and on Astronomical Refractions, 
439 
Laplace arrived at this equation [flee. Cel. vol. v. p. 128.). 
See Poisson, Annales deChimie et dePhysique, tom. xxiii. p. 342*; 
Mecanique, vol. ii. p. 648 ; Navier, Leqons donnks d UEcole desPonts 
et Chaussees^ tom. ii. ^ ^ 
+ V' = A + B^^ 
S S 
y — /c g (1 + a d) (1 + a 0') 
^ and a being constants. 
I will now introduce the additional condition that the heat is^ro- 
portional to the temperature, in which case 
F = C + Z)(1 -4- a 8) 
F' = C + Z)(l +«80 
C and D being constants. These equations include implicitly the 
hypothesis attributed to Watt and also that of Southern, respect- 
ing the vapour of water : on the former Z) = 0. Hence 
V=C + D(\ 4- ^ 
e 
J_ 
V’ = C D [\ + a^') = A + 
If 
1 P 
D 
y-i r 
(1 +«9) -^<j 
0/ 1 
ml 
I Z) y 
P'JL. ] ' " kB^ 
1 
\-^-TbP 
y_^ 
t y 
j 
^ ^ correspond to the boiling point, 8 = 180° 
in Fahrenheit’s scale, if the pressure be measured in atmospheres 
/) = 1, but generally 
1 +«0' = (i + «0) 
i-y 
ip' y -E) 
[1] 
[* A translation of M. Poisson’s raemoir here referred to will be found in Phil. Mag., 
First Series, yol. Ixii. p. 328. — Edit.] 
f This equation must not be confounded with another equation which may be deduced 
from it by making E = 0, and which is not reconcileabie with phaenomena, as was 
long since noticed by M. Poisson in the case of steam. An equation of this kind is given 
by M. Pouillet in the form 
