;!C,4 MAJOR P. A. MAcMAHON: MEMOIR ON Till: 



which, in determinant form, is 



ar(a+2)(l) , 



l-l)(l) , a: (I) (l+l) , 



divided by 



(I) 2 (2) (l+a+1) (l+a+2) (l+b+1) ; 



and it will be shown that it is, in fact, the expression of IL (I ; a, b, c). 

 Art. 26. In a general manner we may take the following view- 

 Recalling a previous notation for the order 3 



, A, = 



, C 8 = (c- 



C x = (c), A = B = C = 1 ; 



and taking a product 



where p, q, r denotes some permutation of the numbers 2, 1,0, suppose 



_ _ 



(l+a+1) (l+a + 2) (l+b+1) 



substituted for IL (I ; a, b, c) is the functional equation. The result on reduction is 



F 



- 



and now writing 





(0 



(l+l) (1) (1-1) 



(1+2) (l+l) 



(I) 



adinf-6 

 '*! 



Fj = <f>ap<f>bg<j>cr ', 



and the inner lattice function IL (I ; a, b, c) is, to a divisor 



(I) 3 (2) (l+a+1) (l+a+2) (l+b+1) 



