The greatest number of straight lines that can lie upon a surface of order n (not being a ruled surface) is unknown, except if n is three. Salmon and Clebsch have shown that the points of contact of lines which have a four-point contact with the surface lie upon a locus of order n (11n – 24), the intersection of the surface of order n with another of order 11n – 24. Since a straight line lying wholly on the former surface must form a part of this locus, the number n (11n – 24) is an upper limit to the number of lines; if n is three, this gives 27, the correct number. But for values of n > 3, it is improbable that this limit1 can be reached.