~Sampling.~--A further consideration in favour of the larger charges is the matter of sampling. In preparing his ore, the student should ask himself what reasonable expectation he has that the portion he puts in the furnace will be of average richness. The larger charges are likely to be nearer than the smaller ones to the average of the parcel of ore from which they are taken. In explanation of this, let us suppose a large heap of 5-dwt. ore, in sand of the coarseness of full-stops, and containing all its gold in particles of 1 milligram, as uniformly distributed as care and labour in the mixing can accomplish. Such a heap could not possibly occur in practice, but it will serve for purposes of illustration. Now, one ton of the sand, however taken, would contain appreciably the same quantity of gold as any other ton. For a ton would contain about 8000 particles of gold; and even if two separate tons differed by as much as 100 particles (which they are just likely to do), this would mean only a difference of 1 or 2 grains to the ton. On the other hand, two portions of 14 lbs., which should contain on the average 50 particles of gold, are likely enough to differ by 10 particles, and this, calculated on a ton, means a difference of 1 dwt. It is easy to see that something like this should be true; for on calculating the 14-lb. lot up to a ton, the deviation from the average, whatever it may be, is multiplied by 160; whereas, if the ton were made up by adding 14-lb. lot to 14-lb. lot, up to the full tale, then a large proportion of the errors (some being in excess and some in defect) would neutralise each other. An average which is practically true when dealing with thousands, and perhaps sufficiently exact with hundreds, would be merely misleading when applied to tens and units. Reasonable safety in sampling, then, is dependent largely on the number of particles of gold in the charge taken, and the risk of an abnormal result is less, the larger the charge taken.