761 



regard to the decrease of b„ stated then, without entering into 

 further details: ''It seems that at liigher temperature the atoms in the 

 molecule may approach one another closer than at loiuer temperature" . 



A further calculation shows us, however, that the above mentioned 

 f{T), which in approximation (see the following paragraph) is 

 proportional with (1 — a\/Ty, do not sufficiently represent the values 

 found of the virial coefficients B above 20° C. (the one fixed point, 

 on which the calculation of ■hn and the coefficient « is based), and 

 especially below 7\ (the second fixed point). ^) Too low values are 

 found. At 200° 0. B would only be =1170.10-6, ^hile 1280 

 would follow from Amagat's experiments. And for — 252°, — 255°, 

 — 257° would follow the only little increasing values 403, 419, 

 and 429 for — B, whereas the rapidly increasing values 480, 500, 

 and 630 (about) would in reality follow from K. Onnes's experiments. 



This course would sooner point to an exponential function of T. 

 In the collisions we shall, indeed, have to take account in the 

 second place of the influence of the field of force on the distribution 

 (density) of the molecules round the considered molecule, e.g. 

 according to the theory of Boltzmann. We then arrive at an expres- 

 sion for b (when we namely assume the same function of the 

 temperature for h^, as was found for a, which would be in contra- 

 diction with Boltzmann's formula) of the form 



*.7 = (^<7)ooX— U«^-l , (9) 



in which [bg)^ represents the limiting value at very high temperature, 

 just as before [bcj)^ = 4?/i denoted the limiting value at very low 

 temperature. 



Now we find better agreement above 20° C. (e.g. i^ = 1280.10— ^ 

 in perfect agreement with Amagat), and also below T^, where we 

 now find 470, 525, and 570 . 10-^ at the above mentioned tempera- 

 tures. But now the values between 20° C. and Tk are almost all 

 somewhat too small. This may perhaps be remedied by also making 

 the first influence (that of the molecule-compression) play a part — 

 though it be an insignificant one — which renders it possible to 

 reduce the exponent «' to a somewhat smaller value, so that the 

 curvature between 20° C. and 7\. becomes somewhat slighter. 



In any case the influence (at least for hydrogen) of the {real) 

 molecule diminution by compression seems, however, in consequence 

 of the rigid atom system, to be very slight compared with the much 



1) I.e. when we assume the same function of the temperature to be valid for 

 a, and therefore make a vary together with b. (See also the Note to § 2). 



