HYPOTHESES. 351 



law of the attractive force, was ascertained in this mode ; by this legitimate 

 employment of the Hypothetical Method. Newton began by an assump- 

 tion that the force which at each instant deflects a planet from its rectihn- 

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

 directly toward the sun. He then proved that if this be so, the planet will 

 describe, 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 would accord with 

 the facts, the assumption was proved ; the hypothesis became an inductive 

 truth. Not only did Newton ascertain by this hypothetical process the 

 direction 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 assumption the remaining two of Kepler's laws might be de- 

 duced ; and, finally, that any other law of variation would give results in- 

 consistent with those laws, and inconsistent, therefore, with the real mo- 

 tions of the planets, of which Kepler's laws were known to be a correct 

 expression. 



I have said that in this case the verification fulfills 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, « J c, and B C, be. A repi'esents central force ; A B C, 

 the planets phis 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 &c (a set of motions) with- 

 out a, or with something else instead of a. This is the Method of Differ- 

 ence 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 de- 

 duction. But that is of no consequence. It is immaterial Avhat is the 

 nature of the evidence from which we derive the assurance that ABC 

 will produce ahc, and BC only be; it is enough that we have that as- 

 surance. 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. I3ut in order that this should hap- 

 pen, 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 aftirmative in- 

 stance, A B C, a 6 c. It is equally necessary that we should be able to ob- 

 tain, as Newton did, the negative instance BC, 6c/ by showing that no 

 antecedent, except the one assumed in the hypothesis, would in conjunc- 

 tion Avith B C produce a. 



Now it appears to me that this assurance can not be obtained, when the 

 cause assumed in the hypothesis is an unknown 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 instance. 

 An inquiry which of the bodies of the solar system causes by its attraction 

 some particular irregularity in the orbit or periodic time of some satellite 



