300 

 and now 



PROFESSOR A. G. GREENHILL ON THE 



aV(l - 8 +2 % 



a'+2y/a"-a4 : 8 ) 



(10). 



In KIEPRRT'S notation ('Math. Ann.,' 32, p. llf>), 



Treating /u. = 24 by the trisection method of 14 applied to p. = 8, we put 



z (1 2z) 1 2z 2 



35 = 2(1-22), y= Y-2 ' 2/+lr i_ z 



so that, putting- f = 2 2 y) in the efjuation (8), 14, it may be written 



/. O x 2= (1-2^)' ;> 3 ( + 4) 



42 2 1 -2 2 4 + l 3 



(12); 



(13). 



To agree with the notation in KLE1N-FRICKE, ' Modul-Functionen,' 1, p. 688, put 



(14), 



=*y 



_ 



256(1 - 



^ + 1/2 = 1 



and denoting the tetrahedron-irrationality by f, 



x = TIS - 2, y = T 12 3 



8 = ( 



18 



and GIEUSTER'S r 12 (' Math. Ann.,' 14) is given by 



36 



36 



_ 3 Q 



t/y O 



So also ^ 48 can be discussed by a trisection of p. = 16, by putting 



(16), 



(17); 



(18), 



(19): 



(20); 

 (21). 



(22). 



