PROGRESSIVE EFFECTS. 35 



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 principles. In fact, 

 this case,, being that of infinitesimal increments, is pre- 

 cisely 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 continu- 

 ally 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 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 intri- 

 cate 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 



D 2 



