_In the case of solids_, the whole mass must be crushed, and, if not already of fairly uniform quality, mixed, before sampling can take place. Most of the material which a sampler is called upon to deal with, is, however, in a more or less divided state and fairly uniform. In practice it is assumed that 5 per cent. of the whole (= 1/20th), if taken in portions of equal weight and at frequent and regular intervals, will represent the mass from which it was taken. Taking a heap of ore, A, and selecting one out of every twenty spade-, bag-, barrow-, or wagon-fuls, according to the quantity of stuff in the heap, there is obtained a second heap, B, containing one-twentieth of the stuff of the heap A. If we crush the stuff in B until this heap contains approximately the same number of stones as A did--which means, crushing every stone in B into about twenty pieces--B will become the counterpart of A. Selecting in the same manner 5 per cent. of B, there is got a third heap, C. This alternate reduction and pulverising must be carried on until a sample of suitable size is obtained. This may be expressed very clearly thus:-- A = 1000 tons of rocks and lumpy ore. B = 50 " " rough stones, 1/20th of A. C = 2.5 " " small stones, 1/20th of B. D = 0.125 " " coarse powder, 1/20th of C. [Illustration: FIG. 1. CONE PARTLY REDUCED CONE PLAN OF FRUSTRUM DIVIDED. ELEVATION OF FRUSTRUM DIVIDED.] If the material to be sampled is already a dry powder, 5 per cent. of it should be heaped in a cone; each lot being added on the apex of the cone already formed, so that it may distribute itself by falling evenly in all directions. When the cone is completed, convert it into a low frustrum of a cone by drawing stuff uniformly and in a direct line from the centre to the circumference. Draw two diameters at right angles to each other, and reserving any two alternate quarters, reject the others. Mix; and form another cone, and proceed until a sample is got of the bulk required. This is the usual plan, and all samples should be treated in this way when the stuff is fine enough to fall evenly down the sides of a cone. Samples as they reach the assay office are seldom in a fit state for the work of the assayer; they are generally too coarse, and ought always to be more than he wants for any particular determination. The portion he requires should never be taken at hap-hazard; the sample must be reduced systematically to the quantity required. 1. _If the sample is a liquid:_ it is sufficient to shake the bottle, and take out a measured or weighed quantity for the assay. 2. _If a liquid with a solid in suspension:_ measure the whole of it. Filter. Make up the filtrate with the wash-water or water to the original bulk. Assay it. Dry and weigh the residue, and make a separate assay of it.