————L <<< 
TRANSACTIONS OF SECTION A. 629 
deduced from this by the usual parabolic difference formula, which gives results in 
practical agreement with the Paris scale. 
Since the discussion of the thermal unit introduced by Griffiths! at the British 
Association Meeting of 1895, and partly in consequence of the general interest 
excited by that discussion, so many new facts have been brought to light, and so 
much experience has been gained of the practical effect of the proposals then 
made, that it appears desirable to discuss more fully the bearing of the present 
work on the general question of the relation between the various thermal units. 
Dieterici (‘ Wied. Ann.’ 33, p. 417, 1888) made a determination of the mean 
specific heat in terms of the electrical units by means of a Bunsen ice-calorimeter. 
His result (when reduced on the assumption that the electrochemical equivalent of 
silver is 00011180 grm. per amp. sec., and that the ohm is the resistance at 0° C. 
of a column of mercury 1 sq. mm. in section and 106-30 em. in length) gives 
4238 joules as the value of the mean specific heat of water in absolute measure 
between the limits 0° and 100° C.? 
Winkelmann (‘ Handbook of Physics,’ vol. ii. part ii. p. 838) endeavoured to 
connect this result with those of Rowland at low temperatures by assuming a 
parabolic formula for the mode of variation, and taking the mmimum value 
at 30°6° C. to be 0:9898 of the value at 0° C. These assumptions give for the 
specific heat s, at any temperature ¢° C., the formula— 
s,= 1 —0:0006684 ¢ + 0:00001092 ¢? ‘ . é . (W) 
and for the mean specific heat between 0° and 2°, which may be written s ‘,, 
s', =1—0-0003342 ¢ + 0:00000364 2?. 
According to this formula, the ratio of the mean specific heat between 0° and 
100° to the specific heat at 20° C, would be 1:0120. According to the formula of 
Regnault, the same ratio would be 1:0038. If we take Rowland’s corrected 
value at 20° C. as 4181 joules, the mean value between 0° and 100° would be 
4-197 joules according to Regnault, but 4°233 joules according to Winkelmann. 
The latter gives a remarkable coincidence with Dieterici, in consequence of which 
the formula (W) has been frequently quoted and employed in physical investiga- 
tions. It must be remarked, however, that Rowland’s curve is not even approxi- 
mately parabolic, and that the range covered by his observations is hardly 
sufficient to justify this method of treatment. It must also be observed that the 
values given by Winkelmann’s formula for the specific heat in the neighbourhood 
of 100°, and still more at higher temperatures, are so large that they cannot 
conceivably be reconciled with the experiments of Regnault and other good 
observers. 
Griffiths (‘ Phil. Trans.’ vii. 1895, pp. 318-323) came to the conclusion from 
a comparison of his experiments on the latent heat of evaporation of water at 30° 
and 40° C. with those of Dieterici at 0° C. expressed in terms of the mean specific 
heat, and with those of Regnault on the total heat of steam at 100° C., that the 
mean specific heat must be very nearly identical with the specific heat at 15° C., 
although Regnault’s direct experiments made the ratio from 0:5 per cent. to 
1 per cent. larger. At his suggestion Professor Joly performed the inverse experi- 
ment of determining the mean specific heat between 12° and 100° with his steam 
calorimeter in terms of the latent heat of steam at 100° taken as 536°63 times the 
thermal unit at 15°C. The result of this experiment was to make the mean 
specific heat appear nearly 0°5 per cent. smaller than the specific heat at 15° C. 
If we suppose that the inversion of the experiment would tend to reverse the 
error of the original determination of the latent heat, the result would appear to 
be strorgly in support of Griffiths’s contention. 
! Griffiths’s ‘The Thermal Unit.’ Phil. Mag. Nov. 1895. 
2 Assuming that the mean caloric melts a quantity of ice sufficient to cause 
15°44 milligrams of mercury to enter the calorimeter. Bunsen gives 15-41 mgm., 
and Velten 15°47 mgm. See also Dieterici, Wied. Ann, 1896, lvil. p. 883, where a 
curve somewhat similar to Winkelmann’s is given, 
