302 



PROFESSOE A. G. GEEENHILL ON THE 



(14), 



as in fj. = 16, so that the bisection formulas can be carried one stage further. 

 We find now 



.AK' V 

 V 



dn :i - 6 - iV _ 



1 + 



+ 



x/( 



-V 



(15). 



50. fji = 40, v = K 

 The relation 



leads to 



or putting m m? = n, 



N 



10 



With 



and with 



= 



+ (/3 2 - j3 + )[(! - 4?i)/3 2 - (1 - &) - ] = 

 /3 = ; , and arranged in powers of w, 



- 1 /72 /<7 i \~\ 2 



- [56 3 + 36 2 + 6 1 + 2a (26 + 1)] bn 

 + 6 2 (6 2 + a) = 



6 _ (1 + 26) 2 - a 4 

 * ~ (1 + 6) 



this becomes 



(b + I) 4 [56 2 - 1 - a (A* - 46 - 1)] 



- (6 + 1) [56 3 + 3/> 2 + 6 - 1 + 2a (3b + 1)] [(26 + I) 2 - a*] 

 + (& 2 + a) [(26 + I) 2 - a*] 2 = 



A factor 1 a may be cancelled and 



. 6 5 + A 2 6 4 + A S 6 3 



06 



(1) 

 (2), 



; 



(3). 



(4), 

 (5) 



(6). 



- a 4 (1 + a + a 2 -|- a 3 + a 4 ) = 

 A 2 = 3a (1 + + a 2 ), A 3 = 0, A, = - a (1 + a + a 2 - a 3 + a* + a fi + a 6 ) 



(8). 



