11& Mr. H. Hilton on van der Waals' Equation. 



equal and opposite ( + ^); the tangential plane at that point 

 isy-40 + 3=O. 



The border-curve may be considered as a twisted curve 

 lying on this surface ; it starts from the point (g, 0, 0), where 

 it touches the line y = 0, x — \ = ^-fi', it touches also the line 

 y = 6=l at the point (1, 1, 1), and touches the axis of x at 

 infinity. 



We discussed in the previous paper the equation of this 

 curve, and the practical method of obtaining points on it, 

 such a series of points is given in Table IV. (owing to the 

 method of obtaining them, the values are only approximate). 



Table IV. 







Points 



on the Border-C 



urve. 



X 









y- 



e. 



GO . 



•333 















) 



*418 







•048 



•500 



, 



•441 







•090 



•625 



4-830, 



•495 







•281 



•750 



3-310, 



•545 







•486 



•844 



2-530, 



•573 







•587 



•875 



1-840, 



•660 







•773 



•937 



1-000, 



1-000 







1000 



] 000 



It is the projections of this curve on the ] lines perpen- 

 dicular to the axes which are shown in figs. 1 and 3 of the 

 present paper and fig. 2 of my previous paper. The projection 

 in fig. 1 touches the axis of 6 where = 0, and the line 

 y — 404-3 = at the point (1, 1); the projection in fig. 3 

 touches that curve of the family there shown for which y = 

 at the point (J-, 0) (and makes an angle tan-*- 1 with the axis 

 of x there): it also touches the line 0=1 at (1, 1), and is 

 asymptotic to the axis of x. 



