XIX. On Mr. Spottiswoode’s contact problems

The present communication consists of two parts. The first part treats of the contact of conics with a given surface at a given point; this class of questions was first treated by Mr. Spottiswoode in his paper “On the Contact of Conics with Surfaces,” and general formulæ applicable to all such questions were given. The results of that paper are here reproduced with some additions; with the exception of a few collateral theorems, these are all contained in the following Table:— Number of five-point conics through fixed point ........................ = 6 Order of surface formed by five-point conics through fixed axis = 8 Number of six-point conics through fixed axis.............................= 9 Number of seven-point conics ................................................. = 70