developed mines where the value is almost wholly prospective. The risks in such enterprises amount to the possible loss of the whole investment, and the possible returns must consequently be commensurate. Such business is therefore necessarily highly speculative, but not unjustifiable, as the whole history of the industry attests; but this makes the matter no easier for the mine valuer. Many devices of financial procedure assist in the limitation of the sum risked, and offer a middle course to the investor between purchase of a wholly prospective value and the loss of a possible opportunity to profit by it. The usual form is an option to buy the property after a period which permits a certain amount of development work by the purchaser before final decision as to purchase.

Aside from young mines such enterprises often arise from the possibility of lateral extension of the ore-deposit outside the boundaries of the property of original discovery (Fig. 3), in which cases there is often no visible ore within the property under consideration upon which to found opinion. In regions where vertical side lines obtain, there is always the possibility of a "deep level" in inclined deposits. Therefore the ground surrounding known deposits has a certain speculative value, upon which engineers are often called to pass judgment. Except in such unusual occurrences as South African bankets, or Lake Superior coppers, prospecting for deep level of extension is also a highly speculative phase of mining.

The whole basis of opinion in both classes of ventures must be the few geological weights,—the geology of the property and the district, the development of surrounding mines, etc. In any event, there is a very great percentage of risk, and the profit to be gained by success must be, proportionally to the expenditure involved, very large. It is no case for calculating amortization and other refinements. It is one where several hundreds or thousands of per cent hoped for on the investment is the only justification.

OPINIONS AND VALUATIONS UPON SECOND-HAND DATA.

Some one may come forward and deprecate the bare suggestion of an engineer's offering an opinion when he cannot have proper first-hand data. But in these days we have to deal with conditions as well as theories of professional ethics. The growing ownership of mines by companies, that is by corporations composed of many individuals, and with their stocks often dealt in on the public exchanges, has resulted in holders whose interest is not large enough to warrant their undertaking the cost of exhaustive examinations. The system has produced an increasing class of mining speculators and investors who are finding and supplying the enormous sums required to work our mines,—sums beyond the reach of the old-class single-handed mining men. Every year the mining investors of the new order are coming more and more to the engineer for advice, and they should be encouraged, because such counsel can be given within limits, and these limits tend to place the industry upon a sounder footing of ownership. As was said before, the lamb can be in a measure protected. The engineer's interest is to protect him, so that the industry which concerns his own life-work may be in honorable repute, and that capital may be readily forthcoming for its expansion. Moreover, by constant advice to the investor as to what constitutes a properly presented and managed project, the arrangement of such proper presentation and management will tend to become an a priori function of the promoter.

Sometimes the engineer can make a short visit to the mine for data purposes,—more often he cannot. In the former case, he can resolve for himself an approximation upon all the factors bearing on value, except the quality of the ore. For this, aside from inspection of the ore itself, a look at the plans is usually enlightening. A longitudinal section of the mine showing a continuous shortening of the stopes with each succeeding level carries its own interpretation. In the main, the current record of past production and estimates of the management as to ore-reserves, etc., can be accepted in ratio to the confidence that can be placed in the men who present them. It then becomes a case of judgment of men and things, and here no rule applies.

Advice must often be given upon data alone, without inspection of the mine. Most mining data present internal evidence as to credibility. The untrustworthy and inexperienced betray themselves in their every written production. Assuming the reliability of data, the methods already discussed for weighing the ultimate value of the property can be applied. It would be possible to cite hundreds of examples of valuation based upon second-hand data. Three will, however, sufficiently illustrate. First, the R mine at Johannesburg. With the regularity of this deposit, the development done, and a study of the workings on the neighboring mines and in deeper ground, it is a not unfair assumption that the reefs will maintain size and value throughout the area. The management is sound, and all the data are given in the best manner. The life of the mine is estimated at six years, with some probabilities of further ore from low-grade sections. The annual earnings available for dividends are at the rate of about £450,000 per annum. The capital is £440,000 in £1 shares. By reference to the table on page 46 it will be seen that the present value of £450,000 spread over six years to return capital at the end of that period, and give 7% dividends in the meantime, is 4.53 x £450,000 = £2,036,500 ÷ 440,000 = £4 12s. 7d. per share. So that this mine, on the assumption of continuity of values, will pay about 7% and return the price. Seven per cent is, however, not deemed an adequate return for the risks of labor troubles, faults, dykes, or poor patches. On a 9% basis, the mine is worth about £4 4s. per share.

Second, the G mine in Nevada. It has a capital of $10,000,000 in $1 shares, standing in the market at 50 cents each. The reserves are 250,000 tons, yielding a profit for yearly division of $7 per ton. It has an annual capacity of about 100,000 tons, or $700,000 net profit, equal to 14% on the market value. In order to repay the capital value of $5,000,000 and 8% per annum, it will need a life of (Table III) 13 years, of which 2-1/2 are visible. The size of the ore-bodies indicates a yield of about 1,100 tons per foot of depth. At an exhaustion rate of 100,000 tons per annum, the mine would need to extend to a depth of over a thousand feet below the present bottom. There is always a possibility of finding parallel bodies or larger volumes in depth, but it would be a sanguine engineer indeed who would recommend the stock, even though it pays an apparent 14%.

Third, the B mine, with a capital of $10,000,000 in 2,000,000 shares of $5 each. The promoters state that the mine is in the slopes of the Andes in Peru; that there are 6,000,000 tons of "ore blocked out"; that two assays by the assayers of the Bank of England average 9% copper; that the copper can be produced at five cents per pound; that there is thus a profit of $10,000,000 in sight. The evidences are wholly incompetent. It is a gamble on statements of persons who have not the remotest idea of sound mining.

GENERAL CONDUCT OF EXAMINATION.

Complete and exhaustive examination, entailing extensive sampling, assaying, and metallurgical tests, is very expensive and requires time. An unfavorable report usually means to the employer absolute loss of the engineer's fee and expenses. It becomes then the initial duty of the latter to determine at once, by the general conditions surrounding the property, how far the expenditure for exhaustive examination is warranted. There is usually named a money valuation for the property, and thus a peg is afforded upon which to hang conclusions. Very often collateral factors with a preliminary sampling, or indeed no sampling at all, will determine the whole business. In fact, it is becoming very common to send younger engineers to report as to whether exhaustive examination by more expensive men is justified.

In the course of such preliminary inspection, the ore-bodies may prove to be too small to insure adequate yield on the price, even assuming continuity in depth and represented value. They may be so difficult to mine as to make costs prohibitive, or they may show strong signs of "petering out." The ore may present visible metallurgical difficulties which make it unprofitable in any event. A gold ore may contain copper or arsenic, so as to debar cyanidation, where this process is the only hope of sufficiently moderate costs. A lead ore may be an amorphous compound with zinc, and successful concentration or smelting without great penalties may be precluded. A copper ore may carry a great excess of silica and be at the same time unconcentratable, and there may be no base mineral supply available for smelting mixture. The mine may be so small or so isolated that the cost of equipment will never be justified. Some of these conditions may be determined as unsurmountable, assuming a given value for the ore, and may warrant the rejection of the mine at the price set.

It is a disagreeable thing to have a disappointed promoter heap vituperation on an engineer's head because he did not make an exhaustive examination. Although it is generally desirable to do some sampling to give assurance to both purchaser and vendor of conscientiousness, a little courage of conviction, when this is rightly and adequately grounded, usually brings its own reward.

Supposing, however, that conditions are right and that the mine is worth the price, subject to confirmation of values, the determination of these cannot be undertaken unless time and money are available for the work. As was said, a sampling campaign is expensive, and takes time, and no engineer has the moral right to undertake an examination unless both facilities are afforded. Curtailment is unjust, both to himself and to his employer.

How much time and outlay are required to properly sample a mine is obviously a question of its size, and the character of its ore. An engineer and one principal assistant can conduct two sampling parties. In hard rock it may be impossible to take more than five samples a day for each party. But, in average ore, ten samples for each is reasonable work. As the number of samples is dependent upon the footage of openings on the deposit, a rough approximation can be made in advance, and a general idea obtained as to the time required. This period must be insisted upon.

REPORTS.

Reports are to be read by the layman, and their first qualities should be simplicity of terms and definiteness of conclusions. Reports are usually too long, rather than too short. The essential facts governing the value of a mine can be expressed on one sheet of paper. It is always desirable, however, that the groundwork data and the manner of their determination should be set out with such detail that any other engineer could come to the same conclusion if he accepted the facts as accurately determined. In regard to the detailed form of reports, the writer's own preference is for a single page summarizing the main factors, and an assay plan, reduced to a longitudinal section where possible. Then there should be added, for purposes of record and for submission to other engineers, a set of appendices going into some details as to the history of the mine, its geology, development, equipment, metallurgy, and management. A list of samples should be given with their location, and the tonnages and values of each separate block. A presentation should be made of the probabilities of extension in depth, together with recommendations for working the mine.

GENERAL SUMMARY.

The bed-rock value which attaches to a mine is the profit to be won from proved ore and in which the price of metal is calculated at some figure between "basic" and "normal." This we may call the "A" value. Beyond this there is the speculative value of the mine. If the value of the "probable" ore be represented by X, the value of extension of the ore by Y, and a higher price for metal than the price above assumed represented by Z, then if the mine be efficiently managed the value of the mine is A + X + Y + Z. What actual amounts should be attached to X, Y, Z is a matter of judgment. There is no prescription for good judgment. Good judgment rests upon a proper balancing of evidence. The amount of risk in X, Y, Z is purely a question of how much these factors are required to represent in money,—in effect, how much more ore must be found, or how many feet the ore must extend in depth; or in convertible terms, what life in years the mine must have, or how high the price of metal must be. In forming an opinion whether these requirements will be realized, X, Y, Z must be balanced in a scale whose measuring standards are the five geological weights and the general industrial outlook. The wise engineer will put before his clients the scale, the weights, and the conclusion arrived at. The shrewd investor will require to know these of his adviser.

CHAPTER VII.

Development of Mines.

Development is conducted for two purposes: first, to search for ore; and second, to open avenues for its extraction. Although both objects are always more or less in view, the first predominates in the early life of mines, the prospecting stage, and the second in its later life, the producing stage. It is proposed to discuss development designed to embrace extended production purposes first, because development during the prospecting stage is governed by the same principles, but is tempered by the greater degree of uncertainty as to the future of the mine, and is, therefore, of a more temporary character.

ENTRY TO THE MINE.

There are four methods of entry: by tunnel, vertical shaft, inclined shaft, or by a combination of the last two, that is, by a shaft initially vertical then turned to an incline. Combined shafts are largely a development of the past few years to meet "deep level" conditions, and have been rendered possible only by skip-winding. The angle in such shafts (Fig. 2) is now generally made on a parabolic curve, and the speed of winding is then less diminished by the bend.

The engineering problems which present themselves under "entry" may be divided into those of:—

1. Method.
2. Location.
3. Shape and size.

The resolution of these questions depends upon the:—

From the point of view of entrance, the coöperation of a majority of these factors permits the division of mines into certain broad classes. The type of works demanded for moderate depths (say vertically 2,500 to 3,000 feet) is very different from that required for great depths. To reach great depths, the size of shafts must greatly expand, to provide for extended ventilation, pumping, and winding necessities. Moreover inclined shafts of a degree of flatness possible for moderate depths become too long to be used economically from the surface. The vast majority of metal-mining shafts fall into the first class, those of moderate depths. Yet, as time goes on and ore-deposits are exhausted to lower planes, problems of depth will become more common. One thing, however, cannot be too much emphasized, especially on mines to be worked from the outcrop, and that is, that no engineer is warranted, owing to the speculation incidental to extension in depth, in initiating early in the mine's career shafts of such size or equipment as would be available for great depths. Moreover, the proper location of a shaft so as to work economically extension of the ore-bodies is a matter of no certainty, and therefore shafts of speculative mines are tentative in any event.

Another line of division from an engineering view is brought about by a combination of three of the factors mentioned. This is the classification into "outcrop" and "deep-level" mines. The former are those founded upon ore-deposits to be worked from or close to the surface. The latter are mines based upon the extension in depth of ore-bodies from outcrop mines. Such projects are not so common in America, where the law in most districts gives the outcrop owner the right to follow ore beyond his side-lines, as in countries where the boundaries are vertical on all sides. They do, however, arise not alone in the few American sections where the side-lines are vertical boundaries, but in other parts owing to the pitch of ore-bodies through the end lines (Fig. 3). More especially do such problems arise in America in effect, where the ingress questions have to be revised for mines worked out in the upper levels (Fig. 7).

If from a standpoint of entrance questions, mines are first classified into those whose works are contemplated for moderate depths, and those in which work is contemplated for great depth, further clarity in discussion can be gained by subdivision into the possible cases arising out of the factors of location, dip, topography, and boundaries.

MINES OF MODERATE DEPTHS.

MINES TO GREAT DEPTHS.

Case I.—Although for logical arrangement tunnel entry has been given first place, to save repetition it is proposed to consider it later. With few exceptions, tunnels are a temporary expedient in the mine, which must sooner or later be opened by a shaft.

Case II. Vertical or Horizontal Deposits.—These require no discussion as to manner of entry. There is no justifiable alternative to a vertical shaft (Fig. 4).

Case III. Inclined Deposits which are intended to be worked from the Outcrop, or from near It (Fig. 5).—The choice of inclined or vertical shaft is dependent upon relative cost of construction, subsequent operation, and the useful life of the shaft, and these matters are largely governed by the degree of dip. Assuming a shaft of the same size in either alternative, the comparative cost per foot of sinking is dependent largely on the breaking facilities of the rock under the different directions of attack. In this, the angles of the bedding or joint planes to the direction of the shaft outweigh other factors. The shaft which takes the greatest advantage of such lines of breaking weakness will be the cheapest per foot to sink. In South African experience, where inclined shafts are sunk parallel to the bedding planes of hard quartzites, the cost per foot appears to be in favor of the incline. On the other hand, sinking shafts across tight schists seems to be more advantageous than parallel to the bedding planes, and inclines following the dip cost more per foot than vertical shafts.

An inclined shaft requires more footage to reach a given point of depth, and therefore it would entail a greater total expense than a vertical shaft, assuming they cost the same per foot. The excess amount will be represented by the extra length, and this will depend upon the flatness of the dip. With vertical shafts, however, crosscuts to the deposit are necessary. In a comparative view, therefore, the cost of the crosscuts must be included with that of the vertical shaft, as they would be almost wholly saved in an incline following near the ore.

The factor of useful life for the shaft enters in deciding as to the advisability of vertical shafts on inclined deposits, from the fact that at some depth one of two alternatives has to be chosen. The vertical shaft, when it reaches a point below the deposit where the crosscuts are too long (C, Fig. 5), either becomes useless, or must be turned on an incline at the intersection with the ore (B). The first alternative means ultimately a complete loss of the shaft for working purposes. The latter has the disadvantage that the bend interferes slightly with haulage.

The following table will indicate an hypothetical extreme case,—not infrequently met. In it a vertical shaft 1,500 feet in depth is taken as cutting the deposit at the depth of 750 feet, the most favored position so far as aggregate length of crosscuts is concerned. The cost of crosscutting is taken at $20 per foot and that of sinking the vertical shaft at $75 per foot. The incline is assumed for two cases at $75 and $100 per foot respectively. The stoping height upon the ore between levels is counted at 125 feet.

From the above examples it will be seen that the cost of crosscuts put at ordinary level intervals rapidly outruns the extra expense of increased length of inclines. If, however, the conditions are such that crosscuts from a vertical shaft are not necessary at so frequent intervals, then in proportion to the decrease the advantages sway to the vertical shaft. Most situations wherein the crosscuts can be avoided arise in mines worked out in the upper levels and fall under Case IV, that of deep-level projects.

There can be no doubt that vertical shafts are cheaper to operate than inclines: the length of haul from a given depth is less; much higher rope speed is possible, and thus the haulage hours are less for the same output; the wear and tear on ropes, tracks, or guides is not so great, and pumping is more economical where the Cornish order of pump is used. On the other hand, with a vertical shaft must be included the cost of operating crosscuts. On mines where the volume of ore does not warrant mechanical haulage, the cost of tramming through the extra distance involved is an expense which outweighs any extra operating outlay in the inclined shaft itself. Even with mechanical haulage in crosscuts, it is doubtful if there is anything in favor of the vertical shaft on this score.

In deposits of very flat dips, under 30°, the case arises where the length of incline is so great that the saving on haulage through direct lift warrants a vertical shaft as an auxiliary outlet in addition to the incline (Fig. 6). In such a combination the crosscut question is eliminated. The mine is worked above and below the intersection by incline, and the vertical shaft becomes simply a more economical exit and an alternative to secure increased output. The North Star mine at Grass Valley is an illustration in point. Such a positive instance borders again on Case IV, deep-level projects.

In conclusion, it is the writer's belief that where mines are to be worked from near the surface, coincidentally with sinking, and where, therefore, crosscuts from a vertical shaft would need to be installed frequently, inclines are warranted in all dips under 75° and over 30°. Beyond 75° the best alternative is often undeterminable. In the range under 30° and over 15°, although inclines are primarily necessary for actual delivery of ore from levels, they can often be justifiably supplemented by a vertical shaft as a relief to a long haul. In dips of less than 15°, as in those over 75°, the advantages again trend strongly in favor of the vertical shaft. There arise, however, in mountainous countries, topographic conditions such as the dip of deposits into the mountain, which preclude any alternative on an incline at any angled dip.

Case IV. Inclined Deposits which must be attacked in Depth (Fig. 7).—There are two principal conditions in which such properties exist: first, mines being operated, or having been previously worked, whose method of entry must be revised; second, those whose ore-bodies to be attacked do not outcrop within the property.

The first situation may occur in mines of inadequate shaft capacity or wrong location; in mines abandoned and resurrected; in mines where a vertical shaft has reached its limit of useful extensions, having passed the place of economical crosscutting; or in mines in flat deposits with inclines whose haul has become too long to be economical. Three alternatives present themselves in such cases: a new incline from the surface (A B F, Fig. 7), or a vertical shaft combined with incline extension (C D F), or a simple vertical shaft (H G). A comparison can be first made between the simple incline and the combined shaft. The construction of an incline from the surface to the ore-body will be more costly than a combined shaft, for until the horizon of the ore is reached (at D) no crosscuts are required in the vertical section, while the incline must be of greater length to reach the same horizon. The case arises, however, where inclines can be sunk through old stopes, and thus more cheaply constructed than vertical shafts through solid rock; and also the case of mountainous topographic conditions mentioned above.

From an operating point of view, the bend in combined shafts (at D) gives rise to a good deal of wear and tear on ropes and gear. The possible speed of winding through a combined shaft is, however, greater than a simple incline, for although haulage speed through the incline section (D F) and around the bend of the combined shaft is about the same as throughout a simple incline (A F), the speed can be accelerated in the vertical portion (D C) above that feasible did the incline extend to the surface. There is therefore an advantage in this regard in the combined shaft. The net advantages of the combined over the inclined shaft depend on the comparative length of the two alternative routes from the intersection (D) to the surface. Certainly it is not advisable to sink a combined shaft to cut a deposit at 300 feet in depth if a simple incline can be had to the surface. On the other hand, a combined shaft cutting the deposit at 1,000 feet will be more advisable than a simple incline 2,000 feet long to reach the same point. The matter is one for direct calculation in each special case. In general, there are few instances of really deep-level projects where a complete incline from the surface is warranted.

In most situations of this sort, and in all of the second type (where the outcrop is outside the property), actual choice usually lies between combined shafts (C D F) and entire vertical shafts (H G). The difference between a combined shaft and a direct vertical shaft can be reduced to a comparison of the combined shaft below the point of intersection (D) with that portion of a vertical shaft which would cover the same horizon. The question then becomes identical with that of inclined versus verticals, as stated in Case III, with the offsetting disadvantage of the bend in the combined shaft. If it is desired to reach production at the earliest date, the lower section of a simple vertical shaft must have crosscuts to reach the ore lying above the horizon of its intersection (E). If production does not press, the ore above the intersection (EB) can be worked by rises from the horizon of intersection (E). In the use of rises, however, there follow the difficulties of ventilation and lowering the ore down to the shaft, which brings expenses to much the same thing as operating through crosscuts.

The advantages of combined over simple vertical shafts are earlier production, saving of either rises or crosscuts, and the ultimate utility of the shaft to any depth. The disadvantages are the cost of the extra length of the inclined section, slower winding, and greater wear and tear within the inclined section and especially around the bend. All these factors are of variable import, depending upon the dip. On very steep dips,—over 70°,—the net result is in favor of the simple vertical shaft. On other dips it is in favor of the combined shaft.

Cases V and VI. Mines to be worked to Great Depths,—over 3,000 Feet.—In Case V, with vertical or horizontal deposits, there is obviously no desirable alternative to vertical shafts.

In Case VI, with inclined deposits, there are the alternatives of a combined or of a simple vertical shaft. A vertical shaft in locations (H, Fig. 7) such as would not necessitate extension in depth by an incline, would, as in Case IV, compel either crosscuts to the ore or inclines up from the horizon of intersection (E). Apart from delay in coming to production and the consequent loss of interest on capital, the ventilation problems with this arrangement would be appalling. Moreover, the combined shaft, entering the deposit near its shallowest point, offers the possibility of a separate haulage system on the inclined and on the vertical sections, and such separate haulage is usually advisable at great depths. In such instances, the output to be handled is large, for no mine of small output is likely to be contemplated at such depth. Several moderate-sized inclines from the horizon of intersection have been suggested (EF, DG, CH, Fig. 8) to feed a large primary shaft (AB), which thus becomes the trunk road. This program would cheapen lateral haulage underground, as mechanical traction can be used in the main level, (EC), and horizontal haulage costs can be reduced on the lower levels. Moreover, separate winding engines on the two sections increase the capacity, for the effect is that of two trains instead of one running on a single track.

Shaft Location.—Although the prime purpose in locating a shaft is obviously to gain access to the largest volume of ore within the shortest haulage distance, other conditions also enter, such as the character of the surface and the rock to be intersected, the time involved before reaching production, and capital cost. As shafts must bear two relations to a deposit,—one as to the dip and the other as to the strike,—they may be considered from these aspects. Vertical shafts must be on the hanging-wall side of the outcrop if the deposit dips at all. In any event, the shaft should be far enough away to be out of the reach of creeps. An inclined shaft may be sunk either on the vein, in which case a pillar of ore must be left to support the shaft; or, instead, it may be sunk a short distance in the footwall, and where necessary the excavation above can be supported by filling. Following the ore has the advantage of prospecting in sinking, and in many cases the softness of the ground in the region of the vein warrants this procedure. It has, however, the disadvantage that a pillar of ore is locked up until the shaft is ready for abandonment. Moreover, as veins or lodes are seldom of even dip, an inclined shaft, to have value as a prospecting opening, or to take advantage of breaking possibilities in the lode, will usually be crooked, and an incline irregular in detail adds greatly to the cost of winding and maintenance. These twin disadvantages usually warrant a straight incline in the footwall. Inclines are not necessarily of the same dip throughout, but for reasonably economical haulage change of angle must take place gradually.

In the case of deep-level projects on inclined deposits, demanding combined or vertical shafts, the first desideratum is to locate the vertical section as far from the outcrop as possible, and thus secure the most ore above the horizon of intersection. This, however, as stated before, would involve the cost of crosscuts or rises and would cause delay in production, together with the accumulation of capital charges. How important the increment of interest on capital may become during the period of opening the mine may be demonstrated by a concrete case. For instance, the capital of a company or the cost of the property is, say, $1,000,000, and where opening the mine for production requires four years, the aggregate sum of accumulated compound interest at 5% (and most operators want more from a mining investment) would be $216,000. Under such circumstances, if a year or two can be saved in getting to production by entering the property at a higher horizon, the difference in accumulated interest will more than repay the infinitesimal extra cost of winding through a combined shaft of somewhat increased length in the inclined section.

The unknown character of the ore in depth is always a sound reason for reaching it as quickly and as cheaply as possible. In result, such shafts are usually best located when the vertical section enters the upper portion of the deposit.

The objective in location with regard to the strike of the ore-bodies is obviously to have an equal length of lateral ore-haul in every direction from the shaft. It is easier to specify than to achieve this, for in all speculative deposits ore-shoots are found to pursue curious vagaries as they go down. Ore-bodies do not reoccur with the same locus as in the upper levels, and generally the chances to go wrong are more numerous than those to go right.

Number of Shafts.—The problem of whether the mine is to be opened by one or by two shafts of course influences location. In metal mines under Cases II and III (outcrop properties) the ore output requirements are seldom beyond the capacity of one shaft. Ventilation and escape-ways are usually easily managed through the old stopes. Under such circumstances, the conditions warranting a second shaft are the length of underground haul and isolation of ore-bodies or veins. Lateral haulage underground is necessarily disintegrated by the various levels, and usually has to be done by hand. By shortening this distance of tramming and by consolidation of the material from all levels at the surface, where mechanical haulage can be installed, a second shaft is often justified. There is therefore an economic limitation to the radius of a single shaft, regardless of the ability of the shaft to handle the total output.

Other questions also often arise which are of equal importance to haulage costs. Separate ore-shoots or ore-bodies or parallel deposits necessitate, if worked from one shaft, constant levels through unpayable ground and extra haul as well, or ore-bodies may dip away from the original shaft along the strike of the deposit and a long haulage through dead levels must follow. For instance, levels and crosscuts cost roughly one-quarter as much per foot as shafts. Therefore four levels in barren ground, to reach a parallel vein or isolated ore-body 1,000 feet away, would pay for a shaft 1,000 feet deep. At a depth of 1,000 feet, at least six levels might be necessary. The tramming of ore by hand through such a distance would cost about double the amount to hoist it through a shaft and transport it mechanically to the dressing plant at surface. The aggregate cost and operation of barren levels therefore soon pays for a second shaft. If two or more shafts are in question, they must obviously be set so as to best divide the work.

Under Cases IV, V, and VI,—that is, deep-level projects,—ventilation and escape become most important considerations. Even where the volume of ore is within the capacity of a single shaft, another usually becomes a necessity for these reasons. Their location is affected not only by the locus of the ore, but, as said, by the time required to reach it. Where two shafts are to be sunk to inclined deposits, it is usual to set one so as to intersect the deposit at a lower point than the other. Production can be started from the shallower, before the second is entirely ready. The ore above the horizon of intersection of the deeper shaft is thus accessible from the shallower shaft, and the difficulty of long rises or crosscuts from that deepest shaft does not arise.

CHAPTER VIII.

Development of Mines (Continued).

Shape of Shafts.—Shafts may be round or rectangular.[*] Round vertical shafts are largely applied to coal-mines, and some engineers have advocated their usefulness to the mining of the metals under discussion. Their great advantages lie in their structural strength, in the large amount of free space for ventilation, and in the fact that if walled with stone, brick, concrete, or steel, they can be made water-tight so as to prevent inflow from water-bearing strata, even when under great pressure. The round walled shafts have a longer life than timbered shafts. All these advantages pertain much more to mining coal or iron than metals, for unsound, wet ground is often the accompaniment of coal-measures, and seldom troubles metal-mines. Ventilation requirements are also much greater in coal-mines. From a metal-miner's standpoint, round shafts are comparatively much more expensive than the rectangular timbered type.[**] For a larger area must be excavated for the same useful space, and if support is needed, satisfactory walling, which of necessity must be brick, stone, concrete, or steel, cannot be cheaply accomplished under the conditions prevailing in most metal regions. Although such shafts would have a longer life, the duration of timbered shafts is sufficient for most metal mines. It follows that, as timber is the cheapest and all things considered the most advantageous means of shaft support for the comparatively temporary character of metal mines, to get the strains applied to the timbers in the best manner, and to use the minimum amount of it consistent with security, and to lose the least working space, the shaft must be constructed on rectangular lines.

[Footnote *: Octagonal shafts were sunk in Mexico in former times. At each face of the octagon was a whim run by mules, and hauling leather buckets.]

[Footnote **: The economic situation is rapidly arising in a number of localities that steel beams can be usefully used instead of timber. The same arguments apply to this type of support that apply to timber.]

The variations in timbered shaft design arise from the possible arrangement of compartments. Many combinations can be imagined, of which Figures 9, 10, 11, 12, 13, and 14 are examples.

The arrangement of compartments shown in Figures 9, 10, 11, and 13 gives the greatest strength. It permits timbering to the best advantage, and avoids the danger underground involved in crossing one compartment to reach another. It is therefore generally adopted. Any other arrangement would obviously be impossible in inclined or combined shafts.

Size of Shafts.—In considering the size of shafts to be installed, many factors are involved. They are in the main:—

It is not to be assumed that these factors have been stated in the order of relative importance. More or less emphasis will be attached to particular factors by different engineers, and under different circumstances. It is not possible to suggest any arbitrary standard for calculating their relative weight, and they are so interdependent as to preclude separate discussion. The usual result is a compromise between the demands of all.

Certain factors, however, dictate a minimum position, which may be considered as a datum from which to start consideration.

First, a winding engine, in order to work with any economy, must be balanced, that is, a descending empty skip or cage must assist in pulling up a loaded one. Therefore, except in mines of very small output, at least two compartments must be made for hoisting purposes. Water has to be pumped from most mines, escape-ways are necessary, together with room for wires and air-pipes, so that at least one more compartment must be provided for these objects. We have thus three compartments as a sound minimum for any shaft where more than trivial output is required.

Second, there is a certain minimum size of shaft excavation below which there is very little economy in actual rock-breaking.[*] In too confined a space, holes cannot be placed to advantage for the blast, men cannot get round expeditiously, and spoil cannot be handled readily. The writer's own experience leads him to believe that, in so far as rock-breaking is concerned, to sink a shaft fourteen to sixteen feet long by six to seven feet wide outside the timbers, is as cheap as to drive any smaller size within the realm of consideration, and is more rapid. This size of excavation permits of three compartments, each about four to five feet inside the timbers.

[Footnote *: Notes on the cost of shafts in various regions which have been personally collected show a remarkable decrease in the cost per cubic foot of material excavated with increased size of shaft. Variations in skill, in economic conditions, and in method of accounting make data regarding different shafts of doubtful value, but the following are of interest:—

In Australia, eight shafts between 10 and 11 feet long by 4 to 5 feet wide cost an average of $1.20 per cubic foot of material excavated. Six shafts 13 to 14 feet long by 4 to 5 feet wide cost an average of $0.95 per cubic foot; seven shafts 14 to 16 feet long and 5 to 7 feet wide cost an average of $0.82 per cubic foot. In South Africa, eleven shafts 18 to 19 feet long by 7 to 8 feet wide cost an average of $0.82 per cubic foot; five shafts 21 to 25 feet long by 8 feet wide, cost $0.74; and seven shafts 28 feet by 8 feet cost $0.60 per cubic foot.]

The cost of timber, it is true, is a factor of the size of shaft, but the labor of timbering does not increase in the same ratio. In any event, the cost of timber is only about 15% of the actual shaft cost, even in localities of extremely high prices.

Third, three reasons are rapidly making the self-dumping skip the almost universal shaft-vehicle, instead of the old cage for cars. First, there is a great economy in labor for loading into and discharging from a shaft; second, there is more rapid despatch and discharge and therefore a larger number of possible trips; third, shaft-haulage is then independent of delays in arrival of cars at stations, while tramming can be done at any time and shaft-haulage can be concentrated into certain hours. Cages to carry mine cars and handle the same load as a skip must either be big enough to take two cars, which compels a much larger shaft than is necessary with skips, or they must be double-decked, which renders loading arrangements underground costly to install and expensive to work. For all these reasons, cages can be justified only on metal mines of such small tonnage that time is no consideration and where the saving of men is not to be effected. In compartments of the minimum size mentioned above (four to five feet either way) a skip with a capacity of from two to five tons can be installed, although from two to three tons is the present rule. Lighter loads than this involve more trips, and thus less hourly capacity, and, on the other hand, heavier loads require more costly engines. This matter is further discussed under "Haulage Appliances."

We have therefore as the economic minimum a shaft of three compartments (Fig. 9), each four to five feet square. When the maximum tonnage is wanted from such a shaft at the least operating cost, it should be equipped with loading bins and skips.

The output capacity of shafts of this size and equipment will depend in a major degree upon the engine employed, and in a less degree upon the hauling depth. The reason why depth is a subsidiary factor is that the rapidity with which a load can be drawn is not wholly a factor of depth. The time consumed in hoisting is partially expended in loading, in acceleration and retardation of the engine, and in discharge of the load. These factors are constant for any depth, and extra distance is therefore accomplished at full speed of the engine.

Vertical shafts will, other things being equal, have greater capacity than inclines, as winding will be much faster and length of haul less for same depth. Since engines have, however, a great tractive ability on inclines, by an increase in the size of skip it is usually possible partially to equalize matters. Therefore the size of inclines for the same output need not differ materially from vertical shafts.

The maximum capacity of a shaft whose equipment is of the character and size given above, will, as stated, decrease somewhat with extension in depth of the haulage horizon. At 500 feet, such a shaft if vertical could produce 70 to 80 tons per hour comfortably with an engine whose winding speed was 700 feet per minute. As men and material other than ore have to be handled in and out of the mine, and shaft-sinking has to be attended to, the winding engine cannot be employed all the time on ore. Twelve hours of actual daily ore-winding are all that can be expected without auxiliary help. This represents a capacity from such a depth of 800 to 1,000 tons per day. A similar shaft, under ordinary working conditions, with an engine speed of 2,000 feet per minute, should from, say, 3,000 feet have a capacity of about 400 to 600 tons daily.

It is desirable to inquire at what stages the size of shaft should logically be enlarged in order to attain greater capacity. A considerable measure of increase can be obtained by relieving the main hoisting engine of all or part of its collateral duties. Where the pumping machinery is not elaborate, it is often possible to get a small single winding compartment into the gangway without materially increasing the size of the shaft if the haulage compartments be made somewhat narrower (Fig. 10). Such a compartment would be operated by an auxiliary engine for sinking, handling tools and material, and assisting in handling men. If this arrangement can be effected, the productive time of the main engine can be expanded to about twenty hours with an addition of about two-thirds to the output.

Where the exigencies of pump and gangway require more than two and one-half feet of shaft length, the next stage of expansion becomes four full-sized compartments (Fig. 11). By thus enlarging the auxiliary winding space, some assistance may be given to ore-haulage in case of necessity. The mine whose output demands such haulage provisions can usually stand another foot of width to the shaft, so that the dimensions come to about 21 feet to 22 feet by 7 feet to 8 feet outside the timbers. Such a shaft, with three- to four-ton skips and an appropriate engine, will handle up to 250 tons per hour from a depth of 1,000 feet.

The next logical step in advance is the shaft of five compartments with four full-sized haulage ways (Fig. 13), each of greater size than in the above instance. In this case, the auxiliary engine becomes a balanced one, and can be employed part of the time upon ore-haulage. Such a shaft will be about 26 feet to 28 feet long by 8 feet wide outside the timbers, when provision is made for one gangway. The capacity of such shafts can be up to 4,000 tons a day, depending on the depth and engine. When very large quantities of water are to be dealt with and rod-driven pumps to be used, two pumping compartments are sometimes necessary, but other forms of pumps do not require more than one compartment,—an additional reason for their use.

For depths greater than 3,000 feet, other factors come into play. Ventilation questions become of more import. The mechanical problems on engines and ropes become involved, and their sum-effect is to demand much increased size and a greater number of compartments. The shafts at Johannesburg intended as outlets for workings 5,000 feet deep are as much as 46 feet by 9 feet outside timbers.

It is not purposed to go into details as to sinking methods or timbering. While important matters, they would unduly prolong this discussion. Besides, a multitude of treatises exist on these subjects and cover all the minutiæ of such work.

Speed of Sinking.—Mines may be divided into two cases,—those being developed only, and those being operated as well as developed. In the former, the entrance into production is usually dependent upon the speed at which the shaft is sunk. Until the mine is earning profits, there is a loss of interest on the capital involved, which, in ninety-nine instances out of a hundred, warrants any reasonable extra expenditure to induce more rapid progress. In the case of mines in operation, the volume of ore available to treatment or valuation is generally dependent to a great degree upon the rapidity of the extension of workings in depth. It will be demonstrated later that, both from a financial and a technical standpoint, the maximum development is the right one and that unremitting extension in depth is not only justifiable but necessary.

Speed under special conditions or over short periods has a more romantic than practical interest, outside of its value as a stimulant to emulation. The thing that counts is the speed which can be maintained over the year. Rapidity of sinking depends mainly on:—

The delays incident to general carrying of ore and men are such that the use of the main haulage engine for shaft-sinking is practically impossible, except on mines with small tonnage output. Even with a separate winch or auxiliary winding-engine, delays are unavoidable in a working shaft, especially as it usually has more water to contend with than one not in use for operating the mine. The writer's own impression is that an average of 40 feet per month is the maximum possibility for year in and out sinking under such conditions. In fact, few going mines manage more than 400 feet a year. In cases of clean shaft-sinking, where every energy is bent to speed, 150 feet per month have been averaged for many months. Special cases have occurred where as much as 213 feet have been achieved in a single month. With ordinary conditions, 1,200 feet in a year is very good work. Rock awkward to break, and water especially, lowers the rate of progress very materially. Further reference to speed will be found in the chapter on "Drilling Methods."

Tunnel Entry.—The alternative of entry to a mine by tunnel is usually not a question of topography altogether, but, like everything else in mining science, has to be tempered to meet the capital available and the expenditure warranted by the value showing.

In the initial prospecting of a mine, tunnels are occasionally overdone by prospectors. Often more would be proved by a few inclines. As the pioneer has to rely upon his right arm for hoisting and drainage, the tunnel offers great temptations, even when it is long and gains but little depth. At a more advanced stage of development, the saving of capital outlay on hoisting and pumping equipment, at a time when capital is costly to secure, is often sufficient justification for a tunnel entry. But at the stage where the future working of ore below a tunnel-level must be contemplated, other factors enter. For ore below tunnel-level a shaft becomes necessary, and in cases where a tunnel enters a few hundred feet below the outcrop the shaft should very often extend to the surface, because internal shafts, winding from tunnel-level, require large excavations to make room for the transfer of ore and for winding gear. The latter must be operated by transmitted power, either that of steam, water, electricity, or air. Where power has to be generated on the mine, the saving by the use of direct steam, generated at the winding gear, is very considerable. Moreover, the cost of haulage through a shaft for the extra distance from tunnel-level to the surface is often less than the cost of transferring the ore and removing it through the tunnel. The load once on the winding-engine, the consumption of power is small for the extra distance, and the saving of labor is of consequence. On the other hand, where drainage problems arise, they usually outweigh all other considerations, for whatever the horizon entered by tunnel, the distance from that level to the surface means a saving of water-pumpage against so much head. The accumulation of such constant expense justifies a proportioned capital outlay. In other words, the saving of this extra pumping will annually redeem the cost of a certain amount of tunnel, even though it be used for drainage only.

In order to emphasize the rapidity with which such a saving of constant expense will justify capital outlay, one may tabulate the result of calculations showing the length of tunnel warranted with various hypothetical factors of quantity of water and height of lift eliminated from pumping. In these computations, power is taken at the low rate of $60 per horsepower-year, the cost of tunneling at an average figure of $20 per foot, and the time on the basis of a ten-year life for the mine.

The size of tunnels where ore-extraction is involved depends upon the daily tonnage output required, and the length of haul. The smallest size that can be economically driven and managed is about 6-1/2 feet by 6 feet inside the timbers. Such a tunnel, with single track for a length of 1,000 feet, with one turn-out, permits handling up to 500 tons a day with men and animals. If the distance be longer or the tonnage greater, a double track is required, which necessitates a tunnel at least 8 feet wide by 6-1/2 feet to 7 feet high, inside the timbers.

There are tunnel projects of a much more impressive order than those designed to operate upper levels of mines; that is, long crosscut tunnels designed to drain and operate mines at very considerable depths, such as the Sutro tunnel at Virginia City. The advantage of these tunnels is very great, especially for drainage, and they must be constructed of large size and equipped with appliances for mechanical haulage.