PROFESSOR G. G. STOKES ON THE COEFFICIENT OF VISCOSITY OF AIR. 701 
acting perpendicularly to tlie plane passing through the axis and the element, the 
expression for which, reckoned positive when it acts in the direction of cr positive, is 
T = ^!wL = /^ 
and the moment of the force taken all over the sphere is 
| T 27 m 2 sin 6.a sin 6 <16 = § 7 wjjtcde i ” t (f\a) 
m 
= 2M 'ix'e h,t [f\a) — 
/(«) 
if [jl'=ii/p, and M' is the mass of the fluid displaced by the sphere. 
Now we have, by (2), (3), 
a) a = e in f(a), 
whence the expression for the moment becomes 
To get the whole moment, the above must be doubled, as there are two spheres. If 
d be the angular distance of the vibrating system from the position of equilibrium, 
we may write dS/dt for a>; and if the mixed imaginary within parentheses, with 
sign changed, be denoted by P + iQ, the real part, P, will be that which affects the 
arc of vibration, the imaginary part falling upon the time, which we do not want. 
The Napierian logarithmic decrement in one vibration will be got by dividing half 
the real part of the expression for the moment of the forces by the moment of inertia, 
or, say, MK 3 . It will therefore be 2M / p/P/MK 3 . 
Now we get, from (G), 
o . 3 
1 _ «/(«) _ . 
/(«) i + JL 
met 
and, taking the real part of this, we get finally, after reduction, 
3 3 
Q /q\ /T/ V& iy 0 o 
XT , 1 2/jL M VCt 22 rcr 
Map. log. dec, = ^^-- - ---r, 
where v 
- 
M I 1 c \ o O 
va 2v i a~ 
(0 
