difference of tensions to be measured is less. Fig.
3, therefore, is the better form.

A numerical calculation here may be useful. Supposing the break set to a
given difference of tension, Q-P, and that in consequence of any cause
the coefficient of friction increases 20 per cent., the difference of
tensions for an ordinary value of the coefficient of friction would
increase from 1.5 P to 2 P in Fig. 2, and from 1.5 P to 1.67 P in Fig.
3. That is, the vibration of the spring, and the possible error of
measurement of the difference of tension would be much greater in Fig. 2
than in Fig. 3. It has recently occurred to the author that a further
change in the dynamometer would make the friction on the pulley still
more independent of changes in the coefficient of friction, and
consequently the measurement of the work absorbed still more accurate.
Suppose the cord taken twice over a pulley fixed on the shaft driven by
the motor and round a fixed pulley, C.

For clearness, the pulleys, A B, are shown of different sizes, but they
are more conveniently of the same size. Further, let the spring balance
be at the free end of the cord toward which the pulley runs. Then it
will be found that a variation of 20 per cent. in the friction produces
a somewhat greater variation of P than in Fig. 3. But P is now so much
smaller than before that Q-P is much less affected by any error in the
estimate of P. An alteration of 20 per cent. in the friction will only
alter the quantity Q-P from 5.25 P to 5.55 P, or an alteration of less
than 6 per cent.

[Illustration: FIG. 4]

To put it in another way, the errors in the use of dynamometer are due
to the vibration of the spring which measures P, and are caused by
variations of the coefficient of friction of the dynamometer. By making
P very much smaller than in the usual form of the dynamometer, any
errors in determining it have much less influence on the measurement of
the work absorbed. We may go further. The cord may be taken over four
pulleys; in that case a variation of 20 per cent. in the frictional
coefficient only alters the total friction on the pulleys 11/4 percent. P
is now so insignificant compared with Q that an error in determining it
is of comparatively little consequence.

[Illustration: FIG. 5]

The dynamometer is now more powerful in absorbing work than in the form
Fig. 3. As to the practical construction of the brake, the author thinks
that simple wires for the flexible