lt, and [mu]
for the coefficient of friction,

Q/P = [epsilon]^{[mu]^{[theta]}},

or for a given arc of contact Q = [kappa]P, where [kappa] depends only
on the coefficient of friction, increasing as [mu] increases, and _vice
versa_. Hence, for the belt to remain at rest with two fixed weights, Q
and P, it is necessary that the coefficient of friction should be
exactly constant. But this constancy cannot be obtained. The coefficient
of friction varies with the condition of lubrication of the surface of
the pulley, which alters during the running and with every change in the
velocity and temperature of the rubbing surfaces. Consequently, in a
dynamometer in this simple form more or less violent oscillations of the
weights are set up, which cannot be directly controlled without
impairing the accuracy of the dynamometer. Professors Ayrton and Perry
have recently used a modification of this dynamometer, in which the part
of the cord nearest to P is larger and rougher than the part nearest to
Q. The effect of this is that when the coefficients of friction
increase, Q rises a little, and diminishes the amount of the rougher
cord in contact, and _vice versa_. Thus reducing the friction,
notwithstanding the increase of the coefficient. This is very ingenious,
and the only objection to it, if it is an objection, is that only a
purely empirical adjustment of the friction can be obtained, and that
the range of the adjustment cannot be very great. If in place of one of
the weights we use a spring balance, as in Figs. 2 and 3, we get a
dynamometer which automatically adjusts itself to changes in the
coefficient of friction.

[Illustration: FIG.2 FIG.3]

For any increase in the coefficient, the spring in Fig. 2 lengthens, Q
increases, and the frictional resistance on the surface of the pulley
increases, both in consequence of the increase of Q, which increases the
pressure on the pulley, and of the increase of the coefficient of
friction. Similarly for any increase of the coefficient of friction, the
spring in Fig. 3 shortens, P diminishes, and the friction on the surface
of the pulley diminishes so far as the diminution of P diminishes the
normal pressure, but on the whole increases in consequence of the
increase of the coefficient of friction. The value of the friction on
the surface of the pulley, however, is more constant for a given
variation of the frictional coefficient in Fig. 3 than in Fig. 2, and
the variation of the