of the Mechanical Theory of Heat, 179 



which we call heat, equilibrium is always effected in this way : — 

 between the vires vivce of the various points a fixed ratio subsists, 

 which is renewed with every alteration that occurs in the total 

 vis viva. The mean vis viva of each point may then be repre- 

 sented by a product of the form mcT, in which m is the mass of 

 the point, and c another constant, determinate for each point, 

 while T denotes a variable quantity which is equal for all the 



771 



points. By the insertion of this product in the place of „ v 2 , 



the preceding equation becomes 



SL=S»icST + S2»jcTSlogi. .... (32) 



Herein the quantity T, as a common factor, can be omitted from 

 the second sum. We could also omit the variation ST from the 

 first sum; but it may be left under the sign of summation. 

 Hence comes 



SL = SmcST + TX2mcS log i 



= T(%mc^- +22mc81og») 



=T(Smc81ogT + 22roc81ogi); . . . (33) 



or, combining the two sums into one and putting the sign of va- 

 riation before the sign of summation, 



SL=m2mc(logT + 21og2), 



for which, finally, we may write 



SL=TS2mclog(T2 2 ) (34) 



15. This last equation, if by T we understand the absolute 

 temperature, agrees perfectly with equation (1) adduced for heat, 



T 



A ' 



in order to explain it on mechanical principles. The disgrega- 

 tion of the body, Z, is according to this represented by the ex- 

 pression 



AXmclog(Tz 2 ). 



It is easy to show also its agreement with another equation of 

 the theory of heat. 



Let us imagine vis viva communicated to our system of mate- 

 rial points by a transitory external influence, and the system then 

 left to itself; this vis viva may partly serve to increase the vis 

 viva present in the system, and partly be expended in mechanical 

 work. Hence, if 8q denotes the vis viva communicated, and h 



N2 



