292 PEOFESSOK A. G. GREENHILL ON THE 



44. ^ = 36, v = K + 2r +-^ K't. 



18 



The relation 



{()-8(9v)}> = (*-)(- 9>) (1) 



leads to 



N 9 _. 1+6 ,, 



D B 1 - b 



ft -.N 9 + D 9 _ *[(c T _2)j + e] 



N,-:D,"jp|y.-f(^:-f + fj 



ami putting 



r -1 = 9, " 1 = ', 2r - 1 = , e ~ l = t, t + 1 = u (4), 



- 



and thereby the superfluous factor a 2 /r is cancelled, and finally 

 aW + ( 1 + 3'< + - G 3 + + - (1 ) 1 s 



- :3 (1 + i - -2rr - 2 :{ ) a :! //' + (3 + - 3- - :i ) (i = (6), 



a cubic equation for b { . 

 Putting as before 



' 3 -"=t ( v~; ) (?) - 



this relation (G3) becomes 



[V<. + 2(1- -) r]- - ( ! - tt ? 1(2 + a) ( .- + (1 + aff = (8), 



<:' + (i ._ ) ( 2 + ) c + 2(1- o-) c + (l - a) (1 + ) 2 = (9), 



and jmtting r = (1 + ^) ry, 



(1 + a) <f> - (1 - n) (2 + '<) 7 - + 2 (1 - ) q + 1 - = (10), 



and arranged as a quadratic in a, 



,,-* - ((/' - ,f - 2? - 1) - (,/ + 1) (f + ,, + 1) = (11), 



Q = /' + 2r/ + 5</' + 10</ :i + 10r/ + 4</ + 1 (13), 



as in /A = 18, 32 ; and 



c = q* + f-2g-i 



2q 



