HYPOTHESES. 



11 



eight in the second, and so forth, in the ratio of the odd 

 numbers, 1, 3, 5, &c.,) the two quantities are found to agree. 

 The order in which the steps are here presented, was not 

 that of their discovery ; but it is their correct logical order, 

 as portions of the proof that the same attraction of the earth 

 which causes the moon's motion, causes also the fall of heavy 

 bodies to the earth : a proof which is thus complete in all its 

 parts. 



Now, the Hypothetical Method suppresses the first of 

 the three steps, the induction to ascertain the law ; and con- 

 tents itself with the other two operations, ratiocination and 

 verification ; the law which is reasoned from, being assumed, 

 instead of proved. 



This process may evidently be legitimate on one suppo- 

 sition, namely, if the nature of the case be such that the final 

 step, the verification, shall amount to, and fulfil the condi- 

 tions of, a complete induction. We want to be assured that 

 the law we have hypothetically assumed is a true one ; and 

 its leading deductively to true results will afford this assu- 

 rance, provided the case be such that a false law cannot lead 

 to a true result ; provided no law, except the very one which 

 we have assumed, can lead deductively to the same conclu- 

 sions which that leads to. And this proviso is often realized. 

 For example, in the very complete specimen of deduction 

 which we just cited, the original major premise of the ratio- 

 cination, the law of the attractive force, was ascertained in 

 this mode; by this legitimate employment of the Hypo- 

 thetical Method. Newton began by an assumption, that the 

 force which at each instant deflects a planet from its recti- 

 lineal 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 would accord with the facts, the assumption was 

 proved ; the hypothesis became an inductive truth. Not only 



