The Character, Training, and Obligations of the Mining Engineering
Profession
Index
PRINCIPLES OF MINING.
CHAPTER I.
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_, _W_1, _V_, _V_1 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_) + (_V_1 _W_1 _L_1 _D_1) + (_V_2 _W_2 _L_2 _D_2,), etc.
---------------------------------------------------------------
(_WLD_) + (_W_1 _L_1 _D_1) + (_W_2 _L_2 _D_2), 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_, _D_1, _D_2
may be considered as equal and the equation becomes:--
(_VWL_) + (_V_1 _W_1 _L_1) + (_V_2 _W_2 _L_2), etc.
---------------------------------------------------
(_WL_) + (_W_1 _L_1) + (_W_2 _L_2), 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_, _L_1, _L_2 becoming thus
equal can in such case be eliminated, and the equation becomes:--
(_VW_) + (_V_1 _W_1) + (_V_2 _W_2), etc.
----------------------------------------
_W_ + _W_1 + _W_2 , 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 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_).
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 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.
============================================
| | 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.
[Illustration: Fig. 1.--Longitudinal section of a mine, showing
classification of the exposed ore. Scale, 400 feet = 1 inch.]
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:--
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.
CHAPTER III.
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 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_).
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 £12 12_s._ 4_d._, £13 3_s._
7_d._, and £17 7_s._ 0_d._ respectively; zinc, £17 14_s._ 10_d._,
£19 3_s._ 8_d._, and £23 3_s._ 0_d._; and standard copper, £48 16_s._
0_d._, £59 10_s._ 0_d._, and £65 7_s._ 0_d._ 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 | £11. |$.035|£17 |$.040|£52 |$.115|£100|$.220| 22_d._|$.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.
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_).
REDEMPTION OR AMORTIZATION OF CAPITAL AND INTEREST.
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%.
=======================================================
Years | 5% | 6% | 7% | 8% | 9% | 10%
-------|-------|-------|-------|-------|-------|-------
1 | .95 | .94 | .93 | .92 | .92 | .91
2 | 1.85 | 1.82 | 1.78 | 1.75 | 1.72 | 1.69
3 | 2.70 | 2.63 | 2.56 | 2.50 | 2.44 | 2.38
4 | 3.50 | 3.38 | 3.27 | 3.17 | 3.07 | 2.98
5 | 4.26 | 4.09 | 3.93 | 3.78 | 3.64 | 3.51
6 | 4.98 | 4.74 | 4.53 | 4.33 | 4.15 | 3.99
7 | 5.66 | 5.36 | 5.09 | 4.84 | 4.62 | 4.41
8 | 6.31 | 5.93 | 5.60 | 5.30 | 5.04 | 4.79
9 | 6.92 | 6.47 | 6.08 | 5.73 | 5.42 | 5.14
10 | 7.50 | 6.98 | 6.52 | 6.12 | 5.77 | 5.45
| | | | | |
11 | 8.05 | 7.45 | 6.94 | 6.49 | 6.09 | 5.74
12 | 8.58 | 7.90 | 7.32 | 6.82 | 6.39 | 6.00
13 | 9.08 | 8.32 | 7.68 | 7.13 | 6.66 | 6.24
14 | 9.55 | 8.72 | 8.02 | 7.42 | 6.91 | 6.46
15 | 10.00 | 9.09 | 8.34 | 7.79 | 7.14 | 6.67
16 | 10.43 | 9.45 | 8.63 | 7.95 | 7.36 | 6.86
17 | 10.85 | 9.78 | 8.91 | 8.18 | 7.56 | 7.03
18 | 11.24 | 10.10 | 9.17 | 8.40 | 7.75 | 7.19
19 | 11.61 | 10.40 | 9.42 | 8.61 | 7.93 | 7.34
20 | 11.96 | 10.68 | 9.65 | 8.80 | 8.09 | 7.49
| | | | | |
21 | 12.30 | 10.95 | 9.87 | 8.99 | 8.24 | 7.62
22 | 12.62 | 11.21 | 10.08 | 9.16 | 8.39 | 7.74
23 | 12.93 | 11.45 | 10.28 | 9.32 | 8.52 | 7.85
24 | 13.23 | 11.68 | 10.46 | 9.47 | 8.65 | 7.96
25 | 13.51 | 11.90 | 10.64 | 9.61 | 8.77 | 8.06
26 | 13.78 | 12.11 | 10.80 | 9.75 | 8.88 | 8.16
27 | 14.04 | 12.31 | 10.96 | 9.88 | 8.99 | 8.25
28 | 14.28 | 12.50 | 11.11 | 10.00 | 9.09 | 8.33
29 | 14.52 | 12.68 | 11.25 | 10.11 | 9.18 | 8.41
30 | 14.74 | 12.85 | 11.38 | 10.22 | 9.27 | 8.49
| | | | | |
31 | 14.96 | 13.01 | 11.51 | 10.32 | 9.36 | 8.56
32 | 15.16 | 13.17 | 11.63 | 10.42 | 9.44 | 8.62
33 | 15.36 | 13.31 | 11.75 | 10.51 | 9.51 | 8.69
34 | 15.55 | 13.46 | 11.86 | 10.60 | 9.59 | 8.75
35 | 15.73 | 13.59 | 11.96 | 10.67 | 9.65 | 8.80
36 | 15.90 | 13.72 | 12.06 | 10.76 | 9.72 | 8.86
37 | 16.07 | 13.84 | 12.16 | 10.84 | 9.78 | 8.91
38 | 16.22 | 13.96 | 12.25 | 10.91 | 9.84 | 8.96
39 | 16.38 | 14.07 | 12.34 | 10.98 | 9.89 | 9.00
40 | 16.52 | 14.18 | 12.42 | 11.05 | 9.95 | 9.05
=======================================================
Condensed from Inwood's Tables.
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 --%.
===================================
Years | 4% | 5% | 6% | 7%
------|------|------|------|-------
1 | .961 | .952 | .943 | .934
2 | .924 | .907 | .890 | .873
3 | .889 | .864 | .840 | .816
4 | .854 | .823 | .792 | .763
5 | .821 | .783 | .747 | .713
6 | .790 | .746 | .705 | .666
7 | .760 | .711 | .665 | .623
8 | .731 | .677 | .627 | .582
9 | .702 | .645 | .592 | .544
10 | .675 | .614 | .558 | .508
| | | |
11 | .649 | .585 | .527 | .475
12 | .625 | .557 | .497 | .444
13 | .600 | .530 | .469 | .415
14 | .577 | .505 | .442 | .388
15 | .555 | .481 | .417 | .362
16 | .534 | .458 | .394 | .339
17 | .513 | .436 | .371 | .316
18 | .494 | .415 | .350 | .296
19 | .475 | .396 | .330 | .276
20 | .456 | .377 | .311 | .258
| | | |
21 | .439 | .359 | .294 | .241
22 | .422 | .342 | .277 | .266
23 | .406 | .325 | .262 | .211
24 | .390 | .310 | .247 | .197
25 | .375 | .295 | .233 | .184
26 | .361 | .281 | .220 | .172
27 | .347 | .268 | .207 | .161
28 | .333 | .255 | .196 | .150
29 | .321 | .243 | .184 | .140
30 | .308 | .231 | .174 | .131
| | | |
31 | .296 | .220 | .164 | .123
32 | .285 | .210 | .155 | .115
33 | .274 | .200 | .146 | .107
34 | .263 | .190 | .138 | .100
35 | .253 | .181 | .130 | .094
36 | .244 | .172 | .123 | .087
37 | .234 | .164 | .116 | .082
38 | .225 | .156 | .109 | .076
39 | .216 | .149 | .103 | .071
40 | .208 | .142 | .097 | .067
===================================
Condensed from Inwood's Tables.
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.
===========================================================================
Annual | Number of years of life required to yield--% interest, and in
Rate of | addition to furnish annual instalments which, if reinvested at
Dividend.| 4% will return the original investment at the end of the period.
---------|-----------------------------------------------------------------
% | 5% | 6% | 7% | 8% | 9% | 10%
| | | | | |
6 | 41.0 | | | | |
7 | 28.0 | 41.0 | | | |
8 | 21.6 | 28.0 | 41.0 | | |
9 | 17.7 | 21.6 | 28.0 | 41.0 | |
10 | 15.0 | 17.7 | 21.6 | 28.0 | 41.0 |
| | | | | |
11 | 13.0 | 15.0 | 17.7 | 21.6 | 28.0 | 41.0
12 | 11.5 | 13.0 | 15.0 | 17.7 | 21.6 | 28.0
13 | 10.3 | 11.5 | 13.0 | 15.0 | 17.7 | 21.6
14 | 9.4 | 10.3 | 11.5 | 13.0 | 15.0 | 17.7
15 | 8.6 | 9.4 | 10.3 | 11.5 | 13.0 | 15.0
| | | | | |
16 | 7.9 | 8.6 | 9.4 | 10.3 | 11.5 | 13.0
17 | 7.3 | 7.9 | 8.6 | 9.4 | 10.3 | 11.5
18 | 6.8 | 7.3 | 7.9 | 8.6 | 9.4 | 10.3
19 | 6.4 | 6.8 | 7.3 | 7.9 | 8.6 | 9.4
20 | 6.0 | 6.4 | 6.8 | 7.3 | 7.9 | 8.6
| | | | | |
21 | 5.7 | 6.0 | 6.4 | 6.8 | 7.3 | 7.9
22 | 5.4 | 5.7 | 6.0 | 6.4 | 6.8 | 7.3
23 | 5.1 | 5.4 | 5.7 | 6.0 | 6.4 | 6.8
24 | 4.9 | 5.1 | 5.4 | 5.7 | 6.0 | 6.4
25 | 4.7 | 4.9 | 5.1 | 5.4 | 5.7 | 6.0
| | | | | |
26 | 4.5 | 4.7 | 4.9 | 5.1 | 5.4 | 5.7
27 | 4.3 | 4.5 | 4.7 | 4.9 | 5.1 | 5.4
28 | 4.1 | 4.3 | 4.5 | 4.7 | 4.9 | 5.1
29 | 3.9 | 4.1 | 4.3 | 4.5 | 4.7 | 4.9
30 | 3.8 | 3.9 | 4.1 | 4.3 | 4.5 | 4.7
===========================================================================
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_).
VALUATION OF MINES WITH LITTLE OR NO ORE IN SIGHT; VALUATIONS ON
SECOND-HAND DATA; GENERAL CONDUCT OF EXAMINATIONS; REPORTS.
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 12_s_.
7_d_. 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 4_s_. 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.
ENTRY TO THE MINE; TUNNELS; VERTICAL, INCLINED, AND COMBINED SHAFTS;
LOCATION AND NUMBER OF SHAFTS.
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:--
a. Degree of dip of the deposit.
b. Output of ore to be provided for.
c. Depth at which the deposit is to be attacked.
d. Boundaries of the property.
e. Surface topography.
f. Cost.
g. Operating efficiency.
h. Prospects of the mine.
[Illustration: Fig. 2.--Showing arrangement of the bend in combined
shafts.]
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).
[Illustration: Fig. 3.--Longitudinal section showing "deep level"
project arising from dip of ore-body through end-line.]
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.
Case I. Deposits where topographic conditions permit the
alternatives of shaft or tunnel.
Case II. Vertical or horizontal deposits, the only practical
means of attaining which is by a vertical shaft.
Case III. Inclined deposits to be worked from near the surface.
There are in such instances the alternatives of either
a vertical or an inclined shaft.
Case IV. Inclined deposits which must be attacked in depth,
that is, deep-level projects. There are the alternatives
of a compound shaft or of a vertical shaft, and
in some cases of an incline from the surface.
MINES TO GREAT DEPTHS.
Case V. Vertical or horizontal deposits, the only way of reaching
which is by a vertical shaft.
Case VI. Inclined deposits. In such cases the alternatives are
a vertical or a compound shaft.
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).
[Illustration: Fig. 4.--Cross-sections showing entry to vertical
or horizontal deposits. Case II.]
[Illustration: Fig. 5.--Cross-section showing alternative shafts
to inclined deposit to be worked from surface. Case III.]
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.
Dip of | Depth of | Length of |No. of Crosscuts| Total Length
Deposit from | Vertical | Incline | Required from | of Crosscuts,
Horizontal | Shaft | Required | V Shaft | Feet
-------------|-------------|-------------|----------------|---------------
80° | 1,500 | 1,522 | 11 | 859
70° | 1,500 | 1,595 | 12 | 1,911
60° | 1,500 | 1,732 | 13 | 3,247
50° | 1,500 | 1,058 | 15 | 5,389
40° | 1,500 | 2,334 | 18 | 8,038
30° | 1,500 | 3,000 | 23 | 16,237
==========================================================================
Cost of |Cost Vertical| Total Cost | Cost of Incline|Cost of Incline
Crosscuts $20| Shaft $75 | of Vertical | $75 per Foot | $100 per Foot
per Foot | per Foot |and Crosscuts| |
-------------|-------------|-------------|----------------|---------------
$17,180 | $112,500 | $129,680 | $114,150 | $152,200
38,220 | 112,500 | 150,720 | 118,625 | 159,500
64,940 | 112,500 | 177,440 | 129,900 | 172,230
107,780 | 112,500 | 220,280 | 114,850 | 195,800
178,760 | 112,500 | 291,260 | 175,050 | 233,400
324,740 | 112,500 | 437,240 | 225,000 | 300,000
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.