284 Mr. J. J. Waterston on the Deviation from 
nO 
§ 8. The formula, § 4, A= W340" expresses the law of the 
deviation, viz. that for a constant difference of density it varies 
directly as the amount of the thermal depression or cooling effect, 
and inversely as the temperature of the experiment reckoned from 
the zero of gaseous tension. In the experiments of Messrs. 
Thomson and Joule with carbonic acid, the cooling effect was 
about four and a half times that of air, giving a deviation of jth 
for a difference of density equal to one atmosphere. 
If the deviation at 100° were the same in absolute amount as 
at 0°, the cooling effect ought to be greater in the ratio of 373° 
to 273°. But if the deviation were less in proportion with the 
diminished density, the cooling effect ought to be unchanged. 
If the cooling effect dimmish as the temperature increases, 
the deviation must diminish for the same constant difference of 
pressure, not only with the density, but also in some inverse 
ratio of the temperature. This last seems to be the case, judging 
from Messrs. Thomson and Joule’s experiments with carbonic 
acid. 
§ 9. M. Regnault’s observations provide us with the coeffi- 
cients of expansion under constant pressure, and of augmenta~ 
tion of pressure with constant volume, all at the temperature of 
50° C. or 273 +50=328° G temperature, or temperature reck- 
oned from the zero of gaseous tension. If we denote this G 
temperature by T, the volume by V, and tension or elastic pres- 
sure by P, the primary laws of gases in their entirety are ex- 
pressed by T=VP, the equation of the hyperbola referred to 
its asymptote, im which we set out with a unit of each of the 
elements as a basis of comparison with standard measures. 
From M. Regnault’s experiments alone, we may infer that the 
actual coordinates of volume and pressure do not trace out this 
curve exactly, because his coefficients increase with the density ; 
but the amount of the deviation cannot be inferred, because only 
one value of V for the same value of T has been supplied. 
The actual coordinates of volume and pressure may neverthe- 
less trace out the exact hyperbola, if they are assumed not to 
have reference to the actual asymptotes, but to a subordinate 
unknown hyperbolic curve lying near to and belonging to the 
same asymptotes, and that expresses by its equation the unknown 
cause of the deviation. Upon this assumption we obtain the 
means of computing the deviation by the coefficients alone. In 
this way the deviation comes out aa This value, compared 
with a7) the value computed by the first process, does not show 
such accordance as to establish the hypothesis, but sufficient per- 
haps to make it worthy of passing remark. 
