264 
ON THE FLEFLECNODAL PLANES OF A SURFACE. 
[675 
where, changing the origin to the point x — 0, y = 0, z = k on the parallel surface, the 
coordinates of the consecutive point are Z — k, X, =(1— ka)%, and Y, =(1 -kb)y. 
We cannot, by any determination of the value of k, make the plane Z — k = 0 
a fleflecnodal plane of the parallel surface; but if 
, _ a/ 2 + bg- 
off 2 + b~g 2 ’ 
then 
and the equation becomes 
t (gV -/V) + O! 2 + by 2 ) (g% +fy); 
viz. the term of the second has here a factor g£ + fy which divides the term of the 
third order, and the plane Z—k= 0 is a flecnodal plane of the parallel surface.