196 Mr. J. C. Maxwell on the Dynamical Theory of Gases. 



the quantity p will represent the mean pressure at a given point, 

 and g 2 p } rfp, and f 2 p will differ from p only by small quantities ; 

 v£p } &p, and %y)p will then be also small quantities with re- 

 spect to p. 



Energy in the Medium. — Actual Heat, 



The actual energy of any molecule depends partly on the 

 velocity of its centre of gravity, and partly on its rotation or 

 other internal motion with respect to the centre of gravity. It 

 may be written 



±M{(u + ff+(v + v y+(w + W\+iUM, . . (65) 



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 



iK + ^ + ^ 2 )p + i(r + ^ 2 + ? 2 )p + Pp. • ■ (66) 



The first term gives the energy due to the motion of transla- 

 tion of the medium in mass, the second that due to the agita- 

 tion 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 (/3 — 1), we may conclude that, except in very 

 violent disturbances, this ratio is always preserved, so that 



E=(/3-l)(P + ^+? 2 ) (67) 



The total energy of the invisible agitation in unit of volume 

 will then be 



m?+n*+?)p,' ..... (68) 

 or 



§fr (69) 



This energy, being in the form of invisible agitation, may be 

 called the total heat in the unit of volume of the medium. 



(7) Transference of Energy across a Plane. — Conduction of Heat. 



Putting 



Q=i^(|2 4 _^ 2 + ? 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 



i/3(? + ¥)*+W)p, (71) 



where £ 3 &c. indicate the mean values of f 3 &c. They are 

 always small quantities. 



