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The double binary form, (at)3(ai-)3, of third order in digredient variables t and T, when equated to zero, defines a space curve of the sixth order on a quadric surface with generators t and r-. This space curve is the complete intersection of the quadric surface and a cubic surface and hence is of genus four. The geometric theory connected with a general (3, 3) form has been discussed by Coble.t He introduced the form, with the interpretation also used by H. S. White,j that is, as the incidence condition of a point of one space cubic curve and a plane of a second space cubic curve. It is the purpose of this paper to discuss the special form

The geometric configuration defined by a special algebraic relation of genus four