8 SirW. Thomson on the Thermoelastic, Thermomagnetic, 



from a body when at temperatures* t, t' respectively, during 

 operations changing its physical state in any way, the sum 



2 — * must vanish for any cycle of changes, if each is of a per- 

 fectly reversible character, and if at the end of all the body 

 is brought back to its primitive state in every respect. Let 

 us consider, for instance, the following cycle, which obviously 

 fulfils both conditions. 



(I.) Let the body, initially in the state (# , y , z , f , rj , to, t), 

 be raised in temperature from t to if, its form and dimensions 

 being maintained constant. 



(II.) Let it be strained from the state (js , y , z , f , Vo, to) 

 to the state {x, y, z, f, rj, f), while its temperature is kept 

 always at if. 



(III.) Let it be lowered in temperature from tf to t, its form 

 and dimensions being retained. 



(IV.) Let it be brought back to the mechanical state 

 (x , y , z , f , rj , J ), while its temperature is kept constantly 

 at t. 



The quantities of heat taken in by the body in these succes- 

 sive operations are respectively : — 



(*•) J { 9{ x o, yo, ?o, fo, Vo, to, ~ <K^o, l/o, z o, %Q> Vo, to, } , 



because the difference of the whole mechanical energies is 

 simply the mechanical value of the heat taken in or emitted in 

 all cases in which no work is either done on the body or re- 

 ceived by it in virtue of the action of applied forces ; 



(II.) f(x, y, z, f, v, t, O-fi^o, yo, z , %o, Vo, to, t'), 

 according to the notation expressed by equation (2) aboA^e ; 



( IIL ) - j {<K®, y, z , ft v, t, 0-<£0> y, z , I, v, t,t)}, 



and 



(IY.) - {f(x, y, z, f, r}, ?, t)-f(x ,y , z o, fo, Vo, to, *)}■ 



* Reckoned on the absolute thermodynamic scale, according to which 

 " temperature " is denned as the mechanical equivalent of the thermal unit 

 divided by " Carnot's function." In a paper " On the Thermal Effects of 

 Fluids in Motion," by Mr. Joule and myself, communicated to the Royal 

 Society last June [1854], and since published in the Philosophical Transac- 

 tions, it is shown that temperature on the absolute thermodynamic scaledoes 

 not differ sensibly from temperature on the ordinary scale of the air-ther- 

 mometer, except by the addition of a constant number, which we find to 

 be about 273*7 for the Centigrade scale. Thus, on the system now adopted, 

 the temperature of melting ice is 2737, that of boiling water is 373-7, 

 aid differences of temperature are sensibly the same as on an ordinary 

 standard Centigrade thermometer. 



