therefore 



Mr Greenhill, Complex Multiplication [Oct. 29, 

 dy 



•)- + - + ( — a — -7-g- J # 2 > V- ^°^ 



(a %c Vac 2 ia'c/ j 



c 



where Jf- V -& (| + i) - ^(« + * ^), 



2 1 



if /5 2 =-- = a+i ° 

 P a 2 J _2_ 



ix 2 c ac 2 



or a 4 + 2t'ca 3 - 2t'ca 4- c 2 = ; 



but this is the equation of which one root is 



a = en ±(K-iK'): 



- en 2u en it 



f ic ic fen* u + 2ic en 3 w — 2ic en w + c 2n 5 



en 3w en u \cn 4 tt — 2ie en 3 u + lie cnu + c i 



ic ic 



With the above values of c and a, the value of M should reduce to 



|(HiV5). 



When ~ = V9, 2&# = (2 - V3) 2 , 



and c = (2 + V3) 2 + 2 JB (2 + V3), 



