1208 
$ 6. In order to find the order and the class of the focal surface 
of the congruence of intersection of two complexes, [ pass two 
a-planes a, and a, through a point P of O?,. The @-plane through 
a ray a, of the plane pencil P, a, cuts «, in a straight line a,. A 
plane y through a, which cuts «, in a straight line a’, and has two 
coinciding points in common with )’,”", touches the curve which 
the space R,=(a,«,) cuts out of V,”"; as this curve is the curve 
of intersection of a surface of the m'* order and a surface of the 
nt order, it has the rank mn (m+n—2); accordingly this is the 
number of the planes through a, intersecting «, in a straight line 
a,‘ and at the same time touching ),”". Between the rays a, and 
a,! belonging to the same ray a,, there exists a [mn (m-—-+-n—2), 
mn (m+n—2)| correspondence, hence there pass through P 2mn(m—+ 
n—2) 3-planes (and as many «-planes) touching V,”". or: 
The focal surface of the congruence of intersection of a complex 
of the m* and a complex of the n® order, has the order and the 
class 2mn(m—+-n—2). 
Of course this result can also be derived from § 4 and § 5. 
