Me. w. m. hicks on the motion of two spheres in a FLUID. 467 
and determining A by the condition that p{= 
we shall find 
and 
and 
(ri-A) 
i-wr 
l-cf* 
1 — Cl 
G—p «_i — + 
6 p'u • 1—g 3 * -8 
« c—p H _~^ l-f‘ l 
. r a -/)^- 1 ! 8 / 
l-g*. j ^ 1 
L x - 27 Tllpllc^Li 
ab{l—cf) q“ 1 ] 3 
~c l-g^J 
Similarly L,= same quantity. 
Therefore, denoting by M' the mass of fluid contained in a sphere of radius unity 
where 
L = — 47rt4 1 w 2 Q'(g r )= — SWupioQ^q) 
Q '(?)= s dr =$;' 8 
(«) 
Tables for Q and Q' are given at the end of the paper for equal spheres, and for the 
case of a=2b. 
7. When the sphere A is moving perpendicularly to B A, the original doublet is one 
perpendicular to the line B A, as also its images. Suppose A is moving along the axis 
of x, A B being the axis of z. Then the normal velocity at a point P on the sphere A 
is v sin 6 cos y, (a. tty) being the polar coordinates of P; and the kinetic energy is given 
by 
2 T= — cdv [ I [<£] sin 3 9 cos y d9d\ 
Jcwo 
Let p, be the magnitude of a doublet at a point distant p from the centre of A; the 
part of r/> depending on this is 
/x?’ sin 0 cos y 
{r 2 + p 2 + 2pr cos 
and the part of 2T depending on this is 
