which it influences.
5. Limits of Rotational Energy. Disruptional Phenomena
It is clear that the material at different parts of the rotating spheroid will be energised to varying degrees. Since the linear velocity of the material in the equatorial regions of the spheroid is greater than that of the material about the poles, the energy of motion of the former will exceed that of the latter, the difference becoming greater as the mass is increasingly energised and assumes more and more the discoidal form.
The question now arises as to how far this process of energising the material mass may be carried. What are its limits? The capacity of the rotating body for energy clearly depends on the amount of work which may be spent on its material in distorting it against the influence of the gravitative attraction. The amount is again dependent on the strength of this attraction. But the value of the gravitative attraction or gravitation field is, by the law of gravitation, in direct proportion to the quantity of material or matter present, and hence the capacity of the body for energy depends on its mass or on the quantity of matter which composes it.
Now if energy be impressed on this mass beyond its capacity a new order of phenomena appears. Distortion will be followed by disruption and disintegration. By the action of the disruptive forces a portion of the primary material will be projected into space as a planetary body. The manner of formation of such a secondary body is perhaps best illustrated by reference to the commonplace yet beautiful and suggestive phenomenon of the separation of a drop of water or other viscous fluid under the action of gravitation. In this process, during the first downward movement of the drop, it is united to its source by a portion of attenuated material which is finally ruptured, one part moving downwards and being embodied in the drop whilst the remainder springs upwards towards the source. In the process of formation of the planetary body we are confronted with an order of phenomena of somewhat the same nature. The planetary orb which is hurled into space is formed in a manner similar to the drop of viscous fluid, and under the action of forces of the same general nature. One of these forces is the bond of gravitative attraction between planet and primary which is never severed, and when complete separation of the two masses finally occurs, the incessant combination of this force with the tangential force of disruption acting on the planet will compel it into a fixed orbit, which it will pursue around the central axis. When all material links have thus been severed, the two bodies will then be absolutely separate masses in space. The term "separate" is here used in its most rigid and absolute sense. No material connection of any kind whatever exists, either directly or indirectly, between the two masses. Each one is completely isolated from the other by interplanetary space, and in reality, so far as material connection is concerned, each one might be the sole occupant of that space. This conception of separate masses in space is of great importance to the author's scheme, but, at the same time, the condition is one which cannot be illustrated by any terrestrial experimental contrivance. It will be obvious that such a device, as might naturally be conceived, of isolating two bodies by placing them in an exhausted vessel or vacuous space, by no means complies with the full conditions of true separation portrayed above, because some material connection must always exist between the enclosed bodies and the containing vessel. This aspect is more fully treated later (§ 30). The condition of truly separate masses is, in fact, purely a celestial one. No means whatever are existent whereby such a condition may be faithfully reproduced in a terrestrial environment.
In their separate condition the primary and planetary mass will each possess a definite and unvarying amount of energy. It is to be noted also, that since the original mass of the primary body has been diminished by the mass of the planet cast off, the capacity for energy of the primary will now be diminished in a corresponding degree. Any further increment of energy to the primary in any form has now, however, no direct influence on the energy of the planet, which must maintain its position of complete isolation in its orbit. But although thus separate and distinct from the primal mass in every material respect, the planet is ever linked to it by the invisible bond of gravitation, and every movement made by the planet in approaching or receding from the primary is made in the field or influence of this attraction. In accordance, therefore, with the general principle already enunciated (§ 4), these actions or movements of the energised planetary mass, being made in the field of the incepting gravitative 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
