Sir James Cockle on a Differential Criticoid. 1 15 



the form 



we shall have the relations 



A a n—l X. , ox 



A =x + ^rx> (3 > 



/ (n-2)(n-8) n-2\X? »-2 X 2 



+ V 3 3^i +_ 3~jr 2+ ^" x- 



This last expression shows the mode of derivation ; but it reduces 

 to 



T» ° / r»x X, . r>x/3ft— 5\X? n— 2 X 9 ... 



^ + (w -l)«|. + (^) 2 , (5) 



12. Now 



A 2 = 

 and 



dK L da _ X, 72-1 X 2 __ tz-1 X? 



dx X ^ X 2 ' 2 X 2 X 2 * 



Hence, X and /x being indeterminates, 



dx 



+ \A 2 + mB=(J +XaH^)p + L^l 



+M x +N S' (7) 



where 



L=(n-2)/A+(n-l)\-l, (8) 



, r n — 2 n — l 



M=~3-^+^-, (9) 



tvt / rtx/3w — 5\ /?z — 1\ 2 ft— 1 ,__. 



N =("- 2 <lTT> + (-2-) x -^- • • < 10 > 



13. Hence M = gives 



^"S^ (U) 



aud (11) combined with L = gives 



x= W=Ty (12) 



