774 
MR. H. TOMLINSON ON THE COEFFICIENT OF VISCOSITY - OF AIR, 
These processes were repeated during some eight or nine hours of each day through a 
period of three days, with the following mean* results :— 
Paper Cylinders on. 
Temperature of the air 
in degrees Centigrade. 
Temperature of the 
wire. 
Barometric height 
in inches. 
Period of a single 
vibration in seconds. 
Logarithmic 
decrement for one 
vibration. 
12-02 
12-43 
29-872 
6-8373 
•0036476f 
Paper Cylinders off. 
12-25 
12-31 
29-817 
6-8202 
•0009103 
The moment of inertia of the whole vibrator when the paper cylinders were on 
was 33773 in centimetre-gramme units. 
Mathematical Formulae necessary for the Investigation. 
Before it can be shown how the results given above were made use of in finding 
the coefficient of viscosity of air, it will be necessary to point out how the requisite 
mathematical formulae can be obtained. I will first take the case of a cylinder 
vibrating horizontally under the influence of the torsional elasticity of a wire attached 
to its centre and hanging vertically. 
Conceive the cylinder divided into elementary slices by planes perpendicular to its 
axis. Let r be the distance of any slice from the middle point, 6 the angle between 
the actual and the mean positions of the axis, c/F that part of the resistance expe¬ 
rienced by the slice which varies as the first power of the velocity. Then, calculating 
the resistance as if the element belonged to an infinite cylinder moving with the same 
linear velocity, we have by Art, 31 of Prof. Stokes’s paper— 
_ PM V dj 
_ T dt’ 
where M/ is the mass of fluid displaced by the slice, r = the vibration-period, 
dV 
and V is a constant, provided the vibration-period, the diameter of the cylinder, and 
the nature of the fluid remain unchanged. 
* I Lave not thought it necessary to give here more than the mean values, as in a portion of a paper 
on the internal friction of metals, which I hope shortly to be able to offer to the Royal Society, I have 
entered fully into the details of experiments very similar to these. 
t Mean of eight trials, each of 200 vibrations, the numbers varying from '0036300 to '0036969. 
