222 PROFESSOR A. G. GREENHILI, ON THE 



4. When r is an aliquot /A th part of the imaginary period 2w :! , so that 



or 



2ra)., 



(1), 



and fjir is congruent to a period, then 



P (/xr) = oo , P (w<>) + P (p. - m) v = 



so that p.P (o) is given by equation (7), 3, by putting n = p. 1, with the 

 additional condition that 



= oo , s (mv) f> (ju, w) v 



or 



Tims 



(3), 

 (4). 



xt/ 



y - 



X 



y 



7]1 = o, P(fr) + P(Gr) = 0, so that adding (11) and (12), 3, 



and, similarly, 



,, = o. 



y x y x if 



y (v ~ x ) z i (v ~ 



' - - 



y, 7 = 0, 17P(v) = 5 



lfl = 0, 19P (v) =3 



7iu 



7io 7n 



