682 * Proceedings of the Poyal Society 
city in the plane perpendicular to the axis is less or greater than 
-— . It is to he remarked that in every case in which the globule 
is drawn in to the axis (except the extreme one in which its 
velocity is infinitely little less than that of the fluid, and its spiral 
path infinitely nearly perpendicular to the radius vector), the spiral 
by which it approaches, although it has always an infinite number 
of convolutions, is of finite length; and therefore, of course, the 
time taken to reach the axis is finite. Considering, for simplicity, 
motion in a plane perpendicular to the axis; at any point infinitely 
distant from the axis, let the globule be projected with a velocity 
v along a line passing at distance p on either side of the axis. 
Then if r denote the velocity of the fluid at distance unity from 
the axis j^which is equal to ~~ J, and if we put 
v L p l 
the polar equation of the path is 
r = 
np 
cos n6 
( 41 ), 
• (42). 
Hence the nearest approach to the axis attained by the glo¬ 
bule is np, and the whole change of direction which it expe¬ 
riences 
is 7r G-0 . The case of - - 2'3 is represented in the 
annexed diagram, copied from Tait and Steele’s book [§ 149 (15), 
Species Y.]. 
