NOTES. 



Art. 2. Through a mistake of the Compositor, the indices belonging 

 to the symbols of operation are not placed in the manner originally intended; 



n 



instead of ^"„. the symbol should have been A. 



m 



Art. 8. The following Theorems are easily demonstrated, and are of 

 constant application : 



1. \n =\n_ . \n + rs . 



m,r »,r m — a, r 



2. \n = [to + 7/1 — 1 . r . 



3. in = Ins . — . 



I I c"* 



m, r m, ri *^ 



4. \n_ = I, and [o^= 1. 



Art. 1 2. If the series is not infinite, it is obvious that we shall have 

 S'a = Sa + Sa , 



2n— 1 - n n— 1 



and Sa = Sa + Sa . 



mm m 2m — 1 m Sm 



Art. 14. It will be sometimes found necessary to give to the indices 

 subscript of the symbols of summation negative, as well positive integral 



n, r 



values. In order to meet this necessity we may use S . a to denote the 



m m 



