82Ó 



of the function h=f{v), and so the particular form of this last 

 function is after all the deeper cause that both ).^ = P.,, and the 

 new relations found by me, viz. Vk — f)k = 2/?^ and hh : b^ = 2y are 

 satisfied. 



I further draw attention to the fact that the above relations only 

 remain valid as long as the law of eqnipartition continues to' hold 

 at very low temperatures. I have convinced myself for argon that 

 the departures from this law even at the lowest temperatures, at 

 which vapour-pressure determinations etc. have still been made 

 below the critical temperature — among others at 90° K. — are 

 still so slight that they remain entirely below the errors of observation. 

 But this will be treated more fully in a following communication. 

 Whether this is the case at the critical temperatures of hydrogen 

 and helium, 1 have not yet examined. It is, however, very well 

 possible that for such exceedingly low absolute temperatures the 

 deviations are large enough to give rise to more or less considerable 

 deviations in the formulae. This can particularly affect the quantity 

 y, as the straight diameter extends to still lower temperatures than 

 the critical temperatures. 



Finally a few remarks on the way in which /> depends on the 

 temperature. It has appeared to me that this variability is exceedingly 

 slight at higher temperatures, so that even at the critical temperature 



of ordinary substances — is still negligible (See § 1 and 2). This is 



in agreement with what I found before for //, '). For 0°, 100°, and 

 200° C. I found, namely, h,, constant = 917 X 10"*^ (P- ^"6, 580 

 and 582 loc. cit.). But />„ varied greatly. That b, varied and even 

 apparently increased according to the relation b,, — b^z=\/yT was 

 entirely owing to the form of the chosen function b =f{v), viz. the 

 wellknown "equation of state of the molecule" of van der Waals. 

 It has, however, become clear to me that this equation does not 

 hold, and is in contradiction to the above given accurate values b'k 

 and ^'k. The fact is this that b decreases at all temperatures, but the 

 more as the temperature is lower. Finally b,, will have become — b, 

 at the absolute zero ; hence no variation of b with the volume will then 

 be possible any more. For at a given temperature b moves between 

 b,j (for v = <x>) and b„ (for v—v,). Now bg is a temperature function, 

 and it moves from b^ (for T large) to b, (for T=0). Hence in a 

 6,?;-diagram at high temperatures the curve b=/{v) will have a 

 pretty steep inclination from b(, = about 1,9 bo (for ordinary substances) 



1) These Proc. of 24 April 1903, p. 573—589. 



