5. But it was not by new processes alone that Klaproth improved the mode of analysis, though they were numerous and important; the improvements in the apparatus contributed not less essentially to the success of his experiments. When he had to do with very hard minerals, he employed a mortar of flint, or rather of agate. This mortar he, in the first place, analyzed, to determine exactly the nature of the constituents. He then weighed it. When a very hard body is pounded in such a mortar, a portion of the mortar is rubbed off, and mixed with the pounded mineral. What the quantity thus abraded was, he determined by weighing the mortar at the end of the process. The loss of weight gave the portion of the mortar abraded; and this portion must be mixed with the pounded mineral. When a hard stone is pounded in an agate mortar it is scarcely possible to avoid losing a little of it. The best method of proceeding is to mix the matter to be pounded (previously reduced to a coarse powder in a diamond mortar) with a little water. This both facilitates the trituration, and prevents any of the dust from flying away; and not more than a couple of grains of the mineral should be pounded at once. Still, owing to very obvious causes, a little of the mineral is sure to be lost during the pounding. When the process is finished, the whole powder is to be exposed to a red heat in a platinum crucible, and weighed. Supposing no loss, the weight should be equal to the quantity of the mineral pounded together with the portion abraded from the mortar. But almost always the weight will be found less than this. Suppose the original weight of the mineral before pounding was _a_, and the quantity abraded from the mortar 1; then, if nothing were lost, the weight should be _a_ + 1; but we actually find it only _b_, a quantity less than _a_ + 1. To determine the weight of matter abraded from the mortar contained in this powder, we say _a_ + 1: _b_:: 1: _x_, the quantity from the mortar in our powder, and _x_ = _b_/_a_ + 1. In performing the analysis, Klaproth attended to this quantity, which was silica, and subtracted it. Such minute attention may appear, at first sight superfluous; but it is not so. In analyzing sapphire, chrysoberyl, and some other very hard minerals, the quantity of silica abraded from the mortar sometimes amounts to five per cent. of the weight of the mineral; and if we were not to attend to the way in which this silica has been introduced into the powder, we should give an erroneous view of the constitution of the mineral under analysis. All the analyses of chrysoberyl hitherto published, give a considerable quantity of silica as a constituent of it. This silica, if really found by the analysts, must have been introduced from the mortar, for pure chrysoberyl contains no silica whatever, but is a definite compound of glucina, alumina, and oxide of iron.