( 800 ) 



§ 3. So we arrive at equation (4) witlioiit making use of the 



equation of tlie virial ajid witiioiit speaking of repulsive forces. That 



the introduction of tliese and tiie determination of the so-called 



"repulsive virial" in the same waj as has been done by Lorentz, 



Tait and Boltzmann, leads to the same result, is easy to see, if we 



|/2rr;i.v- \/2 .ins'' 

 put everv where ,j mstead of — for the number of 



V V 



collisions in the formidae used by fhem. The exi»ression (3 does not 

 depend on any of the integrations and the repulsive virial yields 



J' l> 



iherefore MT — ,i instead of RT -. This is easv to understand, even 



i' 



without following the proofs of I^orentz and Fjoltzma.nn, for it is 



clear that the term which is introduce<l into the equation of the 



virial through the collisions, must l)e ])roportio]ial to the number of 



those collisions, as two collisions can never be of a different kin(P). 



It seems therefore as if theory really leads to the form expected 



by Tait and DiETERifi, ^\ hicli conforms so little with the experiment. 



In reality, however, the result is quite dliferent. For — as I pointed 



out in my other communication — ^i has l)y first approximation not 



5 h 

 the lorm : I -\- ~ — , as .Iagek and Uoltzmann generally write, but we 



b V 



11 h 

 1 



8 V 



find in the wav first indicated bv Clausus — for it, and onlv 



b 

 1 — 2- 



by carrying out the division and by neglecting tlie terms of higher 

 order, we get the form 1 -|- ~ . As I showed, we get, taking the 



o I' 



terms of liigher order into account : 



(5) 



where n is a finite numl>er. 



Xow it is true that the other coefficients of this series, C\ and B 

 excepted, are unknowji, and we might conclude from this, that it 

 must therefore be iiKHfrcreiit for the present, whether the equation 

 of state is wj-itten 



1) KoRTEWEG aud VAN DER Waals have also made use of thi:< property in their 

 derivafion of equation (2) from (1), mentioned on p. 795. 



