PROGRESSIVE EFFECTS. 



effect, we have a progressive series 

 of effects, arising from the accumu- 

 lated influence of a permanent cause. 

 Thus, the contact of iron with the 

 atmosphere causes a portion of it to 

 rust ; and if the cause ceased, the 

 effect already produced would be per- 

 manent, but no further effect would 

 be added. If, however, the cause, 

 namely, exposure to moist air, con- 

 tinues, more and more of the iron 

 becomes rusted, until all which is e.x- 

 posed is converted into a red powder, 

 when one of the conditions of the 

 production of rust, namely, the pre- 

 sence of unoxidised iron, has ceased, 

 and the effect cannot any longer be 

 produced. Again, the earth causes 

 bodies to fall towards it, that is, the 

 existence of the earth at a given in- 

 stant causes an unsupported body to 

 move towards it at the succeeding 

 instant ; and if the earth were anni- 

 hilated, as much of the effect as is 

 already produced would continue ; 

 the object would go on moving in 

 the same direction, with its acquired 

 velocity, until intercepted by some 

 body or deflected by some other force. 

 The earth, however, not being anni- 

 hilated, goes on producing in the 

 second instant an effect similar 

 and of equal amount with the first, 

 which two effects being added to- 

 gether, 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 produc- 

 tion of that effect continue to be 

 realised. 



It is obvious that this state of 

 things is merely a case of the Com- 

 position 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 ■everally produce 

 if they^ actad singly. The progressive 



rusting of the iron is in strictness the 

 sum of the effects of many particles 

 of air acting in succession upon cor- 

 responding particles of iron. The 

 continued action of the earth upon a 

 falling body is equivalent to a series 

 of forces, applied in successive in- 

 stants, each tending to produce a cer- 

 tain 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 pro- 

 duced 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 that instant, the 

 result assumes the form of an ascend- 

 ing series ; a succession of sums, each 

 greater than that which preceded it : 

 and we have thus a progressive effect 

 from the continued action of a cause. 

 Since the continuance of the cause 

 influences the effect only by adding 

 to its quantity, and since the addition 

 takes place according to a fixed law, 

 (equal quantities in equal times,) the 

 result is capable of being computed 

 on mathematical principles. In fact, 

 this case, being that of infinitesimal 

 increments, is precisely the case which 

 the differential calculus was invented 

 to meet. The questions, what effect 

 will result from the continual addition 

 of a given cause to itself, and what 

 amount of the cause, being continually 

 added to itself, will produce a given 

 amount of the effect, j^re evidently 



