A fine sand, such as would pass a 40 sieve but be retained on a 60 sieve, would be fairly represented by particles one-quarter of a millimetre in diameter. This being five times coarser, to contain the same number of particles must be 125 times (the cube of 5) as heavy; therefore 125 grams of it can be taken with the same degree of safety as 1 gram of the finer powder. Of such a sand about this weight should be taken and reduced to the finer powder. If the ore were in coarse sand, say in particles 1 millimetre in diameter, this would be four times as coarse as that last considered, and we should have to take 64 times as much of it: 64 times 125 grams is 8 kilos, or say roughly from 15 to 20 lbs. This should be crushed to the finer size and mixed; then from 100 to 150 grams should be taken and ground to the finest powder.
There is, however, a reason why, on the coarser stuff, a smaller proportion may safely be used. This becomes more evident if we consider a still coarser sample. A heap of ore in stones about 2 inches across would be 50 times coarser than the sand, and an equivalent sample would need to be 125,000 times heavier; this would amount to about 1000 tons. Experienced samplers would say that under such conditions so large a sample was hardly necessary.
This is because I have assumed in the calculations that the grains of copper pyrites, for example, were all copper pyrites and the particles of gangue were free from copper. This would be true or nearly so for the very fine powder, but far from true in the case of the ore heap. In the heap probably few of the stones would be pure ore and still fewer would be free from copper. The stones would differ among themselves in their copper contents only within certain comparatively narrow limits. And it is evident that, if replacing one stone by another, instead of resulting in the gain or loss of all the copper one or other contained, merely affected the result to one-tenth of this amount, then a sample of 1-100th of the weight (say 10 tons) would be equally safe.
It should be remembered, however, that while the man who samples on a large scale can safely and properly reduce the size of his samples on this account, yet the principle is one which counts less and less as the stuff becomes more finely divided, and ought to be ignored in the working down of the smaller samples which come to the assayer.
FOOTNOTES:
[126] The 10 in 20 multiplied by 10 = 100 in 200.
[127] Multiply the errors for 100 by the square root of 10.
[128] Multiply the errors for 100 by the square root of 6990.
[129] Sp. Gr. 5.8. Silver 60 per cent.
[130] Taking 28 as the limit of variation on 100.