Intelligence and Miscellaneous Articles. 79 



Q. *.' 



Let us suppose Q and Q x infinitely small, as well as the arcs of 

 the lines of equal energy corresponding to them. Let us draw, 

 through the intersection of the line of equal energy <J> with the 

 adiabatic line on the left, an infinitely small arc of an isothermal 

 curve stopping at the adiabatic line on the right ; and let us make 

 the same construction for the point of intersection of the curve of 

 equal energy $ x and the left adiabatic line. The quantities of heat 

 Q ' and Q x ' which must be respectively supplied to and withdrawn 

 from the body along the isothermal ares thus traced will, in virtue 

 of Carnot's theorem, be connected by the relation 



Q,'~ r,* 



r and r x being the absolute temperatures corresponding to the iso- 

 thermal lines. 



Now it is easily demonstrated that Q and Q ', Q : and Q,/, re- 

 spectively differ only by infinitely small quantities of the second 

 order. We have therefore 



from which, finally, is deduced the general relation between the 

 mean actual energy $ and the absolute temperature r, 



d>=/3r, 



fl being a specific coefficient depending only on the nature of the 

 body. 



This equation, true for any body or portion of a body whatever, 

 is also true for an atom ; hence the theorem stated above. 



In the second part, I demonstrate that if, as experiment indi- 

 cates, the condition of a body is determined when the atomic ar- 

 rangement produced by a certain equilibrium between the external 

 and internal forces is known and a single quantity, the tempera- 

 ture, is given, tins arises from the circumstance that the atoms, 

 instead of merely being in the presence of each other, are under the 

 influence of the aether — a fluid whose vibration-period has an ex- 

 tremely small duration in comparison with that of the atomic 

 vibration. 



I show that the 3n expressions which determine the mean vires 

 vivce of the n atoms constituting any body whatever contain Sn ar- 

 bitrary constants, so that the vires vivce are independent of the 

 arrangement and mutual forces of the atoms. They are dependent, 

 therefore, only on the action of the aether ; so that the atoms of the 

 body vibrate as if, the body being completely disaggregated, they, 

 immersed in the aether, no longer exerted any action upon one 

 another. 



I hence infer, by very simple considerations, that, if represents 

 the mean vis viva of an atom, or of the centre of gravity of any 



