278 



ROYAL SOCIî:TY OF CANADA 



+ 



Certain of these determinants obviously vanish since they have 

 two rows identical. The others all reduce to the next lower orders, 

 and when added together give the determinant 



Pi 2;?2 p3 

 1 Pi Pi 



of order 2 k — i — 1. 



^ Pi Pi 



000 010 



We have therefore for the coefficient of />; in P D^ 



Vi '^Pz Pi 2p4 

 1 Pi Pi 2;>3 



i-i) 



or 



'k~i-l 







Pi 2^2 Pi 

 1 Pi Pi 



1 Vi 



+ (- 1) 



'k~i 



(-!> 



'k-i-1 



or 



tk-i-l 

 {- 1) Pi 



^ Pi Pi 



^ ^ Pi 



Pi '^Pi Pi 



1 Pi Pi 



\ p^ 



that is^i times the coefficient of pi in D^-x. 



For i = 2k, or 2k — 1 , pi evidently vanishes, and for i == k only 

 part of the coefficient of jp,- is found in A-. 



