( 796 ) 



Now it lias clearly ap]ieared of late, of how prei)0nderalhi_2; an 

 iiiiporlaiicc the kiio\\ie<lge of these corrections is for an accurate 

 equation of slate. Iji the first place Brinkman ^) has succeeded in 

 provin<2,-, that tiie itehaviour of air at 0' between 1 and 3000 atms. 

 can l)e \evy accurately represented bv means of coefïicients which 

 do not differ considerably from the values found by Uoltzmann; 

 then VAN DEH Waai.s ■') has pro\ed — as van Laak "') had done 

 before — that with the aid of these corrections the critical coefficient 



becomes ( — 1 = 3.0 and in this wav one of the great discrepancies 



VFVc 

 between theory and experiment seems to be removed. And this last 

 result makes it again clear, ho^v great from a i)hysical point of 

 view, the difference is between an equation of form (1) and (2), 

 though from a mathematical point of view they may be identical by 

 first, second aiid further approximation. Already a long time ago 

 DiKTERici^j proved, as lately Happei, ') has also done, tliat with an 

 equation of the form : 



7'+ -,=" !+- + «-,+ ...... (3) 



the critical coefficient can reach at the utmost the value 3 with the 

 theoretical values of the coefficients, and that th-s form can therefore 

 never I'epresent the exi)ei-iniental data. It seems therefore iiot devoid 

 of interest to me, to examine the different derivations of the equation 

 of state, in order to find which form must be taken as the correct 

 one. This investigation will at the same time enable ns to form an 

 opinion about the difference between Boltzmann and van dek Waals. 



§ 2. As is well-known, the proof which van der Waals originally 

 ga^■e for his equation of state, rests on \\\() theorems, the first of 

 which is ex[dicitly stated, the other is a.ssumed without argument 

 as self-evident. The first theorem states, that the number of collisions 

 in a gas with s})herical molecules is represented by the before- 



mentioned fornuda P= — ^— . Now I have alreadv pointed ont 



v — b 



in a former paper ^), that this formula is inaccurate, and must 



ij Tliese Proc. YI, p. 510. 



2j BoLTZMANN-Feslschrift, p. 305, 



5) Archives Teyler (2) Vll. 

 •i) Wicd. 69, p. 685. 



-") Drude 13. p. 352. 



6) Tliese Proc. p. 787. 



