. Now, let us suppose that we have two rods of equal weight,
one three feet long, the other six feet long. To an end of each we
fasten a 2-lb. weight. We shall find it much easier to wave the shorter
rod backwards and forwards quickly than the other. Why? Because the
weight of the longer rod has more leverage over the hand than has that
of the shorter rod. Similarly, if, while the mass of the rim of a wheel
remains constant, the length of the spokes varies, the effort needed to
rotate the wheel to and fro at a constant rate must vary also. Graham
got over the difficulty with a rod by means of the compensating
pendulum. Thomas Earnshaw mastered it in wheels by means of the
_compensating balance_, using the same principle--namely, the unequal
expansion of different metals. Any one who owns a compensated watch will
see, on stopping the tiny fly-wheel, that it has two spokes (Fig. 206),
each carrying an almost complete semicircle of rim attached to it. A
close examination shows that the rim is compounded of an outer strip of
brass welded to an inner lining of steel. The brass element expands more
with heat and contracts more with cold than steel; so that when the
spokes become elongated by a rise of temperature, the pieces bend
inwards at their free ends (Fig. 207); if the temperature falls, the
spokes are shortened, and the rim pieces bend outwards (Fig. 208).[39]
This ingenious contrivance keeps the leverage of the rim constant
within very fine limits. The screws S S are inserted in the rim to
balance it correctly, and very fine adjustment is made by means of the
four tiny weights W W. In ships' chronometers,[40] the rim pieces are
_sub_-compensated towards their free ends to counteract slight errors in
the primary compensation. So delicate is the compensation that a daily
loss or gain of only half a second is often the limit of error.

[Illustration: FIG. 206. FIG. 207. FIG. 208. A "compensating" watch
balance, at normal, super-normal, and sub-normal temperatures.]

KEYLESS WINDING MECHANISM FOR WATCHES.

The inconvenience attaching to a key-wound watch caused the Swiss
manufacturers to put on the market, in 1851, watches which dispensed
with a separate key. Those of our readers who carry keyless watches will
be interested to learn how the winding and setting of the hands is
effected by the little serrated knob enclosed inside the pendant ring.

There are two forms of "going-barrel" keyless mechanism--(1) The rocking