University of Virginia Library

THE EVOLUTION OF THE STARS AND THE FORMATION
OF THE EARTH. IV
BY WILLIAM WALLACE CAMPBELL
DIRECTOR OF THE LICK OBSERVATORY, UNIVERSITY OF CALIFORNIA

THE PLANETESIMAL HYPOTHESIS

THE most elaborate structure yet proposed to explain the origin of the solar system is the planetesimal hypothesis by Chamberlin and Moulton. The energy which these investigators have devoted to formulating and testing this hypothesis, in the light of the principles of mechanics, has been commensurate with the importance of the subject. They postulate that the materials now composing the Sun, planets, and satellites, at one time existed as a spiral nebula, or as a great spiral swarm of discrete particles, each particle in elliptic motion about the central nucleus. The authors go further back and endeavor to account for the origin of the spiral nebula, but this phase of the subject is not vital to their hypothesis. However, it conduces to clearness in presenting their hypothesis to begin with the earlier process.

It may happen, once in a while, that two stars will collide. If the collision is a grazing one, they say, a spiral nebula will be formed. However, a fairly close approach of two stars will occur in vastly greater frequency and the effect of this approach will also be to form a spiral nebula or two such nebulæ. The authors recall that our Sun is constantly ejecting materials to a considerable height to form the prominences, and that the attractions of a great star passing fairly close to our solar system would assist this process of expulsion of matter from the Sun. A great outbreak or ejection of matter would occur not only on the side of our Sun turned toward the disturbing body, but on the opposite side as well, for the same reason that tides in our oceans are raised on the side opposite the Moon as well as on the side toward the Moon. As the Sun and disturbing star proceeded in their orbits, the stream of matter leaving our Sun on the side of the disturbing body would try to follow the other star; and the stream of matter leaving the other side of the Sun would shoot out in curves essentially symmetrical with those in the first stream. As the disturbing star approached and receded the paths taken by the ejected matter would be successively along curves such as are represented by the dotted lines in Fig. 28. At any given moment the ejected matter would lie on the two heavy lines. The matter would not be moving along the heavy lines, but nearly at right angles to them, in the directions that the lighter curves are pointing. As the ejections would not be continuous, but on the contrary

intermittent, because of violent pulsations of the Sun's body, there would be irregularities in the two spiral streamers. The materials drawn out of the Sun would revolve around it in elliptic orbits after the disturbing body had passed beyond the distance of effective disturbance,

FIG. 28. THE ORIGIN OF A SPIRAL NEBULA, according to Moulton.

[Description: Illustration of the origin of a spiral nebula. In design, the lines combine to look like a bow tie.]

as illustrated in Fig. 29. The orbits of the different masses would have different sizes and different eccentricities. There would also be a wide distribution of finely-divided material between the main branches of the spiral. All of the widespread gaseous matter, hot when it left the

FIG. 29. THE ORIGIN OF ELLIPTICAL ORBITS OF MATTER EJECTED FROM THE SUN S AT THE TIME A STAR S1—S2 IS PASSING (Moulton)

[Description: Illustration of the origin of elliptical orbits of matter ejected from the sun. In design, the lines combine to look like a figure eight turned on its side.]

Sun, would soon become cold, by expansion and radiation; and only the massive nuclei would remain gaseous and hot.

I see no reason to question the efficiency of this ingenious explanation of the origin of a spiral nebula: the close passage of two massive stars could, in my opinion, produce an effect resembling a spiral nebula, quite in accordance with Moulton's test calculations upon the subject. Some of the spirals have possibly been formed in this way (see Fig. 30);

FIG. 30. SPIRAL NEBULA HI 55 PEGASI. Photographed at the Lick Observatory.

[Description: Photograph of a spiral nubula.]

but that the tens of thousands of spirals known to exist in the sky have actually been produced in this manner is another question, and one which, in my opinion, is open to grave doubt. But to this point we shall return later.

There are marked advantages in starting the evolution of the solar system from a spiral nebula, aside from the fact that spirals are abundant, and therefore represent a standard product of development. The material is thinly and very irregularly distributed in a plane passing through the Sun, and the motions around the Sun are all in the same direction. The great difficulty in the Laplace hypothesis, as to the constancy of the moment of momentum, is here eliminated. There are well-defined condensations of nuclei at quite different distances from the Sun. According to this hypothesis the principal nuclei are the beginnings of the future planets. They draw into themselves the materials with which they come in contact by virtue of the crossings of the orbits of various sizes and various eccentricities. The growth of the planets is gradual, for the sweeping up and combining process must be excessively slow. The satellites are started from those smaller nuclei which happen to be moving with just the right speeds not to escape entirely the attractions of the principal nuclei, nor to fall into them. The planes of the planetary orbits and, in general, the planes of the satellite orbits should agree quite closely with each other, but they could differ and should differ from that of the Sun's equator.

The authors call attention to the fact that the Sun's equator is inclined

at a small angle, 7°, to the common planes of the planetary system, and Chamberlin holds this to be one of the strong points in favor of the planetesimal hypothesis. He reasons thus: the star which passed close to our Sun and drew out the planetary materials in the form of spiral streams must have moved in the plane of the spiral; that is, in the plane of our planetary system. Some of the materials would be drawn out from our Sun only a very short distance and then fall back upon the Sun. Great tidal waves would be formed on opposite sides of the Sun, and these would try to follow the disturbing body. The effect of these waves and of the materials which fall back would be to change the Sun's original rotation plane in the direction of the disturbing body's orbital plane.

Now the chance for a disturbing star's passing around our Sun in a plane making a large angle, say from 45° to 90°, with the Sun's equator, is much greater than for a small angle 0° to 45°. The chances are greatest that the angle will be 90°. Only those disturbing stars which approach our Sun precisely in the plane of the Sun's equator could move around the Sun in this plane. All those approaching along any line parallel to the Sun's equatorial plane, but lying outside of this plane, and all those whose directions of approach make any angle whatever with the equatorial plane, would find it impossible to move in that plane. That the angle under this hypothesis is only 7° is surprising, though, as we are dealing with but a single case, we can not say, I think, that this militates either for or against the hypothesis. We are entitled to say only that unless the approach was so close as to cause disturbances in our Sun to relatively great depths, the angle referred to would have only one chance in ten or fifteen or twenty to be as small as 7°. Any disturbance which succeeded in taking out of the Sun only 1/7 of 1 per cent. of its mass could scarcely succeed in shifting the axis of rotation of the remaining 99 6/7 per cent. very much, I think. If the angle were 30° or 50° or 80°, instead of 7°, the case for the planetesimal hypothesis would be somewhat stronger.

A remarkable fact concerning the Sun is that the equatorial region rotates once around in a shorter time than the regions in higher latitudes require. The rotation period of the Sun's equator is about 24 days; the period at latitude 45° is 28 days; and at 75°, 33 days. The planetesimal hypothesis attributes this equatorial acceleration to the falling back into the Sun of the materials which had been lifted out to a short distance by the disturbing body, and to the forward-rushing tide raised in the equatorial regions by the disturbing body. This may well have occurred. However, we must remember that the same phenomenon exists certainly in Jupiter and Saturn, and quite probably in Uranus and Neptune; that is, in all the bodies in the system that are gaseous and free to show the effect. It seems to be the result of a

principle which has operated throughout the solar system, not requiring, at least not directly requiring, the passage of a disturbing star. I think the most plausible explanation of this curious phenomenon is that great quantities of materials originally revolving around the Sun and around each of the planets have gradually been drawn into these bodies, by preference into their equatorial areas. Such masses of matter moving in orbits very close to these bodies must have traveled with speeds vastly higher than the surface speeds of the bodies. To illustrate, the rotational velocity of a particle now in the Sun's surface at the equator is approximately 2 km. per second. A small body revolving around the Sun close to his surface, rapidly enough to prevent its falling quickly upon the Sun, must have a velocity of more than 400 km. per second. If, now, this small body encounters some resistance it will fall into the Sun, and as it is traveling more than 200 times as rapidly as the solar materials into which it drops, it will both generate heat and accelerate the rotational velocity of the surrounding materials. In the same way the equatorial accelerations in Jupiter and Saturn can receive simple explanation. The point is not necessarily in opposition to the planetesimal hypothesis; but whatever the explanation, it ought to apply to the planet as well as to the Sun.

If the spiral nebulæ have been formed in accordance with Chamberlin and Moulton's hypothesis, the secondary nuclei in them must revolve in a great variety of elliptic orbits. The orbits would intersect, and in the course of long ages the separate masses would collide and combine and the number of separate masses would constantly grow smaller. Moulton has shown that in general the combining of two masses whose orbits intersect causes the combined mass to move in an orbit more nearly circular than the average orbit of the separate masses, and in general in orbit planes more nearly coincident with the general plane of the system. Accordingly, the major planets should move in orbits more nearly circular and more nearly in the plane of the system than do the asteroids; and so they do. If the asteroids should combine to form one planet the orbit of this planet should be much less eccentric than the average of all the present asteroid eccentricities, and the deviation of its orbit plane should be less than the average deviation of the present planes. We can not doubt that this would be the case. Mercury and Mars, the smallest planets, should have, according to this principle, the largest eccentricities and orbital inclinations of any of the major planets. This is true of the eccentricities, but Mars's orbit plane, contrarily, has a small inclination. Venus and the Earth, next in size, should have the next largest inclinations and eccentricities, but they do not; Venus's eccentricity is the smallest of all. The Earth's orbital inclination and eccentricity are both small. Jupiter and Saturn, Uranus and Neptune, should have the smallest orbital inclinations; their

average inclination is about the same as for Venus and the Earth. They should likewise have the smallest eccentricities. Neptune, the smallest of the four, has an orbit nearly circular; Jupiter, Saturn and Uranus have eccentricities more than 4 times those of Venus and the Earth. Considering the four large planets as one group and the four small planets as another group, we find that the inclinations of the orbits of the two groups, per unit mass, are about equal; but the average eccentricity of the orbits of the large planets, per unit mass, is 21 times that of the orbits of the small planets.[1] The evidence, except as to the asteroids and Mercury, is not favorable to the planetesimal hypothesis, unless we make special assumptions as to the distribution of materials in the spiral nebulæ.

The fact that the disturbing body drew 225 times as much matter a great distance to form the four large planets as it drew out a short distance to form the four small planets and the asteroids seems difficult of explanation on the planetesimal hypothesis. However, this distribution of matter is at present a difficulty in any of the hypotheses. The planetesimal hypothesis explains well all west to east rotations of the planets on their axes, but to make Uranus rotate nearly at right angles to the plane of the system, and Neptune in a plane inclined 135° to the plane of the system, is a difficulty in any of the hypotheses, unless special assumptions are made to fit each case.

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 nebulæ 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.

RÉSUMÉ 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 NEBULÆ

I think it is very doubtful whether the spiral nebulæ 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 nebulæ, 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°. 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.

We are sadly in need of information concerning the constitution of the spiral nebulæ. 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 nebulæ.

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 Poincaré 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-Poincaré 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 β Lyræ 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 β Lyræ 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° 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.

5. If the Earth consisted of a thin solid shell upon a liquid interior there would be tides in the liquid interior, the crust would yield to these tides almost as if it were composed of rubber, and the ocean tides would be only an insignificant amount larger than the land tides. As a result we should not see the ocean tides; their visibility depends upon the contrast between the ocean tides and the land tides. If the Earth were absolutely unyielding from surface to center the ocean tides would be relatively 50 per cent. higher than we now see them. The conclusion from these facts is that the Earth yields to the tidal forces a little less than if it were a solid ball of steel, supposing that the well-known rigidity and density existed from surface to center of the ball. This result is established by Darwin's and Schweydar's studies of ocean tides, by studies of the tides in the Earth's surface strata made by Hecker, Paschwitz and others, and by Michelson's recent extremely accurate comparison of land and water tides. Michelson's results establish further that the Earth is highly elastic: though distortion is resisted, there is yielding, but the original form is recovered quickly, almost as quickly as a perfectly elastic body would recover.

6. Some 25 years ago it was discovered by Küstner that the latitudes of points on the Earth's surface are changing slowly. Chandler proved that these variations pass through their principal cycle in a period of 427 days. The entire Earth oscillates slightly in this period. The earlier researches of Euler had shown that the Earth would have a natural oscillation period of 305 days provided it were an absolutely rigid body. Newcomb showed that the period of oscillation would be 441 days if the Earth had the rigidity of steel. As the observed oscillation requires 427 days, Newcomb concluded that the Earth is slightly more rigid than steel.

7. The first waves from a very distant earthquake come to us directly through the Earth. The observed speeds of transmission are the greater, in general, the more nearly the earthquake origin is exactly on

the opposite side of the Earth from the observer; that is, the speeds of transmission are greater the nearer the center of the Earth the waves pass. Now, we know that the speeds are functions of the rigidity and density of the materials traversed. The observed speeds require for their explanation, so far as we can now see, that the rigidity of the Earth's central volume be much greater than that of steel, and the rigidity of the Earth's outer strata considerably less than that of steel. Wiechert has shown that a core of radius 4,900 km. whose rigidity is somewhat greater than that of steel and whose average density is 8.3, overlaid by an outer stony shell of thickness 1,500 km. and average density 3.2, would satisfy the observed facts as to the average density of the Earth, as to the speeds of earthquake waves, as to the flattening of the Earth,—assuming the concentric strata to be homogeneous in themselves,— and as to the relative strengths of gravity at the Poles and at the Equator. The dividing line, 1,500 km. below the surface—1,600 km. would be just one fourth of the way from the surface to the center— places a little over half the volmue in the outer shell and a little less than half in the core. Wiechert did not mean that there must be a sudden change of density at the depth of 1,500 km., with uniform density 8.3 below that surface and uniform density 3.2 above that surface. The change of density is probably fairly continuous. It was necessary in such a preliminary investigation to simplify the assumptions. The observational data are not yet sufficiently accurate to let us say what the law of increase in density and rigidity is as we pass from the surface to the center.

8. The phenomena of terrestrial magnetism indicate that the distribution of magnetic materials in the Earth is far from uniform or symmetrical; the magnetic poles are distant from the Earth's poles of rotation; the magnetic poles are not opposite each other; the lines of equal intensity as to all the magnetic components involved run very irregularly over the Earth's surface. There is reason to believe that iron in the deep interior of the Earth, in view of its high temperature, is devoid of magnetic properties, but we must not state this as a fact. We know that iron is very widely, but very irregularly spread throughout the Earth's outer strata. Whatever may be the main factors in making the Earth a great magnet, to whatever extent the rotation factor may be important, the Earth's magnetic properties point strongly to a very irregular distribution of magnetic materials in the outer strata where the temperatures are below that at which magnetic materials commonly lose their polarity.

9. Irregularities in the direction of the plumb-line and in the force of gravity as observed widely and accurately over the Earth's surface indicate that the surface strata are very irregular as to density. To harmonize the observed facts Hayford has shown the need of assuming

that the heterogeneous conditions extend down to a depth of 122 km. from the surface. Below that level the Earth's concentric strata seem to be of approximately uniform densities.

10. The radio active elements have been found by Strutt and others in practically all kinds of rock accessible to the geologists, but they are not found in significant quantities in the so-called metals which exist in a pure state. These radioactive elements are liberating heat. Strutt has shown that if they existed down to the Earth's center in the same proportion that he finds in the surface strata they would liberate a great deal more heat than the body of the Earth is now radiating to outer space. The conclusion is that they are restricted to the strata relatively near the Earth's surface, and are not in combination with the materials composing the Earth's core. They have apparently found some way of coming to the higher levels. Chamberlin suggests that as they liberate heat they would raise surrounding materials to temperatures above the normals for their strata, and that these expanded materials would embrace every opportunity to approach the surface of the Earth, carrying the radioactive substances with them.

The evidence is exceedingly strong, and perhaps irresistible, to the effect that the Earth is now solid, or acts like a solid, from surface to center, with possibly local, but on the whole negligible, pockets of molten matter here and there; and further, that the Earth existed in a molten, or at the least a thickly plastic, state throughout a long part of its life. The nucleus, whether gaseous or meteoric, from which I believe it has grown, may have been fairly hot or quite cold, and the materials which were successively drawn into the nucleus may have been hot or cold: heat would be generated by the impacts of the incoming materials; and as the attraction toward the center of the mass became strong, additional heat would be generated in the contraction process. The denser materials have been able, on the whole, to gravitate to the center of the structure, and the lighter elements have been able, on the whole, to rise to and float upon the surface very much as the lighter impurities in an iron furnace find their way to the surface and form the slag upon the molten metal. The lighter materials which in general form the surface strata are solid under the conditions of solids known to us in every-day life. The interior is solid or at least acts as a solid, because the materials, though at high temperatures, are under stupendous pressures. If the pressures were removed the deep-lying materials would quickly liquefy, and probably even vaporize.

If the Earth grew from a small nucleus to its present size by the extremely gradual drawing-in of innumerable small masses in its neighborhood, the process would always be slow; much slower at first when the small nucleus had low gravitating powers, more rapid when the body was of good size and the store of materials to draw upon plentiful,

and gradually slower and slower as the supply of building materials was depleted. Meteoric matter still falls upon and builds up the Earth, but at so slow a rate as to increase the Earth's diameter an inch only after the passage of hundreds of millions of years. If the Earth grew in this manner, the growth may now be said to be essentially complete, through the substantial exhaustion of the supply of materials.

Whether the Earth of its present size was ever completely liquefied, that is, from center to surface, at one and the same time, is doubtful. The lack of homogeneity, as indicated by the plumb-line, gravity, terrestrial magnetism and radiaoctive matter, extending in a perceptible degree down to 122 km., and quite probably in lesser and imperceptible degree to a much greater depth, is opposed to the idea.

Solidification would respond to the fall of temperature down to the point required under the existing high pressures, and it is probable that the solidification began at the center and proceeded outwards. It is natural that the plastic state should have developed and existed especially during the age of most rapid growth, for this would be the age of most rapid generation of heat. Later, while the rate of growth was declining, the body could probably have solidified slowly and successively from center out to surface. In later slow depositions of materials, the denser substance would not be able to sink down to the deepest strata: they must lie within a limited depth and horizontal distance from where they fell, and the outer stratum of the Earth would be heterogeneous in density.

The simplest hypothesis we can make concerning the Earth's deep interior is that the chief ingredient is iron; perhaps a full half of the volume is iron. The normal density of iron is 7.8, and of rock formations about 2.8. If these are mixed, half and half, the average density is 5.3. Pressures in the Earth should increase the density and the heat in the Earth should decrease the density. The known density of the Earth is 5.5. We know that iron is plentiful in the Earth's crust, and that iron is still falling upon the Earth in the form of meteorites. The composition of the Earth as a whole, on this assumption, is very similar to the composition of the meteorites in general. They include many of the metals, but especially iron, and they include a large proportion of stony matter. Iron is plentiful in the Sun and throughout the stellar universe. Why should it not be equally plentiful in the materials which have coalesced to form the Earth? It is difficult to explain the Earth's constitution on any other hypothesis.

The Earth's form is that which its rotation period demands. Undoubtedly if the period has changed, the form has changed. Given a little time, solids under great pressure flow quite readily into new forms. Now any great slowing-down of the Earth's rotation period within geological times would be expected to show in the surface features. The

strata should have wrinkled, so to speak, in the equatorial regions and stretched in the polar regions, if the Earth changed from a spheroid that was considerably flatter than it now is, to its present form. Mountains, as evidence of the folding of the rock strata, should exist in profusion in the torrid zone, and be scarce in or absent from the higher latitudes of the Earth. Such differential effects do not exist, and it seems to follow that changes in the Earth's rotation period and in its form could have been only slight while the stratification of our rocks was in progress.

Geologists estimate from the deposition of salt in the oceans, and from the rates of denudation and sedimentation, that the formation of the rock strata has consumed from 60,000,000 to 100,000,000 years. If the Earth had substantially its present form 80,000,000 years ago we are safe in saying that the period of time represented in the building up of the Earth from a small nucleus to its present dimensions has been vastly longer, probably reckoned in the thousands of millions of years.

For more than a century past the problem of the evolution of the stars, including the solar system and the Earth, has occupied the central place in astronomical thought. No one is bold enough to say that the problem has been solved. The chief difficulty proceeds from the fact that we have only one Earth, one solar system and one stellar system available for tests of the hypotheses proposed; we should like to test them on many systems, but this privilege is denied us. However, the search for the truth will undoubtedly proceed at an ever increasing pace, partly because of man's desire to know the truth, but chiefly, as Lessing suggested, because the investigator finds an irresistible satisfaction in the process. There is always with him the certainty that the truth is going to be incomparably stranger and more interesting than fiction.