the variation of the 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