354 
A MEMOIR ON THE THEORY OF RECIPROCAL SURFACES. 
[411 
a' (n — 2) = k — B' + p + 2a', 
V (n' - 2) = p + 2/3' + 3y + 3t\ 
d (n — 2) = 2a + 4/3' + y + 0', 
a’ (n' - 2) <>' - 3) = 2 (S' - C') + 3 (aV - 3a' - X ') + 2 (a'6' - 2p' - /), 
5' (n' - 2) (n' - 3) = 4 A;' + (a'6' - 2 p - j') + 3 (b'c' - 3/3' - 2y' - %), 
d (n' - 2) (n' - 3) = Qh' + (a'd - 3a' - %') + 2 ( b>c ' ~ ~ 2 7 “ »'), 
q' = b'*-b'-2Jc'-3y'-6t', 
r ' = d 2 -d-2h'-3/3', 
together with the equations for /3 and /3'. 
66. The symbols signify as follows; viz. 
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. 
b, order of nodal curve. 
Jc, number of its apparent double points. 
t , number of its triple points. 
q , its class. 
p, number of points where nodal curve is met by curve of contact of tangent cone. 
j , number of pinch-points. 
c, order of cuspidal curve. 
h, number of its apparent double points. 
r, its class. 
а, number of points where cuspidal curve is met by curve of contact of tangent cone. 
б, number of off-points, 
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. 
G, 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. 
8', number of double tangents of curve of intersection.