556 PROFESSOR WILLIAM THOMSON'S ACCOUNT OF 



dp 



M = (l-.)-^.Hr^^^°"°.Hr .... (5). 

 ^ ' k da ^ ' 



* dv 



If we denote the coefficient of H t in these equal expressions by >«, which may be 

 called " Carnot's coefficient," we have 



dp 



d V 



and we deduce the following very remarkable conclusions : — 



(1.) For the saturated vapours of aU different liquids, at the same tempera- 

 ture, the value of 



dp 



a^ d t 



must be the same. 



(2.) For any difiFerent gaseous masses, at the same temperature, the value of 



da 

 dv 



must be the same. 



(3.) The values of these expressions for saturated vapours and for gases, at 

 the same temperature, must be the same. 



31. No conclusion can be drawn a prioi'i regarding the values of this coeffi- 

 cient fj. for different temperatures, which can only be determined, or compared, by 

 experiment. The results of a great variety of experiments, in different branches of 

 physical science (Pneumatics and Acoustics), cited by Carnot and by Clapeyron, 

 indicate that the values of ^ for low temperatures exceed the values for higher tem- 

 peratures; a result amply verified by the continuous series of experiments performed 

 by Regnault on the saturated vapour of water for all temperatures from to 

 230", which, as we shall see below, give values for // gradually diminishing from 

 the inferior limit to the superior limit of temperature. When, by observation, // 

 has been determined as a function of the temperature, the amount of mechanical 

 effect, M, deducible from H units of heat descending from a body at the tempera- 

 ture S to a body at the temperature T, may be calculated from the expression, 



M = bJ ^dt (7) , 



which is, in fact, what either of the equations (1) for the steam-engine, or (4) for 

 the air-engine, becomes, when the notation /x, for Carnot's multiplier, is intro- 

 duced. 



