HYPOTHESES. 



323 



meuou by the Deductive Method, the 

 process must consist of three parts — 

 induction, ratiocination, and verifica- 

 tion. Induction, (the place of which, 

 however, may be supplied by a prior 

 deduction,) to ascertain the laws of 

 the causes ; ratiocination, to compute 

 from those laws how the causes will 

 operate in the particular combination 

 known to exist in the case in hand ; 

 verification, by comparing this calcu- 

 lated effect with the actual phenome- 

 non. No one of these three parts of 

 the process can be dispensed with. In 

 the deduction which proves the iden- 

 tity of gravity with the central force 

 of the solar system, all the three are 

 found. First, it is proved from the 

 moon's motions that the earth attracts 

 her with a force varying as the in- 

 verse square of the distance. This 

 (though partly dependent on prior 

 deductions) corresponds to the first 

 or purely inductive step, the ascer- 

 tainment of the law of the cause. 

 Secondly, from this law, and from 

 the knowledge previously obtained of 

 the moon's mean distance from the 

 earth, and of the actual amount of 

 her deflection from the tangent, it is 

 ascertained with what rapidity the 

 earth's attraction would cause the 

 moon to fall, if she were no farther 

 off and no more acted upon by ex- 

 traneous forces than terrestrial bodies 

 are ; that is the second step, the 

 ratiocination. Finally, this calculated 

 velocity being compared with the ob- 

 served velocity with which all heavy 

 bodies fall, by mere gravity, towards 

 the surface of the earth (sixteen feet 

 in the first second, forty-eight in the 

 second, and so forth, in the ratio of 

 the odd numbers, i, 3, 5, &c,), the 

 two quantities are found to agree. 

 The order in which the steps are here 

 presented was not that of their dis- 

 covery ; 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 complct* in all 

 its parts. 



Now, the Hypothetical Method sup- 

 presses the first of the three steps, 

 the induction to ascertain the law, 

 and contents itself with the other two 

 operations, ratiocination and verifica- 

 tion, the law which is reasoned from 

 being assumed instead of proved. 



This process may evidently be legi- 

 timate on one supposition, namely, tf 

 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 can- 

 not 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 often realised. 

 For example, in the very complete 

 specimen of deduction which we just 

 cited, the original major premise of 

 the ratiocination, the law of the at- 

 tractive force, was ascertained in this 

 mode, by this legitimate employment 

 of the Hypothetical Method. New- 

 ton began by an assumption that the 

 force which at each instant deflects a 

 planet from its rectilineal course, and 

 makes it describe a curve round the 

 sun, is a force tending directly to- 

 wards 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 de- 

 scribe equal areas in equa^ times. It 

 being thus shown that no other hypo- 

 thesis would accord with the facts, 

 the assumption was proved ; the hypo- 

 thesis became an inductive truth. 

 Not only did Newton ascertain by 

 this hypothetical process the direc- 

 tion of the deflecting force, he pro- 

 ceeded in exactly the same manner 

 to ascertain the law of variation of 

 the quantity of that force. Ho as- 

 sumed that the force varied inversely 



