424 Haughton and Reynolds—Eaperiments to determine the 
wire of suspension was 6108 centimeters, and its diameter was 
0°889 millimeter. The diameter of the iron tub was 2 feet 4 
inches, and the depth of water contained in it was 1 foot 9 
inches. 
The method of observation was as follows: the indices of 
the ball having arrived at the zero of rest, the ball was then 
displaced by a torsional movement of the wire, and allowed to 
regain its position of rest by a succession of vibrations of 
sh atime amplitudes. 
uantities observed were, the time of vibration and the 
rate of iminution of the amplitude. 
The equations of motion of the apparatus are thus found :— 
Px 
mee es Seem ()" 1 
. aa X=; (1) 
where «=the varying a of moc tes of the surface of 
the ball measured from the zero of rest; X = ae tangential 
forces bes torsion and drag” acting at she oin 
me that for low Mer el the frieaiin will be 
pivpiobtiohal to’ the velocity, we shall hay 
X=he — f— Th (2) 
where & is a coefficient depending on torsion, and / is a coeffi- 
cient depending on “dra 
It is easy to see that the complete integral of the equation of 
motion, 
dx ee ae 
atte t+He=0, (3) 
must be of the ca 
= ae™ cos nt + be™ sin nt, (4) 
where a and d are wie ail constants, and where m and n have 
the values 
Peal das J 
If we reckon the time from the commencement of the oscil- 
lation, equation (4) reduces to 
xe = ae™ cos nt. (6) 
If T denote the time of a complete double oscillation, we find 
from the above 
fnT 
eP (7) 
where 0 ee of & (n+1)" vibration ; 6,=amplitude 
of the first v ion 
From (7) we aie the following working equation, or use 
in the calculations to cores the coefficient of frictio 
Ss ef nT oS (a =). ®) 
