324 



INDUCTION. 



as the square of the distance, showed 

 that from this assumption the remain- 

 ing two of Kepler's laws might be 

 deduced, and, finally, that any other 

 law of variation would give results 

 inconsistent with those laws, and in- 

 consistent, therefore, with the real 

 motions of the planets, of which Kep- 

 ler's laws were known to be 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, A B C, a 6 c, and B C, 

 be. A represents central force ; 

 ABC, 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 6 c (a set of motions) 

 without a, or with something else in- 

 stead 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 immaterial what 

 is the nature of the evidence from 

 which we derive the assurance that 

 ABC will produce a h c, and B C 

 only be; it is enough that we have 

 that assurance. In the present case, a 

 process of reasoning furnished New- 

 ton with the very instances which, 

 if the nature of the case had admitted 

 of it, he would have sought by experi- 

 ment. 



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 in- 

 stances which the Method of Differ- 

 ence requires. That we are able from 

 the hypothesis to deduce the known 

 f^cts, gives only tJ?e afl&rmative in- 



stance, A B C, a t c. It is equally 

 necessary that we should be able to 

 obtain, as Newton did, the negative 

 instance B C, 6 c, by showing that 

 no antecedent, except the one assumed 

 in the hypothesis, would in conjunc- 

 tion with B C produce a. 



Now it appears to me that this as- 

 surance cannot be obtained when the 

 cause assumed in the hypothesis is an 

 vmknown cause, imagined solely to 

 account for a. When we are only 

 seeking to determine the precise law 

 of a cause already ascertained, or to 

 distinguish the particular agent which 

 is in fact the cause, among several 

 agents of the same kind, one or other 

 of which it is already known to be, 

 we may then obtain the negative in- 

 stance. An inquiry which of the 

 bodies of the solar system causes by 

 its attraction some particular irregu- 

 larity in the orbit or periodic time of 

 some satellite or comet, would be a 

 case of the second description. New- 

 ton's was a case of the first. If 

 it had not been previously known 

 that the planets were hindered from 

 moving in straight lines by some 

 force tending towards the interior of 

 their orbit, though the exact direc- 

 tion was doubtful ; or if it had not 

 been known that the force increased 

 in some proportion or other as the 

 distance diminished, and diminished 

 as it increased, Newton's argument 

 would not have proved his conclusion. 

 These facts, however, being already 

 certain, the range of admissible sup- 

 positions was limited to the various 

 possible directions of a line, and the 

 various possible numerical relations 

 between the variations of the distance, 

 and the variations of the attractive 

 force : now among these it was easily 

 shown that different suppositions 

 could not lead to identical conse- 

 quences. 



Accordingly, Newton could* not 

 have performed his second great 

 scientific operation, that of identify- 

 ing terrestrial gravity with the cen- 

 tral force of the solar system, by the 

 same hypothetical method. When 



