We have now to show that our aetherial medium agrees with this second law of motion in so far as the second law of motion agrees with experience and experiments. To do this, we must review our conception of the universal Aether, and remember that Aether is matter, and being matter, it is atomic and gravitative, possessing density, elasticity, inertia, and kinetic energy, the same as any other moving matter.
In this Aether medium we have, according to this conception, something that can both push and pull, or exert force upon any body with which it comes into contact. Further, the inertia and kinetic energy of the Aether at any part of s.p.a.ce will be regulated by its ma.s.s in that particular part, and if its ma.s.s is denser in some parts than others, that part of the aetherial medium possessing the greatest ma.s.s will also possess the greatest capacity for impressing force upon any body that exists in the medium. Now we have learned from Art. 45 that Aether being gravitative, it is denser nearer to the sun, getting gradually less and less dense, the further it recedes from the central body, except where it is bound or a.s.sociated to some other planet or satellite, and there it gradually gets denser, for the same reason that it is denser nearer to the sun. As, therefore, the Aether gets gradually less dense as it recedes from the sun, the density of the Aether at the mean distance of Mercury, 35,900,000 miles, would not be so great as near the sun"s surface; while the density of the aetherial medium at the distance of Venus, 67,000,000 miles, would be less than the density of the aetherial medium at the distance of Mercury. This principle may be applied right through the sun"s aetherial electro-magnetic field, until we come to the mean distance of Neptune, which is 2,780,000,000 miles, and there the density of the Aether would be less than at any other part of the aetherial electro-magnetic field around the sun.
So that the ma.s.s of the Aether at Mercury, which is equal to the number of aetherial atoms per unit volume, is greater than the ma.s.s at Venus.
Thus the impressed force which the aetherial medium at the mean distance of Mercury can exert upon any body in its neighbourhood, is greater than the impressed force which the Aether can exert upon any body at the distance of Venus, because of its decreased ma.s.s at that distance. In the same way it can be proved that the impressed force which the electro-magnetic Aether exerts on any body at the distance of Venus, is greater than the impressed force which the Aether exerts upon a body at the mean distance of the Earth. So that at the respective mean distances of Mercury, Venus, Earth, Mars, Jupiter, Saturn, Ura.n.u.s and Neptune, the electro-magnetic Aether, if in motion, would exert less force at each of the mean distances of these planets exactly proportionate to the decreased ma.s.s and decreased velocity of the Aether.
Now what is the motion which the Aether possesses, so far as the sun is concerned? because, upon the particular kind of motion which it possesses will depend the direction in which the impressed force will be exerted according to the second law of motion.
In Art. 98 we supposed the sun and planets to be stationary in the solar system, each planet being at its respective mean distance, from which it cannot move owing to the equality of the two forces. Now give to the central sun from whence the electro-magnetic Aether waves flow, a rotatory motion on its own axis, which it really possesses, as it rotates on its axis once in every twenty-six days nearly, and this will give to the Aether medium a circular or rotatory motion. This circular or rotatory motion the Aether has already been proved to possess (Art.
91, where we learned that all solar magnets were caused by electro-magnetic aetherial currents constantly circulating round them).
So that the Aether will actually possess two motions: 1st, a radial motion due to the Aether waves generated by the sun, which are radiated out into s.p.a.ce with the velocity of light; and 2nd, a circular or rotatory motion. This result is in perfect harmony with our hypothesis as to the cause of the electro-magnetism of the sun (Art. 91, where we saw that solar magnetism was due to electric currents circulating round the various planets), and we have proved that the Aether has an electro-magnetic basis; thus the rotatory Aether currents and the rotatory electro-magnetic currents are due to one and the same medium.
Now what will be the effect of these circular or rotatory Aether currents on the bodies situated within their field? It must be remembered that we are no longer dealing with a frictionless medium, but with a medium which possesses inertia and kinetic energy the same as any other moving matter. Therefore, as soon as it is set in motion, it will impress its motions upon all planets that come under its control and influence, with the result that as the impressed force is ever directed in a circular form, the planet will be pushed along through s.p.a.ce by the moving Aether, and the path it describes will be circular also.
Thus the actual result of the rotatory electro-magnetic Aether currents will be, that all dependent and a.s.sociated planets under their influence will be carried by them around the central body which generates the Aether currents. So that they will literally and truly have an orbit, and the circle they describe will be, in its size and circ.u.mference, regulated by the mean distance of each planet, which mean distance will form the radius of the circular orbit.
Further, as we shall see later, if the sun were always stationary, and had no orbital motion of its own, then the orbit of each planet would always be circular, each planet always occupying its mean distance from the sun, because at that mean distance the centripetal and centrifugal forces are equal.
That the actual path of any planet is a circle has been proved by Sir W.
R. Hamilton. Tait, in his _Natural Philosophy_, on this point writes (Art. 38): "The Hodograph for the motion of a planet or comet is always a circle, whatever be the form and dimensions of the orbit." This path has been termed the Hodograph. So that we have in the circling electro-magnetic Aether currents a physical explanation for the Hodograph of any planet.
In applying the rotatory Aether currents to the various planets, and in endeavouring to find out the quant.i.ty of the force impressed upon the various planets at their mean distances, by those currents, we have to take into consideration, as we have already seen, two facts, viz. the ma.s.s of the Aether at any point in s.p.a.ce, and the velocity of the Aether at the same point. We will first take the effect of the difference in ma.s.s. We have seen that at the distance of Mercury from the sun the density of the Aether is greater than at the distance of Venus, and that the density at Mars is greater than the aetherial density at the Earth, the aetherial density decreasing the further the Aether recedes from the sun.
What, therefore, is the effect of the decreased density of the Aether on each planet? Even supposing the velocity of the moving Aether is the same at the respective mean planetary distances, which it is not, the total impressed force at the respective mean planetary distances will gradually be decreased upon the various planets, proportionate to the decrease in the ma.s.s and density of the Aether.
So that on Mercury, which is pushed along by a denser electro-magnetic Aether than Venus, the impressed force, according to Newton"s Second Law of Motion, will be greater than the impressed force exerted by the moving electro-magnetic Aether on Venus; and, consequently, Mercury should have a greater velocity through s.p.a.ce than Venus, due partly to the difference of the aetherial ma.s.s and density, by which the impressed force or motive power that acts upon Mercury is produced.
In the same way, Venus should have a greater velocity through s.p.a.ce than Mars, and Mars a greater velocity than the Earth. The same principle, when applied to the outer planets, equally holds good; with the result, that the greater the mean distance, the less the orbital velocity of each planet, due partly to the decreased aetherial density at the increased distance from the sun. But this is only part of the cause. Not only is there a decrease in density of the Aether, as the distance from the sun is increased, but there is also a decrease in the velocity of the moving Aether, with the result that the Aether at the distance of Mercury, possesses a greater angular velocity than at the distance of Venus.
It may be at once asked, How do we know that? Well, Philosophy alone can give us the key, and Philosophy tells us to base our theories and hypotheses on experience and experiment. Now what does experiment and experience teach us as to the effect of a body revolving in any medium upon that medium? If experience teaches us anything at all, it teaches us that the further away any medium is from the revolving body, the less is the angular velocity of that medium at that distance, while the nearer the medium is to the revolving body, the greater is the angular velocity.
This applies in each and every case, whether the medium is either fluid or gaseous, and I will challenge the reader to perform any experiment on any solid body rotating in a fluid or gaseous medium, and prove by that experiment that the angular velocity of the outermost part of the fluid or gaseous medium is equal to the angular velocity of the medium directly a.s.sociated with the body, or even at a short distance from it.
But we have most conclusive evidence of the fact that a solid body does not communicate all its rotational surface motion to the medium directly in contact with that body in the case of the earth revolving on its axis, surrounded by an atmosphere. If the principle held good anywhere in relation to a revolving body, viz. that the whole of the rotational velocity is communicated to the medium surrounding the body, it should certainly hold good at the surface of the body where the two media, the solid and gaseous media, meet.
If a solid body fails to impart all its rotational velocity to the medium there, then it will certainly fail to impart its full rotational velocity to the enveloping medium 100 miles away, and fail still more at a distance of 1000, and still more at a distance of 100,000,000, and so on proportionate to the distance.
What, then, is the effect of the rotational velocity of the surface of the earth on the atmosphere near to it? We know that the velocity of the surface of the earth is greatest at the equator, as at that place the circ.u.mference of the earth is about 25,000 miles, but the further we get away from the equator, and the nearer we get to the North and South poles, the velocity of the surface decreases, simply because the circ.u.mference of the earth decreases.
Or, to reverse the statement, the velocity of the surface of the earth is least at the poles, but increases the nearer we get to the equator.
It is also familiar knowledge that there are currents of cold air ever moving from the North and South poles to the equatorial regions near the surface of the earth. Thus the cold air currents, in pa.s.sing from the North and South poles, are ever pa.s.sing over surfaces which are increasing in velocity as they journey on their way to the equator. This of course occurs all round the earth, so that the earth is continually revolving in these currents, and if the rotational velocity of the surface of the earth were wholly imparted to the air directly over its surface, then the currents would be always flowing due North and South.
If, however, the earth fails to impart all its rotational velocity to the atmosphere, or the atmosphere fails to pick up the whole of the rotational velocity at once, then the result will be that the atmosphere as it pa.s.ses over the surfaces of greatest velocity will lag behind, because its rotational velocity will be less than the velocity of the earth"s surface.
Now this is exactly what does happen in regard to the atmosphere, with the result, that instead of getting winds blowing due north and south, we get what are known as Trade Winds, which blow north-east in the northern hemisphere and south-east in the southern hemisphere. Here then we have direct experimental proof on a large scale of the very principle I have stated, viz, that a medium surrounding any rotating body does not move through the whole of its extent with the same velocity as its does at the surface. Thus it can be seen that the velocity of the rotating Aether will be greatest at the surface of the sun, but its angular velocity will decrease the further the medium recedes from the sun.
The same principle can easily be proved from an electrical standpoint; for if we consider the Aether currents as electric currents, no one would think of suggesting that the intensity of the currents was the same at a distance of several million miles away, as it is near the source of the currents, which in this case may be looked upon as the sun, because at its surface we have the greatest electric potential (Art. 80).
So that we see from this reasoning, that not only is there a decreased ma.s.s of the Aether at the distance of Venus, compared with Mercury, but there is also a decreased velocity in the rotatory electro-magnetic Aether currents, with the result that the impressed force exerted upon Venus is less than the impressed force exerted upon Mercury, and therefore Venus should move slower through s.p.a.ce than Mercury, which is exactly what happens, as Mercury has an orbital velocity of 29 miles per second, while Venus has an orbital velocity of 22 miles per second.
As the angular velocity decreases in proportion as the distance increases, it follows that at the respective mean distances not only of Venus, but also of Mars, Jupiter, Saturn, Ura.n.u.s and Neptune, the capacity of the Aether to exert its impressed force upon the various planets will decrease as the distance increases, with the result that the farther a planet is from the sun, the less force will the Aether currents exert upon that planet, with the result that its...o...b..tal velocity should decrease as the distance increases, and this is perfectly in accordance with planetary phenomena.
Here, then, we have at once a physical basis for Newton"s Second Law of Motion, the results of which are entirely in harmony with observation and experiment, and whose conception fully satisfies all the Rules of Philosophy; as it is simple in conception, fully agrees with observation and experiment, and satisfactorily explains the Second Law of Motion sought to be explained.
Thus we find that from the physical standpoint, as well as from the mathematical standpoint, "Change of motion is proportional to the impressed force, and takes place in the direction in which the force is impressed," that is, in a circular direction.
We have therefore arrived at exactly the same result that Newton arrived at, except that he had to introduce a third factor, viz. the Parallelogram of Forces, while we have produced the result by a simpler method, which, according to his own rules, is more philosophical, as all effects are produced by the simplest causes, as Newton himself stated in Rule 1. Thus it is the rotatory electro-magnetic Aether currents that urge the planets round the sun; and, as will be shown later, it is the same Aether currents in combination with the other motions that give rise to the physical cause of Kepler"s Laws. It is the electro-magnetic Aether currents that produce the regular decrease in the velocity of the planets in their orbits, because of the regular decrease of the ma.s.s and velocity of the Aether currents themselves.
We have now a physical cause as well as a mathematical explanation of the decrease of the velocity of a planet in its...o...b..t, which physical cause is in perfect harmony with all philosophical rules. The following table shows the gradual decrease in the velocity of each planet as the various planets recede from the sun--
MEAN PERIOD OF VELOCITY IN DISTANCE. REVOLUTION. ORBIT PER HOUR.
Mercury 35,900,000 87.9 days
Venus 67,000,000 224.7 77.000
Earth 92,700,000 365.2 66.500
Mars 141,000,000 686.9 53.000
Jupiter 482,000,000 4,332.6 28.744
Saturn 884,000,000 10,759. 21.221
Ura.n.u.s 1,780,000,000 30,687. 14.963
Neptune 2,780,000,000 60,127. 11.958
ART. 100. _Aether and Third Law of Motion._--We have seen (Art. 16) that action and reaction are equal and opposite, and that it is true of the centripetal force in its application to all matter throughout the universe. If, therefore, the centrifugal force is the exact opposite of the centripetal force, then the Third Law of Motion should equally hold good in relation to that force also.
We have, therefore, to form a physical conception of the application of the third law of motion, as it relates to the centrifugal force. As we have already learned, this force is due to the universal electro-magnetic Aether, which being gravitative, surrounds all atoms and molecules that may exist throughout the whole universe. It can readily be seen, therefore, that if the Aether surrounds every atom and molecule, then each atom repels another atom or molecule when the two forces are in equilibrium with exactly the same intensity with which the atom and molecule attract each other.
But the centrifugal force in each case is due to the pressure of the Aether, which presses always proportionately to the density of the Aether surrounding the atom or molecules, as suggested by Professor Challis.
The mean density, however, of each atomic or molecular atmosphere is regulated solely by the ma.s.s of the atom or planet, therefore the pressure exerted by one atom on another is proportionate to the ma.s.s of each atom, and to that extent is strictly in accordance with the law which governs the proportion of the forces between the two atoms or molecules. If, therefore, we have two atoms, A and B, of different ma.s.ses, then it is true that while A exerts a pressure on B, which pressure takes the form of a repulsion, at the same time B exerts a pressure on A which is equal and opposite in its character and intensity, and in each case the pressure is due to the aetherial medium which surrounds each atom or molecule.
When the atoms are equal in ma.s.s, then the resultant motion produced on each atom would be exactly equal, but when the ma.s.ses vary, the resultant motion produced on each atom would vary also, though the momentum in each case would be exactly equal and opposite, as momentum is a compound term dependent partly upon the ma.s.s of the body concerned.
In Art. 16 we saw that when this third law was applied to planetary phenomena, not only did the sun attract all the planets, but all the planets attracted the sun with equal and opposite forces, and the planets also attracted each other with equal and opposite forces. In the same way it can be proved, that as the sun repels all the planets by the pressure exerted by the aetherial centrifugal force on those planets, the planets repel the sun with an exactly equal and opposite force at their mean distances. In Newton"s conception, however, of the third law of motion, there was simply mathematical data to deal with, by which the law was shown to apply to the planetary and stellar world. In the case, however, of the centrifugal motion, we have a definite physical medium, which by its motions produces the pressure on the planets or suns that exist in s.p.a.ce, which pressure forms the physical centrifugal force that forms the counterpart of Gravitation Attraction.
Let us look at this phase of the case in detail, and by so doing help to establish and confirm the physical existence of the force or motion referred to. We have learned from Chapter IV. that as Aether is gravitative, it surrounds all satellites and planets, suns and stars that exist in the universe.
We have also learned from Art. 86 that Aether has an electro-magnetic basis, as mathematically proved by Maxwell and experimentally proved by Hertz. Thus we came to the conclusion that each satellite and planet, sun and star, was an electrified body (Art. 81), or an electro-magnet (Art. 88), possessing its own electric or electro-magnetic field.
We also learned that in every electro-magnetic field there was a pressure which was ever directed away from the body that generated the electro-magnetic waves. Now, as every satellite and planet, sun and star, is a generator of these waves according to our theory, it follows that every satellite and planet, sun and star, is the centre of a centrifugal force, which centrifugal force is regulated by the ma.s.s of the satellite, planet, sun or star which gives rise to the centrifugal force or motion.
Now, in relation to all electro-magnetic action, it can be experimentally demonstrated, that action and reaction are equal and opposite, so that if we have two electrified or magnetized bodies, then the joint forces of attraction or repulsion between them are equal and opposite. This being so, when we apply the same law of action and reaction to the planets" influence on each other, it follows that the same law must hold good in relation to them.