( 139 ) 



The condition which is required for considering a group of points 

 as a system is, that these points keep always together, whatever 

 may happen and that the quantity ^2 fi r/ keeps constant. 



For the term — V2 ^ (^•''^ + Yy, + Zs^) we may write ^U i^ + ^^1) i'. 

 so that the Latter equation may be written : 



2 1/2 '« T'=^ + -^- V2 i" Vr~ = =5/2 (N + iVj) r — 



- 1/2 ^^ {X~rr + Yy, + Zzr) .... {<!) 



In these equations collisions taking place between material points, 

 cannot furnish a value, as in every point where a collision takes 

 place, there are two forces of opposed direction, which, working 

 at the same point, destroy each other. The forces in the term 

 V2 — .S" (Ar,. -j- Yi/r "t- Zz,.) are simply the attractive forces between 

 the points of the system and possibly also the attractive forces which 

 are exercised on a system by the surrounding ones. 



It is true that in transforming — V2 -^ i^^z + I'»/; + Zz^) to 

 ^2 i^^ -{ ^^1) ^ it has been assumed for these latter forces, that for 

 a system, which does not lie near the surface 2X is equal to 0, 

 but from this does not follow that ^Xx,- is equal to 0. 



If to the moving systems themselves the virial equation is applied, 

 we get the equation 



^^1/2/" Vr^ =-y, ^^ (X'.r, + r'y, + Zz,) . . ) 



provided that in X', F'audZ' all forces, also those which exist on 

 the surfaces as pressures, are taken into account. These systems 

 move in a space, in which the pressure is A' + -^^ per unity of sur- 

 face, and if we were justified in considering the pressure as really 

 exercised on the surface of every system, the value furnished in the 

 second member of tlie equation would be equal to V2 (-^'^+•^^'1)^1, 

 if we represent the volume of all the systems together by b^. 



As this pressure, however, is transferred on every system by the 

 collisions with the other systems, in calculating this value, we 

 must consider that pressure as exercised at a distance twice as 

 great, so on the surface of a volume, whose lineal dimension is 

 twice that of the sytem ; at least for spherical systems. Of the 

 value obtained in this way, the half is to be taken, because a 

 pressure exercised by the first system on the second is at the same 

 time a pressure, which is exercised by the second on the first. The 

 equation (e) becomes then if we put b^ih^ 



