ON THE MECHANICAL EQUIVALENT OF HEAT 415 



Using Wiedemann's value for K, -2389, these become 



= 427-8 ; -^ = 434-0 ; = 427-1 . 

 999 



As Wiedemann, however, used the mercurial thermometer, and as 

 the reduction to the air thermometer would increase these figures from 

 2 to -8 per cent, it is evident that Eegnault's value for K is the more 

 nearly correct. I take the weights rather arbitrarily as follows : 



Weight. J. 



Eontgen 3 430-3 



Amagat 1 436-6 



Velocity of sound 4 429-6 



Mean 430-7 



And this is of course the value referred to water at 14 C. and in the 

 latitude of Baltimore. My value at this point is 427-7. 



This determination of the mechanical equivalent from the properties 

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

 the velocity of sound will produce a great change in the mechanical 

 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, H the heat required to vaporize a unit of mass of 

 the water; also let p be the pressure in absolute units, and // the absolute 

 temperature. Then 



JH 



The quantity H and the relation of p to // 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. 



