78 Intelligence and Miscellaneous Articles* 



Thermodynamics defines the calorie very clearly ; it only indi- 

 rectly defines the temperature, by means of Carnot's theorem : hence 

 the difficult and embarrassed course of the theory. I have proposed 

 to myself to remedy this defect. 



In the first part of the work which I have the honour to submit 

 to the Academy I demonstrate that Carnot's theorem is identical 

 with the f ollowing : — The mean vis viva of an atom forming part of 

 a body, the absolute temperature of which is r, may be expressed by ar, 

 a being a specific coefficient ivhich can only be dependent on the nature 

 of the atom. 



The following is a compendium of the demonstration of this pro- 

 position : — 



If we produce a change in the elementary state of a body sub- 

 mitted at every instant to external forces which balance the internal 

 forces, we shall have 



dX + EdQ = dU. + d$ + d% 



dX being the variation of the external work, cZQ the quantity of 

 heat supplied to the body, dll the variation of the potential function 

 corresponding to the displacement of each atom from its mean po- 

 sition, d<& the variation of the actual energy, and c^p the variation 

 of that part of the potential energy which depends on the vibratory 

 motion. On account of the constant equilibrium between the ex- 

 ternal and internal forces, we have 



and there remains 



dX=dU, 

 'EdQ=d& + d¥. 



Instead of determining, according to custom, the condition of a 

 body at any instant by two quantities such as the pressure ^> and 

 the volume v, I suppose it determined by two auxiliary variables E 

 and B, chosen so that 



EK=2#, ~FdR=dV. 



The fines of equal energy will then be equilateral hyperbolas 



EE=2$ (1) 



The adiabatic lines satisfy the equation 



¥dQ=~Fd~R+dV = 0, 

 or 



EK 3 = const (2) 



Equations (1) and (2) having the same forms as the equations of 

 isothermic and adiabatic lines for perfect gases, analogous conse- 

 quences are deduced from them — namely, that if Q is the quantity 

 of heat supplied to the body, in a cycle analogous to that of Carnot, 

 along the fine of equal energy 4> , and Q x the quantity of heat ex- 

 pended by the body during that cycle along the fine of equal 

 energy $ v 



