Mine Valuation (Continued).

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

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

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

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

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

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

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

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

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

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

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

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

CLASSIFICATION OF ORE IN SIGHT.

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

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

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

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

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

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

They are:—

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

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

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

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