A Sufficient Condition That a C-Characteristic Be Geometric.

These inequalities express the fact that no curve of order k and defined at the p points can meet the net in more than yok points. Coble' has conjectured that the conditions (1) and (2) are sufficient as well as necessary. In this paper we will show that the conditions (2) are actually sufficient. Indeed, the less stringent set of inequalities given in (5) will suffice. The notation and point of view is that used in "Ctemona's Diophantine Equations."2 We begin with the proof of LEMMA: If co > 0 in a solution Ic} of equations (1), then 2co > cl + c2 + c3, where