238 PROFESSOR A. f4. GREENHILL ON THE 



So also 



2-8-0-11) 



,. . 



M" 6Q~b\/(b* + b + I) 



and I' (4r), P (Hr) are obtained from P ('), P (lir) by writing the coefficients in 

 reverse order. 

 We find also 



an = - 6 1 * +2 + 5 8 5 2 + 6 + 12+6 2 5 8 + 5+2 1, 



1,., = - (7,2 - 1 ) (/,< - b : ' - Ir -6+1) (// + - .%' + W - 3b + + 1) (25) ; 



ft fl = & 4 + 2 + 5 + 4 29 26 + 18 + 60 + 18 26 29 + 4 + 5 + 2 1, 



h n = - (b- - 1 ) (IS - !>" - b- -6 + 1) (//' + - W - 1 1 b* - 3/r + 0+1) (26) ; 



M 20// ! v /(6 2 + />+!) 



M :i06 :i x /(6'- + 6+ L) 



and these are unchanged by the substitution (/>, ) . 

 Also m 



P (f,,,) _ - (&s + | ) (// . _ b " _ w _/;+,)_(/,_!) (/> i. + //, _ 6 + /, + 1 ) v/B 

 M 12^^(^ + 6 + 1) 



and 



M- M ( 30 ^- 



With 



(32), 



^ j 



the expressions for M/ ? , are lowered in degree ; for 



M' 



_ (// + o _ 2 - 2 + + 1) /(//- - 36 + 1)] (33), 



= (6 - l)p, v /(/>- + />+!) + / >r/ , y(// -86+1) 

 M'- 266-l* " 



