II. Oil Algehraic Notation. 

 By THOMAS JARRETT, B.A. 



OF CATHARINE HALL. 



[Read Nov. 12, 1827.] 



1 . T^ HE object of this paper is to propose a notation by 

 means of which the analysis of .series may be facilitated, and to 

 suggest a few modilications in the received system of algebraic 

 notation. 



2. The principle of the notation about to be proposed, though 

 sufficiently obvious, and at the same time by no means novel, is 

 one capable of being applied much more extensively than it has 

 hitherto been. It is as follows : if a„. is any function of m, and 

 if A represent that operation by which any quantities ai-e com- 

 bined in a given manner, then the symbol J",„ . (a,,,) may be used 

 to represent the result of such combination applied to n functions, 

 of which the m* is a,„. Again, if y is a function of any quantities, 

 one of which is x, then B^ . (v) may repre.sent the performance 

 on u of any operation in which .v alone is considered as variable, 

 and !?%.(«) will equally represent the result of that operation 

 when repeated w times. 



3. Let then the letter P be taken as an abbreviation of the 

 word product, and P",„ . a^ will denote a product of n factors of 

 which the m* is a,,,. 



Vol. III. Part I. i 



