( 133 ) 



On closer inspection, however, this opinion proves to be unfounded. 



If the double points have not yet yielded to the directing couples 



which they exercise on one another, and if therefore the axes may 



be directed in any direction, the mutual action will as often be a 



repulsion as an attraction, i. e. the mean attraction will be zero. If 



on the other hand we might assume that they had perfectly yielded 



to the directing couples, they would attract each other with forces 



1 

 proportional to — . It is, however, evident that the molecules will 

 r* 



only partially have yielded to the couples, and that they will be 



more perfectly directed according as they have approached each 



other more closely and therefore lie in a stronger field of forces. 



The consequence will be that the resulting molecular action will be 



an attraction which with increasing /■ varies more rapidly than 



1 



— . This circumstance has not escaped the attention of Rkinganum 

 r< 



and of Sutherland. They, however, thought that the law of 



attraction would only slightly deviate from — and assumed this law 



r* 



to be, at least approximately, accurate. 



In 1900 the present writer expressed the supposition that the 



resulting attracting forces would vary more rapidly than — '). It is 



r 7 



true that he founded his calculation on a somewhat different sup- 

 position as to the nature of the molecules, namely that they would 

 act not as constant but as periodical double points, but this difference 

 is probably not essential, as the law of attraction for vibrating 

 double points will not improbably agree in a high degree with the 

 law for constant double points, at least when the mutual distance of 

 the molecules is small compared with the wave-length, which con- 

 dition is satisfied in the case of gas-molecules at pressures of the 

 order of one atmosphere. 



At present it is my intention to investigate more accurately what 

 will be the law of the resulting attraction for constant double points. 

 We shall see that the attraction in this case really varies more 



1 

 rapidly than proportional to — . To render a rigorous treatment of 



r' 



this problem possible, we shall assume the following condition to be 



satisfied : 



] ) J. D. van der Waals Jr., Dissertation, Amsterdam, p. 85. 



