AT THE BOUNDARY OP A LIQUID IN MOTION. 
579 
By Helmholtz and Piotrowski’s paper we see that the ratio of the friction 
8-806 X -142217 
on silver to the friction on Hass is as 1 : ^ - - ^ = 1 : 1‘0022. 
® 8-779 X -I 42 ooo 
The change, if it exists at all, is according to these experiments less than 0'3 per 
cent. 
A modification of Piotrowski’s experiment -was then tried. Instead of filling the 
oscillating flask with water, it was filled with sand, and oscillated as a rigid body in 
a large beaker of water. The temperature could then be accurately observed, and 
the ordinary investigation of the oscillations of a rigid body in a resisting medium, 
and acted on by a force proportional to the displacement, will hold. 
Let k denote the frictional force proportional to the velocity, 
M the moment of inertia, 
X the logarithmic decrement. 
Then it is easily shown that 
XM 
where 
P = 
v/iri-sp)’ 
ju- being the force of restitution for unit displacement. 
. 7 2 _ 
• • — 4^2 + • 
Now in our case X has a value of about 0-2, and X^ can therefore be neglected in 
comparison with iH, 
.•. k = — (approximately). 
When the flask is silvered /r is unchanged, as the weight of silver is much too 
small to appreciably alter the bifilar couple, and, therefore, we get for the ratio of the 
frictions 
k _ _A,!' 
P “ XV^U ~ X'T' ’ 
where T and T' are the respective times of vibration. 
A thick platinum wire was attached to the bulb, and the bifilar arrangement fixed 
to this above the surface of the water. 
At the conclusion of the experiments, the bulb filled with sand was oscillated in air 
and the logarithmic decrement found to be a very small fraction of that observed 
when the bulb was in water. This meets the objection that the chief resistance 
4 E 2 
