582 
[416 
416. 
ON THE THEORY OF RECIPROCAL SURFACES. 
[Published as an Addition by Prof. Cayley in Dr Salmon’s Treatise on the Analytic 
Geometry of Three Dimensions, 4th Ed. (8vo. Dublin, 1882), pp. 592—604.] 
620. In further developing the theory of reciprocal surfaces it has been found 
necessary to take account of other singularities, some of which are as yet only imperfectly 
understood. It will be convenient to give the following complete list of the quantities 
which present themselves: 
n, order of the surface. 
a, order of the tangent cone drawn from any point to the surface. 
8, number of nodal edges of the cone. 
k, number of its cuspidal edges. 
p, class of nodal torse. 
cr, class of cuspidal torse. 
h, order of nodal curve. 
k, number of its apparent double points. 
f number of its actual double points. 
t, number of its triple points. 
j, number of its pinch-points. 
q, its class. 
c, order of cuspidal curve. 
h, number of its apparent double points.