1, 2, according to the number of seconds a
day by which they will accelerate; and the pendulum adjusted at first
to lose a little, perhaps a second a day, when there are no weights on
the collar, so that it may always have some weight on, which can be
diminished or increased from time to time with certainty, as the rate
may vary.

Compensation.

The length of pendulum rods is also affected by temperature and also,
if they are made of wood, by damp. Hence, to ensure good time-keeping
qualities in a clock, it is necessary (1) to make the rods of
materials that are as little affected by such influences as possible,
and (2) to provide means of compensation by which the effective length
of the rod is kept constant in spite of expansion or contraction in
the material of which it is composed. Fairly good pendulums for
ordinary use may be made out of very well dried wood, soaked in a thin
solution of shellac in spirits of wine, or in melted paraffin wax; but
wood shrinks in so uncertain a manner that such pendulums are not
admissible for clocks of high exactitude. Steel is an excellent
material for pendulum rods, for the metal is strong, is not stretched
by the weight of the bob, and does not suffer great changes in
molecular structure in the course of time. But a steel rod expands on
the average lineally by .0000064 of its length for each degree F. by
which its temperature rises; hence an expansion of .00009 in. on a
pendulum rod of 39.14 in., that is .000023 of its length, will be
caused by an increase of temperature of about 4 deg. F., and that is
sufficient to make the clock lose a second a day. Since the summer and
winter temperatures of a room may differ by as much as 50 deg. F., the
going of a clock may thus be affected by an error of 12 seconds a day.
With a pendulum rod of brass, which has a coefficient of expansion of
.00001, a clock might gain one-third of a minute daily in winter as
compared with its rate in summer. The coefficients of linear expansion
per degree F. of some other materials used in making pendulums are as
follows: white deal, .0000024; flint glass, .0000048; iron, .000007;
lead, .000016; zinc, .000016; and mercury, .000033. The solid or
cubical expansions of these bodies are three times the above
quantities respectively.

The first method of compensating a pendulum was invented in 1722 by
George Graham, who proposed to