'284 PROFESSOR A. G. GREENHILL ON THE 



41. In the general case a distinction must be made between /a odd or even. 

 I. Jfi = 2n + 1, ft = 8n + 4. 



r i 2r -4- 1 vf - _ r< 



X, = C n + 20^ x 2 = (05, x) (x, + a;) 



X 2 = C 2C r x x z = (.r, + x) (x z x) 



jCn ' KJC i 



GO = V/O?, S 3 ) (Sj -^) = .S' (2, + 1) V S 



20, = /(*, - . 3 ) - /fo - 3 ) = 2P (2n + 1 

 2C C, = I ?>' (2n + 1) r = Q (2 + 1) u 



1 



- 



O 



(i); 

 (2), 



(3), 



(4), 

 (5), 

 (6), 



(7), 



(8), 



where o denotes the octahedron irrationality X /K; so that if the expressions are 

 normalised by the homogeneity factor M = v /0,,, 



X,, X ; = 1 Or - x-, = ' - ,> 



,T, = , ,r., = o, .c = osn(K mf.) 



/"K' = ' S3 = " = K D = - D, zn/K' = 



M 



(9), 



(10); 

 (11). 



No 



w 



I() = J 



M M 3 



D - x" 



2n + I 



cos" 



(D - x*) 



. , R n 4- R, 



" P (2n 



/i x 



= (- l)", 



(12). 



Q (w) _ 



M 3 



(13). 



