12 INDUCTION. 



did Newton ascertain by this hypothetical process the direc 

 tion of the deflecting force; he proceeded in exactly the 

 same manner to ascertain the law of variation of the quantity 

 of that force. He assumed that the force varied inversely as 

 the square of the distance ; showed that from this assump 

 tion the remaining two of Kepler s laws might he deduced; 

 and finally, that any other law of variation would give results 

 inconsistent with those laws, and inconsistent, therefore, with 

 the real motions of the planets, of which Kepler s laws were 

 known to he a correct expression. 



I have said that in this case the verification fulfils the 

 conditions of an induction : but an induction of what sort ? 

 On examination we find that it conforms to the canon of the 

 Method of Difference. It affords the two instances, ABC, 

 a b c, and B C, b c. A represents central force ; A B C, the 

 planets plus a central force ; B C, the planets apart from a 

 central force. The planets with a central force give a, areas 

 proportional to the times ; the planets without a central force 

 give b c (a set of motions) without a, or with something else 

 instead of a. This is the Method of Difference in all its 

 strictness. It is true, the two instances which the method 

 requires are obtained in this case, not by experiment, but by a 

 prior deduction. But that is of no consequence. It is imma 

 terial what is the nature of the evidence from which we derive 

 the assurance that ABC will produce a b c, and B C only 

 b c ; it is enough that we have that assurance. In the present 

 case, a process of reasoning furnished Newton with the very 

 instances, which, if the nature of the case had admitted of it, 

 he would have sought by experiment. 



It is thus perfectly possible, and indeed is a very common 

 occurrence, that what was an hypothesis at the beginning of 

 the inquiry, becomes a proved law of nature before its close. 

 But in order that this should happen, we must be able, either 

 by deduction or experiment, to obtain both the instances which 

 the Method of Difference requires. That we are able from 

 the hypothesis to deduce the known facts, gives only the 

 affirmative instance, A B C, a b c. It is equally necessary 

 that we should be able to obtain, as Newton did, the negative 



