Then, writing upon the definite relationship of these equivalents in compounds, he states (Art. 835): “Electro-chemical equivalents are always consistent, that is, the same number which represents the equivalent of a substance A when it is separating from a substance B will also represent A when separating from a third substance C. Thus 8 is the electro-chemical equivalent of oxygen, whether separating from hydrogen, tin, or lead; and 103.5 is the electro-chemical equivalent of lead, whether separating from oxygen, or chlorine, or iodine.”
Here, then, from the pen of one of the greatest thinkers and experimentalists of modern times we have confirmatory evidence that the mass of any body is practically synonymous with the quantity of electricity associated with that body. For if the principle is true in its application to atoms, it is true in its application to molecules; and if it is true in relation to molecules, it is equally true in relation to small bodies composed of molecules. And if it holds good in relation to small bodies, the principle is equally true in its application to larger bodies, as the earth, and therefore is of universal application and proves the statement already made, that the masses of bodies and quantities of electricity in association with that mass are always proportionate to each other.
We are now in a position to compare the proportion of the centripetal and centrifugal forces. The attractive power of the former, between two bodies, is equal to the product of their masses; the repulsive power of the latter is equal to the product of the quantities of electricity bound to them, and that, as we have seen, is regulated by the respective mass of each body. Let us apply this fact to the solar system and see how it works.
Taking the mass of the earth as unity, we find that the mass of the sun is 324,000 greater, so that the attractive power of the two bodies would be represented by the product of the two numbers; but because the sun is that number of times greater, its aetherial and, therefore, its electric field would be so many times greater, with the result that the proportion of the repulsive forces between the two bodies would be exactly the same as the attractive forces between the two bodies, that is, if the mean distance remains the same.
In the same way, it can be shown that the attractive forces between the earth and Jupiter exactly equal the repulsive forces between the two planets at their mean distance, or the attractive forces between any two planets or satellites are exactly counterbalanced by the repulsive power of the centrifugal force at their mean distances.
Thus the centrifugal force of every body is the exact opposite of its centripetal force at their mean distance, because the laws governing the centrifugal force are the exact counterpart of the laws governing the centripetal force. A comparison of the two will prove this. From [Arts. 20], [21], and [Art. 22] we have seen that the centripetal force is exerted along the straight lines joining the attracting bodies, that the intensity of the attracting body is inversely as the square of the distance, while the total force is proportionate to the product of their masses.
From the phenomena of light, heat, and electricity, we learn that the centrifugal force due to aetherial pressure is exerted along straight lines, that the intensity is inversely as the square of the distance, while the total force between two bodies is equal to the product of the quantities of electricity, which are regulated by the product of their masses.
Thus, if every planet and satellite could be conceived to be motionless in space, and these two forces could be set in operation without producing rotation or translation in space, which is impossible, then every planet and satellite would occupy, by the joint exercise of these two forces, the same position in relation to the sun represented by their mean distances, as long as the solar system existed as a separate system in the realm of aetherial space. We have therefore discovered by strict philosophical reasoning, based on Newton's Rules of Philosophy, a real tangible centrifugal force existing throughout the universe; because it is entirely due to the pressure of an universal Aether, whose operation is ever directed from a central body, which force was indicated by Herschel, and its existence to his mind was demonstrated by the repulsion exhibited in connection with the tails of comets.
We have now to go a step further, and show that the same pressure also includes the magnetic phenomena, as indicated by Clerk Maxwell, and that magnetic phenomena are also due to the aetherial medium, and then we shall have linked together in one common medium the majority of the forms of energy, as light, heat, electricity and magnetism, with which we are familiar.
If it be demonstrated that these two forces, the centrifugal force and the centripetal force, can conjointly account for all the motions of the celestial bodies, then we shall have conclusive evidence that one of the forces is physical and due to the pressure of a physical medium. After that it will be comparatively easy to show that the centripetal force is also due to the same aetherial medium, and then we shall have accomplished that which we set out to accomplish, viz. the establishment of a physical cause for universal Gravitation, which physical cause is alone to be found in the pressures, tensions and motions of an universal Aether.