14 INDUCTION. 



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 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 

 could accord with the facts, the assumption was 

 proved ; the hypothesis 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 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 deduced ; and, finally, that 

 any other law of variation would give results incon- 

 sistent with those laws, and inconsistent, therefore, 

 with the real motions of the planets, of which Kepler's 

 laws were known to be a correct expression. 



It is thus perfectly possible, and indeed is a very 

 common occurrence, 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 determine the precise law of a 

 cause already ascertained. If it had not been already 

 known that the planets were hindered from moving in 

 straight lines by some force tending towards 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 



