First, it had to be universal ([Art. 19]). Second, it had to follow exactly the same path as the centripetal force or motion, which was that of a straight line joining the centre of gravity of two bodies, as for example the earth and the sun ([Art. 20]). Third, the centrifugal force or motion must be equal to the product of the masses, in the same way that the centripetal force was governed by such a law ([Art. 21]). Fourth, its intensity was to be governed by the law of inverse squares, the same as the centripetal force or Gravitation Attraction was governed ([Art. 22]).
Now all these conditions are satisfactorily fulfilled, and have been shown to be satisfactorily fulfilled, from the phenomena of heat, light, and electricity in their relation to the universal Aether. For in [Art. 43] we saw that the Aether was universal, and therefore if the centrifugal motion is produced and originated by the Aether, then such motions must be as universal as that medium, which under qualifying conditions gives rise to these motions.
From [Arts. 65] and [Art. 76] we have learned that the path of this centrifugal motion is that of a straight line, and follows exactly the same path that the centripetal force of gravity takes. In [Art. 85] we learned that the centrifugal force between any two bodies was equal to the product of their masses, which is exactly the same as the centripetal force that exists between any two bodies; and, lastly, from the phenomena of heat, light, and electricity we learned that the intensity of this centrifugal motion due to aetherial pressure was inversely as the square of the distance, which is the law governing the intensity of its counterpart, the centripetal force. Thus we have learned that there is in existence throughout universal space, a physical force or motion due to a physical medium, the universal Aether, which force or motion is the exact opposite of the centripetal force or Gravitation Attraction, which may be stated as follows--
Every particle in the universe repels every other particle with a force whose direction is in the line joining the centres of gravity of the two bodies, and whose magnitude is directly as the product of their masses, and inversely as the square of the distance between them, at their mean distances.
We shall see that it is by the conjoint working of these two forces, the Centripetal and Centrifugal, in combination with other motions of the Aether, that the harmonious working of the whole celestial mechanism is maintained and perpetuated. In confirmation of the existence of the centrifugal force, I should like to draw the attention of the reader to certain phenomena relative to the solar system, which phenomena violate the centripetal force as at present recognized, and can alone be accounted for by the existence of another force or motion existing in space, such as the centrifugal motion already proved and demonstrated.
We know that the law governing the centripetal force, or Gravitation Attraction, is regulated by the product of the masses of the two attracting bodies. So that if there were three bodies in space whose masses are respectively represented by 2, 3 and 100, the proportion of the attractive force of gravitation between the largest and the other two, would be 200 (100 × 2) and 300 (100 × 3) respectively. So that if the centripetal force, or the Attraction of Gravitation, is the only governing force in the universe, then it naturally follows that the two bodies, between which the attractive force is greater, will be closer together than the two bodies between which the attractive force is less.
Thus the two bodies, whose product of their masses is represented by 300, will, according to the Law of Gravitation, be closer together than the two bodies, the product of whose masses is represented by only 200. Unless this is so, we should have a violation of the Law of Gravitation, and it would at once cease to be a law.
Let us therefore apply the centripetal force, or Gravitation Attraction, to the solar system, and see how it works out. The law strictly defined is given in [Art. 18], from which we learn that the attractive force between two bodies is as the product of their masses. Now what are the masses of some of the bodies in the solar system?
We find that the sun, with its diameter of 865,000 miles, is about 324,000 times greater in mass than our earth, so that it would take about 324,000 bodies of the size and density of our earth to equal a body of the size and density of the sun. It has been calculated, however, by Von Asten, from observations made on comets by the planet Mercury, that the mass of Mercury is about 1/24 of the mass of the Earth. Therefore the mass of the sun must exceed the mass of Mercury 324,000 × 24 = 7,776,000; the exact relation according to Von Asten is 7,636,440. Again, the planet Jupiter, with its diameter of 85,000 miles and its density of 1.38, is only 1/1048 part of the mass of the sun, so that it would take about 1048 Jupiters to equal the mass of the sun, therefore Jupiter must weigh about 7400 times the mass of Mercury.
If the mass of Mercury, therefore, be represented by 1, the mass of the Earth would be represented by 24, the mass of Jupiter by 7400, and the mass of the sun by 7,636,400. So that the attractive forces between the planets as regards their masses only will be represented numerically as follows--