PROFESSOR G. G. STOKES ON THE COEFFICIENT OF VISCOSITY OF AIR. 787 
very simple if we treat the distance between the disks as very small compared with 
the radius, neglect the special actions about the edge, and further neglect the inertia 
of the air, as we safely may, since it was small in Maxwell’s experiments, especially 
those in which the disks were at a small distance apart, and therefore the influence of 
viscosity the greatest; or those again in which the air was rarefied. 
Let the plane of a movable disk in its position of equilibrium be taken for the 
plane of x, y, the axis of figure for the axis of z, and the intersection of a horizontal 
plane with the plane of the disk for the axis of y ; and let the opposed fixed plane be 
parallel to the plane of x, y, and at a distance h from it. Let a be the radius of the 
disk. 
First, as regards motion round the axis of figure. Let oj be the angular velocity of 
the disk. Then, according to the simplifications adopted, the motion of the fluid will be 
a motion of simple shearing, such that the velocity at a point whose semi-polar coordi¬ 
nates are r, 0, z, will be ojr(li—z)jh in a direction perpendicular to the radius vector. 
It will suffice to write down the moment of the force which this calls into play, which 
is 
TTyCdoj 
2 h ' 
Next, for motion round the axis of y. Let oj' be the angular velocity; u. v, w, the 
components of the velocity; U, V, the mean values of u, v, from 0 to h. Consider the 
prism of fluid standing on the base dx dy, and extending between the planes. As the 
volume of the prism is diminished at the base by oj'x dx dy dt in the time dt, the excess 
of the volume of the fluid which flows out across the face hdy, whose abscissa is 
x-\-dx, over that which flows in across the face hdy, whose abscissa is x, plus the 
similar difference for the pair of faces hdx, must equal oj'x dx dy dt. This leads to the 
equation 
7 dJJ. 7 dY 
h—-\-h - ■ = oj x. 
dx dy 
( 1 ) 
But, for motion between two close parallel planes, the velocity parallel to the plane, 
and its components in two fixed directions in that plane, vary as z(h—z), and there¬ 
fore 
^ _GflA—y) y ....... ( 2 ) 
/r n~ v ' 
The first equation of motion is 
dp 
dx 
(dhc d~u dh/\ 
ysp+Ar+sy 
( 3 ) 
Now, on account of the smallness of h, the space-variations of the components u, v, 
5 H 2 
