318 INDUCTION. 



which cancel one another, while many others do not appear distinguisha- 

 bly, but merge in one sum ; forming altogether a result, between which 

 and the causes whereby it was produced there is often an insurmountable 

 difficulty in tracing by observation any fixed relation whatever. 



The genei'al idea of the Composition of Causes has been seen to be, that 

 though two or more laws interfere with one another, and apparently frus- 

 trate or modify one another's operation, yet in reality all are fulfilled, the 

 collective effect being the exact sum of the effects of the causes taken sepa- 

 rately. A familiar instance is that of a body kept in equilibrium by two 

 equal and contrary 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 toward 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 toward the east as far as the other would carry 

 it — that is, precisely the same distance; being ultimately left Avhei'e 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. Motion, 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 alternate instants instead of acting in the same 

 instant (saving that if we suppose two forces to act successively whicli ai"e 

 in truth simultaneous we must of course allow them double the time). It 

 is evident, therefore, that each force has had, during each instant, all the 

 effect which belonged to it; and that the modifying influence 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 ])redicting, calcula- 

 ting, or explaining their joint result, causes which compound 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 assertion 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 invei'sely ; 

 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, retarded by the action of gravity and other resisting 

 forces, and at last stopped altogether ; it is clear that the general proposi- 

 tion, though it would be true under a certain hypothesis, would not ex- 

 press' the facts as they actually occur. To accommodate the expression of 

 the law to the real phenomena, w^e must say, not that the object moves, but 



