PRINCIPLES OF MINING
Published by the McGraw-Hill Book Company New York Successors to the Book Departments of the McGraw Publishing Company Hill Publishing Company Publishers of Books for Electrical World The Engineering and Mining Journal Engineering Record Power and The Engineer Electric Railway Journal American Machinist Metallurgical and Chemical Engineering
PRINCIPLES OF MINING
VALUATION, ORGANIZATION AND ADMINISTRATION
COPPER, GOLD, LEAD, SILVER, TIN AND ZINC
HERBERT C. HOOVER
Member American Institute of Mining Engineers, Mining and Metallurgical Society of America, Societe des Ingenieurs Civils de France, Fellow Royal Geographical Society, etc.
McGRAW-HILL BOOK COMPANY
239 WEST 39TH STREET, NEW YORK
BOUVERIE STREET, LONDON, E.C.
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.
Valuation of Copper, Gold, Lead, Silver, Tin, and Zinc Lode Mines
Determination of average metal content; sampling, assay plans, calculations of averages, percentage of errors in estimate from sampling.
Mine Valuation (Continued)
Calculation of quantities of ore, and classification of ore in sight.
Mine Valuation (Continued)
Prospective value. Extension in depth; origin and structural character of the deposit; secondary enrichment; development in neighboring mines; depth of exhaustion.
Mine Valuation (Continued)
Recoverable percentage of the gross assay value; price of metals; cost of production.
Mine Valuation (Continued)
Redemption or amortization of capital and interest.
Mine Valuation (Concluded)
Valuation of mines with little or no ore in sight; valuations on second-hand data; general conduct of examinations; reports.
Development of Mines
Entry to the mine; tunnels; vertical, inclined, and combined shafts; location and number of shafts.
Development of Mines (Continued)
Shape and size of shafts; speed of sinking; tunnels.
Development of Mines (Concluded)
Subsidiary development: stations; crosscuts; levels; interval between levels; protection of levels; winzes and rises. Development in the prospecting stage; drilling.
Methods of ore-breaking; underhand stopes; overhand stopes; combined stope. Valuing ore in course of breaking.
Methods of Supporting Excavation
Timbering; filling with waste; filling with broken ore; pillars of ore; artificial pillars; caving system.
Conditions bearing on mine equipment; winding appliances; haulage equipment in shafts; lateral underground transport; transport in stopes.
Mechanical Equipment (Continued)
Drainage: controlling factors; volume and head of water; flexibility; reliability; power conditions; mechanical efficiency; capital outlay. Systems of drainage,—steam pumps, compressed-air pumps, electrical pumps, rod-driven pumps, bailing; comparative value of various systems.
Mechanical Equipment (Concluded)
Machine drilling: power transmission; compressed air vs. electricity; air drills; machine vs. hand drilling. Workshops. Improvement in equipment.
Ratio of Output to the Mine
Determination of possible maximum; limiting factors; cost of equipment; life of the mine; mechanical inefficiency of patchwork plant; overproduction of base metal; security of investment.
Labor efficiency; skill; intelligence; application coordination; contract work; labor unions; real basis of wages.
Accounts and technical data and reports; working costs; division of expenditure; inherent limitations in accuracy of working costs; working cost sheets. General technical data; labor, supplies, power, surveys, sampling, and assaying.
The Amount of Risk in Mining Investments
Risk in valuation of mines; in mines as compared with other commercial enterprises.
The Character, Training, and Obligations of the Mining Engineering Profession
PRINCIPLES OF MINING.
Valuation of Copper, Gold, Lead, Silver, Tin, and Zinc Lode Mines.
DETERMINATION OF AVERAGE METAL CONTENT; SAMPLING, ASSAY PLANS, CALCULATIONS OF AVERAGES, PERCENTAGE OF ERRORS IN ESTIMATE FROM SAMPLING.
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:—
a. The profit that may be won from ore exposed; b. The prospective profit to be derived from extension of the ore beyond exposures; c. The effect of a higher or lower price of metal (except in gold mines); d. 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:—
W = Width in feet of ore sampled. L = Length in feet of ore represented by the sample. D = Depth into the block to which values are assumed to penetrate.
We may also let:—
C = The number of cubic feet per ton of ore. V = Assay value of the sample.
Then WLD/C = tonnage of the prismoid.* V WLD/C = total metal contents.
[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:—
_V(_WLD_/_C_) + _V_1 (_W_1 _L_1 _D_1/_C_) + _V_2 (_W_2 _L_2 _D_2/_C_) ——————————————————————————————————- _WLD_/_C_ + _W_1 _L_1 _D_1/_C_ + _W_2 _L_2 _D_2/_C_ = average value.
This may be reduced to:—
(VWLD) + (V1 W1 L1 D1) + (V2 W2 L2 D2,), etc. ———————————————————————————————- (WLD) + (W1 L1 D1) + (W2 L2 D2), etc.
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:—
(VWL) + (V1 W1 L1) + (V2 W2 L2), etc. —————————————————————————- (WL) + (W1 L1) + (W2 L2), etc.
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:—
(VW) + (V1 W1) + (V2 W2), etc. ———————————————————— W + W1 + W2 , etc.
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 regime 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%.
Mine Valuation (Continued).
CALCULATION OF QUANTITIES OF ORE, AND CLASSIFICATION OF ORE IN SIGHT.
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 formulae 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.
============================================ Number of Weight per Cubic Feet Cubic Foot per Ton of 2000 lb. Antimony 417.50 4.79 Sulphide 285.00 7.01 Arsenical Pyrites 371.87 5.37 Barium Sulphate 278.12 7.19 Calcium: Fluorite 198.75 10.06 Gypsum 145.62 13.73 Calcite 169.37 11.80 Copper 552.50 3.62 Calcopyrite 262.50 7.61 Bornite 321.87 6.21 Malachite 247.50 8.04 Azurite 237.50 8.42 Chrysocolla 132.50 15.09 Iron (Cast) 450.00 4.44 Magnetite 315.62 6.33 Hematite 306.25 6.53 Limonite 237.50 8.42 Pyrite 312.50 6.40 Carbonate 240.62 8.31 Lead 710.62 2.81 Galena 468.75 4.27 Carbonate 406.87 4.81 Manganese Oxide 268.75 6.18 Rhodonite 221.25 9.04 Magnesite 187.50 10.66 Dolomite 178.12 11.23 Quartz 165.62 12.07 Quicksilver 849.75 2.35 Cinnabar 531.25 3.76 Sulphur 127.12 15.74 Tin 459.00 4.35 Oxide 418.75 4.77 Zinc 437.50 4.57 Blende 253.12 7.90 Carbonate 273.12 7.32 Silicate 215.62 9.28 Andesite 165.62 12.07 Granite 162.62 12.30 Diabase 181.25 11.03 Diorite 171.87 11.63 Slates 165.62 12.07 Sandstones 162.50 12.30 Rhyolite 156.25 12.80 ============================================
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:—
Quartz, 96% x 12.07 = 11.58 Iron Pyrite, 4% x 6.40 = .25 ——- 11.83 cubic feet per ton.
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:—
Positive Ore Ore exposed on four sides in blocks of a size Ore Developed / variously prescribed. Ore Blocked Out Ore exposed on three sides within reasonable distance of each other. Probable Ore Ore Developing / Ore exposed on two sides.
Possible Ore The whole or a part of the ore below the Ore Expectant / lowest level or beyond the range of vision.
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.
Proved Ore Ore where there is practically no risk of failure of continuity.
Probable Ore Ore where there is some risk, yet warrantable justification for assumption of continuity.
Prospective Ore Ore which cannot be included in the above classes, nor definitely known or stated in any terms of tonnage.
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.
Mine Valuation (Continued).
PROSPECTIVE VALUE.[*] EXTENSION IN DEPTH; ORIGIN AND STRUCTURAL CHARACTER OF THE DEPOSIT; SECONDARY ENRICHMENT; DEVELOPMENT IN NEIGHBORING MINES; DEPTH OF EXHAUSTION.
[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:— (a) Their solubility, and therefore susceptibility to replacement. (b) Their influence as a precipitating agent on solutions. (c) Their influence as a source of metal itself. (d) 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." (e) 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 reequipment. 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 preeminently, 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 reenforced 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.
Mine Valuation (Continued).
RECOVERABLE PERCENTAGE OF THE GROSS ASSAY VALUE; PRICE OF METALS; COST OF PRODUCTION.
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 L12 12s. 4d., L13 3s. 7d., and L17 7s. 0d. respectively; zinc, L17 14s. 10d., L19 3s. 8d., and L23 3s. 0d.; and standard copper, L48 16s. 0d., L59 10s. 0d., and L65 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."]
========================================================================== Lead Spelter Copper Tin Silver - London N.Y. Lon. N.Y. Lon. N.Y. Lon. N.Y. Lon. N.Y. Ton Pound Ton Pound Ton Pound Ton Pound Per oz. Per oz. - - - - - - Basic Price L11. $.035 L17 $.040 L52 $.115 L100 $.220 22d. $.44 Normal Price 13.5 .043 21 .050 65 .140 130 .290 26 .52 ==========================================================================
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.