MR. CLERK MAXWELL ON THE DYNAMICAL THEORY OF GASES. 71 
where ^EM is the internal part of the energy of the molecule, the form of which is at 
present unknown. Summing for all the molecules in unit of volume, the energy is 
+i(P+d*+r)?+iE» (66) 
The first term gives the energy due to the motion of translation of the medium in 
mass, the second that due to the agitation of the centres of gravity of the molecules, and 
the third that due to the internal motion of the parts of each molecule. 
If we assume with Clausius that the ratio of the mean energy of internal motion to 
that of agitation tends continually towards a definite value (f 3 — 1), we may conclude that, 
except in very violent disturbances, this ratio is always preserved, so that 
E=(/3-lXr+W 2 ) (67) 
The total energy of the invisible agitation in unit of volume will then be 
i(3(?+»*+r)s> • • (68) 
or 
§@P (69) 
This energy being in the form of invisible agitation, may be called the total heat in 
the unit of volume of the medium. 
(y) Transference of Energy across a Plane — Conduction of Heat. 
Putting 
Q=i/3(f+^+^ 2 )M, and u=u', (70) 
we find for the quantity of heat carried over the unit of area by conduction in unit of time 
wv+w+Wh (7i) 
where | 3 , &c. indicate the mean values of | 3 , &c. They are always small quantities. 
On the Bate of Variation of Q in an Element of Volume, Q being any property of the 
Molecules in that Element. 
Let Q be the value of the quantity for any particular molecule, and Q the mean value 
of Q for all the molecules of the same kind within the element. 
The quantity Q may vary from two causes. The molecules within the element may 
by their mutual action or by the action of external forces produce an alteration of Q, or 
molecules may pass into the element and out of it, and so cause an increase or diminution 
of the value of Q within it. If we employ the symbol & to denote the variation of Q 
due to actions of the first kind on the individual molecules, and the symbol B to denote 
the actual variation of Q in an element moving with the mean velocity of the system of 
molecules under consideration, then by the ordinary investigation of the increase or 
diminution of matter in an element of volume as contained in treatises on Hydrodynamics, 
-|{(»-»')QN+^Q N |-g((®-w')QN+?QN}, 
• • ( 72 ) 
