434 MR W. J. M. RANKINE ON THE CENTRIFUGAL THEORY OF ELASTICITY, 
of volume 6 Y. Let 6. Q be divided into two parts 
r) Q + 6 g= é. Q 
of which 6 Q, being directly employed in varying the velocity of the particles, is 
the variation of the actual or sensible heat possessed by the body; while 6 Q’, 
being employed in varying their orbits, represents the amount of the mutual 
transformation of heat with expansive power and molecular action, or the varia- 
tion of what is called the /atent heat ; that is to say, of a molecular condition con- 
stituting a source of power, out of which heat may be developed. (6 Q’ in this 
paper corresponds to — 6 Q/ in my former papers. ) 
The variation of sensible heat has evidently this value 
OQ=kdr Plas evi) Sn tae 
Let 62, dy, 62, be the displacements of the orbit of the particles of atomic 
atmosphere at the point (v,y, 2.) A molecule edadydzis acted upon by the 
accelerative forces (see equation 3 A.) 
=3@e"; 2952; - 2Q2f, 
parallel to the three axes respectively. 
The sum of the actions of those forces on the molecule e d x dy d = during the 
change of temperature and volume, is 
-29 (22 d2+4 ree ae rf 8y+ F002) gaedyds 
=~ bene 
The sum of such actions upon all the particles in unity of weight is equal in 
amount and opposite in sign to the variation of latent heat: that is to say, 
8q= EIT], ee bardyas | ee ET 
To determine the value of the variation > ¢, let it be divided into two parts, 
thus :— 
dp=b 9,404 
where a fp=-—9, 
First, With respect to 6 @,, it is obvious that because, according to equations 
(6, 7) 
Pp kag 
Mv=imvf_ ye Yad 
we must have 
OV=kV 0d, and 6 $,= 
Hence the first part . the integral (23) is 
Hob [ff edeavas= she ov 
: ~ 
"> ~ig! = —=—se 
