292 INDUCTION. 



the induction to ascertain the law ; and contents itself with the other 

 two operations, ratiocination and verification ; the law, which is rea- 

 soned from, being assumed, instead of proved. 



This process may evidently be legitimate upon one supposition, 

 namely, if the nature of the case be such that the final step, the verifi- 

 cation, shall amount to, and fulfill the conditions of, a complete induc- 

 tion. We want to be assured that the law we have hypothetically 

 assumed is atrue one ; and its leading deductively to true results will 

 afford this assurance, provided the case he such that a false law can- 

 not lead to a true result ; provided no law, except the very one which 

 we have assumed, can lead deductively to the same conclusions which 

 that leads to. And this proviso is very often realized. For example, 

 in that perfect specimen of deduction which we just cited, the original 

 mgj or premiss of the ratiocination, the law of the atti'active force, was 

 ascertained in this very mode ; by this legitimate employment of the 

 Hypothetical Method. Newton began by an assumption, that the 

 force which at each instant deflects a planet from its rectilineal course, 

 and makes it describe a curve round the sun, is a force tending directly 

 towards the sun; He then proved that if this be so, the planet will de- 

 scribe, as we know by Kepler's first law that it does describe, equal 

 areas in equal times ; and, lastly, he proved that if the force acted in 

 any other direction whatever, the planet would not describe equal 

 areas in equal times. It being thus shown that no other hypothesis 

 could accord with the facts, the assumption was proved; the hypothe- 

 sis became a law, established by the Method of Difference. Not only 

 did Newton ascertain, by this hypothetical process, the direction of the 

 deflecting force ; he proceeded in exactly the same manner to ascer- 

 tain 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 assumption the remaining two of Kepler's laws might be 

 deduced'; and, finally, that any other law of variation would give re- 

 sults inconsistent with those laws, and inconsistent, therefore, with the 

 real motions of the planets, of wliich Kepler's laws were k■now^l to be 

 a correct expression. 



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

 rence, that what is an hypothesis at the beginning of the inquiry 

 becomes a proved law of nature before its close. But this can only 

 happen when the inquiry has for its object, not to detect an unknown 

 cause, but to detennine the precise law of a cause already ascertained. 

 If it had not been already known that the planets were hindered from 

 mo\ang in straight lines by some force tending towards the interior of 

 their orbit, though the exact du-ection was doubtful ; or if it had not 

 been known tliat the force inci'eased in some proportion or other as the 

 distance diminished, and diminished as it-irncreased ; Newton's argu- 

 ment would not have proved his conclusion. These facts, however, 

 being already certain, the range of admissible suppositions 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 

 philosophical operation, that of identifying teiTestrial giavity with the 



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