466 



Intelligence and Miscellaneous Articles. 



Stations. 



Latitude. 



Longitude. 



Date. 



Horizontal 

 intensity. 



Dip. 



Namthabad 

 Deyrah .... 



15 06 00 



30 20 00 



77 36 00 



78 06 00 



April 1868 

 Jan. 1867 



037401 

 033604 



11 40 56 

 41 27 34 



■Proceedings of the Asiatic Society of Bengal, February 181 



ON MOLECULAR ATTRACTION IN ITS RELATIONS WITH THE 

 TEMPERATURE OF BODIES. BY M. LEVY. 



The demonstration which we have given, in our last communica- 

 tion, of a general law upon the dilatation of bodies rests on the two 

 fundamental propositions of thermodynamics, and upon this other 

 proposition — that the mutual actions of the molecules of a bodv are 

 independent of their temperatures. 



This last proposition we have assumed as an hypothesis ; we wish 

 now to prove that it flows from the first proposition of thermody- 

 namics, so that our law itself will be found to be built solely upon 

 the two propositions which serve as a foundation for that science. 



To justify this assertion, let us conceive any body in motion under 

 the influence of :— (1) external forces, F ; (2) mutual actions, /, on 

 the nature of which we will make no hypothesis ; (3) a certain quan- 

 tity of heat received from without. 



Let d'Q be the quantity, positive or negative, of heat received 

 during an infinitely short interval of time dt (we will employ the 

 characteristic d! for the infinitely small quantities which are not 

 exact differentials or which are not known a priori to be so) : a 

 portion d'q of this heat is employed for increasing the temperatures 

 of the various points of the body; the surplus, or d'Q — d'q, is trans- 

 formed into work, and gives rise to a quantity of work E(^'Q — d'q), 

 E being the mechanical equivalent of heat. 



Suppose that the body describes any complete cycle, which meaus 

 not only that all its points describe closed curves and resume their 

 velocities at the end of the orbit, hut also that they resume their tem- 

 peratures. If to this cycle we apply the theorem of the vires vivce, 



We get 0= JsCeF+JsCeZ+Ejrf'Q-Ej^, 



C c denoting an elemental work. 



But, in virtue of the first proposition of thermodynamics, 



jSC.F-fE JVQ=0, 

 whence 



J(2C e /- 



■Bd'q) = 0, (a) 



which is equivalent to saying that the quantity under the symbol f 



is the total differential of a certain function of all the variables, 

 which resume their values at the end of the cycle— that is, not only 

 of the coordinates x { , y { , zi of the various points of the material 

 system considered, and which we suppose to be n in number (so 

 that » = 1, 2, 3, ...n), but also of the temperatures T,. of those 



