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.

Mining Guide

Principles of Mining

Mine Valuation

Prospective value

Price of Metals

Amortization of Capital

Valuation of Mines

Development of Mines

Shape of Mining Shafts

Subsidiary Development

Methods of Ore-Breaking

Methods of Supporting Excavation

Mechanical Equipment

Drainage-Controlling Factors

Machine Drilling

Ratio of Output to the Mine

Labor Efficiency

Working Costs

Administrative Reports

Amount of Risk in Mining Investments

Mining Engineering

Principles of Mining

Mine Valuation

Prospective value

Price of Metals

Amortization of Capital

Valuation of Mines

Development of Mines

Shape of Mining Shafts

Subsidiary Development

Methods of Ore-Breaking

Methods of Supporting Excavation

Mechanical Equipment

Drainage-Controlling Factors

Machine Drilling

Ratio of Output to the Mine

Labor Efficiency

Working Costs

Administrative Reports

Amount of Risk in Mining Investments

Mining Engineering