Mine Valuation

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 formulć 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.