[ 347 J ¥ Ip 
XLI. On the Viscosity of Pitch-like Substances. / By Prof. F. 
T. Trouton, F.R.S., and Mr. HE. 8. ANpREws, B.Sc.* 
HE various methods which have been proposed for 
measuring viscosity meet with difficulties when it is 
attempted to.apply them to the measurement of the viscosity 
of bodies such as pitch. The girder method has been applied 
to examine the viscosity of ice as well as methods depending 
on direct extension and compression ; but these apparently did 
not lead readily toa numerical determination of the coefficient 
of viscosity. The application of Stokes’ method, depending on 
the rate at which a spherical body—say a lead bullet—sinks 
through the material, seems apparently to have been pre- 
vented by the difficulty of knowing exactly its velocity in the 
middle of the substance, the terminal effects leaving consi- 
derable uncertainty. As described later, this particular diffi- 
culty was surmounted by the use of Roéntgen rays in some 
experiments made to compare the coefficient obtained by this 
method and that by the method described in this paper. 
To obviate some of the difficulties, a method was proposed 
involving the torsion of a cylindrical bar. In this method a 
constant torque was applied to a cylinder of the substance, 
and the relative motion of the ends observed. From these and 
the dimensions of the body the viscosity was calculated. 
From symmetry we may assume that any two planes in 
the body, lying at right angles to the axis of the cylinder, 
moye over each other, about the common axis, remaining 
plane all the while. 
Let dz be the distance apart of the two planes. Then, 
if w is the coefficient of viscosity of the material of the 
cylinder (supposed independent of the velocity), and dw the 
relative angular velocity of the planes, we have 
bo (°F 
i Yt 
6x 0 
where T is the torque applied. 
Thus we have 
T=27p °dr, 
Sree 
p= aU R”’ 
where U is the relative angular velocity per centimetre of 
length of the cylinder, and R is its radius. 
The form finally adopted for applying the method consisted 
in a shaft turning freely on anti-friction wheels with a 
pulley attached, from which hung a weight for the purpose of 
* Communicated by the Physical Society: read June 12, 1903. 
