Geometry on the Cubic Scroll of the First Kind. 35 



7) y = H^Pq(Pq — q" + q — 5) + q(q^ — 2q' + llq — 2j + 



8p - (2H + 3ß) (4pq - 2q' + 2q - 1) + 



C2H + 3ßf-f 6(3H + 4ß)] 



8) g = i[9(2pq-q'-pf4-4(3H + 4ßf-(3H + 4ß). 



[l2(2pq-q'-p)-14] + 2H-22q(2p-q) + 



27p + 5q] 



9) D = p(q — 1) — iq(q + l)+l-H-ß 



where D^ deficiency. 



The number of varieties of curve of each species (p , q) is 



(D 4- 1) (D 4- 2) 



