STRAIN ON THE PHYSICAL PROPERTIES OF MATTER. 
815 
Equation (4) does not take into account the effect of the air due to the rotation of 
the cylinders about their axes ; the correction required for this is, however, very 
slight.* When necessary, this correction was made by means of the following 
formula: t 
2M ' fJLT ^ 
J p ^ ^9 .(7) 
where \ a is the natural logarithmic decrement due to the rotation of both cylinders 
about their axes, M' is the mass of fluid displaced by each cylinder, and 
P= / m.u 0-375 0-4922 
\/2 ' ' \/2f y/2f» 
( 8 ) 
f being put, by way of abbreviation, for a ^/— • cc, where a is the radius of the cylinder, 
The Extent to which the Internal Friction of Metals depends upon the Vibration-Period. 
We are now in a position to examine how far the loss of energy, resulting from 
internal friction, depends upon the vibration-period of the wire. I propose, therefore, 
to give, in illustration, the results of four sets of experiments on piano-steel, on copper, 
on zinc, and on tin. 
Experiment III. 
Unannealed Piano-Steel 0’0824 centim. in diameter and 602 centims. in length. 
Bar B x and Cylinders C 2 . 
Vibration-period 
in seconds. 
Observed logarithmic 
decrement for one 
vibration. 
Logarithmic decrement 
due to the 
resistance of the air.J 
Logarithmic decrement 
due to 
internal friction. 
Temperature in 
degrees Centigrade. 
3-9337 
•0010497 
•0006950 
•0003547 
10-00 
5-5210 
•0009563 
•0006459 
•0003104 
10-64 
8-1750 
•0009633 
•0005918 
■0003715 
10-12 
12-5130 
•0010710 
•0007077 
•0003633 
9-70 
16-9720 
•0012052 
•0008502 
•0003550 
11-38 
Mean 
.. 
•0003510 
10-37 
* Would not in any case exceed f per cent, of tire whole, 
f Kindly furnished by Prof. G. G. Stokes. 
J It will he observed that the numbers in this column at first decrease with the time of swing and 
then increase. This arises from the fact that the time of swing, as well as the dimensions of the 
vibrator, come into the equations used for determining the logarithmic decrement due to the resistance 
of the air. 
