292 



INDUCTION. 



the phenomenon to be investigated ; 

 on the contrary, they still take place, 

 but are intermingled with, and dis- 

 guised by, the homogeneous and 

 closely allied effects of other causes. 

 They are no longer a, 6, c, d, e, ex- 

 isting side by side, and continuing 

 to be separately discernible ; they 

 are ■¥ a, a,- ^ 6, - 6, 2 6, &c. ; some 

 of which cancel one another, while 

 many others do not appear distinguish- 

 ably, but merge in one sum : forming 

 altogether a result, between which 

 and the causes whereby it was pro- 

 duced there is often an insurmount- 

 able difficulty in tracing by observa- 

 tion any fixed relation whatever. 



The general idea of the Composi- 

 tion of Causes has been seen to be, 

 that though two or more laws inter- 

 fere with one another, and apparently 

 frustrate or modify one another's 

 operation, yet in reality all are ful- 

 filled, the collective effect being the 

 exact sum of the effects of the causes 

 taken separately. A familiar in- 

 stance is that of a body kept in 

 equilibrium by two equal and con- 

 trary forces. One of the forces if 

 acting alone would carry the body 

 in a given time a certain distance to 

 the west, the other if acting alone 

 would carry it exactly as far towards 

 the east ; and the result is the same 

 as if it had been first carried to the 

 west as far as the one force would 

 carry it, and then back towards the 

 east as far as the other would carry 

 it, that is, precisely the same dis- 

 tance ; being ultimately left where it 

 was found at first. 



All laws of causation are liable to 

 be in this manner counteracted, and 

 seemingly frustrated, by coming into 

 conflict with other laws, the separate 

 result of which is opposite to theirs, 

 or more or less inconsistent with it. 

 And hence, with almost every law, 

 many instances in which it really is 

 entirely fulfilled do not, at first sight, 

 appear to be cases of its operation at 

 all. It is so in the example just 

 adduced : a force, in mechanics, means 

 neither more nor less than a cause of 



motion, yet the sum of the effects of 

 two causes of motion may be rest. 

 Again, a body solicited by two forces 

 in directions making an angle with 

 one another moves in the diagonal; 

 and it seems a paradox to say that 

 motion in the diagonal is the sum of 

 two motions in two other lines. Mo- 

 tion, however, is but change of place, 

 and at every instant the body is in 

 the exact place it would have been in 

 if the forces had acted during alter- 

 nate instants instead of acting in the 

 same instant, (saving that if we sup- 

 pose two forces to act successively 

 which are in truth simultaneous, we 

 must of course allow them double the 

 time.) It is evident, therefore, that 

 each force has had, during each in- 

 stant, all the effect which belonged 

 to it ; and that the modifying influ- 

 ence which one of two concurrent 

 causes is said to exercise with respect 

 to the other may be considered as 

 exerted not over the action of the 

 cause itself, but over the effect after 

 it is completed. For all purposes of 

 predicting, calculating, or explaining 

 their joint result, causes which com- 

 pound their effects may be treated as 

 if they produced simultaneously each 

 of them its own effect, and all these 

 effects co-existed visibly. 



Since the laws of causes are as 

 really fulfilled when the causes are 

 said to be counteracted by opposing 

 causes as when they are left to their 

 own undisturbed action, we must be 

 cautious not to express the laws in 

 such terms as would render the asser- 

 tion of their being fulfilled in those 

 cases a contradiction. If, for instance, 

 it were stated as a law of nature that 

 a body to which a force is applied 

 moves in the direction of the force, 

 with a velocity proportioned to the 

 force directly, and to its own mass 

 inversely ; when in point of fact some 

 bodies to which a force is applied do 

 not move at all, and those which do 

 move (at least in the region of our 

 earth) are, from the very first, re- 

 tarded by the action of gravity and 

 other resisting forces, and at last 



