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. | |