130 THE PRINCIPLES OF SCIENCE. [CHAP 



Diamond = combustible gem. 

 In a similar manner we ascertain that 



Mercury = metal liquid at ordinary temperatures, 

 Substance of least density = substance of least atomic 



weight. 



Two or three objects may occasionally enter into the 

 induction, as when we learn that 



Sodium -I- potassium = metal of less density than 



water, 



Venus -|- Mercury -|- Mars = major planet devoid of 

 satellites. 



Induction of Partial Identities. 



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 pro- 

 position 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 im- 

 possible 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 propo- 

 sitions 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 gravi- 

 tation. But of course it is not to be asserted that all 

 bodies obeying the law of gravitation, or shining by 



