330 Mr. W. H. L. Russell on Symbolical Expansions. [June 15, 



And we must first eudeavour to find a suitable expression for 



2(w r+l)2(n r+2)S(w r+3) . . . . 2. 

 "With this purpose let us assume 



S( n _ r +i)2(ra r+2) 2ra= 



A?>(n-2r+ 1) ( w _2r + 2) . . . . 



( 2r + 3) . . . . n 



2r+4) 

 Whence 



2r 

 This will give us 



2r(2r-2)(2r 4) 2 



A ' 2)= (2r-l)(2r-3) 1 S '. 2r(2r-2) 2 ~ 



&c.=&c. 



A(3) _ } (r-l)(2f2)(2r-4)....2 



r (2r-2)(2r-4) 2 (2r 1) (2r-3) 1 



2r(2r-2)(2r-4)....2 



