556 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF 

dp 
M=(-9-— Hea Ebete He pe Re STE, 
: sie 
If we denote the coefficient of H z in these equal expressions by «, which may be 
called ‘“‘ Carnot’s coefficient,” we have 

dp 
fa ie 
e=(Sn = anes epbehiuadas evel (Gp) 
and we deduce the following very remarkable conclusions :— 
(1.) For the saturated vapours of all different liquids, at the same tempera- 
ture, the value of 
dp 
(1) di 

must be the same. 
(2.) For any different gaseous masses, at the same temperature, the value of 
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 @ prior? regarding the values of this coeffi- 
cient » 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; aresult amply verified by the continuous series of experiments performed 
by Reenavtt on the saturated vapour of water for all temperatures from 0° 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, 
S 
M=H CBG: Or Ee ett ale 7 
af @) P 
“which is, in fact, what either of the equations (1) for the steam-engine, or (4) for 
the air-engine, becomes, when the notation », for CarNnot’s multiplier, is intro- 
duced. 

