The likelihood of two very faulty assays being concordant is remote; but with very important work, as in selling parcels of ore, even this risk should be avoided, as concordance in these cases is demanded in the reports of two or more assayers. The following actual reports on a disputed assay will illustrate this: (a) 5 ozs. 1 dwt.; (b) 5 ozs. 10 dwts. 12 grains; (c) 5 ozs. 11 dwts.; (c) 5 ozs. 11 dwts. 12 grs. The mean result of several assays, unless there be some fault in the method, will be very fairly exact; and individual assays, with an uncertainty of 1 in 20, may, by repetition, have this reduced to 1 in 100 or less. ~Assay Tons, etc.~--Having decided on taking a larger or smaller portion, the exact quantity to be used will be either some round number of grams, such as 50 or 100, easily calculable into percentage; or it will be that known as the "Assay Ton" (see page 13) or some simple multiple or fraction of it, which is easily calculable into ounces. The reports, too, are at least as often made as ounces in the short ton of 2000 lbs., as on the more orthodox ton of 2240 lbs. Now the short ton is equal to 29,166.6 troy ounces; and the corresponding "assay ton" is got from it by replacing ounces by milligrams. The advantage of its use is that if one assay ton of ore has been taken, the number of milligrams of gold obtained is also the number of ounces of gold in a ton of the ore, and there is absolutely no calculation. Even if half an assay ton has been taken the only calculation needed is multiplying the milligrams by two. On the other hand with a charge of two assay tons the milligrams need halving. Where weights of this kind (_i.e._, assay tons) are not at hand they may be easily extemporised out of buttons of tin or some suitable metal, and it is better to do this than to array out the grams and its fractions at each weighing. The sets of "assay tons," however, are easily purchased. As stated on page 13, the assay ton for 2240 lbs. is 32.6667 grams; and for the short ton, 29.1667 grams. If, however, the round number of grams be used and the result brought by calculation to the produce on 100 grams, the conversion to ounces to the ton may be quickly effected by the help of the table on page 107. As this table only deals with the ton of 2240 lbs., it is supplemented here by a shortened one dealing only with _the produce of 100 grams_ and stating the result in _ounces troy to the short ton of 2000 lbs_. ~Estimation of Small Quantities of Gold.~--_By the Balance._ In estimating minute quantities of gold there are one or two points, of importance to an assayer only in this assay, where they will often allow one to avoid the working of inconveniently large charges. One of these is known as "weighing by the method of vibrations."