If in a certain kinematic correlation the time-system it be correlated to (), then is called the time-system of () 'proper' to that correlation. The 'proper' time-system of an event-particle always refers to a certain kinematic correlation implicitly understood. Furthermore () is the velocity at () due to the implicitly understood kinematic correlation at the -time . Then, being the proper time-system at (), Then equations (iii) of 52.2 can be written The kinematic symmetry as between and is now apparent in the formulae. The first of equations (ii) can be replaced by 52.7 In considering the elliptic type of kinematics put for . The equations of article 51 are now embodied in the scheme , , , , 0, 0, 0, 1, 0, 0 0, 0, 1, 0 0, 0, The fundamental distinction between space and time, i.e. between rects and point-tracks, has failed to find any expression in the formulae for measurement relations. Accordingly with this type of kinematics, it would be natural to suppose that the distinction does not exist and that every rect was a point-track and every point-track a rect. This conception is logically possible but does not appear to correspond to the properties of the external world of events as we know it. Furthermore the electromagnetic equations lose their invariant property. Altogether there appear to be good reasons for putting aside the elliptic type of kinematics as inapplicable to nature. 52.8 In the parabolic type of kinematics we put Hence Then from (ii) of 51.1 and (ii) of 50.3 and (iii) of 50.1 Thus equations (i) of 49.7 give These are the formulae for the ordinary Newtonian relativity. These formulae are well in accordance with common sense and are in fact the formulae naturally suggested by ordinary experience. To some extent the hyperbolic formulae lead to unexpected results, though, if be a velocity not less than that of light, the divergences from the deliverances of common sense take place in respect to phenomena which are not manifest in ordinary experience. But when by refined methods of observation the divergences between the two types of kinematics should be apparent to the senses, experiment has, so far, pronounced in favour of the hyperbolic type. Accordingly it is this type which we consider in the sequel.