A NEW FORM OF FLEXIBLE BAND DYNAMOMETER.

[Footnote: Read before Section G of British Association.]

By Professor W.C. UNWIN.


[Illustration: Fig. 1.]

In the ordinary strap dynamometer a flexible band, sometimes carrying
segments of wood blocks, is hung over a pulley rotated by the motor, the
power of which is to be measured. If the pulley turns with left-handed
rotation, the friction would carry the strap toward the left, unless the
weight, Q, were greater than P. If the belt does not slip in either
direction when the pulley rotates under it, then Q-P exactly measures
the friction on the surface of the pulley; and V being the surface
velocity of the pulley (Q-P)V, is exactly the work consumed by the
dynamometer. But the work consumed in friction can be expressed in
another way. Putting [theta] for the arc embraced by the belt, 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