Neither statement is by itself a statement of observable fact, nor does it refer to any intrinsic property of clocks or of light; it is simply an announcement of the rule by which we propose to extend fictitious time-partitions through the world. But the mutual agreement of the two statements is a fact which could be tested by observation, though owing to the obvious practical difficulties it has not been possible to verify it directly. We have here given a theoretical proof of the agreement, depending on the truth of the fundamental axiom of \SecRef{1}. The two alternative forms of the convention are closely connected. In general, in any system of time-reckoning, a change~$du$ in the velocity of a clock involves a change of rate proportional to~$du$, but there is a certain turning-point for which the change of rate is proportional to~$du^{2}$. In adopting a time-reckoning such that this stationary point corresponds to his own motion, the observer is imposing a symmetry on space and time with respect to himself, which may be compared with the symmetry imposed in assuming a constant velocity of light in all directions. Analytically we imposed the same general symmetry by adopting \Eq{(4.6)} instead of~\Eq{(4.7)} as the form for~$ds^{2}$, making our space-time reckoning symmetrical with respect to the interval and therefore with respect to all observational criteria. \Section{12.}{Momentum and mass} \index{Momentum!elementary treatment}% Besides possessing extension in space and time, matter possesses inertia. \index{Inertia!elementary treatment}% We shall show in due course that \emph{inertia, like extension, is expressible in terms of the interval relation}; but that is a development belonging to a later stage of our theory. Meanwhile we give an elementary treatment based on the empirical laws of conservation of momentum and energy rather than on any deep-seated theory of the nature of inertia.