352 INDUCTION. 



or comet, would be a case of the second description. Newton's was a case 

 of the first. If it had not been previously known that the planets wei'e 

 hindered from moving in straight lines by some force tending toward the 

 interior of their orbit, though the exact direction 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 ar- 

 gument would not have proved his conclusion. These facts, however, be- 

 ing 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 sup- 

 positions could not lead to identical consequences. 



Accordingly, Newton could not have performed his second great scien- 

 tific operation : that of identifying terrestrial gravity with the central force 

 of the solar system by the same hypothetical method. When the law of 

 the moon's attraction had been proved from the data of the moon itself, 

 then, on finding the same law to accord with the phenomena of terrestrial 

 gi'avity, he was warranted in adopting it as the law of those phenomena 

 likewise; but it would not have been allowable for him, without any lunar 

 data, to assume that the moon was attracted toward the earth with a force 

 as the inverse square of the distance, merely because that ratio would 

 enable him to account for terrestrial gravity ; for it would have been im- 

 possible for him to prove that the observed law of the fall of heavy bodies 

 to the earth could not result from any force, save one extending to the 

 moon, and proportional to the inverse square. 



It appears, then, to be a condition of the most genuinely scientific hy- 

 pothesis, that it be not destined always to remain an hypothesis, but be of 

 such a nature as to be either proved or disproved by comparison with ob- 

 served facts. This condition is fulfilled when the effect is already known to 

 depend on the very cause supposed, and the hypothesis relates only to the 

 precise mode of dependence ; the law of the variation of the effect according 

 to the variations in the quantity or in the relations of the cause. With these 

 may be classed the hypotheses which do not make any supposition with re- 

 gard to causation, but only with regard to the law of correspondence between 

 facts which accompany each other in their variations, though there may be 

 no relation of cause and effect between them. Such were the different 

 false hypotheses which Kepler made respecting the law of the refraction 

 of light. It was knowm that the direction of the line of refraction varied 

 with every variation in the direction of the line of incidence, but it was 

 not known how ; that is, what changes of the one corresponded to the dif- 

 ferent changes of the other. In this case any law different from the true 

 one must have led to false results. And, lastly, we must add to these all 

 hypothetical modes of merely representing or describing phenomena ; such 

 as the hypothesis of the ancient astronomers that the heavenly bodies 

 moved in circles ; the various hypotheses of eccentrics, deferents, and epi- 

 cycles, which were added to that original hypothesis; the nineteen false 

 hypotheses which Kepler made and abandoned respecting the form of the 

 planetary orbits; and even the doctrine in which he finally rested, that 

 those orbits are ellipses, which was but an hypothesis like the rest until 

 verified by facts. 



In all these cases, verification is proof ; if the supposition accords with 

 the phenomena there needs no other evidence of it. But in order that this 

 may be the case, I conceive it to be necessary, when the hypothesis relates 



