424 PROCEEDINGS OF THE AMERICAN ACADEMY. 



.'. v = —BTr or B= , 



Hence finally 



V 

 W = (f) + ilj/ = - (iTT — log t). (b) 



TT 



Take now in equation (a) 



a = o > 1 



wliich becomes 



1 — or _ Vt — a + Vt + 1 



z=c(V{t-a)it+l) + ^—-^\og 



\ ^ Vt — a — '\/t + I 



. /- , Vt — a + i V a (t + \) \ , ^ 



— % Va log , ^ ^ + r . (c) 



Vt — a — i V a{t-V\) J 



Make the origin in the 2-plane correspond to i = — 1 and let C = — ^ D, 

 then 



z ■=! o -^ i 



i D { — s— ^og 1 — « Va log 1 + r j 



from which follows r = 0. 



When < = a z =^ g -\- hi^ 



then 



2 = ^ + hi = - Z»/ r^^' log (- 1) - i Va log (- 1) j 



= — D i i ;- TTt t Vet TT ^ j . 



From which follows, equating real and imaginary parts, 



A = — D Vci TT I 



} — a and D = 



, — It — /— . 



g — + D — - — TT Va TT 



