THE PROPERTIES OF WATER AND OF STEAM. 
Ill 
“ Unwin” (‘Phil. Mag.,’ 1886, p. 299). His formula is logy> = 7‘5030 _7 ' 679//l U 
“ Antoine ” refers to the last formula given by Ch. Antoine (‘ Annales de Chimie,’ 
1891, vol. 22,’ p. 283). It is logy) = 7' 921 -1638/< + 225 . It has the merit of allowing 
temperature to be calculated from pressure, as easily as the converse; the results, 
however, calculated in each way, are not absolutely the same, but do not differ to any 
important extent. 
“ Buff ” (‘Liebig’s Annalen,’ Suppl. 2, 1862-3, p. 137) uses the formula 
log P = log o ^3 + log (273 + t) + 
a = 0-06479 + 0'0001722 t 
log (273 + t) — log 373 
a 
— o-ooooooi t\ 
Rankine” (‘ Steam Engine,’ 9th Ed., p. 237) gives the formula 
, * , B , c 
lo gp = A + - + 
‘ Broch ” (‘ Travaux et Memoires du Bureau Internat. des Poids et Mesures,’ 
vol. 1, p. 19, et seq.). His formula is 
P 
= a. 10 
It + ct 2 + dt 3 + et* + ft & 
1 + a.t 
M. Broch has undertaken a most laborious investigation of the formulae employed 
for the calculation of the vapour-pressures of water, adopting finally the one given in 
the table. The utmost care was taken to obtain the best possible results from the 
data taken; but, unfortunately, M. Broch has accepted Regnault’s conclusion that 
the curve representing the vapour-pressures of ice is continuous with that obtained 
from the vapour-pressures of water, and he has employed the whole of the data from 
— 32° to 100°. By the method of calculation of the constants for the formula, this 
source of error has been to a certain extent eliminated, as is shown by the comparison 
(p. 31) of Regnault’s individual observations with the pressures calculated from the 
formula. In this table it is seen that below — 5°, out of 31 comparisons, the 
calculated pressures are higher than those observed in every case but one. The 
error is, however, only partially eliminated, and this probably explains the fact that 
the formula, with the constants given, will not bear extrapolation above 100° even to 
120°, though it is supposed to hold good through a range of 132°. 
It is to be feared that the results between 0° and 100° may even be to some extent 
vitiated by this source of error—a most unfortunate circumstance, considering the 
enormous amount of labour bestowed on the work, and the fact that the pressures 
calculated from the formula have received the imprimatur of the Bureau Inter¬ 
national. 
It is to be noticed that Regnault’s formula K gives results nearest the truth, but 
that fairly approximate results are also obtainable by the use of Unwin’s and of 
Antoine’s formulae. These formulae, it need hardly be remarked, are all empirical. 
