750] 
225 
750. 
ON THE THEORY OF RECIPROCAL SURFACES. 
[From Salmons Treatise on the analytic geometry of three dimensions, (3rd ed., 1874), 
pp. 539—550.] 
600. In farther 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. 
5, number of nodal edges of the cone. 
k, number of its cuspidal edges. 
p, class of nodal torse. 
a, 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. 
6, number of its points of an unexplained singularity. 
number of its close-points. 
C. XI. 
29