350 Sir W. Thomson on Thermodynamic Motivity. 



" in order that the system of measuring temperature here 

 " adopted may agree approximately with that of the air-ther- 

 " mometer. Then we have 



ij>= 



(2) 



t + a 



It was only to obtain agreement with the zero of the ordi- 

 nary Centigrade scale of the air-thermometer that the cc was 

 needed ; and in the joint paper by Joule and myself, published 

 in the Transactions of the Royal Society (London) for June 

 1854, we agreed to drop it, and to define temperature simply 

 as the reciprocal of Carnot's function, with a constant coeffi- 

 cient proper to the unit or degree of temperature adopted. 

 Thus definitively, in equation (6) of § 5 of that paper, we took 



t= — , and have used this expression ever since as the expres- 

 sion for temperature on the arbitrarily assumed thermody- 

 namic scale. With it we have 



. .-&'"•-!; (3) 



and by substitution (1) becomes 



W=J^((d^4^dzCcdt(l-jY . . (4) 



Suppose now B to be surrounded by other matter all at a 

 common temperature T. The work obtainable from the given 

 distribution of temperature in B by means of perfect thermo- 

 dynamic engines is expressed by the formula (4). If, then, 

 there be no circumstances connected with the gravity, or elas- 

 ticity, or capillary attraction, or electricity, or magnetism of 

 B in virtue of which work can be obtained, that expressed by 

 (4) is what I propose to call the whole Motivity of B in its 

 actual circumstances. If, on the other hand, work is obtain- 

 able from B in virtue of some of these other causes, and if V 

 denote its whole amount, then 



Pl=Y + W (5) 



is what I call the whole Motivity of B in its actual circum- 

 stances according to this more comprehensive supposition. 



We may imagine the whole Motivity of B developed in an 

 infinite variety of ways. The one which is obvious from the 

 formula (5) is first to keep every part of B unmoved, and to 

 take all the work producible by perfect thermodynamic en- 

 gines equalizing its temperature to T ; and then keeping it 

 rigorously at this temperature, to take all the work that can 



