We found in the last section that the complete identity of two classes is almost always discovered not by direct observation of the fact, but by first establishing two partial identities. There are also a multitude of cases in which the partial identity of one class with another is the only relation to be discovered. Thus the most common of all inductive inferences consists in establishing the fact that all objects having the properties of A have also those of B, or that A = AB. To ascertain the truth of a proposition of this kind it is merely necessary to assemble together, mentally or physically, all the objects included under A, and then observe whether B is present in each of them, or, which is the same, whether it would be impossible to select from among them any not-B. Thus, if we mentally assemble together all the heavenly bodies which move with apparent rapidity, that is to say, the planets, we find that they all possess the property of not scintillating. We cannot analyse any vegetable substance without discovering that it contains carbon and hydrogen, but it is not true that all substances containing carbon and hydrogen are vegetable substances. The great mass of scientific truths consists of propositions of this form A = AB. Thus in astronomy we learn that all the planets are spheroidal bodies; that they all revolve in one direction round the sun; that they all shine by reflected light; that they all obey the law of gravitation. But of course it is not to be asserted that all bodies obeying the law of gravitation, or shining by reflected light, or revolving in a particular direction, or being spheroidal in form, are planets. In other sciences we have immense numbers of propositions of the same form, as, for instance, all substances in becoming gaseous absorb heat; all metals are elements; they are all good conductors of heat and electricity; all the alkaline metals are monad elements; all foraminifera are marine organisms; all parasitic animals are non-mammalian; lightning never issues from stratous clouds; pumice never occurs where only Labrador felspar is present; milkmaids do not suffer from small-pox; and, in the works of Darwin, scientific importance may attach even to such an apparently trifling observation as that “white tom-cats having blue eyes are deaf.” The process of inference by which all such truths are obtained may readily be exhibited in a precise symbolic form. We must have one premise specifying in a disjunctive form all the possible individuals which belong to a class; we resolve the class, in short, into its constituents. We then need a number of propositions, each of which affirms that one of the individuals possesses a certain property. Thus the premises must be of the forms A = B ꖌ C ꖌ D ꖌ .... ꖌ P ꖌ Q B = BX C = CX ... ... ... ... Q = QX.