CONTINUOUS ELECTRIC CALORIMETRY. 
99 
are some objections to be considered. Chappuis’ formula (2) refers to the constant- 
volume nitrogen-thermometer at 100 centims. of mercury initial pressure, whereas 
the difference-formula (l) was obtained with a constant-pressure air-thermometer at 
76 centims. pressure. Moreover, formula (2) makes the difference negative between 
73° and 100°, as shown in the second column of Table IV., so that the correction to 
the specific heat would change from —2 in 10,000 at 80° to +6 in 10,000 at 100°. 
The negative differences are of the same order as the probable errors of the 
observations. Chappuis himself considered them to be impossible, and gave a 
revised formula for the mean coefficient of expansion of nitrogen, from which the 
“corrected” values in the third column have been calculated. He has since recal¬ 
culated the values on a slightly different assumption, namely that the pressure- 
coefficient- ( dp/dt)/p 0 of nitrogen at an initial pressure p 0 = 100 centims., reaches a 
minimum value '0036738 at 80° C., and then remains constant at all higher tempera¬ 
tures. Taking the fundamental coefficient (0° — 100°) as being '00367466, the 
difference of the scales above 100° C. would be linear, and would amount to '023° per 
100°. The effect of this assumption between 0° and 100° does not differ materially 
from M. Chappuis’ first “ corrected ” results. 
It is interesting to compare Chappuis’ results with those calculated from the 
observations of Joule and Thomson. In order to represent the results of these 
observers more accurately, especially in the case of hydrogen, I have added a term b to 
their formula, to represent the “ co-volume,” as in the later equations of Hirn and 
Van der Waals. The equation of Joule and Thomson then becomes 
v-b = R 6/p - A/6' 2 , .(3) 
which is practically equivalent for moderate pressures to the formula devised by 
Clausius to represent the divergences of C0 3 from Van der Waals’ formula. The 
differences calculated from this formula for nitrogen and hydrogen at constant-volume 
and 100 centims. initial pressure, are of the same order of magnitude, but not quite 
so large, as the “ corrected ” differences of Chappuis. On the whole the agreement 
appears very satisfactory. It would have been still closer if the nitrogen-differences 
observed by Chappuis in the second series of his observations between 0° and 25° 
had not been raised by '007° in order to make the curve pass through the zero point. 
(See Callendar, ‘ Proc. Phys. Soc.,’ March, 1902, where the subject is more fully 
discussed.) It should be remarked, on the other hand, that the observations of 
Joule and Thomson can be represented well within the limits of experimental error 
by the formula of Van der Waals. According to the latter formula the pressure at 
constant-volume is a linear function of the temperature, and the differences between 
the scales of all constant-volume thermometers should be identically zero. The 
evidence of the experiments of Joule and Thomson taken alone is therefore incon¬ 
clusive, but it may be stated that the observations of Amagat, Witkowski, and 
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