1885.] molecular energy on an absolute scale. 31 ( J 



Now suppose the engine to be worked backwards so as to 

 restore S to its original state, taking as much energy as possible 

 from S ; then BW is the least amount of work which must be 

 done upon 8 to restore to it its original energy E at potential V, 

 and therefore E — BW is the amount of energy which must be 

 supplied to S in addition to the work BW done upon it. E — BW 

 must therefore be the energy of S when at the potential V , 

 because no energy could pass spontaneously from S Q to S at a 

 higher potential, and BW is the minimum amount of energy which 

 must be derived from without to raise the potential from V 

 to V. 



Next let us measure V on such a scale that BV bears a constant 

 ratio to BW when E is increased or diminished; and let S Q be so 

 changed in its state by external agency that the potential of E 

 is reduced to V — B V; then by means of a perfect engine working 

 between S which has energy E — BW at potential V , and S 

 maintained with its energy E at potential V — SV, a second 

 quantum of work, equal to the former quantity BW since BV is 

 the same and is always proportional to BW, can be got out of 

 E—BW, and we shall have 



.(2). 



Since the work that can be got out of each unit of energy 

 in E is the same fraction of BW, that one unit of energy is of E 

 we may write in the above equation dW : dE, the rate of work 

 obtainable per unit of E, instead of B W : E, and make B V always in 

 a constant ratio to dW/dE . BE, where BE is an arbitrary increment 

 of E which may be the unit of energy. BV, the increment of V, 

 is then wholly independent of the nature of S and of the amount 

 of energy E, and we have a method of measurement of V ap- 

 plicable to all forms of kinetic molecular energy, and we can 

 make the magnitude of our degrees of potential the same for all. 

 When the energy in question is heat, and V is temperature, the 

 equation (2) becomes that which is usually given in text-books for 

 the relation between the amount of work which can be got out 

 of a supply of heat E at temperature V on the absolute dynamic 

 scale when the refrigerator is at temperature V — B V. 



