( 140 ) 



r ^ y, K i;2 = ^'c {N + A-,) /' - 'U ^ ^ (^•'V 4 yHr + ^'^r) . ( ƒ) 



If (ƒ) is subtracted from ('/) the well-know equation is obtained 



3/„ (A' f A'l) {v — h) = Vs ^ m T'/. 



The equation (ƒ) may be considered to contain the condition for 

 the stationary state of the molecules themselves. In the form given 

 it is, however only applicable, if the molecule is supposed to be 

 composed of material points, whicli do not form again separate 

 systems. If the latter is the case, the equilibrium of every separate 

 system will give rise to a new equation, which, however, will not 

 change the equation ^/j (A" + A"i) (u — h) = V2 ^i"- ^-~- 



For a mixture consisting of n-^ + ?(2 molecules, we find the virial- 

 value of the surface-pressure of all the molecules together through the 

 observation, that the amount of the pressure ou the unity of surface 

 for the two kinds of molecules is p)oportionate to the numbers 

 which are found in unity of volume and therefore also proportionate 

 to nj and W2- For collisions with a molecule of the first kind, a 



surface-pressure amounting to {N -(- N{) must be assumed, and 



"1 + "2 

 for collisions with molecules of the second kind a surface-pressure of 

 "2 



"1 + "2 



We find for the quantity with which ^/^ (A' -|- N{) is to bo multi- 

 plied in order to indicate the value of the viiial of the pressure, 

 which is exercised on the surfaces of the moving systems, the same 

 value as Mr. Lorentz (Wiod. Ann. ISSl, lid. XII, TIeft 1) has 

 found, viz. : 



I — Vs ^ { "{" "1^ + <'%^ "2" + 2 0^ «1 11-2) 

 "1 + "2 



It is easy to deduce, by the pniccding way of obtaining the characte- 

 ristic equation that the value oi l> is equal to 4 times the volume of 

 the molecules only in case of infinite rarefaction, and that it must 

 be smaller in case of less great rarefaction; it is not even difficult 

 in that case, to give a first approximation of the way, in which b 

 depends on the volume of the substance. By the calculation of the 

 equation (ƒ) we find the value of the virial of the pressure on the 

 moving systems to amount to half the value of the virial of a pros- 

 sure A' + Ny , exorcised on as many surfaces as there are systems, 



