148 PROCEEDINGS OF THE AMERICAN ACADEMY 



This determination of the mechanical equivalent from the proper- 

 ties of air is at most very imperfect, as a very slight change in either 

 y or the velocity of sound will produce a great change in the mechan- 

 ical equivalent. 



From Theory of Vapors. 



Another important method of calculating the mechanical equivalent 

 of heat is from the equation for a body at its change of state, as for 

 instance in vaporization. Let v be the volume of the vapor, and 

 v' the volume of the liquid, and H the heat required to vaporize a 

 unit of mass of the water ; also let p be the pressure in absolute 

 units, and y. the absolute temperature. Then 



JH 



\t//t/» 



The quantity ^Tand the relation of p to p have been determined with 

 considerable accuracy by Regnault. To determine J it is only 

 required to measure the volume of saturated steam from a given 

 weight of water ; and the principal difficulty of the process lies in 

 this determination, though the other quantities are also difficult of 

 determination. 



This volume can be calculated from the density of the vapor, but 

 this is generally taken in the superheated state. 



The experiments of Fairbairn and Tate * are probably the best 

 direct experiments on the density of saturated vapor, but even those 

 do not pretend to a greater accuracy than about 1 in 100. With 

 Regnault's values of the other quantities, they give about Joule's value 

 for the equivalent, namely 42.3. Him, Herwig, and others have 

 also made the determination, but the results do not agree very well. 

 Herwig even used a Giessler standard thermometer, which I have 

 shown to depart very much from the air thermometer. 



Indeed, the experiments on this subject are so uncertain, that 

 physicists have about concluded to use this method rather for the de- 

 termination of the volume of saturated vapors than for the mechanical 

 equivalent of heat. 



From the Steam- Engine and Expansion of Metals. 



The experiments of Ilirn on the steam-engine and of Edlund on 

 the expansion and contraction of metals, are very excellent as illustrat- 



* Phil. Mag., ser. 4, xxi. 230. 



