PROGRESSIVE EFFECTS. 33 



that instant, the result assumes the form of an ascending 

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

 ceded 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 prin- 

 ciples. In fact, this case, being that of infinitesimal incre- 

 ments, 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, are evidently mathe- 

 matical 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 deductive investigation, 

 this is especially true in the case now examined, the continual 

 composition of a cause with its own previous effects ; since 

 such a case is peculiarly amenable to the deductive method, 

 while the undistinguishable manner in which the effects are 

 blended with one another and with 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 does 

 not merely continue in action, but undergoes, during the same 

 time, a progressive 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 it is no 

 longer by the addition of equal quantities in equal times ; the 

 quantities added are unequal, and even the quality may now be 

 different. If the change in the state of the permanent cause 

 be progressive, the effect will go through a double series of 

 changes, arising partly from the accumulated action of the 

 .cause, and partly from the changes in its action. The effect 



VOL. II. 3 



