MR. H. TOMLINSON ON THE COEFFICIENT OF VISCOSITY OF AIR. 
769 
which held in my experiments on the internal friction of metals, I have employed the 
torsional vibrations of cylinders or spheres attached to a horizontal cylindrical bar 
and moving in a sufficiently unconfined space. The mathematical difficulties con¬ 
nected with the use of vibrating spheres are not so serious, but those in which cylinders 
are concerned are very considerable. They both, however, have been surmounted by 
Professor G. G. Stokes in his valuable paper “ On the Effect of the Internal Friction of 
Fluids on the Motion of Pendulums,”* and to this paper I am indebted for the 
mathematics essential to the purpose of the present inquiry. 
Description of Apparatus and Mode of Experimenting. 
A wire, a b (Plate 42, fig. 1), was suspended in the axis of an air-chamber, W, made of 
two concentric copper cylinders enclosing between them a layer of water. The outer 
diameter of the air-chamber was 4 inches, the inner diameter 2 inches, and the length 
4-| feet. Resting on the top of the air-chamber and wedged into it was a stout 
T-shaped piece of brass, C, to the lower extremity of which was clamped one end of 
the wire. The lower extremity of the wire was soldered or clamped at b to a vertical 
cylindrical copper bar b Q, which was in turn clamped at Q to the centre of a 
horizontal bar V V. The bar V V consisted of a piece of thin, hollow, drawn brass 
tubing, of which the length was 30'70 centims. and the diameter P420 centim. This 
bar was graduated into millimetres and carried two suspenders, S, S, which were 
clamped to it at equal distances from the centre (fig. 3). The suspenders were each 
provided with an index such that their positions on the bar V V could be readily 
estimated to one-tenth of a millimetre. The mean diameter of the cylindrical portion, 
S K, of each suspender was 0‘3366 centim., and the length of this portion 8 - 50 centims. 
To the ends, K, of the suspenders could be screwed (fig. 3) hollow cylinders of stiff 
paper or metal, or spheres of wood ; when the former were employed the suspenders 
were provided with disks, m, m, of the same diameter as the cylinders, and about 
2 millims. in thickness. Two brass caps, D, D (fig. 4), provided with screws about 
8 centims. in length and 2 millims. in diameter, fit one into each end of the hollow 
bar V V, and can be easily removed from or placed in the latter. 
To begin with, two cylinders or two spheres were screwed on to the ends of the 
suspenders (in the former case right up to the disks m, m), and the logarithmic 
decrement and the time of vibration determined from a very large number of 
vibrations. The cylinders or spheres were now unscrewed, and, the brass caps, D, D, 
having been temporarily removed for the purpose, two brass cylinders, h, h (fig. 4), 
each of the same mass as either of the vertical cylinders or spheres which had just 
been removed, were, by means of companion-screws, cut along their axes, adjusted on 
to the screws attached to the caps D, D, and at such a distance from the latter as 
preliminary experiments had proved would give nearly the same vibration-period, 
when the caps should be replaced in the bar V V, as had existed before the vertical 
* ‘ Carnb. Phil. Soc. Trans.,’ vol. 9, No. X. (1850). 
MDCCCLXX XVI. 
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