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CHAPTER II.
ОглавлениеMine 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.
| Weight per Cubic Foot | Number of Cubic Feet 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% × | 12.07 | = | 11.58 | |
| Iron Pyrite, | 4% × | 6.40 | = | .25 | |
| 11.83 | cubic feet per ton. |
Most engineers, to compensate porosity, would allow twelve to thirteen cubic feet per ton.
