With ores of tin, silver, and gold, the result is stated as so many cwts., lbs., or ozs., in the ton. With dressed tin ores as they are sent to the smelter, the produce is given in cwts. and quarters to the ton. The corresponding percentage may be obtained by multiplying by five; or, inversely, if the percentage is given, the produce may be got by dividing by five. A produce of 13-1/2 equals a percentage of 13.5×5 = 67.5; and a percentage of 70.0 equals a produce of 70/5 = 14. With tin ores as raised (in which the percentage is small) the reduction must be carried to pounds per ton. One per cent. equals 22.4 lbs. to the ton; consequently, if we multiply the percentage by 22.4, the produce will be given. Thus, if an ore contains 6.7 per cent. of oxide of tin, the produce is 6.7×22.4 = 150 lbs. (or 1 cwt., 1 quarter, and 10 lbs.) to the ton. With gold and silver ores, the proportion of precious metal is small, and it is necessary to carry the reduction to ozs. and dwts. to the ton; and since gold and silver are sold by troy weight, whilst the ton is avoirdupois, it is of importance to remember that the ounces in the two systems are not the same. A ton contains 15,680,000 grains, which equal 653,333.3 dwts. or 32,666.6 ozs. (troy). The following rules are useful:-- To get ozs. (troy) per ton, multiply parts per 100,000 by 0.327; To get dwts. per ton, multiply parts per 100,000 by 6.53; To get grains per ton, multiply parts per 100,000 by 156.8. Where liquids are being assayed, cubic centimetres are held to be equivalent to grams, and the usual method of statement is, "so many parts by weight in so many by measure." Where the statement is made as grams per litre or grains per gallon, there can be no doubt as to what is meant; and even if it be expressed in parts per 100,000, parts by weight in a measured volume must be understood unless the contrary is expressly stated. In some cases, where the density of the solution differs greatly from that of water, the percentage by weight may be given; and in others, mixtures of two or more liquids, the percentages may be given by volume or by weight; as so many c.c. in 100 c.c., or as so many grams in 100 grams, or even as so many grams in 100 c.c. In such cases it must be distinctly shown which method of statement is adopted. One grain per gallon means 1 grain in 70,000 grain-measures, or one part in 70,000. Dividing by 7 and multiplying by 10 will convert grains per gallon into parts per 100,000. Inversely, dividing by 10 and multiplying by 7, will convert parts per 100,000 into grains per gallon. Grams per litre are parts per 1000; multiplying by 100 will give parts per 100,000, and multiplying by 70 will give grains per gallon.