434 Mr. W. H. L. Russell on the Calculus of Symbols. 

 This equation may be written 



which may be treated as before. 



In order to find the most general form of equation to which the symbols 



^^~y^ iu^+y^ give rise, we must determine the expansion of 

 «/ 



^lkj~~^^ix) ' '^^^ likewise combine according to 



0?— J to avoid the 



negative sign. 



Now the expansion of ^^^^ consist of all the terms of the 



form 



\ %/ y dec/ \ dy) y dx) 



in which 



« + . , . +a+/3+ . . . =?i. 



We shall write Ix for ~, and ly for where it is to be understood that 

 dx " dy 



Ix and ly do not apply to the subject. 



Moreover we shall use, as in the third memoir, 



^ a—\ a — 2 a—r-\-\ 

 ar for a, 3-... 



Then we shall have, if a + a=^, 



d\«r d\^ „ „ d'' . „ d""-^ . „ d''~^ 



dx' 



' -^-^ dy^-Hx^ 



Again, a4-a + ^=^^, 



Vdcc) Vdy) Vd^J 



~^ drd^' dy-dx--^^-^^ ^ d^^d^bZ-^ 



