II. 



ON THE FUNDAMENTAL FORMULA OF STATISTICAL 

 MECHANICS, WITH APPLICATIONS TO ASTRONOMY 

 AND THERMODYNAMICS. 



[Proceedings of the American Association for the Advancement of Science, 

 vol. xxxin. pp. 57, 58, 1884.J 



(ABSTRACT.) 



SUPPOSE that we have a great number of systems which consist 

 of material points and are identical in character, but different in 

 configuration and velocities, and in which the forces are determined 

 by the configuration alone. Let the number of systems in which the 

 coordinates and velocities lie severally between the following limits, 



viz., between 



x l and 



y l and 



z and 



x 2 and 



etc., 



^ and 

 2/i and 

 z^ and 

 XQ ano. Xa ~T~ ct/Xa , 



etc., 

 be denoted by 



L dx 1 dy l dz l dx 2 etc. dx t dy l dz^ dx 2 etc. 



The manner in which the quantity L varies with the time is given 

 by the equation 





 dt ~ ^Ldx dx 



where t, x lt y 1} z l} x%, etc., x lt y lt z lt x 2 , etc., are the independent 

 variables, and the summation relates to all the coordinates. 



The object of the paper is to establish this proposition (which is not 

 claimed as new, but which has hardly received the recognition which 

 it deserves) and to show its applications to astronomy and thermo- 

 dynamics. 



