use a bob of mercury, taking advantage
of the high coefficient of expansion of that metal. As now employed,
the mercurial pendulum consists of a rod of steel terminating in a
stirrup of the same metal on which rests a glass vessel full of
mercury, having its centre of gravity about 39 in. below the point of
suspension of the pendulum. For each Fahrenheit degree of temperature
the centre of gravity of the bob is lowered by the expansion of the
rod about 1/4000 of an inch. The glass vessel and the mercury in it
have therefore to be so contrived, that their centre of gravity will
rise 1/4000 in. per degree F. The glass having a small coefficient of
expansion, the lateral expansion of the mercury will be checked by it,
and this will help to raise the column. For the linear coefficient of
expansion of glass is .0000048 per degree F., whence the sectional
area of a glass vessel increases by .0000096 per degree F., and
therefore the coefficient of vertical expansion of a column of mercury
whose volumetric expansion coefficient is .0001 per degree F. is
(.0001 - .0000096) = .0000904. Let x be the height of the vessel
necessary to compensate a steel rod upon the bottom of which it rests.
Then, the coefficient of expansion of steel being .0000066 per degree
F., we have

x
--- (.0000904 - .0000066) = .0000066 X 39.14, whence x = 6-1/4 in.
2

It must, however, be remembered that the glass jar has some weight and
that it does not rise by anything like the amount of the mercury. This
tends to keep the centre of gravity down. So that the height of
mercury of 6-1/4 in. will not be sufficient to effect the compensation,
and about 6-3/4 to 7 in. will be required. Some authors specify 7 in.;
this is when the diameter of the jar is small. A certain amount of
negative compensation must also be deducted to allow for the changes
of temperature in the air, as will presently be seen; this amounts in
the case of mercury to about 1/5 in.

In consequence of the complication of all these calculations it is
usual to allow about 6-3/4 to 7 in. of mercury in the glass vessel and to
adjust the exact amount of mercury by trial.

Another very good form of mercurial pendulum was proposed by E. J.
Dent; it consists of a cast-iron jar into the top of which the steel
pendulum rod is screwed, having its end plunged into the mercury
contained in the jar. By this means the