318 Prof. Liveing, On the measurement of kinetic [Oct. 26, 



being that when two forms of energy are at the same poten- 

 tial in the same substance there is no tendency for either to 

 be increased at the expense of the other; but that if they are 

 at unequal potentials there is a tendency to an equalization ; also 

 that when two bodies have their energies at equal potentials there 

 is no tendency for the energy of one to increase at the expense 

 of the other, while if they are at unequal potentials there is a 

 tendency to equalization by the passage of energy from one body 

 to the other. 



It remains to construct a scale of measurement which shall 

 be applicable to all kinds of kinetic molecular energy. 



Let 8 and S be two systems each homogeneous in regard to 

 both matter and energy, and let E, E A be their respective energies 

 in such forms e , e t , e 2 &c. as are from the nature of the systems 

 capable of being freely transformed into each other, and freely 

 transmitted from 8 to 8 or vice versa when 8 and 8 are placed in 

 communication ; e for instance may be heat, e t the energy of motion 

 of translation of the molecules of a gas, e 2 the energy of chemical 

 separation and so on. Ewill be the sum of e + e 1 + e 2 + &c. for S ; 

 and E the corresponding sum for 8 . S and S may have besides 

 E and E other energies which are not freely transformable into 

 any of the forms included in E and E . If 8 and 8 are each in 

 equilibrium, e , e 1} e 2 , &c. in $ will all be at the same potential V, 

 and e Q , e t , e 2 , &c. in S will also all be at one potential V . Also 

 if when 8 and S are put in communication there is no tendency 

 for any part of E to transfer itself to 8 , or for any part of E to 

 transfer itself to 8, then V = V ; but if part of E passes to S, 

 V is greater than V, and if part of E passes to S , V is greater 

 than V . 



Suppose V greater than V and the difference to be B V, then 

 it follows, on Carnot's principle, that no more work can be got out 

 of E in consequence of the equalization of the potentials of E 

 and E when S and S are put into communication by any means 

 than can be obtained by means of a perfect reversible engine 

 working between 8 and S ; and hence the greatest amount of 

 work which can be got out of E by such means will depend only 

 on V and 8 V when 8 V is very small. 



Let us suppose 8 Q to be maintained by external agency in a 

 constant state, so that the potential of E is always V during the 

 operation of transferring part of E to $ and converting the rest 

 into mechanical work by help of the reversible engine. Then 

 if BW be the greatest amount of work which can be got out of E 

 by this means, we shall have 



BW : E=BV : F(V) ••■••(I), 



when F(V) is some function of V. 



