760 



584.10-'^. (We s^hall i id mediately see that this is somewhat too low, 

 as it must lie between 588 and 594.10-6). 



When we now assume the value 2,545 also for 20° C. for the 

 ratio bg : a, we easily calculate from RTbg — a = 657,12 . lO^^: 



a2oo = 379,9. 10-6; (6^)ooo r^ 966,8 . 10-6 ... (7) 



As the values for 0° C. will certainly not be far from this, it is 

 clear that the value ar=i300.10~6 assumed before by us and others 

 is much too low, and must be raised to about 380 . 10—6^ and b 

 from 900 . 10-6 ^o about 970 . 10-6. 



Accordingly the value of a (hence also that of bg) has increased 

 between 0° C. (273° abs.) and Tk = 33° abs. in ratio of 380 to 486, 

 i.e. from 1 to almost 1,3. And we shall presently see that this in- 

 crease below Tk (to about 7i ^/fc) still extends from 486 to about 

 740, i.e. that the attraction at 16° abs. is almost 1,5 times larger 

 than that at the critical temperature. It is, therefore, as we remarked 

 above, quite unnecessary to make the quantity a increase with the 

 volume below 7\. The increase found is already perfectly covered 

 by the direct injiuence of the temperature. 



VI. General Considerations on the Dependence on ihe 

 Temperature. 



For the fact that b decreases at higher temperature a theoretical 

 ground can be adduced in the circumstance that the value of b is 

 exclusively determined at the moment of the collisions, and by these 

 collisions of the molecules. When in the first place the atoms inside 

 the molecule show a certain position of equilibrium with respect to 

 each other, this will necessarily be modified at the collision. The 

 atoms will approach each other more closely till the normally 

 directed relative velocity of the colliding molecules is exhausted ; 

 not until then will the colliding molecule be rebuffed by the other 

 in consequence of the repulsive force excited by the shifting out of 

 the state of equilibrium. When we now calculate the value of the 

 virial of collision on the supposition of the vai*ying size of /; during 

 the impact, we obtain an expression (see § VII) of the form 



hg^AmXf{T) (8) 



which can account for the decrease of bg with the temperature. At 

 low temperature the mean velocity at the impact will, indeed, be 

 very small, so that the molecule will be comparatively little com- 

 pressed, whereas at higher temperature the velocity, and consequently 

 also the compression will be considerably greater. 



Already in my paper of 1903 (loc. cit. p. 580) 1 remarked with 



