776 
MR, H. TOMLINSON ON THE COEFFICIENT OF VISCOSITY OF AIR. 
in which a is the radius of each sphere. 
( 5 ) 
W 
Application of the Mathematical Formulae to the Results of Experiment I. 
It will be seen that the logarithmic decrement with the paper cylinders on is 
‘0036476, whilst with the paper cylinders off it is '0009103 ; therefore the logarithmic 
decrement due to the resistance of the air on the cylinders only is approximately 
'0027373. I write ‘ approximately’ because there are certain corrections to be applied 
which I will now proceed to describe. In the first place, the vibration-period, when 
the paper cylinders were on, though nearly the same as when the cylinders were off, 
was not quite the same. I therefore determined approximately the value of p, 
without making this or the other small corrections to be mentioned presently, and 
used this value to obtain approximately the logarithmic decrement which would be 
due to the resistance of the air on the cylindrical bar W and the cylindrical portions 
S, K, of the suspenders. The logarithmic decrement due to the resistance of the air 
on the other portions of the suspenders and on the disks m, m, was obtained by making 
independent observations, in which the bar was vibrated first with the suspenders on 
the bar, and then with the suspenders off, but with cylinders of equal mass placed 
inside the hollow bar W, so that the time of vibration should remain unaltered. 
Suppose that X represents the logarithmic decrement due to the resistance of the 
air on the bar and the suspenders, and that t v t 2 , are the vibration-periods with and 
without the paper cylinders respectively, then, with a sufficient degree of approxima¬ 
tion, provided t i does not differ much from p, we have the amount to be added to the 
uncorrected logarithmic decrement equal to 
Again, the temperature of the air and the pressure of the atmosphere were not 
quite the same with and without the paper cylinders. It can, however, be shown 
that for the small differences of temperature and pressure which we have here the 
logarithmic decrement will be independent of the temperature * and vary directly 
* The logarithmic decrement will not be independent of the temperature unless /i varies as the 
absolute temperature. If we adopt the results of recent experiments, the logarithmic decrement should 
approximately vary as / \/ !r-g p p w ^ere t is the temperature in degrees Centigrade. The correction 
which this would entail I have neglected, as being inappreciable in these experiments. 
