OF THK 



UNIVERSITY 



MOTIVE POWER OF HEAT. 159 



increased in the ratio of 1 to 1 -|- E(t -\- T), where 

 E is very nearly equal to .00366 (the Centigrade 

 scale of the air-thermometer being referred to), 

 whatever be the gas employed, according to the 

 researches of Regnault and of Magnus on the ex- 

 pansion of gases by heat. If, now, the volume be 

 altered arbitrarily with the temperature continually 

 at t -f- 7? the product of the pressure and volume 

 will remain constant ; and therefore we have 



pv = p v {l + fi(t + r)}. 

 Similarly, 



Hence, by subtraction, we have 

 or, neglecting the product 00$, 



Hence the preceding expression for mechanical 

 effect, gained in the cycle of operations, becomes 



p v . Er . dv/v. 

 Or, as we may otherwise express it, 



vdq/dv ' * 



Hence, if we denote by M the mechanical effect due 

 to H units of heat descending through the same 

 interval T, which might be obtained by repeating 



