584 



Mr. H. Hilton on van der Waals 9 Equation. 

 Table II. 









[ Values of y for Different 



X. 



3a?— 1. 



3 

 a? 2 



Values 



of 8 6>. 



80=4. 



80=-8. 



•3 



-1 



33-333 



- 73-333 



46-667 



•25 



-•25 



48-000 



- 64-000 



- 16-000 



•2 



-•4 



75000 



- 85-000 



- 55-000 



■15 



-•55 



133-333 



-140606 



-118-788 



■1 



— •7 



300-000 



-305-814 



-288-571 



- -5 



- 2-5 



12-000 



- 13-600 



-8-800 



-1-0 • 



- 4-0 



3-000 



-4-000 



-1-000 



-1-5 



- 5-5 



1-333 



-2-060 



•121 



-2-0 



- 7-0 



•750 



-1-321 



•393 



-25 



- 8-5 



•480 



- -951 



•461 



-3-0 



-10-0 



•333 



- -733 



•467 



-3-5 



-11-5 



•241 



- -589 



•455 



-4-0 



—130 



•187 



- -495 



•428 



-4-5 



—145 



•148 



- -424 



•404 



-5-0 



—160 



•120 



- -370 



•380 



Differentiating (a) we have 



dy -240 



dx 



w 



3 • 



(3^-l) 2 



.*. The tangent is parallel to y = when (?>x — l) 2 = 4# 3 #. 

 Eliminating between this equation and (a), we have 



(3*-2)=y* 3 , (0) 



as the curve through the points where y has a maximum or 

 minimum value. 



Differentiating (/3) we have 



dy _ 6 (1-*) „„,, cVy _ 6(8*-4) 



dx 



6Ji=£) and p 2 



x dx 2 



.'. (/3) has a tangent parallel to the axis of x at point (1, 1) 



and an inflexion at the point {$•> 32/ • This curve cuts y = 



where #=3, has a triple point at infinity at which tangents 

 coincide with «z'=0, and has an inflexion at infinity at which 

 the tangent is y = 0. It is of degree 4, class 4, and deficiency 

 zero; has 1 double point and 2 cusps (coinciding in the multiple 

 point at infinity) , 1 double tangent and 2 inflexions (one at 

 infinity) . 



It passes through the points ( — 6; "093) ( — 5; *136) 

 (-4; -169) (-3; -407) (-2; l)(-l-5; 1-926) (-1; 5) 

 (-•5; 28) (-1; -1700) (-2; -175) (-3 ; -40-741) 



