14 
Proceedings of Royal Society of Edinburgh. [sess. 
axes of x and y, and two on each octant line. The coordinates of 
these points are ( ± 2, 0), (0 ± 2), and ( ± ^2/ JS, ± J2/J3). 
Since the number of double points is ten, the maximum which a 
sextic curve can have, it follows that the curve is unicursal. This 
might have been seen from the original parametric representation 
of the curve given by the equations (1). In fact, if £ = tan \ 6 , we 
get 
a? = (1 - £ 2 )(£ 4 - 14£ 2 + V)/(ft + 1)(£ 4 - 6£ 2 + !) \ 
y = 2t(3t 2 - 1 )(^ 2 — 3)j(t 2 + 1 )(£ 4 - 6^ 2 + 1) j 
a rational parametric representation of the curve. 
