( 399 ) 

 instead of the planets we iina,U'iiic muleciiles inoxiiig' in a oiie-dinieiisioiial 

 iiiotioii, we f^'et : S^, z=z i . . \ i'' Lxj L" dl^ . .</[., iiM\ liieli /^ 2.t — /j, 







2.T -j- /, etc. iiiiisl he taken together in the eah-uhitioii of P'. 



We meet with still another transition ease when we eoiisider an 

 cnsend)le of systems of one moleeule each, moving freely in a vessel 

 having the shape of a i-ight-angied parallelopiped with the edges r/, 6 

 and c. This motion may l)e tlionght as composed of three motions parallel 

 to the edges, which we may each treat as in the tirst transition case. 

 If we call the coordinates with respect to the sides .r, // and z, 

 the combinations of .r, 2(i — .c, 2(f-\-,r etc. with //, '2h — //, 2/0-[-// etc. 

 and ~, 2c' — -, '2c-\-: etc. come to the same thing with regard to 

 place. So we now get the J^' hy integrating for the 1^ with regard 

 to the components of the velocity, and by then sn nun ing for all these 



J "'a /' b /"• c 

 I I ^^ ^"'.1 ^^' '^'^ ^^11 ^^~ decreases again 







till the minimnm value is reached. A molecule chosen at random 

 from the ensemble will have an equal chance to any place in the 

 vessel. When the dimensions of the molecules are not neglected 

 planes take the place of the walls of the vessel at a distance r 

 parallel to them. 



If we mav disreuard the collisions of the molecules inter se of a 

 gas mass, we might always consider each of the // molecules as chosen 

 arbitrarily from such an ensemble, and hence at last these // mole 

 cules would probal»ly be distributed oxer the vessel about uniformly. 



§ 4. Finally we shall coJisider an ensend)le of systems consisting 

 of )i nujlecules moving in a vessel having the shape of a right-angled 

 |)aralleloi)iped. If we take the coordiiuites with regard to the side 

 faces as variables, the comi)onents of the xelocities may also be 

 negative and the representing i)oint of a system may occupy any 

 place within the space 



/•"-'■ T'^-'' r^~'' r+.'^ .. r+"* r\.''^' 



in which we need only take into consideration that during the motion 

 the kinetic energy or also the 2£i-'' remains constant. So we shall 

 now have to examine which [larts of the phase extension will give the 

 same an-aiigement of the molecules, and which the same molecular 



27 



Proceedings Koyal Acad. Amsterdam. Vol. X. 



