MR. H. TOMLINSON ON THE COEFFICIENT OF VISCOSITY" OF AIR. 
781 
from rest to rest, M' is the mass of fluid displaced by each sphere, a is the radius of 
the sphere, and 
— Vi- 
In the case of the cylinders, which were hollow, we have to take into account the 
effect of the air both inside and outside. For the air outside we may take 
2M>t 
K= -j^-log 10 eP, 
where P is the real part of the imaginary expression 
• • ( 8 ) 
1 + 
6.6 
- + 
1.3.5.7 
P.3.5.7.9 , 1 3 .3 2 .5.7.9.11 
ma 
1(8 ma) ' 1.2(8 ma) 2 1.2.3(8ma) 3 "*"l.2.3.4(8ma) 4 
1 + 
1.3 
1 2 .3.5 1 2 .3 2 .5.7 
* ‘ 1 O O 
where 
to 
l(6ma) 1.2(8 maf 1.2.3(8ma) 3 
= (cos 45°+ \/ — 1 sin 45°). 
On expanding P in descending powers of a, we get 
P = 
fMT 
0-375 0-4922 
where 
JL _L L 5 . —_ 
^ 2 + •' ' \/2 f y/2 f 
/= 
( 9 ) 
This series may be used with advantage in all the experiments relating to the 
cylinders to estimate approximately the effect of the air outside, but, unless the value 
of f is decidedly larger, the value of \ a is best found from the formula 
N 4MVt ! _ /d + // 2 -1 
i P l °g™ e \k- 1)»+^’ 
( 10 ) 
where h, k', are the quantities tabulated at p. 46 of Professor Stokes’s paper. 
The corrections, as calculated from both formulae, were found to agree satisfactorily. 
For the air inside we may use, for such values of /y — a as we have here, the 
formula 
^ = 2 j^“(-Q) lo gi0 e, . . . 
( 11 ) 
