350 INDUCTION. 



the phenomena to a fluid emitted from all luminous bodies, the other (now 

 generally received) attributing them to vibratory motions among the par- 

 ticles 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 proc- 

 ess must consist of three parts : induction, ratiocination, and verification. 

 Induction (the place of which, however, may be supplied by a prior deduc- 

 tion), 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 ef- 

 fect with the actual phenomenon. 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 at- 

 tracts her with a force varying as the inverse square of the distance. I'his 

 (though partly dependent on prior deductions) corresponds to the first, or 

 purely inductive, step : the ascertainment of the law of the cause. Second- 

 ly, 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 de- 

 flection 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. P^inally, this calculated velocity being 

 compared with the observed velocity with which all heavy bodies fall, 

 by mere gravity, toward 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 num- 

 bers, 1, 3, 5, etc.), 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 com])lete 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 vei'ification ; the law which is reasoned from 

 being assumed instead of proved. 



This process may evidently be legitimate on one supposition, namely, if 

 the nature of the case be such that the final step, the verification, shall 

 amount to, and fulfill the conditions 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 assurance, pro- 

 vided the case be such that a false law can not lead to a true result ; pro- 

 vided no law, except the very one which we have assumed, can lead deduct- 

 ively to the same conclusions 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 ratiocination, the 



* Vide supra, book iii., chap. xi. 



