10 in. below it, the
distance varying according to the shape of the bob, so that the heat
expansion of the bob may cause its centre of gravity to rise and
compensate the effect of its increased moment of inertia. Again the
suspension spring is measured for isochronism, and an alloy of steel
prepared for it which does not alter its elasticity with change of
temperature. Moreover, since rods of invar steel subjected to strain
do not acquire their final coefficients of expansion and elasticity
for some time, the invar is artificially "aged" by exposure to strain
and heat.

These considerations serve as a guide in arranging for the
compensation of the expansion of the rod and bob due to change of
temperature. But they are not the only ones required; we have also to
deal with changes due to the density of the air in which the pendulum
is moving. A body suspended in a fluid loses in weight by an amount
equal to the weight of the fluid displaced, whence it follows that a
pendulum suspended in air has not the weight which ought truly to
correspond to its mass. M remains constant while M_g_ is less than in
a vacuum. If the density of the air remained constant, this loss of
weight, being constant, could be allowed for and would make no
difference to the time-keeping. The period of swing would only be a
little increased over what it would be _in vacuo_. But the weight of a
given volume of air varies both with the barometric pressure and also
with temperature. If the bob be of type metal it weighs less in air
than in a vacuum by about .000103 part, and for each 1 deg. F. rise in
temperature (the barometer remaining constant and therefore the
pressure remaining the same), the variation of density causes the bob
to gain .00000024 of its weight. This, of course, makes the pendulum
go quicker. Since the time of vibration varies as the inverse square
root of _g_, it follows that a small increment of weight, the mass
remaining constant, produces a diminution of one half that increment
in time of swing. Hence, then, a rise of temperature of 1 deg. F. will
produce a diminution in the time of swing of .00000012th part or .0104
second in a day. But in making this calculation it has been assumed
that the mass moved remains unaltered by the temperature. This is not
so. A pendulum when swinging sets in motion a volume of air dependent
on the size of the bob, but in a 10 lb