SLOCUM. — FINITE CONTINUOUS GROUPS. 107 



If this transformation is denoted by T a , then from the symbolic equation 

 T b T a = T c we obtain the five relations 



(27) e f * t/=I1 + e~ c ° * '~ l = £ (e'' 3 v ~ x + e~ h V=1 ) (e" 3 v -=1 + e ~ " 3 V=i ) 



(28) « r » 4/=I1 - e~ Cs V31 = i (e' 3 V ~ l + e~ ''* ' ^ (e 3 ^ - e~ " 3 V '~ 1 ) 



(29) c 3 = a 3 + 6 3 , 



(30) ^- (e^- 1 + e-^'" 1 - 2) - ^^i (e^" 1 - ^ V ~ 1 ) 



'% ■" «-3 





X 





+ VzLi (e V-i_ e -M-i } 



(31) -^ (^ v - i + e-^-i - 2) + ^=^ C^ 1 ^- e ~ r3V '- 1 ) 



ii_ (e 's v - 1 + e - * 8 <=i „ 2) + ^vpi (e , 3 *- 1 _ e - * V_ I, 



Z 3 ii 3 



12<7 3 V 2a 3 J 



+ :V/ ~ J (^ V - 1 -^ M - 1 ) 



1 2 « 3 2 o 3 7 



Denoting the right-hand members of equations (30) and (31) by x tiut l $ 

 respectively, and solving for c 1 , c 2 > c 3 , we have 



