MR. H. TOMLINSON ON THE COEFFICIENT OF VISCOSITY OF AIR. 
775 
Let G be tbe moment of the resistance, l the whole length of the cylinder, a the 
radius of the cylinder, and p the density of the fluid ; then 
and 
whence 
M' = 7 t pet'dr, 
n*tfpa*l 9 dd 
G = 
logv dec. = 
12t dt ’ 
TT~k' paH* 
241 ’ 
I being the moment of inertia of the whole vibrator ; thus 
, , irVdpaH 3 . 
log 10 dec. = 24I log 10 e. 
(1) 
When we have a pair of cylinders of equal mass and dimensions suspended 
vertically from points equally distant from the axis of the wire, we can easily prove in 
a manner similar to the above that the logarithmic decrement due to the resistance of 
the air on the cylinders is expressed by the formula 
log¬ 
ic 
, it*p&Wk’ i 
dec. = —jgf — logic 
(?)* 
If the logarithmic decrement be known, we can determine from (2) k' , and hence, 
by interpolation, from the table given on p. 46 of Prof. Stokes’s paper, m, this last 
being connected with p, the coefficient of viscosity, by the formula— 
( 3 ) 
Since /3, r, and p are known, we can from (3) find p. 
In the case of two spheres of equal mass and dimensions there is no difficulty in 
obtaining the following formulae from the data on p. 32 of Prof. Stokes’s paper :— 
logio dec. 
Trim'dd . 
4(1 + 2 kW) ° g ’ 10 
( 4 ) 
where I is the moment of inertia of the whole vibrator, Mf the mass of fluid displaced 
by each sphere, and k and k! are connected with p by the equations— 
* In this equation and in equation (4) the effect of the rotation of the cylinders about the axes is 
neglected. For the necessary correction see the end of the paper. 
