10 , INDUCTION. 



buting them to vibratory motions among the particles of an 

 ether pervading all space. Of the existence of either fluid 

 there is no evidence, save the explanation they are calculated 

 to afford of some of the phenomena ; but they are supposed to 

 produce their effects according to known laws ; the ordinary 

 laws of continued locomotion in the one case, and in the other, 

 those of the propagation of undulatory movements among the 

 particles of an elastic fluid. 



According to the foregoing remarks, hypotheses are 

 invented to enable the Deductive Method to be earlier applied 

 to phenomena. But* in order to discover the cause of any 

 phenomenon 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 calculated effect 

 with the actual phenomenon. No one of these three parts of 

 the process can be dispensed with. In the deduction which 

 proves the identity 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 inverse square of the distance. This (though 

 partly dependent on prior deductions) corresponds to the first, 

 or purely inductive, step, the ascertainment of the law of the 

 cause. Secondly, from this law, and from the knowledge pre- 

 viously obtained of the moon's mean distance from the earth, 

 and of the actual amount of her deflexion from the tangent, it 

 is ascertained with what rapidity the earth's attraction would 

 cause the moon to fall, if she were no further off, and no more 

 acted upon by extraneous forces, than terrestrial bodies are : 

 that is the second step, the ratiocination. Finally, this calcu- 

 lated velocity being compared with the observed velocity with 

 which all heavy bodies fall, by mere gravity, towards the 

 surface of the earth, (sixteen feet in the first second, forty - 



* Vide supra, book iii. ch. xi. 



