50 
ON THE ENVELOPE OF A CERTAIN QUADRIC SURFACE. 
[495 
49 
The result thus is 
(7 - P + fA 2 ) 3 - 27 (J- Q + ¿AP - ^A 3 ) 2 = 0, 
or, what is the same thing, it is 
(7- p)3 _ 27 (J - Q) 2 - 9 AP ( J - 2Q) 
+ A 2 (4/ 2 - 8/P + P 2 ) 
+ 8A 3 (J-2Q) 
+ A 4 .-f-/ = 0, 
where the left-hand side is of the order 24 in (x, y, z, w). I apprehend that the 
order should be =12 only; for writing (x, y, z, w) in place of (x 2 , y 2 , z 2 , w 2 ), the 
equations which connect (a, b, c, d) express that these quantities are the coordinates 
of a point on a plane cubic; and the problem is in fact that of finding the reciprocal 
of the plane cubic: this is a sextic cone, or restoring (x 2 , y 2 , z 2 , w 2 ) instead of 
(x, y, z, w), we should have a surface of the order 12. I cannot explain how the 
reduction is effected. 
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