INTERMIXTURE OF EFFECTS. 521 



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 diago- 

 nal ; 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 in- 

 stant; (saving that if we suppose two forces to act suc- 

 cessively 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 instant, 

 all the effect which belonged to it ; and that the modi- 

 fying 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 predicting, calculating, 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 in- 

 stance, it were stated as a law of nature that a body 

 to which a force is applied moves in the direction of 



