780 Dr. J. W. Nicholson on 



Again, 



_|2 4r + 1.2m-2r.2m + 2r-f 1 



2m-2r-1.2m + 2r + 2.2m-2r + 1.2m-f 2r 



J 2r+l.P 8r+1 + 2rP 2r .n 

 * I 4r + l | 



- ■» 4r + 3.P 2 ,- +1 



2 o 2m-2r-1.2m + 2r-f 2' 



After a fair amount of reduction, this becomes 



.2m + 2r + 3.Par+i 



in y «> 4r + 3.2m-2r.2wi — 2r — 2.2ro + 2r + l 



sUfe-ts- Z 2 m -2r_3 . 2ro-2r-l . 2m-2r-f 1 



. 2m -f 2r . 2??i -f2r + 2. 2m + 2r+'4 



and indications of a general formula are already apparent. 

 Continuing this procedure, we are able to show that 



— 2 ^62»i -l 3 



. (2m + 2r- 1 . 2m + 2r + 1 . 2m <f 2r + 3) 

 _^oo 4r + 3 (2m-2r+ 2 . 2m -2r . 2m- tr-2) 

 ~ o (2m - 2r-3 . 2m-2r-l . 2m — 2r + l . 2m- 2r + 3) 

 . (2m. + 2r . 2m + 2r + 2" . 2m + 2r 4- 4 . 2m + 2?> + 6) . 

 These forms may be shortened to 

 in P -V 00 4r-t-3.P 2r+1 



Tn x 2r. 



o 9 



2m.2m + l-2r + 1.2r + 2' 



in p _ v " 4r+l.P 2r 



2 ^ 2mri ~ 2 'o 2m.2m + l-2r-fl.2r + 2 



2m.2m + l-2r.2r + l 



— 2 ^2«i P 2 = ^ 



"2m.2m+l-2f— 1.2r' 

 4r + 3P 2r+1 



2m.2m-f l~2r+1.2r + 2 



2m.2m+l — 2r.2r + l 

 2m.2m-fT-2r-l.2r 



2m.2m-f l-2r+2 .2?'+3 

 2m.2m+l — 2r + 3.2r-t 4 



