HYPOTHESES. 13 



calculated velocity being compared with the observed 

 velocity with which all heavy bodies fall, by mere 

 gravity, towards the surface of the earth, (namely 

 sixteen feet in the first second, forty-eight in the 

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

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

 The order in which I have here presented the three 

 steps was not the exact order 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 contents itself with the other two operations, 

 ratiocination and verification j the law, which is 

 reasoned 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 verification, shall amount 

 to, and fulfil the conditions of, a complete induction. 

 We want to be assured that the law we have hypo- 

 thetically assumed is a true one ; and its leading 

 deductively to true results will afford this assurance, 

 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 

 conclusions which that leads to. And this proviso is 

 very often realised. For example, in that perfect speci- 

 men of deduction which we just cited, the original major 

 premiss of the ratiocination, the law of the attractive 

 force, was ascertained in this very mode ; by this 

 legitimate employment of the Hypothetical Method. 

 Newton began by an assumption, that the force which 



