Chapter 26

The authors succeed well, I think, in showing that the satellites should prefer to revolve around their planets in the direction of the planetary revolution and rotation, especially for close satellites, and, on the basis of special assumptions, in the reverse direction for satellites at a greater distance. They show that the chances favor small eccentricities for satellites revolving about their planets in the west to east, or direct sense, and large eccentricities for satellites moving in retrograde directions. The inner satellite of Mars and the rings of Saturn make no special difficulty under the planetesimal hypothesis.

The evidence of the comets, as bona fide members of the solar system which approach the Sun almost, and perhaps quite, indifferently from all directions, is that the volume of space occupied by the parent structure of the system was of enormous dimensions, both at right angles to the present principal plane of the system and in that plane. We are accustomed to think of the spiral nebulae as thin relatively to their major diameters. To this extent the planetesimal hypothesis does not furnish a good explanation of the origin of comets, unless we assume that a small amount of matter was widely scattered in all directions around the parent spiral; and this conception leads to some apparent difficulties. The origin of the comets is difficult to explain under any of the hypotheses.

RESUME OF HYPOTHESES

Kant's hypothesis had the great defect of trying to prove too much. It started from matter AT REST, and came to grief in trying to give a motion of rotation to the entire mass through the operation of internal forces alone--an impossibility. Kant's idea of nuclei or centers of gravitational attraction, scattered here and there throughout the chaotic mass, which grew into the planets and their satellites, is very valuable.

Laplace's hypothesis had the great advantage of starting with an extended mass already in rotation, but it violated fatally the law of constancy of moment of momentum. We should expect this hypothesis to create a solar system free from irregularities, very much as if it were the product of an instrument-maker's precision lathe. The solar system as it exists is a combination of regularities and many surprising irregularities.

Chamberlin and Moulton's hypothesis has the advantage of a parent mass in rotation, practically in a common plane, and with the materials distributed at distances from the nucleus as nearly in harmony with the known distribution of matter in the solar system as we care to have them, except perhaps as to the comets. In effect it retains all the advantageous qualities of Kant's proposals. It seems to have the flexibility required in meeting the irregularities that we see in our system.

CONCERNING THE ORIGIN OF SPIRAL NEBULAE

I think it is very doubtful whether the spiral nebulae have in general been formed by the close approaches of pairs of stars, as the authors have postulated for the assumed solar spiral.[2] The distribution of the spirals seems to me to negative the idea. To witness the close approach of two stars we must look in the direction where the stars are. To the best of present-day knowledge the stars are in a spheroid whose longer axes are coincident with the plane of the Milky Way. If this is so, the close approach of pairs of stars should occur preeminently in the Milky Way, and we should find the spirals prevailingly in and near the Milky Way. This is precisely where we do not find them. In fact, they seem to abhor the Milky Way. The new stars, which are credibly explained as the products of collisions of stars with nebulae, are found preeminently in the Milky Way and almost negligibly in the regions outside of the Milky Way. Again, the spirals are believed to be, on the whole, of enormous size. They are too far away to let us measure their distances by the usual methods, and they move too slowly on the surface of the sphere to have let us determine their proper motions. Slipher's recent work with a spectrograph seems to show that the dozen spirals observed by him are moving with high speeds of approach and recession; from 300 km. per second approach in the case of the Andromeda nebula to 1,100 km. per second recession in the case of several objects. If the spirals are moving at random their speeds at right angles to the line of sight must be even greater than their speeds of approach and recession. Unless they are very distant bodies their proper motions should be detected by observations extending over only a few years. My colleague Curtis has this year compared recent photographs of some 25 spirals with photographs of the same object made by Keeler fifteen years ago. They reveal no appreciable proper motions, or rotations. In this same interval Neptune has revolved more than 30 degrees. Slipher has recently measured the rotational speed of one "spindle" nebula, believed to be a spiral. He finds it to be enormously rapid; no motions in the solar system approach it in magnitude. The evidence is to the effect that the spirals are in general very far away;[3] perhaps on or beyond the confines of our stellar system, but not certainly so. Accordingly, we are led to believe that the spirals studied thus far have diameters 20 times or 100 times, or in some cases several thousand times, the diameter of our solar system. It is difficult to avoid the conclusion that in general they are immensely more massive than is our solar system. The spiral which has been assumed as the forerunner of our system must have been of diminutive size as compared with the larger and brighter spirals which we see to-day.

[2] It would seem that all rotating nebulae should in reality possess some of the attributes of spiral motion. Whether the spiral structure should be visible or invisible to a terrestrial observer would depend upon the sizes and distances of the nebulae, upon the distribution of materials composing them, and perhaps upon other factors. See developed the hypothesis that spiral nebulae owe their origin to the collision of two nebulae. Collisions of this kind could readily occur because of the enormous dimensions of the nebulae, and motions of rotation and consequently spiral structure might readily result therefrom. The abnormally high speeds of the spiral nebulae are apparently a very strong objection to the hypothesis.

[3] Bohlin found a parallax of 0"17 for the Andromeda Nebula, and Lampland thinks that Nebula N.G.G. 4594 has a proper motion of approximately 0"05 per annum.

We are sadly in need of information concerning the constitution of the spiral nebulae. Their spectra appear to be prevailingly of the solar type, except that a very small proportion contain some bright lines in addition to the continuous spectrum. So far as their spectra are concerned, they may be great clusters of stars, or they may consist each of a central star sending its light out upon surrounding dark materials and thus rendering these materials visible to us. The first alternative is unsatisfactory, for all parts of spirals have hazy borders, as if the structure is nebulous or consists of irregular groups of small masses; and the second alternative is unsatisfactory, for in many spirals the most outlying masses seem to be as bright as masses of the same areas situated only one half as far from the center, whereas in general the inner area should be at least four times as bright as the outer area. All astronomers are ready to confess that we do not know much about the conditions existing in spiral nebulae.

THE EARTH-MOON SYSTEM

Our Earth and Moon form a unique combination in that they are more nearly of the same size than are any other planet and its satellites in our system. It required a 26-inch telescope on the Earth to discover the tiny moons of Mars; but an astronomer on Mars does not need any telescope to see the Earth and Moon as a double planet--the only double planet in the solar system.

According to the Kantian school of hypotheses the Earth and Moon owe their unique character to the accident that two centers of condensation--two nuclei--not very unequal in mass, were formed close to each other and were endowed with or acquired motions such that they revolved around each other. They drew in the surrounding materials; one of the two bodies got somewhat the advantage of the other in gravitational attraction; it succeeded in building itself up more than the other nucleus did; and the Earth and the Moon were the result.

According to the Laplacean hypothesis, on the contrary, the Earth and Moon were originally one body, gaseous and in rotation. This ball of gas radiated heat, diminished in size, rotated more and more rapidly, and finally abandoned a ring of nebulosity, which later broke up and eventually condensed into one mass called the Moon. The central mass composed the Earth. It is a curious fact that Venus, which is only a shade smaller than the Earth, should not have divided into two bodies comparable with the Earth and Moon. Have the tides on Venus produced by the Sun always been strong enough to keep the rotation and revolution periods equal, as they are thought to be now, and thus to have given no opportunity for a rapidly rotating Venus to divide into two masses?

A third hypothesis of the Moon's origin is due principally to Darwin. He and Poincare have shown that a great rotating mass of fluid matter, such as the Earth-Moon could be assumed to have been, by cooling, contracting and increasing rotation speed, would, under certain conditions thought to be reasonable, become unstable and eventually divide into two bodies revolving around their common center of mass, at first with their surfaces nearly in contact. Here would begin to act a tide-raising force which must have played, according to Darwin's deductions, a most important part in the further history of the Earth and Moon. The Earth would produce enormous tides in the Moon, and the Moon much smaller tides in the Earth. Both bodies would contract in size, through loss of heat, and would try to rotate more and more rapidly. The two rotating bodies would try to carry the matter in the tidal waves around with the rest of the materials in the bodies, but the pull of each body upon the wave materials in the other would tend to slow down the speed of rotation. The tidal resistance to rotation would be slight if the bodies at any time were attenuated gaseous masses, for the friction within the surface strata would be slight. Nevertheless, there would eventually be a gradual slowing down of the Moon's rotation, a gradual slowing down of the Earth's rotation, and a slow increase in the distance between the two bodies. In other words, the Moon's day, the Earth's day and our month would gradually increase in length. Carried to its logical conclusion, the Moon would eventually turn the same face to the Earth, the Earth would eventually turn the same face to the Moon, and the Earth's day and the Moon's day would equal the month in length. The central idea in this logic is as old as Kant: in 1754 he published an important paper in which he said that tidal interactions between Earth and Moon had caused the Moon to keep the same face turned toward us, that the Earth's day was being very slowly lengthened, and that our planet would eventually turn the same face to the Moon. Laplace, a half-century later, proposed the action of such a force in connection with the explanation of lunar phenomena, and Helmholtz, just 100 years after Kant's paper was published, lent his support to this principle; but Sir George Darwin has been the great contributor to the subject. His popular volume, "The Tides," devotes several chapters to the effects of tidal friction upon the motions of two bodies in mutual revolution. We must pass over the difficult and complicated intermediate steps to Darwin's conclusions concerning the Earth and Moon, which are substantially as follows: the Earth and Moon were originally much closer together than they now are: after a very long period of time, amounting to hundreds of millions of years, the Moon will revolve around the Earth in 55 days instead of in 27 days as at present; and the Moon and Earth will then present the same faces constantly to each other. The estimated period of time required, and the final length of day and month, 55 days, are of course not insisted upon as accurate by Darwin.

These tidal forces were unavoidably active, it matters not if the Earth and Moon were originally one body, as Laplace and Darwin have postulated, or originally two bodies, growing up from two nuclei, in accordance with the Kantian school. Whether these forces have been sufficiently strong to have brought the Earth and Moon to their present relation, or will eventually equalize the Moon's day, the Earth's day, and the month, is a vastly more difficult question. Moulton's researches have cast serious doubt upon this conclusion. All such investigations are enormously difficult, and many questionable assumptions must be made if we seek to go back to the Moon's origin, or forward to its ultimate destiny.

Tidal waves, in order to be effective in reducing the rotational speed of a planet, must be accompanied by internal friction; and this requires that the planet be to some extent inelastic. It was the view of Darwin and others that the viscous state of the Earth and Moon permitted wave friction to come into play. Michelson has recently proved that the Earth has a high degree of elasticity. It deforms in response to tidal forces, but quickly recovers from the action of these forces. It therefore seems that the rate of tidal evolution of the Earth-Moon system at present and in the future must be extremely slow, and possibly almost negligible. What the conditions within the Earth and Moon were in the distant past is uncertain, but these bodies probably passed through viscous stages which endured through enormously long periods of time. No one seriously doubts that Jupiter, Saturn, Uranus and Neptune are now largely gaseous, and that they will evolve, through various degrees of viscosity, into the solid and comparatively elastic state. It is natural to assume that the Earth has already passed through an analogous experience.

The Moon turns always the same hemisphere toward the Earth. Observations of Venus and Mercury are prevailingly to the effect that those planets always turn the same hemispheres toward the Sun. Many, and perhaps all, of the satellites of Jupiter and Saturn seem to turn the same hemispheres always toward their respective planets. This widely prevailing phenomenon is no doubt due to a widely prevailing cause, which astronomers have all but unanimously attributed to tidal action.

BINARY STAR SYSTEMS

That an original mass actually divided to form the Earth and Moon, according to the Laplacian or the Darwin-Poincare principle, seems to be extremely doubtful, especially on account of their diminutive sizes, and I greatly prefer to think that the Earth and Moon were built up from two nuclei; but that very much greater masses, masses larger on the average than our Sun, composing highly attenuated stars, have divided each into two masses to form many or most of our double stars, I firmly believe. The two component stars would in such a case at first revolve around each other with their surfaces almost or quite in contact. Tidal forces would very gradually cause the bodies to move in orbits of larger and larger size, with correspondingly longer periods of revolutions, and the orbits would become constantly more eccentric. While these processes were under way the component bodies would be radiating heat and growing smaller, and their spectra would be changing into the more advanced types. We can not hope to watch such changes as they occur, but we can, I think, find abundant illustrations of these processes in the double stars. I have given reasons for believing that one star in every two and one half, as a minimum proportion, is not the single star which it appears to be to the eye or in the telescope, but is a system of two or more suns in mutual revolution. The formation of double stars, therefore, is not a sporadic process: it is one of the straightforward results of the evolutionary process.

Some of the variable stars offer strong evidence as to the early life of the double stars. The so-called beta Lyrae variables vary continuously in brightness, as if they consist in each case of two stars so close together that their surfaces are actually in contact in some pairs and nearly in contact in others, so that from our point of view the two stars mutually eclipse each other. When the two stars are in line with us we have minimum brightness. When they have moved a quarter-revolution farther, and the line joining them is at right angles to our line of sight, so to speak, we have maximum brightness. In every known case the beta Lyrae pairs of stars have spectra of the very early types. Some of them even contain bright lines in their spectra. The densities of these great stars are known to be exceedingly low, in some cases much lower on the average than that of the atmosphere which we breathe.

About 80 Algol variable stars are known. These are double stars whose light is constant except during the short time when one of the components in each system passes between us and the other component. All double stars would be Algol variables if we were exactly in the planes of their orbits. That so few Algols have been observed amongst the tens of thousands of double stars, is easily explained. The two component stars in the few known Algol systems are so great in diameter, in proportion to the size of their orbits, that eclipses are observable throughout a wide volume of space, and the eclipses are of long duration relatively to the revolution period. Their densities are, so far as we have been able to determine them, on an average less than 1/10th of the Sun's density. Let us note well that their spectra, so far as we have been able to determine them, are of the early types; mostly helium and hydrogen stars, and a very few of the Class F, intermediate between the hydrogen and solar stars. There are no known Algols of the Classes G, K, and M: these stars are very condensed and therefore small in size, as compared with stars of Classes B and A; and the components of double stars of these classes are on the average much denser and therefore smaller in size than the components in Classes B and A double stars; the components are much farther apart in Classes G to M doubles than in Classes B and A doubles; and for these reasons eclipses in Classes G to M doubles occur but rarely for observers scattered throughout space. It is difficult to avoid the conclusion that the components of double stars separate more and more widely with the progress of time. The conclusions which we have earlier drawn from visual double stars are in full harmony with the argument.

It is agreed by all, I think, that tidal action has been responsible for at least a part of the separation of the Earth and Moon, for at least a part of the gradual separation of the components of double stars, and for at least a part of the eccentricity of their orbits. See's investigations of 25 years ago led him to the conclusion that this force is sufficient to account for all the observed separation of the components of double stars, and for the well-known high eccentricities of their orbits. In recent years Moulton and Russell have seriously questioned the sufficiency of this force to account for the major part of the separation and eccentricity in the double star systems. I think, however, that if the tidal force is not competent to account for the observed facts as described, some other separating force or forces must be found to supply the deficiency.

THE FORMATION OF THE EARTH

Does the condition of the Earth's interior give evidence on the question of its origin? There are certain important facts which bear upon the problem.

1. The evidence supplied by the volcanoes, by the hot springs, and by the rise in temperature as we go down in all deep mines, is unmistakably to the effect that there is an immense quantity of heat in the Earth's interior. Near the surface the temperature increases at the average of 1 degrees Centigrade for every 30 meters of depth. If this rate were maintained we should at 60 km. in depth arrive at a temperature high enough to melt platinum, the most refractory of the known metals. What the law of temperature-increase at great depths is we do not know, but the temperature of the Earth's deep interior must be very high.

2. The pressures in the Earth increase from zero at the surface to the order of 3,000,000 atmospheric pressures at the center. We know that rock structure, or iron or other metals, can be slightly compressed by pressure, but the experiments at very high pressures, notably those conducted by Bridgman, give no indications that matter under such pressures breaks down and obeys different or unknown laws. It should be said, however, that laboratory pressure-effects alone are not a safe guide as to conditions within the Earth, where high pressures are accompanied by high temperature. Unfortunately it has not been found possible to combine the high-temperature factor with the high-pressure factor in the laboratory experiments. It is well known that the melting points of metals, including rocks, increase with increase of pressure; and although the temperatures in the Earth's interior are very high, it is easy to conceive that the materials of the Earth's interior are nevertheless in the solid state, or that they act like solids, because of the high pressures to which they are subjected.

3. The specific gravity of the entire Earth is 5.5 on the scale of water as one, whereas the density of the stratified rocks averages only 2.75; that is, the stratified rocks have but one half the density of the Earth as a whole. The basaltic rocks underlying the stratified attain occasionally the density 3.1, and perhaps a little higher. It follows absolutely that the density of the materials of the Earth's interior must be considerably in excess of 5.5. If the interior is composed chiefly of substances which are plentiful in the Earth's surface strata, our choice of materials which principally compose the interior is reduced to a few elements, notably the denser ones.

4. The observed phenomena of terrestrial precession can not be explained on the basis of an Earth with a thin solid surface shell and a liquid interior, for the attractions of the Moon and Sun upon the Earth's equatorial protuberance would cause the surface shell to shift over the fluid interior, instead of swinging the entire Earth.