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-comes impossible, because the ice from such water has no definite
■volume at its melting point. 1
We may simplify the calculation without the least injury
to the exactness of the results, by assuming pi = p in the
■quotient
Pit, —pt
^ t, -t
for temperatures not exceeding the limits — 10° and + 10° C.
The formula (4) then becomes
(5) w = Lg-Qq + qp. + ^
w
It is self-evident, that instead of the volumes L, Q, p, pi, W
we may as well substitute in the formula the weights of the
corresponding quantities of mercury.
On page 261 I have alluded to the grave inconvenience,
which the uncertainty of the real value of the coefficient of
■expansion of mercury involves. I will now trjr to show, how
the errors arising from this deficiency in the present state of
science can be counterbalanced and for a great part eliminated
from the results by a special arrangement.
The quantities dependent upon the value ascribed to q in
formula (5) are
Lg — Qq.
and
qpi-
The latter quantity is almost devoid of influence upon the
result, on account of its smallness. We may also reduce the
influence of the former considerably by selecting the
quantities of mercury and of water so, that
Lg — Qq = 0.
In this case the quantity
Pi — P
ti — t ’
which is independant of q and can be determined by direct
observations with great exactness, will be predominating in
the result, and the influence of erroneous assumptions of the
values of q and g will be immaterial. 2
In the series of determinations of the volumes of the
frozen water I, A given in chapter 3
1 This fact (hitherto unnoticed) is the reason, why I have referred the
coefficients of dilatation to the quantity of liquid (instead of solid) water
contained in 1 cc. at 0° C.
- It must be remembered, that the values of q and g are dependent on
each other and must vary in the same sense.
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