The concept of Existence Velocity within the Relativistic Domain D₀, both as have been defined in this paper, has, using methods identical to those of classical mechanics, enabled a simplified mathematical formulation of the kinematics and kinetics of the Special Theory of Relativity, for one particular case, rectilinear motion. In doing so, it has also provided a clearer insight into the relativistic nature of an applied spatial force, and the associated kinetic energy that it produces in a spatially accelerated point mass. In Sections 4 and 5 this simplified method has been used to examine two further relativistic kinematic situations, linear planar, and central orbital motion, as demonstrations of its application.

It must be noted that these concepts are only valid within the domain D₀ i.e. Pseudo-Euclidean Space - Time, (see Appendix A). For other relativistic domains, such as one containing gravitation, it is necessary to change the characteristics of the Domain accordingly. This will be the subject of the next paper where a new theroem for gravitation will be presented using a suitably modified Relativistic Domain. This new theroem will differ from that of the General Theory of Relativity in that although the modified Domain will differ from Pseudo-Euclidean Space-Time, it will still be one exhibiting a linear co-ordinate system.

One final note. In the Special Theory, the limiting spatial velocity is generally accepted to be the velocity of electromagnetic radiation in a vacuum, i.e. light. In this paper the limiting velocity has been termed the "Spatial Terminal Velocity" and no reference has been made to the velocity of light. This approach has been adopted because it has not been conclusively proven that the limiting spatial velocity in the Special Theory is indeed the velocity of light. It may well be that the true limiting velocity is slightly different from this. This is believed possible because from the Special Theory it is known that matter possessing mass and thus energy, cannot be accelerated to the velocity of light within a finite time. Yet it is also known that electromagnetic radiation possesses energy and must therefore also possess mass, however small. Thus it is considered probable that the velocity of light may well be slightly lower than the true limiting spatial velocity in the Special Theory and therefore also in D₀.