The axiom can be explained as follows: Let α and β be the names of two time-systems. The directions of motion in the space of α due to rest in a point of β is called the 'β-direction in α' and the direction of motion in the space of β due to rest in a point of α is called the 'α-direction in β.' Consider a motion in the space of α consisting of a certain velocity in the β-direction of α and a certain velocity at right-angles to it. This motion represents rest in the space of another time-system--call it π. Rest in π will also be represented in the space of β by a certain velocity in the α-direction in β and a certain velocity at right-angles to this α-direction. Thus a certain motion in the space of α is correlated to a certain motion in the space of β, as both representing the same fact which can also be represented by rest in π. Now another time-system, which I will name σ, can be found which is such that rest in its space is represented by the same magnitudes of velocities along and perpendicular to the α-direction in β as those velocities in α, along and perpendicular to the β-direction, which represent rest in π. The required axiom of kinetic symmetry is that rest in σ will be represented in α by the same velocities along and perpendicular to the β-direction in α as those velocities in β along and perpendicular to the α-direction which represent rest in π. A particular case of this axiom is that relative velocities are equal and opposite. Namely rest in α is represented in β by a velocity along the α-direction which is equal to the velocity along the β-direction in α which represents rest in β. Finally the sixth axiom of congruence is that the relation of congruence is transitive. So far as this axiom applies to space, it is superfluous. For the property follows from our previous axioms. It is however necessary for time as a supplement to the axiom of kinetic symmetry. The meaning of the axiom is that if the time-unit of system α is congruent to the time-unit of system β, and the time-unit of system β is congruent to the time-unit of system γ, then the time-units of α and γ are also congruent. By means of these axioms formulae for the transformation of measurements made in one time-system to measurements of the same facts of nature made in another time-system can be deduced. These formulae will be found to involve one arbitrary constant which I will call k. It is of the dimensions of the square of a velocity. Accordingly four cases arise. In the first case k is zero. This case produces nonsensical results in opposition to the elementary deliverances of experience. We put this case aside. In the second case k is infinite. This case yields the ordinary formulae for transformation in relative motion, namely those formulae which are to be found in every elementary book on dynamics.