238 NKW MODE OF REPRESENTING 



' h ~ I ^ 1.2 "■ + 1^23 ~^ ^^- ^'^■ 



Now, if h takes only the values 1, 2, 3, 4, &c. 

 &c. between the limits <r = o and x — a, or the 

 increment of x be equal to unity ; then, it is the 

 object of the calculus of finite differences to cal- 

 culate, in every possible function of x, the value 



of y - y. 



But, if h takes every value between the limits 



cT = and X — a, or the increment of x be equal to 



nothing ; then, it is the object of the differential 



calculus to calculate in every function of x the 



value o^t^lMi when h — o. 

 n 



Hence, by referring to (Art. 2), we shall 

 readily see, that if the curve ACC be generated 

 by a law which is invariable, and a, b, c, &c. &c. 

 be taken equal to 1, 2, 3, &c. &c. respectively, 

 we shall then have a variation which corresponds 

 to the calculus of finite differences. 



(5). If we suppose .r to take every magnitude 



