228 



Mr. K/Ussell on the Calculus of Symbols. [April 28, 



solved by the rules which apply to ordinary algebraical equations ; for there 

 are certain functions of the symbols of partial differentiation which com- 

 bine with certain functions of the independent variables according to the 

 laws of combination of common algebraical quantities. In the first part of 

 this memoir I have investigated the nature of these symbols, and apphed 

 them to the solution of partial differential equations. In the second part I 

 have applied the calculus of symbols to the solution of functional equa- 

 tions. For ^this purpose I have worked out some cases of symbolical 

 division on a modified type, so that the symbols may embrace a greater 

 range. I have then shown how certain functional equations may be 

 expressed in a symbolical form, and have solved them by methods analo- 

 gous to those already explained. 



The Society then adjourned to Thursday, May 12th. 



JULY 11, isa. 



