491] 
ON THE QUARTIC SURFACES (*$£7, V, Tf) 2 =0. 
27 
other points 8, S' (real or imaginary) situate symmetrically in regard to MN; we have 
thus the required pair of points which generate the nodal circle. 
A meridian section of the torus (or section through the axis 00') is a quartic 
curve symmetrical in regard to this axis, and having two (real or imaginary) nodes 
the intersections of the plane by the nodal circle: see fig. 3, which shows the section 
for the surface generated by a conic such as in fig. 2. The quartic curve has 8 double 
tangents, 2 of them at right angles to the axis 00', the remaining 6 forming 3 pairs 
of tangents situate symmetrically in regard to this axis; so that attending only to 
one tangent of each pair, we may say that there are 3 oblique bitangents: one of 
these is the line TT'; and the section of the torus by a plane through this line at 
right angles to the plane of the meridian section is in fact the two conics of fig. 2, 
either of which by its rotation about 00' generates the torus. But taking either of 
the other two oblique bitangents, the section by a plane through the bitangent at 
right angles to the meridian plane is in like manner a pair of conics situate 
symmetrically in regard to the bitangent, and such that either of them by its rotation 
4—2