119 



i new arbitrary constants represented by A, ^, .—^, ^—r^ l 



the remainder of the developement of c ' " , c " &c. will ul- 

 timately disappear, leaving the i terms Ac" ^,A'c * ''. a-. A" c" '^. .r "' 



j,„ ax 3 .,„ &c. a X (i — 1) . , 



^ c . s , A c ' X , as part of the expression of 



It appears then that the form of the function <f}.x is in its na- 

 ture, as I stated in the beginning of this paper, exponential; and 

 that the algebraic functions, that occur in it in certain cases, are 

 no more than the remains, or, if I may use the expression, the 

 skeletons of exponential ones; the rest of which have disappeared, 

 in consequence of the evanescent factors, by which they were 

 inultiplied,. 



