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q =0.oooi8ii6
in the first case g is = O.00002753 [q = 0.ooo 17905 Reg.]
» » second g » =0.00002974 [q = O.00018H6 Wulln.] •
This uncertainty, which does not amount to more than
O.00000221, will perhaps seem to be very unimportant but would
indeed be most fatal, if it was not neutralized to a great degree
by a stratagem in the method. An easy calculation shows
that the influence, which this uncertainty, as to the real
coefficient of expansion of mercury, excercises upon the final result,
is in some cases about 5 to 10 times greater than the
disturbance caused by unavoidable errors of observation. I think,
that the original number O.00017905 of Regnault represents the
average coefficient of dilatation of mercury below zero more
closely than O.oooisno. Therefore the following results are
calculated by means of the constants
q = 0.00017905 g = 0.00002753
The volumes of pure wafer and ice are also calculated by
means of
q = 0.00018116 g = 0.00002974
to facilitate the comparison with the calculations of Pliicker
and Geissler, which are founded upon a similar
assumption. 1 In both cases the values of q and g arg supposed to
be constant within the temperatures of observation.
This assumption is of course not correct, but is an almost
unavoidable consequence of the prevailing uncertainty, as to
the real dilatation of mercury - at low temperatures and from
the chosen standard of temperature, which involves:
q — g = constant
from which it follows, that the variations of q and g must
be equal. The value of g being only 1/6 of q, it follows, that
the expansion of glass varies 6 times more rapidly than that
of mercury. In order to avoid the application of this
consequence, which is hardly acceptable, if q is supposed to vary
below zero in the ratio given by the formulae, I have
supposed both q and g to remain constant and consequently to
1 q = 0.00018058.
2 In the course of this research the author has gained the conviction,
that the dilatation of mercury below zero is not exactly represented by the
formulae and the coefficients given by Regnault a. O. for higher
temperatures, and that this subject highly needs a repeated experimental research.
The alteration in the coefficient of dilatation, which begins to appear on
approaching the point of solidification of mercury, is the real cause of the
discrepancy between the air-thermometer and the mercury thermometers.
The author hopes to return to this subject in a future paper.
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