792 PROFESSOR G. G. STOKES OK THE COEFFICIENT OF VISCOSITY OF AIR. 
In the case of the cylinder the motion is in two dimensions, and is most con¬ 
veniently referred to polar coordinates r, 9, the origin being in the axis. The radius 
of the cylinder will be denoted by a, the outer or inner radius according as we are 
dealing with the air outside or inside. 
The mode of proceeding is precisely analogous to that in the case of the sphere, 
and, q being the whole velocity, we have 
q = e^f^r), .(8) 
where 
/.» + ;/.'M - = 0 ;.(9) 
and the condition at the surface gives 
e ini f x (a) — coct .(10) 
If T be the tangential pressure on the cylinder, 
. (n) 
the sign being + or — according as we are dealing with the air outside or inside. 
The moment of this pressure on a length, l, of the cylinder is 
± 2*paW(f{(a)---JM)) = ± 2MV -1)*>..(12) 
The equation (9) cannot be integrated in finite terms. Nevertheless, in the case of 
the air outside, the expression (12) for the moment may be obtained in a finite form 
in terms of two functions, k, k', which I had occasion to tabulate for the purpose of 
finding the resistance of a viscous fluid to a pendulum of the form of a cylindrical 
rod. 
Putting, as in my former paper, 
fi( r ) = /o'M».(13) 
(/i,/ 0 , are the functions there denoted by F g , F 3 ), we have 
fo\ r )+;Jo{ r )- m ¥o( r ) = 0 .( 14 ) 
Now in both problems (that of my former paper and that of the present note) the 
function f 0 (r) satisfies the same differential equation (14) and the same condition of 
