MR. W. SPOTTISWOODE ON DIFFERENTIAL RESOLVENTS. 231 



-{-2a'c{6ac'-—gb''c + abd) 

 + 2a'd'{a'-d+ gb^ — gabc) 

 —()b'c'a{ad—;^bc) 

 -heb'd'aiiac — ^b"-) 



+ ^{9(E'G-EG0 



+ 2^la'-d{2c^-2bd) 



^gb'^-acd 



-\-()c"-a''d 



-^-d'-a'-b 



+ '^a'yad'- 



+ 6aJdd['^b^ — 2ac) 



+ a!d'[6ac''—()b'-c + abd) 



^iWdabd 



-\-2^'d'a{—ad+2^^) 

 -bc'd'a^c]}, 



or, as it may be more concisely written, 



+ {|^^'+f(3.E-«F)}.' 



E E' 



+ 



. E E' 

 I F F 

 .:«' G G' 



+ 2E 



• «' 3*' 3c' d' 



a 2b' 2c d' . 



. « 36 'ic d 



a 'if) ^c d . 



a 2b c 



. a 2b c . 



=0. 



As regards ulterior developments, I have at present only 

 to add that it may be readily shown by the method of 

 compound determinants that the part of 



. E E' 

 I F F' 

 ^ G G' 



