To mining men the word "assaying" conveys a sufficiently clear meaning, but it is difficult to define. Some writers limit it to the determination of silver and gold, and others imagine that it has only to do with "furnace-work." These limitations are not recognised in practice. In fact, assaying is becoming wider in its scope, and the distinction between "assayers" and "analysts" will in time be difficult to detect. We have endeavoured rather to give what will be of use to the assayer than to cover the ground within the limits of a faulty definition. At first our intention was to supply a description of those substances only which have a commercial value, but on consideration we have added short accounts of the rarer elements, since they are frequently met with, and occasionally affect the accuracy of an assay. Under the more important methods we have given the results of a series of experiments showing the effect of varying conditions on the accuracy of the process. Such experiments are often made by assayers, but seldom recorded. Statements like those generally made--that "this or that substance interferes"--are insufficient. It is necessary to know under what conditions and to what extent. Students learning any particular process cannot do better than repeat such a series of experiments. By this means they will, at the same time, acquire the skill necessary for performing an assay and a confidence in their results based upon work under different conditions. The electrolytic method of copper assaying given under _Copper_ is a modification of Luckow's; it was introduced by us into the offices of the Rio Tinto Copper Company, and has been in use for many years with success. This modification is now employed in copper-works in Spain, Germany, and England, and is used in place of the dry assay for the commercial valuation of copper ores. We have adhered to the gram and the "c.c." as the units of weight and volume. Those who prefer working with grains and grain-measures can use the figures given, multiplied by ten. For example:--When 1 gram is mentioned, 10 grains should be used, and 10 grain-measures take the place of 1 "c.c." It is not advisable to mix the two systems, as by using gram weights and grain-measures. We have intentionally to a large extent omitted to mention the names of those who have originated or modified the various processes. The practice of naming a process after its discoverer has developed of late years, and is becoming objectionable. It is a graceful thing to name a gas-burner after Bunsen, or a condenser after Liebig; but when the practice has developed so far that one is directed to "Finkenerise" a residue, or to use the "Reichert-Meissl-Wollny" process, it is time to stop.