AND ITS CONNECTION WITH THE THEORY OF HEAT. 431 
(5.) Case of a Perfect Gas.—As a substance is rarefied, it gradually approaches 
a condition in which the pressure, under like circumstances as to heat, varies pro- 
portionally to the density. This is because the effect of the molecular attrac- 
tions and repulsions on the pressure diminishes with the density, so that @, , 
and G approximate to constant quantities. In the limiting or perfectly gaseous 
condition, therefore, 
and 
_hpO_ hp (2Q 
(6.) Equilibrium of Heat: Nature of Temperature and Real Specific Heat— 
When the atmospheres of atoms of two different substances are in contact at their 
common bounding surface, it is necessary to a permanent condition, that the pres- 
sure in passing that surface should vary continuously. 
Let (a) and (0b) be taken as characteristics, to distinguish the specific quantities 
peculiar to the two media respectively. Let dm denote the volume of an indefinitely 
thin layer, close to the bounding surface. Then the following equations must be 
fulfilled, to ensure a permanent condition :— 
P (@)=p (6); = oF (@)= ar) FRG pg ey ae) 
By making the proper substitutions in equation (4), it appears, that 
4 (9-9) 
p=pe nil gras 
Ww, 
Hence 
os 
iba d (kp) + 
oF =p)= p (o-2) 5 =) 
1 
2 2 Cee 
Now p is the same for both media: ats . t= eh “is either a maximum 
at 
or a minimum, so that its differential is null; and dm is a continuous function 
of k , so that gus) (a)= A (6). There remains only the function of heat 
é= oe 
Therefore the condition of a permanent state of molecular motion, that is to 
say, the condition of equilibrium of heat, is that this function shall be the same 
for the two substances ; or that 
Ga + AE dee oh: pianciaemmer cia C5 


