102 MAJOR P. A. MxcMAHON: MEMOIR ON THE 



But I have shown in Part II. of this Memoir that 



subject to the stated conditions is GF(n-4, 2, 3). 

 In general I thus establish that 



L,( oo, 2, n) = *-<' +I) GF(n-a-l, 2, s) ; 

 so that I am able to write 



GFfl 2, n) ,-'> - 8 - GF(n-,-l. 2, ,) ; 



the expression of GF (/, 2, n) is thus made to depend upon the expression of 

 GF (/', 2, n'), where I', n' have all values such that 



Now assume 



GFtf 2 - 

 ('' 2 ' n 



so that 



GY(l 2 n) - > f' ;c c.^(l-- 



-n 

 or 



GF(/> 2> n) = (i+n+2) - (t+2n) 



_ It is easy to show that (1+2), (1+3), ... (l+n) are each of them factors of the 

 right-hand side ; the remaining factor is free from I, and is, in fact, the lattice function 

 Mo,2,n). 

 Giving I to the special value zero, we readily find 



and thence 



OF(/, 2, n) = (1+,1) ld+2). .. 



as was to be shown. 



