1884.] identified with Sir J. Cockle's Criticoids. 53 



n=3, the formula gives Professor Malet's function I 2 already noticed. 

 See Article 11, equation (1 2 ). Making n=4, we have 



12Q 1 * + 22Q 1 8-27Q 8 12P 1 ' + 22P 1 2-27P 2 ; t , 



o? = p} • ' 



Compai'e Malet on p. 775, where J x is written in the form 



54P 2 -44P2-24-^ 

 2 1 dx • 



Other criticoids of the second class may be derived from the general 

 quantoid by the foregoing process. I give two examples, 

 p 



13. First. Since Q«=^, we have 

 and therefore 



9,>XQ 1 Q,=^{ p„'+xP 1 P»+2|^\--. J5 i )p /! T } , 



which, on making X— ^ n , becomes 

 n — 1 



or, as it may be written, 



(n-l)Q,; + 2nQ,Q n (n-l)P/ + 2nP 1 P, 



n+l = n+l ' 



a formula which holds for all values of n. When n=2, the formula 

 gives Professor Malet's function J, viz., 



Q2 < + 4Q 1 Q 2 _ P 2 '-f4P 1 P 2 m 



See Malet, pp. 763, 764. When n=3, it gives the function I l5 the 

 form of which is exhibited in equation of Article 11 ; and when 

 w=4, it gives Professor Malet's function J 3 , viz. : — ■ 



3Q; + 8Q 1 Q 4 __ 3P 1 ' + 8P 1 P 4 (J) 



See Malet, p. 775. 



(d \ n 

 T— J sufficiently far 



/ d y- 3 



to determine the coefficient of ( J , we find 



