HELMHOLTZ ON THE CONSERVATION OF FORCE. 137 



the quantity of free and of latent heat, is just the same in the 

 more expanded gases as in the denser ones of the same tem- 

 perature. According to this, a gas which expands without 

 producing work must exhibit no change of temperature, which 

 indeed appears to follow from the above-mentioned experiment 

 of Joule; and thus the increase and diminution of temperature 

 by compression and dilatation would, under ordinary circum- 

 stances, be due to the excitation of heat by mechanical force, 

 and vice versa. In support of the correctness of Holtzmann's 

 law, a great number of consequences from it which agree with 

 experiment might be adduced ; more particularly the deduction 

 of the formula for the elasticity of the vapour of water at different 

 temperatures. 



Joule determines from his own experiments the force-equivalent, 

 which Holtzmann, from the experiments of others, reckons at 

 374, to be 481, 464, 479 ; while, by friction, the force-equivalent 

 for the unit of heat he found to be 452 and 521. 



The formula of Holtzmann for gases coincides with that of 

 Clapeyron, only in the former the undetermined function C of 

 the temperature is found, and by this means the complete de- 

 termination of the integral is rendered possible. The^former 

 formula is 



pv da da 

 a dv ^ dp 



where a is the force- equivalent of the unit of heat ; the formula 

 of Clapeyron is 



"" dv ^dp 



Both are therefore coincident, when C= — ; or, as jo = -( 1 -j-aA 



where a is the coefficient of expansion, and A: is a constant, when 

 1 a 



Y Clapeyron 

 this formula, as is shown by the following table : — 



The values found by Clapeyron for ^ agree pretty well with 



