164. Since two points must have some relation, and the passivity of space proves this to be independent of external reference 165 165. There can be only one such relation 166 166. This must be measured by a curve joining the two points, 166 167. And the curve must be uniquely determined by the two points 167 168. Spherical Geometry contains an exception to this axiom, 168 169. Which, however, is not quite equivalent to Euclid's 168 170. The exception is due to the fact that two points, in spherical space, may have an external relation unaltered by motion, 169 171. Which, however, being a relation of linear magnitude, presupposes the possibility of linear magnitude 170 172. A relation between two points must be a line joining them 170 173. Conversely, the existence of a unique line between two points can be deduced from the nature of a form of externality, 171 174. And necessarily leads to distance, when quantity is applied to it 172 175. Hence the axiom of distance, also, is _à priori_ in a double sense 172 176. No metrical coordinate system can be set up without the straight line 174 177. No axioms besides the above three are necessary to metrical Geometry 175 178. But these three are necessary to the direct measurement of any continuum 176 179. Two philosophical questions remain for a final chapter 177 CHAPTER IV. PHILOSOPHICAL CONSEQUENCES. 180. What is the relation to experience of a form of externality in general? 178 181. This form is the class-conception, containing every possible intuition of externality; and some such intuition is necessary to experience 178 182. What relation does this view bear to Kant's? 179 183. It is less psychological, since it does not discuss whether space is given in sensation, 180 184. And maintains that not only space, but any form of externality which renders experience possible, must be given in sense-perception 181 185. Externality should mean, not externality to the Self, but the mutual externality of presented things 181