438 
Proceedings of the Royal Society 
figured dimensions in the accompanying diagram (fig. 4), makes an 
admirably convenient and sensitive thermometer for temperatures 
from + 20° to something far below - 30°, as we see from the 
results of Regnault’s measurements. 
To sum up, we have, in the preceding description and drawings, 
a complete series of steam-pressure thermometers, of sulphurous 
acid, of water, and of mercury, adapted to give absolutely definite 
and highly sensitive thermometric indications throughout the wide 
range from something much below - 30° to considerably above 
520° of the centigrade scale. The graduation of the scales of these 
thermometers to show absolute temperature is to be made by 
calculation from the thermodynamic formula — 
where t denotes the absolute temperature corresponding to steam- 
pressure p ; p 0 to the absolute temperature corresponding to steam- 
pressure p 0 ; k the latent heat of the steam per unit mass ; p the 
to the density of the liquid in contact with it. When the requisite 
experimental data, that is to say, the values of cr and pK for different 
values of p throughout the range for which each substance is to be 
used as thermometric fluid are available, the graduation of the 
scales of these thermometers to show absolute temperature can be 
performed in practice by calculation from the formula. Hitherto 
these requisites have not been all given by direct experiment for any 
one of the three substances with sufficient accuracy for our thermo- 
metric purpose through any range whatever. Water, naturally, is 
the one for which the nearest approach to the requisite information 
has been obtained. For it Regnault’s experiments have given, no 
doubt with great accuracy, the values of p and of k for all tempera- 
tures reckoned by his normal air thermometer, which we now 
regard merely as an arbitrary scale of temperature, through the 
range from - 30° to + 230°. If he, or any other experimenter, had 
given us with similar accuracy through the same range the values of 
p and cr for temperatures reckoned on the same arbitrary scale, we 
should have all the data from experiment required for the graduation 
of our water-steam thermometer to absolute thermodynamic scale. 
density of the steam ; and a the ratio of the density of the steam 
