Intelligence and Miscellaneous Articles. 467 



points. Thus 2€ e /-Ed'2= -EdU, (6) 



U being a function of the 4n variables x h y u z h T,-. This function 

 is no other than that which is called the internal heat. 



The equation (a), or its equivalent (6), is the only one that can 

 be directly deduced from the first proposition of the mechanical 

 theory of heat, if no preconceived idea on the nature of heat be ad- 

 mitted ; and we do not understand the reasonings by which some 

 have attempted to deduce from it that SC e / is a differential. It 

 has certainly been proved that, for certain particular cyles, during 

 which the temperature or the quantity of heat received remains 

 invariable, we have J2© e /=0; but from this it is not permissible 



to conclude that 2C e / is a differential. 



I now say that, whatever idea may be formed of the nature of heat, 

 the quantity of heat d'q employed to raise the temperatures of the 

 various points of the body, without displacement of those points, is 

 necessarily the exact differential of a function of the n variables % . 



In fact, the quantity of heat necessary for raising by dTi the 

 temperature of a molecule of mass m t is necessarily an expression 

 of the form m^y^T;, as yi can only depend on the temperature T t - of 

 the molecule and on the specific constants relating to the material 

 of which it is composed. 



Therefore the total quantity of heat remaining in the sensible 

 state is ^=2.m i y^T i =^2m i Jy i ^ i : 



d'q being thus a differential, so also is 2T e /, in virtue of (a) ; and 

 as this sum is an expression of the form 



containing no term in dTi, it cannot but be the differential of a 

 function not containing the variables T { , consequently containing 

 only the coordinates x h y { , z t . 



It follows from this :— first, that molecular attractions admit a 

 function of the forces; secondly, that this function remains the 

 same whatever may be the temperatures of the various points of 

 the body ; and, thirdly, that consequently the mutual action of two 

 molecules of a body is quite independent of the temperature — which 

 completely justifies the law laid down in our last communication, 

 and places it among the necessary consequences of the two propo- 

 sitions of thermodynamics. 



That law, that the pressure of a body heated under constant 

 volume varies linearly with the temperature, proves that the empiric 

 definition of temperature adopted by Dulong and afterwards by 

 Eegnault, viz. the pressure of a gaseous mass with constant volume, 

 might be easily extended to the case in which, instead of a gaseous 

 mass, any other body was in question. 



Finally, without wishing here to draw from this law all the con- 

 sequences which it admits of, we will nevertheless make the follow- 

 ing remark : — 



In a previous communication we have sought to discover what 

 are the data strictly necessary to be derived from experiment to 

 enable one to study a body from the thermodynamic point of view ; 



