788 PROFESSOR G. G. STOKES ON THE COEFFICIENT OF VISCOSITY OF AIR, 
of the velocity are much greater for z than for x or y. Hence in (3), and the corre¬ 
sponding equation for v, the first two terms in the right-hand members may be 
omitted, giving, by (2), 
and then, from (1), 
or, in polar coordinates, 
# _^TT 
dx Id ’ 
ddpdrp _ 
dx" dy 2 
ddp . 1 dp 1 d' 2 p 
'd? + rdr + ?dd 2 
clp _ _12 /£ 
dy h? : 
12 /iw 
h 3 
x, 
12/mo 
Id 
r cos 6 
(4) 
and if we take, as we may, p to mean the excess of pressure over the pressure in 
equilibrium, we have the conditions that p shall vanish when r—a, and that p shall 
not become infinite at the centre. 
The equation (4) and the conditions at the mouth and centre may be satisfied by 
taking 
P =f(r) cos 9, 
which gives, from (4), 
The integral of this equation is 
/M 
_ 3 
B 
2 Td r3 + Ar+ r’ 
where A, B, are arbitrary constants. The conditions at the centre and mouth give 
whence 
o / o 
_ . ollco a M 
B = 0, A = 
p = 008 
Tlie moment of this pressure about the axis of y is \\p.r cos 9.rdrd9, or 
7 r/iw'cd 
8 Id ' 
• (B) 
The moments (B) and (A) are as a 2 o/ to 4/fw, and the works of these moments in 
the time dt are as era/ 2 to 4/e 2 oj 2 . If this ratio be denoted by n to e, and io, a/, are 
the components of an angular velocity round an axis in the plane of xz, inclined at an 
angle 8 to the axis of 2 , 
I Cl Q 4 /('“ 
fair o = ,-n. 
cr 
