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INDUCTION. 



that is, the uniformities respecting 

 which we cannot yet decide whether 

 they are cases of causation or mere 

 results of it. Not only has the order 

 in which the facts of organisation and 

 life successively manifest themselves, 

 from the first germ of existence to 

 death, been found to be uniform, and 

 very accurately ascertainable ; but, 

 by a great application of the Method 

 of Concomitant Variations to the en- 

 tire facts of comparative anatomy and 

 physiology, the characteristic organic 

 structure corresponding to each class 

 of functions has been determined 

 with considerable precision. Whether 

 these organic conditions are the whole 

 of the conditions, and in many cases 

 whether they are conditions at all, or 

 mere collateral effects of some common 

 cause, we are quite ignorant ; nor are 

 we ever likely to know, unless we 

 could construct an organised body, 

 and try whether it would live. 



Under such disadvantages do we, 

 in cases of this description, attempt 

 the initial or inductive step in the 

 application of the Deductive Method 

 to complex phenomena. But such, 

 fortunately, is not the common case. 

 In general, the laws of the causes on 

 which the effect depends may be ob- 

 tained by an induction from com- 

 paratively simple instances, or, at the 

 worst, by deduction from the laws 

 of simpler causes, so obtained. By 

 simple instances are meant, of course, 

 those in which the action of each 

 cause was not intermixed or inter- 

 fered with, or not to any great extent, 

 by other causes whose laws were un- 

 known ; and only when the induc- 

 tion which furnished the premises to 

 the Deductive Method rested on such 

 instances has the application of such 

 a method to the ascertainment of the 

 laws of a complex effect been attended 

 with brilliant results. 



§ 2. When the laws of the causes 

 have been ascertained, and the first 

 atage of the great logical operation 

 now under discussion satisfactorily 

 {«,ocomplished, the tecond part follows ; 



that of determining from the laws of 

 the causes what effect any given 

 combination of those causes will pro- 

 duce. This is a process of calcula- 

 tion, in the wider sense of the term, 

 and very often involves processes of 

 calculation in the narrowest sense. 

 It is a ratiocination ; and when our 

 knowledge of the causes is so perfect 

 as to extend to the exact numerical 

 laws which they observe in producing 

 their effects, the ratiocination may 

 reckon among its premises the theo- 

 rems of the science of number, in the 

 whole immense extent of that science. 

 Not only are the most advanced truths 

 of mathematics often required to 

 enable us to compute an effect the 

 numerical law of which we already 

 know, but, even by the aid of those 

 most advanced truths, we can go but 

 a little way. In so simple a case as 

 the common problem of three bodies 

 gravitating towards one another, with 

 a force directly as their mass and in- 

 versely as the square of the distance, 

 all the resources of the calculus have 

 not hitherto sufficed to obtain any 

 general solution but an approximate 

 one. In a case a little more complex, 

 but still one of the simplest which 

 arise in practice, that of the motion 

 of a projectile, the causes which affect 

 the velocity and range (for example) 

 of a cannon-ball may be all known 

 and estimated ; the force of the gun- 

 powder, the angle of elevation, the 

 density of the air, the strength and 

 direction of the wind ; but it is one 

 of the most difficult of mathematical 

 problems to combine all these, so as 

 to determine the effect resulting from 

 their collective action. 



Besides the theorems of number, 

 those of geometry also come in as 

 premises, where the effects take place 

 in space, and involve motion and 

 extension, as in mechanics, optics, 

 acoustics, astronomy. But when the 

 complication increases, and the effects 

 are under the influence of so many 

 and such shifting causes as to give no 

 room either for fixed numbers or for 

 straight lines and regular curves, (as 



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