STRAIN ON THE PHYSICAL PROPERTIES OF MATTER. 
813 
the vibrator without at the same time altering the mass in order to prove the second 
law deduced above, I failed entirely, and, though I adopted numerous changes of the 
mass of the vibrator, of the amplitude of vibration, of the vibration-period, and of the 
nature of the metal, in no case was I able to get a step further towards proving the 
above-mentioned law. On the contrary, when I had eliminated' the effect of the 
resistance of the air in the manner now to be described, I found the logarithmic 
decrement nearly independent of the vibration-period in some cases and increasing 
with it in others. 
Mode of eliminating the Effect of the Resistance of the Air. 
In a paper quite recently presented to the Royal Society, I have shown that the 
following formulse for finding the logarithmic decrement due to the resistance of the 
air may be deduced from Prof. G. G. Stokes’s valuable memoir “ On the Effect of the 
Internal Friction of Fluids on the Motion of Pendulums”:—* 
For a cylinder vibrating horizontally 
. , 7 dk'pcdP . 
log 10 dec. = 2 ” x - log 
10 e > 
( 3 ) 
where p is the density of the air, a the radius of the cylinder, l the length of the 
cylinder, I the moment of inertia of the vibrator, and k! is a constant, provided the 
vibration-period, the diameter of the cylinder, and the nature of the fluid remain 
unchanged. 
For a pair of cylinders of equal mass and dimensions, suspended vertically at equal 
distances from the axis of the wire, 
log 10 dec. = 
161 
togio 
( 4 ) 
where (3 is the diameter and l the length of each cylinder, and d is the distance 
between the two axes of the cylinders. 
We further have from Prof. Stokes’s paper the formula 
. <»> 
where t is the vibration-period and g. is the coefficient of viscosity of air. When m 
has been determined, k’ can also be determined by the aid of the Table given on p. 46 
of Prof. Stokes’s paper. 
By several very carefully executed series of experiments with vibrating cylinders 
* (1850) ‘ Carab. Phil. Soc. Trans.,’ vol. 9 No. X. 
