Mr, H. Hilton on van der WaaW Equation, 

 Table III. 



115 



X. 



Values of 9 for Different Values of y. 



5. 



-2-5. 



-40. 





•625. 



-•3125. 



-5. 



•25 



- 1-656 



- 1-422 



- -250 



2 



- 4000 



- 3-625 



- 1-750 



•15 



- 9511 



- 8-995 



- 6-417 



•1 



-26-687 



-26031 



-22-750 



_ -4 



- 6 532 



- 4-470 





— *5 



- 5-312 



- 2-969 





-10 



- 4000 



- -250 





-1*5 



- 4-354 



•802 





-20 



- 5 031 



1-531 





-2-5 



- 5-822 



2146 





-30 



- 6-667 



2-708 





-3a 



- 7-539 



3-241 





-4-0 



- 8 429 



3-758 





-45 

 -50 





4-263 

 4-760 













The area between the curve and the lines x = x h x=x 2i 



6» = 0, is 



9 



Differentiating (a), we have 



8 ° a?, & C ^ a^a 1 > 



dd 3 f 3 L 2 •) 



7/1 



Hence where — =0, L e. tangent is parallel to axis of x, 

 ?/= ; and eliminating ?/ between this equation and (V) 



we have 



= 



(:v-i) 2 



4* 3 ' 



or 4^ 8 = (3^~1) 2 . . . 



Table I. gives a series of points on the curve. 

 Differentiating (ff) we have 



(0) 



(W 



(t.r 



d 2 6 



3 



4r 

 3 



i(3a-l)(a-l), 



I 2 



