821 



to h^. But at low temperatures tliis curve will approach the straight 

 line b = bo more and more, mo^'ing from />, to /;„. 



Now as lias been said, the decrease of br/ with T is so slow at 

 first that b,, = b^ at 7' very great is not very different from b,/ at 

 Tk, when namely 7\ is comparatively high, as for all "ordinary" 

 substances. Only at k)wer temperatures b,, decreases rapidly to b^. 



In consequence ot this —, will, therefore, be comparatively very small 



in the neighbourhood of Tk, but — — will assume a much greater 



value. 



So this accounts for the fact that for substances with low critical 

 temperatures, as 0^, Argon, H^ and Helium the ratio bic-.b^ becomes 

 smaller and smaller (see the table), which will cause the type to 

 approach more and more to that of the so-called ideal substance, 

 where van der Waals' ideal equation of state with constant b will 

 hold. For once more: at lower temperatures b,j approaches bg more 

 and more, and the distance between b,^ and b^ disappears. 



But that this is nol the onh/ cause of the change of type, so that 



e.g. Xenon with a comparatively high critical temperature (-[- 16°,6 C.) 



is identical in its behaviour with 0^, where Tk= — 119°C. — this is 



perhaps owing to this that a second circumstance can be of influence 



v 

 on the course of b as function of v, namely that the relation — , 



which will probably depend on the structure of the molecule (com- 

 pound or simple as for argon, helium etc.), need not always be 

 = 1. This too will be discussed later. 



Both the varying value of b;j with decrease of temperature, and 

 the variable value of v^ ■ b^ according to the nature of the different 

 substances: these are the principal causes of the preservation of the 

 individuality of the great majority of substances sdso in their reduced 

 equation of state, so that these substances may be divided into diffe- 

 rent classes, ranging from the class of the "limiting substance" with 

 high molecular weight, and of the ordinary substances, to that of 

 the "ideal" substance with extremely low critical temperature, for 

 which would hold ƒ =4, r = S and s = ^/^. But even helium (see 

 the table) is still a long way from this. 



In a following paper we shall treat the form of the function 

 b=f{v), and test the found expressions by the values of b which 

 I have calculated for Argon. 



I will communicate already here, that of the many expressions 

 which satisfy the relations (21), i.e. which at jfit give the values of 



