influence, will be accompanied by transformations, and thus the energy of the planet, although unvarying in its totality, may vary in its form or distribution with the inward or outward movement of the planet in its orbital path. As the planet recedes from the primary it gains energy of position, but this gain is obtained solely at the expense, and by the direct transformation of its own orbital energy of motion. Its velocity in its orbit must, therefore, decrease as it recedes from the central axis of the system, and increase as it approaches that axis. Thus from energy considerations alone it is clear that, if the planetary orbit is not precisely circular, the velocity of the planet must vary at different points of its path.

6. Passive Function and General Nature of Gravitation Field

From the phenomena described above, it will be observed that, in the energy processes of transformation occurring in both primary and planet, the function of the gravitation field or influence is entirely passive in nature. The field is, in truth, the persistent moving or directing power behind the energy processes, the incepting energy influence or agency which determines the nature of the transformation in each case without being, in any way, actively engaged in it. In accelerating or retarding the transformation process it has thus absolutely no effect. These features are controlled by other factors. Neither does this incepting agency affect, in any way, the limits of the transformation process, these limits being prescribed by the physical or energy qualities of the acting materials. In general nature the gravitation field appears to be simply an energy influence—a peculiar manifestation of certain passive qualities of energy. This aspect will, however, become clearer to the reader when the properties of gravitation are studied in conjunction with those of other incepting energy influences (§§ 17, 18, 19).

7. Limit of Gravitation Transformation

In the case of a planetary body, there is a real limit to the extent of the transformation of its orbital energy of motion under the influence of the gravitation field. As the orbit of the planet widens, and its mean distance from the primary becomes greater, its velocity in its orbital path must correspondingly decrease. As already pointed out (§ 5), this decrease is simply the result of the orbital energy of motion being transformed or worked down into energy of position. But since this orbital energy is strictly limited in amount, a point must ultimately be reached where it would be transformed in its entirety into energy of position. When this limiting condition is attained, the planet clearly could have no orbital motion; it would be instantaneously at rest in somewhat the same way as a projectile from the earth's surface is at rest at the summit of its flight in virtue of the complete transformation of its energy of motion into energy of position. In this limiting condition, also, the energy of position of the planet would be the maximum possible, and its orbital energy zero. The scope of the planetary orbital path is thus rigidly determined by the planetary energy properties. Assuming the reduction of gravity with distance to follow the usual law of inverse squares, the value of the displacement of the planet from the central axis when in this stationary or limiting position may be readily calculated if the various constants are known. In any given case it is obvious that this limiting displacement must be a finite quantity, since the planetary orbital energy which is being worked down is itself finite in amount.

8. Interactions of Two Planetary Bodies—Equilibrium Phenomena

Up to the present point, the cosmical system has been assumed to be composed of one planetary body only in addition to the primary mass. It is clear, however, that by repetition of the process already described, the system could readily evolve more than one planet; it might, in fact, have several planetary masses originating in the same primary, each endowed with a definite modicum of energy, and each pursuing a persistent orbit round the central axis of the system. Since the mass of the primary decreases as each successive planet is cast off, its gravitative attractive powers will also decrease, and with every such decline in the central restraining force the orbits of the previously constituted planets will naturally widen. By the formation in this way of a series of planetary masses, the material of the original primary body would be as it were distributed over a larger area or space, and this separation would be accompanied by a corresponding decrease in the gravitative attraction between the several masses. If the distributive or disruptive process were carried to its limit by the continuous application of rotatory energy to each separate unit of the system, this limit would be dependent on the capacity of the system for energy. As is shown later (§ 20), this capacity would be determined by the mass of the system.

For simplicity, let us consider the case in which there are two planetary bodies only in the system in addition to the primary. In virtue of the gravitative attraction or gravitation field between the two, they will mutually attract one another in their motion, and each will, in consequence, be deflected more or less out of that orbital path which it would normally pursue in the absence of the other. This attraction will naturally be greatest when the planets are in the closest proximity; the planet having the widest orbit will then be drawn inwards towards the central axis, the other will be drawn outwards. The distance moved in this way by each will depend on its mass, and on the forces brought to bear on it by the combined action of the two remaining masses of the system. Moving thus in different directions, the motion of each planet is carried out in the lines of the gravitation field between the two. One planet, therefore, gains and the other loses energy of position with respect to the central axis of the system. The one planet can thus influence, to some extent, the energy properties of the other, although there is absolutely no direct energy communication between the two; as shown hereafter, the whole action and the energy change will be due simply to the motion carried out in the field of the incepting gravitation influence.

It is clear, however, that this influence is exerted on the distribution of the energy, on the form in which it is manifested, and in no way affects the energy totality of either planet. Each, as before, remains a separate system with conservative energy properties. That planet which loses energy of position gains energy of motion, and is correspondingly accelerated in its orbital path; the other, in gaining energy of position, does so at the expense of its own energy of motion, and is retarded accordingly. The action is really very simple in nature when viewed from a purely