This is only effected for the more complex expressions, or in trivial cases, where a special implication is involved. First it should be noted from (4.7) and (4.18) that the gravitational radius of a gravitational source can be expressed as

so that when u = 1, a = 0 and therefore, from (4.18) and (4.21)

Section 2.

(i) Eq.(2.11), Existence Velocity

(a) Reduction to the Special Relativistic version is effected by putting u = 1

(b) Reduction to the classical equivalent. In (G3) when c ® ¥

as found in [1] and in classical studies the temporal term is ignored.

Section 3.

(ii) Eq.(3.6), Mass

(a) Reduction to the Special Relativistic version is effected by putting u = u₀ = 1

This can be compared with [1], Eq.(3.7) by putting w = w₀ =0_.

(b) Reduction to the classical equivalent. When in (G.5) c ® ¥

(iii) Eq.(3.10), Rate of change of momentum.

(a) Reduction to the Special Relativistic version is effected by putting u = 1

which becomes with insertion of (G.5)

This can be compared with [1], Eq.(3.9) by putting w = 0.

(b) Reduction to the classical equivalent. When in (G.8) c® ¥

(iv) Eq.(3.14), Spatial gradient of energy.

(a) Reduction to the Special Relativistic equivalent is effected by putting u = 1

which is the same as the magnitude of (G.7) and therefore shows that gravitation only exists within the Special Theory of Relativity as an axiomatic addition as it does in classical theory.

Section 5.

The planetary orbit. This is most easily reduced to the classical equivalent by first putting a = 0 in (5.30) which gives

So that this gives in (5.28)

and therefore in (5.11)

the equation of a standard conic section, and in which the eccentricity, e, is reduced from (5.24) to

where

and where now m₀=1/r₀

(v) Eq.(5.8), Equation of the orbit.

First express (5.8) as

To reduce (G.16) to its classical equivalent put a = 0 and then put

to yield

the classical equation in mechanics.

Appendix A

(vi) Eq.(A.4), The equation of free planar motion in the axes of D₀ .

Substituting for a from (4.6) gives

and then assuming c to be infinitely large reduces this to the classical equation

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