226 
PROFESS OE CAYLEY OX RECIPROCAL SURFACES. 
Q , number of off- points. 
X, number of close-points. 
/3, number of intersections of nodal and cuspidal curves, stationary points on cuspidal 
curve. 
y , number of intersections, stationary points on nodal curve. 
i number of intersections, not stationary on either curve. 
B, number of binodes of surface. 
C, number of cnicnodes. 
67. And the accented letters have the like significations in regard to the reciprocal 
surface ; or, referring them to the original surface, we have 
n ! , class of the surface. 
a! , class of curve of intersection by any plane. 
y , number of double tangents of curve of intersection. 
, number of its inflexions. 
V , class of node-couple torse. 
W , number of its apparent double planes. 
t' , number of its triple planes. 
q' , its order. 
g' , order of node-couple curve. 
j number of pinch-planes. 
c' , class of spinode torse. 
h ! , number of its apparent double planes, 
r' , its order. 
o ’ , order of spinode curve. 
§ , number of off-planes. 
yj , number of close-planes. 
f3 ' , number of common planes of node-couple and spinode torses, stationary planes of 
the spinode torse. 
y ' , number of common planes, stationary planes of node-couple torse. 
i' , number of common planes, not stationary planes of either torse. 
B', number of bitropes of surface. 
C', number of its cnictropes. 
68. It is hardly necessary to recall that a spinode plane is a tangent plane meeting 
the surface in a curve having at the point of contact a spinode or cusp ; the envelope 
of the spinode planes is the spinode torse, and the locus of their points of contact the 
spinode curve. And similarly a node-couple plane is a double tangent plane, or plane 
meeting the surface in a curve having two nodes ; the envelope of the planes is the 
node-couple torse, and the locus of the points of contact the node-couple curve ; the 
other terms made use of are all explained in the present Memoir. 
