32 INDUCTION. 



annihilated, as much of the effect as is already produced would 

 continue ; the object would go on moving in the same direc 

 tion, with its acquired velocity, until intercepted by some 

 body or deflected by some other force. The earth, however, 

 not being annihilated, goes on producing in the second 

 instant an effect similar and of equal amount with the first, 

 which two effects being added together, there results an 

 accelerated velocity ; and this operation being repeated at 

 each successive instant, the mere permanence of the cause, 

 though without increase, gives rise to a constant progressive 

 increase of the effect, so long as all the conditions, negative 

 and positive, of the production of that effect, continue to be 

 realized. 



It is obvious that this state of things is merely a case 

 of the Composition of Causes. A cause which continues in 

 action, must on a strict analysis be considered as a number of 

 causes exactly similar, successively introduced, and producing 

 by their combination the sum of the effects which they would 

 severally produce if they acted singly. The progressive rusting 

 of the iron is in strictness the sum of the effects of many par 

 ticles of air acting in succession upon corresponding particles 

 of iron. The continued action of the earth upon a falling body 

 is equivalent to a series of forces, applied in successive instants, 

 each tending to produce a certain constant quantity of motion ; 

 and the motion at each instant is the sum of the effects of the 

 new force applied at the preceding instant, and the motion 

 already acquired. In each instant, a fresh effect, of which 

 gravity is the proximate cause, is added to the effect of which 

 it was the remote cause : or (to express the same thing in 

 another manner) the effect produced by the earth s influence at 

 the instant last elapsed, is added to the sum of the effects of 

 which the remote causes were the influences exerted by the 

 earth at all the previous instants since the motion began. The 

 case, therefore, comes under the principle of a concurrence of 

 causes producing an effect equal to the sum of their separate 

 effects. But as the causes come into play not all at once, but 

 successively, and as the effect at each instant is the sum of the 

 effects of those causes only which have come into action up to 



