Aether and Gravitation. William George Hooper
or cork, or even a piece of iron would take exactly the same time falling through the same space, provided that the feather or cork could be screened from the resistance of the air.
The distance, however, through which a body falls in one second varies at different parts of the earth's surface, being least at the equator, and greatest at the North and South Poles. This is accounted for by the fact that the polar diameter is only 7899 miles, while the equatorial diameter is 7925 miles, thus the distance from the centre of the earth to either pole is about 3950 miles, or 13 miles less than the equatorial radius of the earth. Now the force of gravity decreases upwards from the earth's surface inversely as the square of the distance from the earth's centre of gravity, but decreases downwards simply as the distance from the centre decreases. Thus if a ball were taken down 2000 miles, that is half the distance to the centre, it would only weigh half-a-pound, while if it were taken to the centre of the earth, it would have no weight at all; while a pound weight at the equator would not weigh one pound at the poles, because it would be nearer the centre of the earth by 13 miles.
Thus a pound weight is not always a pound weight. It varies as we carry it to different parts of the earth's surface, depending upon its relation to the centre of the earth for its exact weight. The point which I wish to make perfectly clear, as it will be necessary for future reference, is, that there is no such thing as weight apart from the gravity of the earth; or, if we apply the principle to the solar system, there is no gravitating force in that system apart from the gravitating force of the central body, the sun, or the planets and other bodies which form the solar system.
Let us look at this matter from another standpoint, in order to prove this truth and make the same perfectly clear. If a pound weight were put in a spring-balance, then at the surface of the earth it would weigh one pound. Now, we will suppose that we have taken the weight to a height of 4000 miles above the surface of the earth, that is exactly double the distance from the centre of the earth, the radius of the earth being approximately 4000 miles. According to the law of inverse squares, the force of Gravitation decreases inversely as the square of the distance. The distance having been doubled, the proportion of the forces at the two places, i.e. the earth's surface and 4000 miles above it, are as 1 to ¼.
Thus at a distance of 4000 miles the weight which weighed one pound at the earth's surface, now only weighs a quarter of a pound. At a distance of 8000 miles, the distance would be trebled, therefore the force of Gravitation is one-ninth, and the weight would weigh one-ninth of a pound. If we could take the pound weight to the moon, the attractive force of the earth would be reduced to 1–3600, as the moon is 240,000 miles distant, that is sixty times the earth's radius. The square of 60 is 3600, and if we invert that we get 1–3600, so that the weight which weighs a pound at the earth's surface, would only weigh 1–3600 part of a pound at the distance of the moon. This again proves, that apart from the Attraction of Gravitation, there is no such thing as weight, and that the weight so called of any body, such as a planet or satellite, increases or decreases as its distance increases or decreases from its central attracting body.
Art. 24. Centrifugal Force.--I have already shown in Art. 10 that the Centripetal Force and Universal Attraction are one and the same; as the Centripetal Force always acts towards the centre, and must therefore be in its operation and influence a gravitating or attractive power.
I have also pointed out in the same article, the necessity of another force, which is to be the complement, and the counter part of Gravitation Attraction. That complement and counter force was conceived by Newton, and called by him the Centrifugal Force. The very nature of the Centripetal Force demands and necessitates a force which in its mode of operation is exactly the opposite of the Centripetal Force. Unless there were such a force, a repellent and repulsive force, then instead of there being that harmonious working of the universe that now exists, there must inevitably be a gradual drawing together of all planets and satellites, of all stars and suns, into one vast, solitary, and ruinous body.
There are also other phenomena which demand a Centrifugal Force in the universe. It is a well-known fact, that there exist between the orbits of Jupiter and Mars, what are called planetoids, about 500 in number, which are supposed to be the remnants of a broken or shattered world. As may be expected from such an accumulation, they present the most extraordinary diversities and eccentricities in the orbits that can possibly be conceived. They are of all shapes and sizes, and besides their orbits round the sun, have orbits among themselves. They are so clustered together that their orbits intersect each other at numerous points, and when in conjunction are said to suffer great perturbations, being pulled great distances this way and that by each other's attractive influence. It is further stated that their orbits so intersect each other, that if they were imagined to be material rings, they would be inseparable, and the whole could be suspended by taking any one of them up at random. Here, then, is presented to us a kind or order of celestial phenomena for whose well-being and effectual working the Centripetal Force or the Attraction of Gravitation cannot possibly account. In their case another force is demanded which shall be the exact complement and counterpart of the Centripetal Force. There needs therefore a force, not an imagined one, simply conceived to fill a want, but a real Force, as real and as plainly to be understood as the Centripetal Force. A force existing in each world just like the Attraction of Gravitation, only the reverse of Gravitation, a repellent, repulsive Force, acting in the reverse mode, and way, to universal attraction. This Force must be governed by the same rules and laws that govern the Centripetal Force, if it is to work in harmony with the same. It must be universal in its character, having a proportion of forces equal to the product of the masses of the two bodies which are concerned, and its path must coincide with the path of gravitational attraction, that is, in the straight line which joins the centres of gravity of the two bodies. Further, and what is perhaps the most important of all, it must act as a repelling or repulsive force which shall be in the same proportion in regard to distance, as the law governing Centripetal Force, that is, inversely as the square of the distance.
Again, and briefly, there are also in existence small bodies called meteors, which are said to exist by myriads, which float in space, and circle round the sun. They are of all shapes and sizes, from one ounce to a ton or even tons, thousands of them coming into contact with our earth's atmosphere every year, especially in August and November. All of these small bodies have orbits among themselves, and gravitate round one another, as they revolve round the sun. Now if the orbits of the planetoids be such an entangled mass, what must be the orbits of these meteors? What an indescribable, unimaginable mass of labyrinthian motions must exist among these myriads of little bodies! How they must intersect, cross and intermingle each other's orbits! What attraction and counter-attraction they must exert upon each other! Let me ask any man to sit down and try to imagine how the present recognized Centripetal and Centrifugal Forces can account for the effectual working of these meteors. As illustrating the necessity of a real and physical Centrifugal Force which is to be the exact counterpart of the Centripetal Force, I would call the attention of the reader to Herschel's view of this matter. In dealing with the phenomena of comets' tails he writes:[1] “Beyond a doubt, the widest and most interesting prospect of future discovery, which this study holds out to us, is, that distinction between gravitating and levitating matter, that positive and irrefutable demonstration in nature of a repulsive force, co-extensive with, but enormously more powerful than the attractive force we call gravity which the phenomena of their tails afford.” I premise that this prophecy of Herschel's will be fully demonstrated and proved in the succeeding pages of this work. For, in the theory of the Aether that is to be afterwards perfected, it will be philosophically proved that the physical medium so conceived will satisfactorily account for a force or motion from the centre of all bodies; which motions fulfil all the conditions required by that Centrifugal Force, which is the complement and counterpart of the Attraction of Gravitation. At the present time, with the conception of a frictionless Aether, it is impossible to harmonize the existence of such a force or motion with our theory of the Aether. Yet Professor Lebedew of Moscow, and Nichols and Hull of America, have incontrovertibly demonstrated by actual experiments the existence of such a force. Therefore it follows, that if our present theory of the Aether fails to agree with experimental evidence, such