424 PROCEEDINGS OF THE AMERICAN ACADEMY. 

 .'. v = —±f7r or B — . 



7T 



Hence finally 



v . . 



W = CJ) + l i]/ = - (l TT — log t). (b) 



7T 



Take now in equation (a) 



a — a > 1 

 b = -l 

 c = 

 which becomes 



. = c ( v(« -«x« + i) + 1=5 io g vr^a + vr+i 



\ l V t — a — \/t + 1 



. /- . Vt — a + i V a (t + 1 ) \ 



- « V « log -— , . ^ / + T ). (c 



Make the origin in the 2-plane correspond to t = — 1 and let C = — i X>, 

 then 



z 



o-\-oi = — iDy — - — log 1 — * V« l°g 1 + T ) 



from which follows T = 0. 



When t = a z = g + hi, 



then 



z = g + hi = - 2)i f^p log (- 1) - i Va log (- 1)) 



n ■(}_-" ■ ■ r \ 



— — JJl I 7T I — i v a IT I \. 



From which follows, equating real and imaginary parts, 



h = — D \/a 7r h 



\ _ a and D 



g = + D — — - 7t Va tt' 



