The determinantal quartic primal in [4], represented on [3] by quartic surfaces passing through a decimic curve of genus eleven, has already been the subject of a number of papers. The primal for which the base curve is a general curve C10 has twenty nodes, mapped by the twenty quadrisecant lines of the curve. If the C10 breaks up into a number of curves of lower order, the primal has, in addition, other nodes, mapped by the neighbourhoods of the intersections of two simple branches of the base curve. When the C10 consists of ten lines, having twenty mutual intersections to preserve the virtual genus eleven, the primal has forty nodes; the two primals of this type which contain no planes are the subject of a paper by Todd (3). Further specialization of the ten lines, giving more additional nodes, is possible; it has been shown in another paper (Todd (4)) that there is a quartic primal with forty-five nodes (the maximum number) which is determinantal. The figure in [3] formed by the base curve is described there; for a description of the configuration formed by the nodes in [4], and many other interesting properties of this primal, the reader is referred to two recent works (Baker (1) and Todd (5)). Further details about the general quartic primal, and references to a number of special cases, may be found in Room (2), chapters XV and XVI.
