302 INDUCTION. , 



without increase, gives rise to a constant progressive increase of the 

 effect, so long as all the conditions, negative and positive, of the pro- 

 duction of that effect continue to be realized. 



' It must be 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 progi-essive rusting of the iron is in strictness the sum of the 

 effects of many particles of air acting in succession upon coiTespond- 

 ing 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 of the motion already acquired. 

 In each instant, a fVesh 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 a^iother 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 influ^ncee exerted by the earth 

 at a^l the previous instants since the rhotion began. The case, there- 

 fore, comes under the principle of a concun^ence of causes producing 

 ,ail effect equal to the suin 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 suto of the effects of those causes only which have 

 come into action up to that instant, the result assumes the form of an 

 ascending series; a succession of sums, each greater than that which 

 preceded it ; and we have thus a progressiva effect, ^om 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 coTuputed on mathematical princijjles.. In fact, this case, being 

 that of infinitesimal increments, is precisely the case which the differ- 

 ential 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/? are evidently mathematical questions, and 

 to be treated, therefore, deductively. If, as we have seen, cases of the 

 Composition of Causes are seldom adapted for any other than deduc- 

 tive investigation, this is especially true in the case now examined, the 

 continual composition of a cause with its own previous effects ; since 

 such a ease is peculiarly amenable to the deductive method, while the 

 undistinguishahle manner in which the effects are blended with one 

 another and vdth the causes, must make the treatment of such an 

 instance experimentally, still more chimerical than in any other case. 



§ 2. We shall next advert to a rather more intricate operation of the 

 same principle, namely, when the cause docs not merely continue in 

 action, but undergoes, during the same time, a progi-essive change in 

 those of its circumstances which contribute to determine the effect. In 

 this case, as in the former,. the total effect goes on accumulating, by 

 the continual addition of a fresh effect to that already produced, but 



