136 HELMHOLTZ ON THE CONSERVATION OF FORCE. 



where q denotes the quantity of heat contained by one body, t its 

 temperature, both expressed as functions of the volume v, and the 



pressure p. p is the mechanical work which the unit of heat 



(which can raise 1 kilogramme of water 1° Centigrade) produces 

 when it passes into a temperature 1° lower. This is stated to be 

 identical for all natural bodies, but to vary with the temperature. 

 For gases the formula is 



"" dv ^dp 



Clapeyron's inferences from the general validity of this formula, 

 at least in the case of gases, have many analogies on their 

 side which agree with experience. His deduction of the law can 

 only be admitted when the quantity of heat is regarded as un- 

 changeable. Further, his more special formulas for gases, which 

 alone are supported by experiment, follow also from the formula 

 of Holtzmann, as we shall immediately show. With regard to 

 the general formula, he has only sought to show that the law 

 which follows from it is at least not contradicted by experiment. 

 This law is, that when the pressure on different bodies, taken at 

 the same temperature, is a little increased, quantities of heat will 

 be developed which are proportional to the expansibility of the 

 bodies by heat. I will here merely draw attention to what must 

 be regarded as at least a very improbable consequence of this law. 

 Compression of water at the point of maximum density would 

 develope no heat, and between this and the freezing-point it 

 would develope cold. 



Holtzmann sets out from the consideration that a certain quan- 

 tity of heat which enters a gas can cause in it either an increase 

 of temperature or an expansion. The quantity of work thus 

 produced by the heat he assumed to be the mechanical equi- 

 valent of the heat ; he calculated from the experiments of Dulong 

 upon sound, that the heat which raises the temperature of 1 ki- 

 logramme of water 1° Centigrade, would raise a weight of 374 

 kilogrammes I metre. This method of calculation, regarded 

 from our point of view, is only admissible when the entire vis 

 viva of the heat communicated is actually returned as mecha- 

 nical force, hence the sum of the vis viva and tensions, that is, 



