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by zero of this part [the reservoir and stem] is denoted by L.
Let Q be the volume of the mercury in the reservoir, the
capillary and the stem unto A and B. The stand of the mercury
column in the scale-tube at zero is 0. When the temperature
of the mercury bath has risen t degrees above zero, the mercury
index is supposed to have moved f millimetres. If the
temperature rises to ti degrees, the mercury index will indicate
fi millimetres. The scale-tube is supposed to possess
the-tem-perature of the room, which was regulated so as never to vary
more than from 2 to 4 degrees from zero, and the mercury
columns measured in the experiments are reduced to zero. I
think this calculation, which is almost without any influence
upon the results, may be safely omitted in the following
for-mulæ.
q is the coefficient of absolute dilatation of mercury
g the coefficient of absolute dilatation of glass [see p. 261]
x the total dilatation of the water between 0° and t°
Xi » total » » » » » 0° » ti°
p » volume in cc. corresponding to / m.m.
pi » » » » » » f\ »
W is the volume in eub-centim. at 0° of the water in the
instrument. Then suppose the temperature of the instrument
to rise from 0° to t°. In this case
(1 )...........x = [Lg — Qq] t + p + pqt
and if the temperature rises from 0° to ti°,
(2 )..........xi = [Lg — Qq] ti + pi + piqti.
By subtraction of (1) from (2) we obtain :
x, — x = [Lg — Qq] (ti — t) + pi — p + (piti — pt) q
X, —X T ^ , p.— p , Pit,— pt
(3 ) TT=r = Ls — Qt + + ‘1 t.-t "
The coefficient of expansion »w> of water between t° and
ti° referred to the unit of volume at 0° will be
^ , Pi —P , Piti —pt
(4) w = Lg-Qq + T—t+q tl-t
w
This formula also holds good below zero, whether the water
in the instrument is frozen or liquid. The standard unit in
either case is the cub. centim. of liquid water at zero. Only
in the case of pure ice another unit of volume is also
introduced, viz. the cub. centim. of the ice at its melting point. In
the case of ice from salt or brackish water this calculus be-
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