RADIANT POINT
| Name of Shower | R. A. | Decl. | Date of Shower |
| Quadrantids | 230° | +53° | Jan. 2-4 |
| Zeta Cepheids | 331° | +56° | Jan. 25 |
| Alpha Leonids | 155° | +14° | Feb. 19-March 1 |
| Tau Leonids | 166° | +4° | March 1-4 |
| Beta Ursids | 161° | +58° | March 13-24 |
| Lyrids | 271° | +33° | April 20-22 |
| Gamma Aquarids | 338° | -2° | May 1-6 |
| Zeta Herculids | 246° | +29° | May 18-26 |
| Eta Pegasids | 330° | +28° | May 30-June 4 |
| Theta Boötids | 213° | +53° | June 27-28 |
| Alpha Capricornids | 304° | -12° | July 15-28 |
| Delta Aquarids | 339° | -11° | July 25-30 |
| Perseids | 45° | +57° | Aug. 10-12 |
| Omicron Draconids | 291° | +60° | Aug. 15-25 |
| Zeta Draconids | 262° | +63° | Aug. 21-Sept. 2 |
| Piscids | 348° | +2° | Sept. 4-14 |
| Alpha Andromedids | 4° | +28° | Sept. 27 |
| Epsilon Arietids | 40° | +20° | Oct. 11-24 |
| Orionids | 92° | +15° | Oct. 17-24 |
| Epsilon Perseids | 61° | +35° | Nov. 5 |
| Leonids | 150° | +23° | Nov. 13-15 |
| Epsilon Taurids | 64° | +22° | Nov. 14-25 |
| Andromedids | 25° | +43° | Nov. 17-23 |
| Beta Geminids | 119° | +31° | Dec. 1-12 |
| Geminids | 108° | +33° | Dec. 1-14 |
| Alpha Ursæ Majorids | 161° | +58° | Dec. 18-21 |
| Kappa Draconids | 194° | +68° | Dec. 18-28 |
The year 1916 was exceptional in providing an abundant and previously unknown shower on June 28, and its stream has nearly the same orbit as that of the Pons-Winnecke periodic comet. Useful observations of meteors are not difficult to make, and they are of service to professional astronomers investigating the orbits of these bodies, among whom are Mitchell and Olivier of the University of Virginia.
CHAPTER XLIII
METEORITES
Meteorites, the name for meteors which have actually gone all the way through our atmosphere, are never regular in form or spherical. As a rule the iron meteorites are covered with pittings or thumb marks, due probably to the resistance and impact of the little columns of air which impede its progress, together with the unequal condition and fusibility of their surface material. The work done by the atmosphere in suddenly checking the meteor's velocity appears in considerable part as heat, fusing the exterior to incandescence. This thin liquid shell is quickly brushed off, making oftentimes a luminous train.
But notwithstanding the exceedingly high temperature of the exterior, enforced upon it for the brief time of transit through the atmosphere, it is probable that all large meteorites, if they could be reached at once on striking the earth, would be found to be cold, because the smooth, black, varnishlike crust which always incases them as a result of intense heat is never thick. On one occasion a meteor which was seen to fall in India was dug out of the ground as quickly as possible, and found to be, not hot as was expected, but coated thickly over with ice frozen on it from the moisture in the surrounding soil.
As to the composition of shooting stars, and their probable mass, and its effect upon the earth, our data are quite insufficient. The lines of sodium and magnesium have been hurriedly caught in the spectroscope, and, estimating on the basis of the light emitted by them, the largest meteors must weigh ounces rather than pounds. Nevertheless, it is interesting to inquire what addition the continual fall of many millions daily upon the earth makes to its weight: somewhere between thirty and fifty thousand tons annually is perhaps a conservative estimate, but even this would not accumulate a layer one inch in thickness over the entire surface of the earth in less than a thousand million years.
Many hundreds of the meteors actually seen to fall, together with those picked up accidentally, are recovered and prized as specimens of great value in our collections, the richest of which are now in New York, Paris, and London. The detailed investigation of them is rather the province of the chemist, the crystallographer and the mineralogist than of the astronomer whose interest is more keen in their life history before they reach the earth. To distinguish a stony meteorite from terrestrial rock substances is not always easy, but there is usually little difficulty in pronouncing upon an iron meteorite. These are most frequently found in deserts, because the dryness of the climate renders their oxidation and gradual disappearance very slow.
The surface of a suspected iron meteorite is polished to a high luster and nitric acid is poured upon it. If it quickly becomes etched with a characteristic series of lines, or a sort of cross-hatching, it is almost certain to be a meteorite. Occasionally carbon has been found in meteorites, and the existence of diamond has been suspected. The minerals composing meteorites are not unlike terrestrial materials of volcanic origin, though many of them are peculiar to meteorites only. More than one-third of all the known chemical elements have been found by analysis in meteorites, but not any new ones.
Meteoric iron is a rich alloy containing about ten per cent of nickel, also cobalt, tin, and copper in much smaller amount. Calcium, chlorine, sodium, and sulphur likewise are found in meteoric irons. At very high temperatures iron will absorb gases and retain them until again heated to red heat. Carbonic oxide, helium, hydrogen, and nitrogen are thus imprisoned, or occluded, in meteoric irons in very small quantities; and in 1867, during a London lecture by Graham, a room in the Royal Institution was for a brief space illuminated by gas brought to earth in a meteorite from interplanetary space. Meteorites, too, have been most critically investigated by the biologist, but no trace of germs of organic life of any type has so far been found. Farrington of Chicago has published a full descriptive catalogue of all the North American meteorites.
Recent investigations of the radioactivity of meteorites show that the average stone meteorite is much less radioactive than the average rock, and probably less than one-fourth as radioactive as in average granite. The metallic meteorites examined were found about wholly free from radioactivity.
From shooting stars, perhaps the chips of the celestial workshop, or more possibly related to the planetesimals which the processes of growth of the universe have swept up into the vastly greater bodies of the universe, transition is natural to the stars themselves, the most numerous of the heavenly bodies, all shining by their own light, and all inconceivably remote from the solar system, which nevertheless appears to be not far removed from the center of the stellar universe.
CHAPTER XLIV
THE UNIVERSE OF STARS
Our consideration of the solar system hitherto has kept us quite at home in the universe. The outer known planets, Uranus and Neptune, are indeed far removed from the sun, and a few of the comets that belong to our family travel to even greater distances before they begin to retrace their steps sunward. When we come to consider the vast majority of the glistening points on the celestial sphere—all in fact except the five great planets, Mercury, Venus, Mars, Jupiter, and Saturn—we are dealing with bodies that are self-luminous like the sun, but that vary in size quite as the bodies of the solar system do, some stars being smaller than the sun and others many hundred fold larger than he is; some being "giants," and others "dwarfs." But the overwhelming remoteness of all these bodies arrests our attention and even taxes our credulity regarding the methods that astronomers have depended on to ascertain their distances from us.
Their seeming countlessness, too, is as bewildering as are the distances; though, if we make actual counts of those visible to the naked eye within a certain area, in the body of the "Great Bear," for example, the great surprise will be that there are so few. And if the entire dome of the sky is counted, at any one time, a clear, moonless sky would reveal perhaps 2,500, so that in the entire sky, northern and southern, we might expect to find 5,000 to 6,000 lucid stars, or stars visible to the naked eye.
But when the telescope is applied, every accession of power increases the myriads of fainter and fainter stars, until the number within optical reach of present instruments is somewhere between 400 and 500 millions. But if we were to push the 100-inch reflector on Mount Wilson to its limit by photography with plates of the highest sensitiveness, millions upon millions of excessively faint stars would be plainly visible on the plates which the human eye can never hope to see directly with any telescope present or future, and which would doubtless swell the total number of stars to a thousand millions. Recent counts of stars by Chapman and Melotte of Greenwich tend to substantiate this estimate.
What have astronomers done to classify or catalogue this vast array of bodies in the sky? Even before making any attempt to estimate their number, there is a system of classification simply by the amount of light they send us, or by their apparent stellar magnitudes—not their actual magnitudes, for of those we know as yet very little. We speak of stars of the "first magnitude," of which there are about 20, Sirius being the brightest and Regulus the faintest. Then there are about 65 of the second, or next fainter, magnitude, stars like Polaris, for example, which give an amount of light two and a half times less than the average first magnitude star. Stars of the third magnitude are fainter than those of the second in the same ratio, but their number increases to 200; fourth magnitude, 500; fifth magnitude, 1,400; sixth magnitude, 5,000, and these are so faint that they are just visible on the best nights without telescopic aid.
Decimals express all intermediate graduations of magnitude. Astronomers carry the telescopic magnitudes much farther, till a magnitude beyond the twentieth is reached, preserving in every case the ratio of two and one-half for each magnitude in relation to that numerically next to it. Even Jupiter and Venus, and the sun and moon, are sometimes calculated on this scale of stellar magnitude, numerically negative, of course, Venus sometimes being as bright as magnitude -4.3, and the sun -26.7.
Knowing thus the relation of sun, moon, and stars, and the number of the stars of different magnitudes, it is possible to estimate the total light from the stars. This interesting relation comes out this way: that the stars we cannot see with the naked eye give a greater total of light than those we can because of their vastly greater numbers. And if we calculate the total light of all the brighter stars down to magnitude nine and one-half, we find it equal to 1/80th of the light of the average full moon.
Many stars show marked differences in color, and strictly speaking the stars are now classified by their colors. The atmosphere affects star colors very considerably, low altitudes, or greater thickness of air, absorbing the bluish rays more strongly and making the stars appear redder than they really are. Aldebaran, Betelgeuse and Antares are well-known red stars, Capella and Alpha Ceti yellowish, Vega and Sirius blue, and Procyon and Polaris white. Among the telescopic stars are many of a deep blood-red tint, variable stars being numerous among them. Double stars, too, are often complementary in color. There is evidence indicating change of color of a very few stars in long periods of time; Sirius, for example, two thousand years ago was a red star, now it is blue or bluish white. But the meaning of color, or change of color in a star is as yet only incompletely ascertained. It may be connected with the radiative intensity of the star, or its age, or both.
The late Professor Edward C. Pickering was famous for his life-long study and determination of the magnitudes of the stars. Standards of comparison have been many, and have led to much unnecessary work. Pickering chose Polaris as a standard and devised the meridian photometer, an ingenious instrument of high accuracy, in which the light of a star is compared directly with that of the pole star by reflection. All the bright stars of both the northern and the southern skies are worked into a standard system of magnitudes known as HP, or the Harvard Photometry.
Astronomers make use of several different kinds of magnitude for the stars: the apparent magnitude, as the eye sees it, often called the visual magnitude; the photographic magnitude, as the photographic plate records it, and these are now determined with the highest accuracy; the photovisual magnitude, quite the same as the visual, but determined photographically on an isochromatic plate with a yellow screen or filter, so that the intensity is nearly the same as it appears to the eye. The difference between the star's visual or photovisual magnitude and its photographic magnitude is called its color-index, and is often used as a measure of the star's color. Light of the shorter wave lengths, as blue and violet, affects the photographic plate more rapidly than the reds and yellows of longer wave length by which the eye mainly sees; so that red stars will appear much fainter and blue stars much brighter on the ordinary photographic plate than the eye sees them.
So great are the differences of color in the stars that well-known asterisms, with which the eye is perfectly familiar, are sometimes quite unrecognizable on the photographic plate, except by relative positions of the stars composing them. White stars affect the eye and the plate about equally, so that their visual or photovisual and photographic magnitudes are about equal. The studies of the colors of the stars, the different methods of determining them, and the relations of color to constitution have been made the subject of especial investigation by Seares of Mount Wilson and many other astronomers.
Centuries of the work of astronomers have been faithfully devoted to mapping or charting the stars and cataloguing them. Just as we have geographical maps of countries, so the heavens are parceled out in sections, and the stars set down in their true relative positions just as cities are on the map. Recent years have added photographic charts, especially of detailed regions of the sky; but owing to spectral differences of the stars, their photographic magnitudes are often quite different from their visual magnitudes. From these maps and charts the positions of the stars can be found with much precision; but if we want the utmost accuracy, we must go to the star catalogues—huge volumes oftentimes, with stellar positions set down therein with the last degree of precision.
First there will be the star's name, and in the next column its magnitude, and in a third the star's right ascension. This is its angular distance eastward around the celestial sphere starting from the vernal equinox, and it corresponds quite closely to the longitude of a place which we should get from a gazetteer, if we wished to locate it on the earth. Then another column of the catalogue will give the star's declination, north or south of the equator, just as the gazetteer will locate a city by its north or south latitude.
CHAPTER XLV
STAR CHARTS AND CATALOGUES
Who made the first star chart or catalogue? There is little doubt that Eudoxus (B. C. 200) was the first to set down the positions of all the brighter stars on a celestial globe, and he did this from observations with a gnomon and an armillary sphere. Later Hipparchus (B. C. 130) constructed the first known catalogue of stars, so that astronomers of a later day might discover what changes are in progress among the stars, either in their relative positions or caused by old stars disappearing or new stars appearing at times in the heavens. Hipparchus was an accurate observer, and he discovered an apparent and perpetual shifting of the vernal equinox westward, by which the right ascensions of the stars are all the time increasing. He determined the amount of it pretty accurately, too. His catalogue contained 1,080 stars, and is printed in the "Almagest" of Ptolemy.
Centuries elapsed before a second star catalogue was made, by Ulugh-Beg, an Arabian astronomer, A. D. 1420, who was a son of Tamerlane, the Tartar monarch of Samarcand, where the observations for the catalogue were made. The stars were mainly those of Ptolemy, and much the same stars were reobserved by Tycho Brahe (A. D. 1580) with his greatly improved instruments, thus forming the third and last star catalogue of importance before the invention of the telescope.
From the end of the seventeenth century onward, the application of the telescope to all the types of instruments for making observations of star places has increased the accuracy many-fold. The entire heavens has been covered by Argelander in the northern hemisphere, and Gould in the southern—over 700,000 stars in all. Many government observatories are still at work cataloguing the stars. The Carnegie Institution of Washington maintains a department of astrometry under Boss of Albany, which has already issued a preliminary catalogue of more than 6,000 stars, and has a great general catalogue in progress, together with investigations of stellar motions and parallaxes. This catalogue of star positions will include proper motions of stars to the seventh magnitude.
In 1887 on proposal of the late Sir David Gill, an international congress of astronomers met at Paris and arranged for the construction of a photographic chart of the entire heavens, allotting the work to eighteen observatories, equipped with photographic telescopes essentially alike. The total number of plates exceeds 25,000. Stars of the fourteenth magnitude are recorded, but only those including the eleventh magnitude will be catalogued, perhaps 2,000,000 in all. The expense of this comprehensive map of the stars has already exceeded $2,000,000, and the work is now nearly complete. Turner of Oxford has conducted many special investigations that have greatly enhanced the progress of this international enterprise.
Other great photographic star charts have been carried through by the Harvard Observatory, with the annex at Arequipa, Peru, employing the Bruce photographic telescope, a doublet with 24-inch lenses; also Kapteyn of Groningen has catalogued about 300,000 stars on plates taken at Cape Town. Charting and cataloguing the stars, both visually and photographically, is a work that will never be entirely finished. Improvements in processes will be such that it can be better done in the future than it is now, and the detection of changes in the fainter stars and investigation of their motions will necessitate repetition of the entire work from century to century.
The origin of the names of individual stars is a question of much interest. The constellation figures form the basis of the method, and the earliest names were given according to location in the especial figure; as for instance, Cor Scorpii, the heart of the Scorpion, later known as Antares or Alpha Scorpii. The Arabians adopted many star names from the Greeks, and gave about a hundred special names to other stars. Some of these are in common use to-day, by navigators, observers of meteors and of variable stars. Sirius, Vega, Arcturus, and a few other first magnitude stars, are instances.
But this method is quite insufficient for the fainter stars whose numbers increase so rapidly. Bayer, a contemporary of Galileo, originated our present system, which also employs the names of the constellations, the Latin genitive in each case, prefixed by the small letters of the Greek alphabet, from alpha to omega, in order of decreasing brightness; and followed by the Roman letters when the Greek alphabet is exhausted.
If there were still stars left in a constellation unnamed, numbers were used, first by Flamsteed, Astronomer Royal; and numbers in the order of right ascension in various catalogues are used to designate hundreds of other stars. The vast bulk of the stars are, however, nameless; but about one million are identifiable by their positions (right ascension and declination) on the celestial sphere.
CHAPTER XLVI
THE SUN'S MOTION TOWARD LYRA
If Hipparchus or Galileo should return to earth to-night and look at the stars and constellations as we see them, there would be no change whatever discernible in either the brightness of the stars or in their relative positions. So the name fixed stars would appear to have been well chosen. Halley in the seventeenth century was the first to detect that slow relative change of position of a few stars which is known as proper motion, and all the modern catalogues give the proper motions in both right ascension and declination. These are simply the small annual changes in position athwart the line of vision; and, as a whole, the proper motions of the brighter stars exceed the corresponding motions of the fainter ones because they are nearer to us. The average proper motion of the brightest stars is 0".25, and of stars of the sixth magnitude only one-sixth as great.
A few extreme cases of proper motion have been detected, one as large as 9", of an orange yellow star of the eighth magnitude in the southern constellation Pictor, and Barnard has recently discovered a star with a proper motion exceeding 10"; several determinations of its parallax give 0".52, corresponding to a distance of 6.27 light years. Nevertheless, two centuries would elapse before these stars would be displaced as much as the breadth of the moon among their neighbors in the sky. The proper motions of stars are along perfectly straight lines, so far as yet observed. Ultimately we may find a few moving in curved paths or orbits, but this is hardly likely.
As for a central sun hypothesis, that pointing out Alcyone in particular, there is no reliable evidence whatever. Analysis of the proper motions of stars in considerable numbers, first by Sir William Herschel, showed that they were moving radially from the constellation Hercules, and in great numbers also toward the opposite side of the stellar sphere. Later investigation places this point, called the sun's goal, or apex of the sun's way, over in the adjacent constellation Lyra; and the opposite point, or the sun's quit, is about halfway between Sirius and Canopus. By means of the radial velocities of stars in these antipodal regions of the sky, it is found that the sun's motion toward Lyra, carrying all his planetary family along with him, is taking place at the rate of about 12 miles in every second.
While the right ascensions of the solar apex as given by the different investigations have been pretty uniform, the declination of this point has shown a rather wide variation not yet explained. For example, there is a difference of nearly ten degrees between the declination (+34°.3) of the apex as determined by Boss from the proper motions of more than 6,000 stars, and the declination (+25°.3) found by Campbell from the radial velocities of nearly 1,200 stars. Several investigations tend to show that the fainter the stars are, the greater is the declination of the solar apex. More remarkable is the evidence that this declination varies with the spectral type of the stars, the later types, especially G and K, giving much more northerly values. On the whole the great amount of research that has been devoted to the solar motion relative to the system of the stars for the past hundred years may be said to indicate a point in right ascension 18h. (270°) and declination 34° N. as the direction toward which the sun is moving. This is not very far from the bright star Alpha Lyræ, and the antipodal point from which the sun is traveling is quite near to Beta Columbæ.
So swift is this motion (nearly twenty kilometers per second) that it has provided a base line of exceptional length, and very great service in determining the average distance of stars in groups or classes. After thousands of years the sun's own motion combined with the proper motions of the stars will displace many stars appreciably from their familiar places. The constellations as we know them will suffer slight distortions, particularly Orion, Cassiopeia and Ursa Major. Identity or otherwise of spectra often indicates what stars are associated together in groups, and their community of motion is known as star drift. Recent investigation of vast numbers of stars by both these methods have led to the epochal discovery of star streaming, which indicates that the stars of our system are drifting by, or rather through, each other, in two stately and interpenetrating streams. The grand primary cause underlying this motion is as yet only surmised.
CHAPTER XLVII
STARS AND THEIR SPECTRAL TYPE
When in 1872 Dr. Henry Draper placed a very small wet plate in the camera of his spectroscope and, by careful following, on account of the necessarily long exposure, secured the first photographic spectrum of a star ever taken, he could hardly have anticipated the wealth of the new field of research which he was opening. His wife, Anna Palmer Draper, was his enthusiastic assistant in both laboratory and observatory, and on his death in 1882, she began to devote her resources very considerably to the amplification of stellar spectrum photography. At first with the cooperation of Professor Young of Princeton, and later through extension of the facilities of Harvard College Observatory, whose director, the late Professor Edward C. Pickering, devoted his energies in very large part to this matter, all the preliminaries of the great enterprise were worked out, and a comprehensive program was embarked upon, which culminated in the "Henry Draper Memorial," a catalogue and classification of the spectra of all the stars brighter than the ninth magnitude, in both the northern and southern hemispheres.
One very remarkable result from the investigation of large numbers of stars according to their type is the close correlation between a star's luminosity and its spectral type. But even more remarkable is the connection between spectral type and speed of motion. As early as 1892 Monck of Dublin, later Kapteyn, and still later Dyson, directed attention to the fact that stars of the Secchi type II had on the average larger proper motions than those of type I. In 1903 Frost and Adams brought out the exceptional character of the Orion stars, the radial velocities of twenty of which averaged only seven kilometers per second.
Soon after, with the introduction of the two-stream hypothesis, a wider generalization was reached by Campbell and Kapteyn, whose radial velocities showed that the average linear velocity increases continually through the entire series B, A, F, G, K, M, from the earliest types of evolution to the latest. The younger stars of early type have velocities of perhaps five or six kilometers per second, while the older stars of later type have velocities nearly fourfold greater.
The great question that occurs at once is: How do the individual stars get their motions? The farther back we go in a star's life history, the smaller we find its velocity to be. When a star reaches the Orion stage of development, its velocity is only one-third of what it may be expected to have finally. Apparently, then, the stars at birth have no motion, but gradually acquire it in passing through their several types or stages of development.
More striking still is the motion of the planetary nebulæ, in excess of 25 kilometers per second, while type A stars move 11 kilometers, type G 15 kilometers, and type M 17 kilometers per second. Can the law connecting speed of motion and spectral type be so general that the planetary nebula is to be regarded as the final evolutionary stage? Stars have been seen to become nebulæ, and one astronomer at least is strongly of the opinion that a single such instance ought to outweigh all speculation to the contrary, as that stars originate from nebulæ.
In his discussion of stellar proper motions, Boss has reached a striking confirmation of the relation of speed to type, finding for the cross linear motion of the different types a series of velocities closely paralleling those of Kapteyn and Campbell.
Concerning the marked relation of the luminosities of the stars to their spectral types, there is a pronounced tendency toward equality of brightness among stars of a given type; also the brightness diminishes very markedly with advance in the stage of evolution. There has been much discussion as to the order of evolution as related to the type of spectrum, and Russell of Princeton has put forward the hypothesis of giant stars and dwarf stars, each spectral type having these two divisions, though not closely related. One class embraces intensely luminous stars, the other stars only feebly luminous. When a star is in process of contraction from a diffused gaseous mass, its temperature rises, according to Lane's law, until that density is reached where the loss of heat by radiation exceeds the rise in temperature due to conversion of gravitational energy into heat. Then the star begins to cool again. So that if the spectrum of a star depends mainly on the effective temperature of the body, clearly the classification of the Draper catalogue would group stars together which are nearly alike in temperature, taking no note as to whether their present temperature is rising or falling.
Another classification of stars by Lockyer divides them according to ascending and descending temperatures. Russell's theory would assign the succession of evolutionary types in the order, M1, K1, G1, F1, A1, B, A2, F2, G2, K2, M2, the subscript 1 referring to the "giants," and 2 to the dwarf stars. In large part the weight of evidence would appear to favor the order of the Harvard classification, independently confirmed as it is by studies of stellar velocities, Galactic distribution, and periods of binary stars both spectroscopic and visual, where Campbell and Aiken find a marked increase in length of period with advance in spectral type. At the same time, a vast amount of evidence is accumulating in support of Russell's theory. Investigations in progress will doubtless reveal the ground on which both may be harmonized.
The publication of the new Henry Draper Catalogue of Stellar Spectra is in progress, a work of vast magnitude. The great catalogue of thirty years ago embraced the spectra of more than ten thousand stars, and was a huge work for that day; but the new catalogue utterly dwarfs it, with a classification much more detailed than in the earlier work, and with the number of stars increased more than twenty-fold. This work, projected by the late director of the Harvard Observatory, has been brought to a conclusion by the energy and enthusiasm of Miss Annie J. Cannon through six years of close application, aided by many assistants. The catalogue ranges over the stars of both hemispheres, and is a monument to masterly organization and completed execution which will be of the highest importance and usefulness in all future researches on the bodies of the stellar universe.
CHAPTER XLVIII
STAR DISTANCES
So vast are the distances of the stars that all attempts of the early astronomers to ascertain them necessarily proved futile. This led many astronomers after Copernicus to reject his doctrine of the earth's motion round the sun, so that they clung rather to the Ptolemaic view that the earth was without motion and was the center about which all the celestial motions took place. The geometry of stellar distances was perfectly understood, and many were the attempts made to find the parallaxes and distances of the stars; but the art of instrument making had not yet advanced to a stage where astronomers had the mechanisms that were absolutely necessary to measure very small angles.
About 1835, Bessel undertook the work of determining stellar parallax in earnest. His instrument was the heliometer, originally designed for measuring the sun's diameter; but as modified for parallax work it is the most accurate of all angle-measuring instruments that the astronomers employ. The star that he selected was 61 Cygni, not a bright star, of the sixth magnitude only, but its large proper motion suggested that it might be one of those nearest to us. He measured with the heliometer, at opposite seasons of the year, the distance of 61 Cygni from another and very small star in the same field of view, and thus determined the relative parallax of the two stars. The assumption was made that the very faint star was very much more distant than the bright one, and this assumption will usually turn out to be sound. Bessel got 0".35 for his parallax of 61 Cygni, and Struve by applying the same method to Alpha Lyræ, about the same time, got 0".25 for the parallax of that star.
These classic researches of Bessel and Struve are the most important in the history of star distances, because they were the first to prove that stellar parallax, although minute, could nevertheless be actually measured. About the same time success was achieved in another quarter, and Henderson, the British astronomer at the Cape of Good Hope, found a parallax of nearly a whole second for the bright star Alpha Centauri.
Although the parallaxes of many hundreds of stars have been measured since, and the parallaxes of other thousands of stars estimated, the measured parallax of Alpha Centauri, as later investigated by Elkin and Sir David Gill, and found to be 0".75, is the largest known parallax, and therefore Alpha Centauri is our nearest neighbor among the stars, so far as we yet know. This star is a binary system and the light of the two components together is about the same as that of Capella (Alpha Aurigæ). But it is never visible from this part of the world, being in 60 degrees of south declination: one might just glimpse it near the southern horizon from Key West.
How the distances of the stars are found is not difficult to explain, although the method of doing it involves a good deal of complication, interesting to the practical astronomer only. Recall the method of getting the moon's distance from the earth: it was done by measuring her displacement among the stars as seen from two widely separated observatories, as near the ends of a diameter of the earth as convenient. This is the base line, and the angle which a radius of the earth as seen from the center of the moon fills, or subtends, is the moon's parallax.
So near is the moon that this angle is almost an entire degree, and therefore not at all difficult to measure. But if we go to the distance of even Alpha Centauri, the nearest of the stars, our earth shrinks to invisibility; so that we must seek a longer base line. Fortunately there is one, but although its length is 25,000 times the earth's diameter, it is only just long enough to make the star distances measurable. We found that the sun's distance from the earth was 93 million miles; the diameter of the earth's orbit is therefore double that amount. Now conceive the diameter of the earth replaced by the diameter of the earth's orbit: by our motion round the sun we are transported from one extremity of this diameter to the opposite one in six month's time; so we may measure the displacement of a star from these two extremities, and half this displacement will be the star's parallax, often called the annual parallax because a year is consumed in traversing its period. And it is this very minute angle which Bessel and Struve were the first to measure with certainty, and which Henderson found to be in the case of Alpha Centauri the largest yet known.
Evidently the earth by its motion round the sun makes every star describe, a little parallactic ellipse; the nearer the star is the larger this ellipse will be, and the farther the star the smaller: if the star were at an infinite distance, its ellipse would become a point, that is, if we imagine ourselves occupying the position of the star, even the vast orbit of the earth, 186 million miles across, would shrink to invisibility or become a mathematical point.
Measurement of stellar parallax is one of many problems of exceeding difficulty that confront the practical astronomer. But the actual research nowadays is greatly simplified by photography, which enables the astronomer to select times when the air is not only clear, but very steady for making the exposures. Development and measurement of the plates can then be done at any time. Pritchard of Oxford, England, was among the earliest to appreciate the advantages of photography in parallax work, and Schlesinger, Mitchell, Miller, Slocum and Van Maanen, with many others in this country, have zealously prosecuted it.
How shall we intelligently express the vast distances at which the stars are removed from us? Of course we can use miles, and pile up the millions upon millions by adding on ciphers, but that fails to give much notion of the star's distance. Let us try with Alpha Centauri: its parallax of 0".75 means that it is 275,000 times farther from the sun than the earth is. Multiplying this out, we get 25 trillion miles, that is, 25 millions of million miles—an inconceivable number, and an unthinkable distance.
Suppose the entire solar system to shrink so that the orbit of Neptune, sixty times 93 million miles in diameter, would be a circle the size of the dot over this letter i. On the same scale the sun itself, although nearly a million miles in diameter, could not be seen with the most powerful microscope in existence; and on the same scale also we should have to have a circle ten feet in diameter, if the solar system were imagined at its center and Alpha Centauri in its circumference.
So astronomers do not often use the mile as a yardstick of stellar distance, any more than we state the distance from London to San Francisco in feet or inches. By convention of astronomers, the average distance between the centers of sun and earth, or 93 million miles, is the accepted unit of measure in the solar system. So the adopted unit of stellar distance is the distance traveled by a wave of light in a year's time: and this unit is technically called the light-year. This unit of distance, or stellar yardstick, as we may call it, is nearly 6 millions of million miles in length. Alpha Centauri, then, is four and one-third light-years distant, and 61 Cygni seven and one-fifth light-years away.
For convenience in their calculations most astronomers now use a longer unit called the parsec, first suggested by Turner. Its length is equal to the distance of a star whose parallax is one second of arc; that is, one parsec is equal to about three and a quarter light-years. Or the light-year is equal to 0.31 parsec. Also the parsec is equal to 206,000 astronomical units, or about 19 millions of million miles.
We have, then four distinct methods of stating the distance of a star: Sirius, for example, has a parallax of 0".38 or its distance is two and two-thirds parsecs, or eight and a half light-years, or 50 millions of million miles. It is the angle of parallax which is always found first by actual measurement and from this the three other estimates of distance are calculated.
So difficult and delicate is the determination of a stellar distance that only a few hundred parallaxes have been ascertained in the past century. The distance of the same star has been many times measured by different astronomers, with much seeming duplication of effort. Comprehensive campaigns for determining star parallaxes in large numbers have been undertaken in a few instances, particularly at the suggestion of Kapteyn, the eminent astronomer of Groningen, Holland. His catalogue of star parallaxes is the most complete and accurate yet published, and is the standard in all statistical investigations of the stars.
That we find relatively large parallaxes for some of the fainter stars, and almost no measurable parallax for some of the very bright stars is one of the riddles of the stellar universe. We may instance Arcturus, in the northern hemisphere and Canopus in the southern; the latter almost as bright as Sirius. Dr. Elkin and the late Sir David Gill determined exhaustively the parallax of Canopus, and found it very minute, only 0".03, making its distance in excess of a hundred light-years. The stupendous brilliancy of this star is apparent if we remember that the intensity of its light must vary inversely as the square of the distance; so that if Canopus were to be brought as near us as even 61 Cygni is, it would be a hundredfold brighter than Sirius, the brightest of all the stars of the firmament.
In researches upon the distribution of the more distant stars, the method of measuring parallaxes of individual stars fails completely, and the secular parallax, or parallactic motion of the stars is employed instead. By parallactic motion is meant the apparent displacement in consequence of the solar motion which is now known with great accuracy, and amounts to 19.5 kilometers per second. Even in a single year, then, the sun's motion is twice the diameter of the earth's orbit, so that in a hundred or more years, a much longer base line is available than in the usual type of observations for stellar parallax. If we ascertain the parallactic motion of a group of stars, then we can find their average distance. It is found, for example, that the mean parallax of stars of the sixth magnitude is 0".014. Also the mean distances of stars thrown into classes according to their spectral type have been investigated by Boss, Kapteyn, Campbell and others. The complete intermingling of the two great star streams has been proved, too, by using the magnitude of the proper motions to measure the average distances of both streams. These come out essentially the same, so that the streaming cannot be due to mere chance relation in the line of sight.
Most unexpected and highly important is the discovery that the peculiar behavior of certain lines in the spectrum leads to a fixed relation between a star's spectrum and its absolute magnitude, which provides a new and very effective method of ascertaining stellar distances. By absolute magnitudes are meant the magnitudes the stars would appear to have if they were all at the same standard distance from the earth.
Very satisfactory estimates of the distance of exceedingly remote objects have been made within recent years by this indirect method, which is especially applicable to spiral nebulæ and globular clusters. The absolute magnitude of a star is inferred from the relative intensities of certain lines in its spectrum, so that the observed apparent magnitude at once enables us to calculate the distance of the star. Adams and Joy have recently determined the luminosities and parallaxes of 500 stars by this spectroscopic method. Of these stars 360 have had their parallaxes previously measured; and the average difference between the spectroscopic and the trigonometric values of the parallax is only the very small angle 0".0037, a highly satisfactory verification.
An indirect method, but a very simple one, and of the greatest value because it provides the key to stellar distances with the least possible calculation, and we can ascertain also the distances of whole classes of stars too remote to be ascertained in any other way at present known.
The problem of spectroscopic determinations of luminosity and parallax has been investigated at Mount Wilson with great thoroughness from all sides, the separate investigations checking each other. A definitive scale for the spectroscopic determination of absolute magnitudes has now been established, and the parallaxes and absolute magnitudes have already been derived for about 1,800 stars.
CHAPTER XLIX
THE NEAREST STARS
Of especial interest are the few stars that we know are the nearest to us, and the following table includes all those whose parallax is 0".20 or greater. There are nineteen in all and nearly half of them are binary systems. The radial motions given are relative to the sun. The transverse velocities are formed by using the measured parallaxes to transform proper motions into linear measures. They are given by Eddington in his "Stellar Movements":
| Star's Name | Magnitude | Parallax in Seconds of Arc | Proper Motion in Seconds of Arc | Linear Velocity Km. per sec. | Radial Velocity Km. per sec. | Spectral Type | Luminosity (Sun=1) | Star Stream | |||
| Groombridge 34 | 8.2 | 0.28 | 2.85 | 48 | ‥ | Ma | 0.010 | I | |||
| Eta Cassiop | 3.6 | 0.20 | 1.25 | 30 | +10 | F8 | 1.4 | I | |||
| Tau Ceti | 3.6 | 0.33 | 1.93 | 28 | -16 | K | 0.50 | II | |||
| Epsilon Erid | 3.3 | 0.31 | 1.00 | 15 | +16 | K | 0.79 | II | |||
| CZ 5h 243 | 8.3 | 0.32 | 8.70 | 129 | +242 | G-K | 0.007 | II | |||
| Sirius | -1.6 | 0.38 | 1.32 | 16 | -7 | A | 48.0 | II | |||
| Procyon | 0.5 | 0.32 | 1.25 | 19 | -3 | F5 | 9.7 | I ? | |||
| Lal. 21185 | 7.6 | 0.40 | 4.77 | 57 | ‥ | Ma | 0.009 | II | |||
| Lal. 21258 | 8.9 | 0.20 | 4.46 | 106 | ‥ | Ma | 0.011 | I | |||
| OA (N) 11677 | 9.2 | 0.20 | 3.03 | 72 | ‥ | ‥ | 0.008 | I | |||
| Alpha Centauri | 0.3 | 0.76 | 3.66 | 23 | -22 | G,K5 |
| I | |||
| OA (N) 17415 | 9.3 | 0.27 | 1.31 | 23 | ‥ | F | 0.004 | II | |||
| Pos. Med. 2164 | 8.8 | 0.29 | 2.28 | 37 | ‥ | K | 0.006 | I | |||
| Sigma Draco | 4.8 | 0.20 | 1.84 | 43 | +25 | K | 0.5 | II | |||
| Alpha Aquilæ | 0.9 | 0.24 | 0.65 | 13 | -33 | A5 | 12.3 | I | |||
| 61 Cygni | 5.6 | 0.31 | 5.25 | 80 | -39 | K5 | 0.10 | I | |||
| Epsilon Indi | 4.7 | 0.28 | 4.67 | 79 | -62 | K5 | 0.25 | I | |||
| Krüger 60 | 9.2 | 0.26 | 0.92 | 17 | ‥ | ‥ | 0.005 | II | |||
| Lacaille 9352 | 7.4 | 0.29 | 7.02 | 115 | +12 | Ma | 0.019 | I | |||
These stars are distant less than five parsecs (about 16 light-years) from the sun, so they make up the closest fringe of the stellar universe immediately surrounding our system. The large number of binary systems is quite remarkable. Why some stars are single and others double is not yet known. By the spectroscopic method the proportion is not so large; Campbell finding that about one quarter of 1,600 stars examined are spectroscopic binaries, and Frost two-fifths to a half. The exceptional number of large velocities is very remarkable; the average transverse motion of the nineteen stars is fifty kilometers per second, whereas thirty is about what would have been expected.
As to star streams to which these nearest stars belong, eleven are in Stream I and eight in Stream II, in close accord with the ratio 3:2 given by the 6,000 stars of Boss's catalogue. "We are not able," says Eddington, "to detect any significant difference between the luminosities, spectra, or speeds of the stars constituting the two streams. The thorough interpenetration of the two star streams is well illustrated, since we find even in this small volume of space that members of both streams are mingled together in just about the average proportion."
The Ring Nebula in Lyra. This is the best example of the annular and elliptic nebulæ, which are not very abundant. (Photo, Mt. Wilson Solar Observatory.)
The Dumb-bell Nebula of Vulpecula. To take the photograph required an exposure of five hours. (Photo, Mt. Wilson Solar Observatory.)
CHAPTER L
ACTUAL DIMENSIONS OF THE STARS
We have seen that the distances of the stars from the solar system are immense beyond conception, and millions upon millions of them are probably forever beyond our power of ascertaining by direct measurement what their distance really is. After we had found the sun's distance and measured the angle filled by his disk, it was easy to calculate his actual size. This direct method, however, fails when we try to apply it to the stars, because their distances are so vast that no star's disk fills an angle of any appreciable size; and even if we try to get a disk with the highest magnifying powers of a great telescope our efforts end only in failure. There is, indeed, no instrumentally appreciable angle to measure.
How then shall we ascertain the actual dimensions of the vast spheres which we know the stars actually are, as they exist in the remotest regions of space? Clearly by indirect methods only, and it must be said that astronomers have as yet no general method that yields very satisfactory results for stellar dimensions. The actual magnitude of the variable system of Algol, Beta Persei, is among the best known of all the stars, because the spectroscope measures the rate of approach and recession of Algol when its invisible satellite is in opposite parts of the orbit; the law of gravitation gives the mass of the star and the size of its orbit, and so the length of the eclipse gives the actual size of the dark, eclipsing body. This figures out to be practically the same size as that of our sun, while Algol's own diameter is rather larger, exceeding a million miles.
If we try to estimate sizes of stars by their brightness merely, we are soon astray. Differences of brightness are due to difference of dimensions, of course, or of light-giving area; but differences of distance also affect the brightness, inversely as the squares of the distances, while differences of temperature and constitution affect, in very marked degree, the intrinsic brilliance of the light-emitting surface of the star. There are big stars and little stars, stars relatively near to us and stars exceedingly remote, and stars highly incandescent as well as others feebly glowing.
We have already shown how the angular diameters subtended by many of the stars have been estimated, through the relation of surface brightness and spectral type. Antares and Betelgeuse appear to be the most inviting for investigation, because their estimated angular diameters are about one-twentieth of a second of arc. This is the way in which their direct measurement is being attempted.
As early as 1890, Michelson of Chicago suggested the application of interference methods to the accurate measurement of very small angles, such as the diameters of the minor planets, and the satellites of Jupiter and Saturn, as well as the arc distance between the components of double stars. Two portions of the object glass are used, as far apart as possible on the same diameter, and the interference fringes produced at the focus of the objective are then the subject of observation. These fringes form a series of equidistant interference bands, and are most distinct when the light comes from a source subtending an infinitesimal angle. If the object presents an appreciable angle, the visibility is less and may even become zero.
Michelson tested this method on the satellites of Jupiter at the Lick Observatory in 1891, and showed its accuracy and practicability. Nevertheless, the method has not been taken up by astronomers, until very recently at the Mount Wilson Observatory, where Anderson has applied it to the measurement of close double stars. It is found that, contrary to general expectation, the method gives excellent results, even if the "seeing" is not the best—2 on a scale of 10, for instance.
To simplify the manipulation of the interferometer, a small plate with two apertures in it is placed in the converging beam of light coming from the telescope objective or mirror. The interference fringes formed in the focal plane are then viewed with an eyepiece of very high power, many thousand diameters. The resolving power of the interferometer is found to be somewhat more than double that of a telescope of the same aperture. By applying the interferometer method to Capella, arc distances of much less than one-twentieth of a second of arc were measured. More recently the method has been applied to the great star Betelgeuse in Orion, whose angular diameter was found to be 0".46, corresponding to an actual diameter of 260,000,000 miles, if the star's parallax is as small as it appears to be.
CHAPTER LI
THE VARIABLE STARS
Spectacular as they are to the layman, novæ, or temporary stars, are to the astronomers simply a class among many thousands of stars which they call variables, or variable stars. There are a few objects classified as irregular variables, one of which is very remarkable. We refer to Eta Argus, an erratic variable in the southern constellation Argo and surrounded by a well-known nebula. There is a pretty complete record of this star. Halley in 1677 when observing at Saint Helena recorded Eta Argus as of the fourth magnitude. During the 18th century, it fluctuated between the fourth magnitude and the second. Early in the 19th it rapidly waxed in brightness, fluctuating between the first and second magnitudes from 1822 to 1836. But two years later its light tripled, rivaling all the fixed stars except Canopus and Sirius. In 1843 it was even brighter for a few months, but since then it has declined fairly steadily, reaching a minimum at magnitude seven and a half in 1886, with a slight increase in brightness more recently. A period of half a century has been suggested, but it is very doubtful if Eta Argus has any regular period of variation.
Another very interesting class of variables is known as the Omicron Ceti type. Nearly all the time they are very faint, but quite suddenly they brighten through several magnitudes, and then fade away, more or less slowly, to their normal condition of faintness. But the extraordinary thing is that most of these variables go through their fluctuations in regular periods: from six months to two years in length. The type star, Omicron Ceti, or Mira, is the oldest known variable, having been discovered by Fabricius in 1596. Most of the time it is a relatively faint star of the 12th magnitude; but once in rather less than a year its brightness runs up to the fourth, third and sometimes even the second magnitude, where it remains for a week or ten days, and afterward it recedes more slowly to its usual faintness, the entire rise and decline in brightness usually requiring about 100 days. The spectrum of Omicron Ceti contains many very bright lines, and a large proportion of the variable stars are of this type.
Another class of variables is designated as the Beta Lyræ type. Their periods are quite regular, but there are two or more maxima and minima of light in each period, as if the variation were caused by superposed relations in some way. Their spectra show a complexity of helium and hydrogen bands. No wholly satisfactory explanation has yet been offered. Probably they are double stars revolving in very small orbits compared with their dimensions, their plane of motion passing nearly through the earth.
But the most interesting of all the variables are those of the Algol type, their light curves being just the reverse of the Omicron Ceti type; that is, they are at their maximum brightness most of the time, and then suffer a partial eclipse for a relatively brief interval. Algol goes through its variations so frequently that its period is very accurately known; it is 2d. 20h. 48m. 55.4s. For most of this period Algol is an easy second magnitude star; then in about four and a half hours it loses nearly five-sixths of its light, receding to the fourth magnitude. Here at minimum it remains for fifteen or twenty minutes, and then in the next three and a half hours it regains its full normal brilliancy of the second magnitude. During these fluctuations the star's spectrum undergoes no marked changes. The spectra of all the Algol variables are of the first or Sirian type.
To explain the variation of the Algol type of variables is easy: a dark, eclipsing body, somewhat smaller than the primary is supposed to be traveling round it in an orbit lying nearly edgewise to our line of sight. The gravitation of this dark companion displaces Algol itself alternately toward and from the earth, because the two bodies revolve round their common center of gravity. With the spectroscope this alternate motion of Algol, now advancing and now receding at the rate of 26 miles per second, has been demonstrated; and the period of this motion synchronizes exactly with the period of the star's variability.
Russell and Shapley have made extended studies of the eclipsing binaries, and developed the formulæ by which the investigations of their orbits are conducted. Heretofore, visual binaries and spectroscopic binaries afforded the only means of deriving data regarding double systems, but it is now possible to obtain from the orbits of eclipsing variables fully as much information relating to binary systems in general and their bearing on stellar evolution. After an orbit has been determined from the photometric data of the light curve, the addition of spectroscopic data often permits the calculation of the masses, dimensions and densities in terms of the sun. Shapley's original investigation included the orbits of ninety eclipsing variables, and with the aid of hypothetical parallaxes, he computed the approximate position of each system in space. The relation to the Milky Way is interesting, the condensation into the Galactic plane being very marked; only thirteen of the ninety systems being found at Galactic latitudes exceeding 30 degrees.
If we can suppose the variable stars covered with vast areas of spots, perhaps similar to the spots on the sun, and then combine the variation of these spot areas with rotation of the star on its axis, there is a possibility of explanation of many of the observed phenomena, especially where the range of variation is small. But for the Omicron Ceti type, no better explanation offers than that afforded by Sir Norman Lockyer's collision theory. First he assumes that these stars are not condensed bodies, but still in the condition of meteoric swarms, and the revolution of lesser swarms around larger aggregations, in elliptic orbits of greater or less eccentricity, must produce vast multitudes of collisions; and these collisions, taking place at pretty regular periods, produce the variable maximum light by raising hosts of meteoric particles to a state of incandescence simultaneously.
The catalogues of variable stars now contain many thousands of these objects. They are often designated by the letters R, S, T, and so on, followed by the genitive form of the name of the constellation wherein they are found. Most of the recently found variables have a range of less than one magnitude. They are so distributed as to be most numerous in a zone inclined about 18 degrees to the celestial equator, and split in two near where the cleft in the Galaxy is located. Nearly all the temporary stars are in this duplex region. Bailey of Harvard a quarter century ago began the investigation of variables in close star clusters, where they are very abundant, with marked changes of magnitude within only a few hours.
Many amateur astronomers afford very great assistance to the professional investigator of variable stars by their cooperation in observing these interesting bodies, in particular the American Association of Observers of Variable Stars, organized and directed by William Tyler Olcott.
For a high degree of accuracy in determining stellar magnitudes the photo-electric cell is unsurpassed. Stebbins of Urbana has been very successful in its application and he discovered the secondary minimum of Algol with the selenium cell. His most recent work was done with a potassium cell with walls of fused quartz, perfected after many trial attempts. The stars he has recently investigated are Lambda Tauri, and Pi Five Orionis. Combining results with those reached by the spectroscope, the masses of the two component stars of the former are 2.5 and 1.0 that of the sun, and the radii are 4.8 and 3.6 times the sun's.
Russell of Princeton thinks it probable that similar causes are at work in all these variables. In the case of the typical Novæ there is evidence that when the outburst takes place a shell of incandescent gas is actually ejected by the star at a very high velocity. What may be the forces that cause such an explosion can only be guessed. Repeated outbursts have not, in the case of T Pyxidis, destroyed the star, because it has gone through this process three times in the past thirty years. Russell inclines to regard it as a standard process occurring somewhere in the stellar universe probably as often as once a year.
Novæ, then, cannot be due to collisions between two stars, for even if we suppose the stars to be a thousand millions in number, no two should collide except at average intervals of many million years. The idea is gaining ground that the stars are vast storehouses of energy which they are gradually transforming into heat and radiating into space. "Under ordinary circumstances, it is probable that the rate of generation of heat is automatically regulated to balance the loss by radiation. But it is quite conceivable that some sudden disturbance in the substance of the star, near the surface, might cause an abrupt liberation of a great amount of energy, sufficient to heat the surface excessively, and drive the hot material off into infinite space, in much the form of a shell of gas, as seems to have been observed in the case of Nova Aquilæ…. With the rapid advance of our knowledge of the properties of the stars on one hand, and of the very nuclei of atoms on the other, we may, perhaps before many years have passed, find ourselves nearer a solution of the problem."
The Cepheid variables increase very rapidly in brightness from their least light to their maximum, and then fade out much more slowly, with certain irregularities or roughnesses of their light-curves when declining. Their spectral lines also shift in period with their variations of light. In the case of these variables, whose regular fluctuation of light cannot be due to eclipse, and is as a rule embraced within a few days, there is a fluctuation in color also between maximum and minimum, as if there were a periodic change in the star's physical condition. Eddington and Shapley advocate the theory of a mechanical pulsation of the star as most plausible. Knowledge of the internal conditions of the stars make it possible to predict the period of pulsation within narrow limits; and for Delta Cephei this theoretical period is between four and ten days. Its observed period is five and one-third days, and corresponding agreement is found in all the Cepheids so far tested.
Shapley of Mount Wilson finds that the Cepheid variables with periods exceeding a day in length all lie close to the Galactic lane. So greatly have the studies of these objects progressed that, as before remarked, when we know the star's period, we can get its absolute magnitude, and from this the star's distance. On all sides of the sun, the distances of the Cepheids range up to 4,000 parsecs. So they indicate the existence of a Galactic system far greater in extent than any previously dealt with.
CHAPTER LII
THE NOVÆ, OR NEW STARS
New stars, or temporary stars, we have already mentioned in connection with variables. They are, next to comets, the most dramatic objects in the heavens. They may be variable stars which, in a brief period, increase enormously in brightness, and then slowly wane and disappear entirely, or remain of a very faint stellar magnitude.
In the ancient historical records are found accounts of several such stars. For instance, in the Chinese annals there is an allusion to such a stellar outburst in the constellation of Scorpio, B. C. 134. This was observed also by Hipparchus and, no doubt, it was the immediate incentive which led to his construction of the first known catalogue of stars, so that similar happenings might be detected in the future. In November, 1572, Tycho Brahe observed the most famous of all new stars, which blazed out in the constellation Cassiopeia. In something over a year it had completely disappeared.
In 1604-1605 a new star of equal brightness was seen in Ophiuchus by Kepler; it also faded out to invisibility in 1606. Kepler and Tycho printed very complete records of these remarkable objects. The eighteenth century passed without any new stars being seen or recorded. There was one of the fifth magnitude in 1848, and another of the seventh magnitude in 1860; and in May, 1866, a star of the second magnitude suddenly made its appearance in Corona Borealis; and one of the third magnitude in Cygnus in November, 1876. The latter was fully observed by Schmidt of Athens and became a faint telescopic star within a few weeks. It is now of the fifteenth magnitude.
In 1885 astronomers were surprised to find suddenly a new star of the sixth magnitude very close to the brightest part of the great nebula in Andromeda; it ran its course in about six months, fading with many fluctuations in brightness, and no star is now visible in its position even with the telescope. Stars of this class are known to astronomers as Novæ, usually with the genitive of the constellation name, as Nova Andromedæ.
In 1891-1892 Nova Aurigæ made its spectacular appearance and yielded a distinctly double and complex spectrum for more than a month. Many pairs of lines indicated a community of origin as to substance, and accurate measurement showed a large displacement with a relative velocity of more than 500 miles per second. For each bright hydrogen line displaced toward the red there was a dark companion line or band about equally displaced toward the violet much as if the weird light of Nova Aurigæ originated in a solid globe moving swiftly away from us and plunging into an irregular nebulous mass as swiftly approaching us. Parallax observations of Nova Aurigæ made it immensely remote, perhaps within the Galaxy, and it still exists as a faint nebulous star.
In February, 1901, in the constellation Perseus appeared the most brilliant nova of recent years. It was first discovered by Dr. Anderson, an amateur of Glasgow, and at maximum on February 23 it outshone Capella. There were many unusual fluctuations in its waning brightness. Its spectrum closely resembled that of Nova Aurigæ, with calcium, helium, and hydrogen lines. In August, 1901, an enveloping nebula was discovered, and a month later certain wisps of this nebulosity appeared to have moved bodily, at a speed seventy-fold greater than ever previously observed in the stellar universe.
According to Sir Norman Lockyer's meteoritic hypothesis, a vast nebulous region was invaded, not by one but by many meteor swarms, under conditions such that the effects of collision varied greatly in intensity. The most violent of these collisions gave birth to Nova Persei itself, and the least violent occurred subsequently in other parts of the disturbed nebula, perhaps immeasurably removed. This explanation would avoid the necessity of supposing actual motion of matter through space at velocities heretofore unobserved and inconceivably high. A recent photograph of Nova Persei, by Ritchey, reveals a nebulous ring of regular structure surrounding the star. The great power of the 60-inch has made it possible to photograph even the spectra of many of the novæ of years ago which are now very faint. After the lapse of years the characteristic lines of the nebular spectrum generally vanish, as if the star had passed out of the nebula—a plunge into which is generally thought to be the cause of the great and sudden outburst of light.
Many novæ have recently been found in the spiral nebulæ, especially in the great nebula of Andromeda.
CHAPTER LIII
THE DOUBLE STARS
Examining individual stars of the heavens more in detail, thousands of them are found to be double; not the stars that appear double to the naked eye, as Theta Tauri, Mizar, Epsilon Lyræ, and others; but pairs of stars much closer together, and requiring the power of the telescope to divide or separate them. Only a very few seconds apart they are or, in many cases, only the merest fraction of a second of arc. Some of them, called binaries, are found to be revolving around a common center, sometimes in only a few years, sometimes in stately periods of hundreds of years. Many such binary systems are now known, and the number is constantly increasing. Castor is one, Gamma Virginis another, Sirius also is one of these binaries, and a most interesting one, having a period of revolution of about 52 years.
Aitken, of the Lick Observatory, in his work on binary stars, directs special attention to the correlation between the elements of known binary orbits and the star's spectral type, and presents a statistical study of the distribution of 54,000 visual double stars, of which the spectra of 3919 are known. That the masses of binary systems average about twice that of the sun's mass has long been known, and this fact can be employed with confidence in estimates of the probable parallax of these systems. Aitken applies the test to fourteen visual systems for which the necessary data are available, and deduces for them a mean mass of 1.76 times that of the sun. For the spectroscopic binaries the masses are much greater.
Triple, quadruple and multiple stars are less frequent; but many exceedingly interesting objects of this class exist. Epsilon Lyræ is one, a double-double, or four stars as seen with slender telescopic power, and six or seven stars with larger instruments. Sigma Orionis and 12 Lyncis, also Theta Cancri and Mu Bootis are good examples of triple stars.
CHAPTER LIV
THE STAR CLUSTERS
From multiple stars the transition is natural to star clusters although the gap between these types of stellar objects is very broad. The familiar group of the winter sky known as the Pleiades is a loose cluster, showing relatively very few stars even in telescopes or on photographic plates. The "Beehive," or cluster known as Praesepe in Cancer, and a double group in the sword-handle of Perseus, both just visible to the naked eye, are excellent examples of star clusters of the average type. When the moon is absent, they are easily recognized without a telescope as little patches of nebulous light; but every increase of optical power adds to their magnificence.
Then we come in regular succession to the truly marvelous globular clusters, that for instance in Hercules. Messier 13, a recent photograph of which, taken by Ritchey with the 60-inch reflector on Mount Wilson, reveals an aggregation of more than 50,000 stars. But the finest specimens are in the southern hemisphere. Sir John Herschel spent much time investigating them nearly a century ago at the Cape of Good Hope. His description of the cluster in the constellation of Centaurus is as follows: "The noble globular cluster Omega Centauri is beyond all comparison the richest and largest object of the kind in the heavens. The stars are literally innumerable, and as their total light when received by the naked eye affects it hardly more than a star of the fifth or fourth to fifth magnitude, the minuteness of each star may be imagined."
Others of these clusters are so remote that the separate stars are not distinguishable, especially at the center, and their distances are entirely beyond our present powers of direct measurement, although methods of estimating them are in process of development. If gravitation is regnant among the uncounted components of stellar clusters, as doubtless it is, these stars must be in rapid motion, although our photographs of measurements have been made too recently for us to detect even the slightest motion in any of the component stars of a cluster. The only variations are changes of apparent magnitude, of a type first detected in a large number of stars in Omega Centauri, by Bailey of Harvard, who by comparison of photographs of the globular clusters was the first to find variable stars quite numerous in these objects. Their unexplained variations of magnitude take place with great rapidity, often within a few hours.
There are about a hundred of these globular clusters, and the radial velocities of ten of them have been measured by Slipher and found to range from a recession of 410 to an approach of 225 kilometers per second. These excessive velocities are comparable with those found for the spiral nebulæ. Shapley has estimated the distances of many of these bodies, which contain a large number of variable stars of the Cepheid type. By assuming their absolute magnitudes equal to those of similar Cepheids at known distances, he finds their distance represented by the inconceivably minute parallax of 0".00012, corresponding to 30,000 light-years. This research also places the globular clusters far outside and independent of our Galactic system of stars. The distribution of the globular clusters has also been investigated, and these interesting objects are found almost exclusively in but one hemisphere of the sky. Its center lies in the rich star clouds of Scorpio and Sagittarius. Success in finding the distances of these objects has made it possible to form a general idea of their distribution in three-dimensional space.
The numerous variable stars in any one cluster are remarkable for their uniformity. Accepting variables of this type as a constant standard of absolute brightness, and assuming that the differences of average magnitude of the variables in different clusters are entirely due to differences of distance, the relative distances of many clusters were ascertained with considerable accuracy. Then it was found that the average absolute magnitude of the twenty-five brightest stars in a cluster is also a uniform standard, or about 1.3 magnitudes brighter than the mean magnitude of the variables. This new standard was employed in ascertaining the distances of other clusters not containing many variables.
Shapley further shows that the linear dimensions of the clusters are nearly uniform, and the proper relative positions in space are charted for sixty-nine of these objects. We can determine the scale of the charts, if we know the absolute brightness of our primary standard—the variable stars; and this is deduced from a knowledge of the distances of variables of the same type in our immediate stellar system.
The most striking of all the globular clusters, Omega Centauri, comes out the nearest; nevertheless it is distant 6.5 kiloparsecs. A kiloparsec is a thousand parsecs, and is the equivalent of 3,256 light-years. At the inconceivable distance of sixty-seven kiloparsecs, or more than 200,000 light-years, is the most remote of the globular clusters, known to astronomers as N.G.C. 7006, from its number in the catalogue which records its position in the sky, the New General Catalogue of nebulæ by Dreyer of Armagh.
The clusters are widely scattered, and their center of diffusion is about twenty kiloparsecs on the Galactic plane toward the region of Scorpio-Sagittarius. Marked symmetry with reference to this plane makes it evident that the entire system of globular clusters is associated with the Galaxy itself. But to conceive of this it is necessary to extend our ideas of the actual dimensions of the Galactic system. Almost on the circumference of the great system of globular clusters our local stellar system is found, and it contains probably all the naked-eye stars, with millions of fainter ones. Its size seems almost diminutive, only about one kiloparsec in diameter. The relative location of our local stellar system shows why the globular clusters appear to be crowded into one hemisphere only.
Shapley suggests that globular clusters can exist only in empty space, and that when they enter the regions of space tenanted by stars, they dissolve into the well-known loose clusters and the star clouds of the Milky Way. Strangely the radial velocities of the clusters already observed show that most of them are traveling toward this region, and that some will enter the stellar regions within a period of the order of a hundred million years.
The actual dimensions of globular clusters are not easy to determine, because the outer stars are much scattered. To a typical cluster, Messier 3, Shapley assigns a diameter of 150 parsecs, which makes it comparable with the size of the stellar cluster to which the sun belongs. Also on certain likely assumptions, he finds that the diameter of the great cluster in Hercules, the finest one in our northern sky, is about 350 parsecs, and its distance no less than 30,000 parsecs; in other words, the staggering distance that light would require 9,750,000 years to travel over. While these distances can never be verified by direct measurement, it lends great weight to the three methods of indirect measurement, or estimation, (1) from the diameter of the image of the clusters, (2) from the mean magnitude of the twenty-five brightest stars, and (3) from the mean magnitude of the short period variables, that they are in excellent agreement.
CHAPTER LV
MOVING CLUSTERS
Recent researches on the proper motions of stars have brought to light many groups of stars whose individual members have equal and parallel velocities. Eddington calls these moving clusters. The component stars are not exceptionally near to each other, and it often happens that other stars not belonging to the group are actually interspersed among them. They may be likened to double stars which are permanent neighbors, with some orbital motion, though exceedingly slow.
The connection is rather one of origin; occurring in the same region of space, perhaps, from a single nebula. They set out with the same motion, and have "shared all the accidents of the journey together." Their equality of motion is intact because any possible deflections by the gravitative pull of the stellar system is the same for both. Mutual attraction may tend to keep the stars together, but their community of motion persists chiefly because no forces tend to interfere with it. In this way physically connected pairs may be separated by very great distances.
So with the moving clusters: their component stars may be widely separate on the celestial sphere, but equality of their motions affords a clue to their association in groups. The Hyades, a loose cluster in Taurus, is a group of thirty-nine stars, within an area of about 15 degrees square, which has been pretty fully investigated, especially by the late Professor Lewis Boss; and no doubt many fainter stars in the same region will ultimately be found to belong to the same group.
If we draw arrows on a chart representing the amount and direction of the proper motions of these stars, these arrows must all converge toward a point. This shows that their motions are parallel in space. It is a relatively compact group, and the close convergence shows that their individual velocities must agree within a small fraction of a kilometer per second. Radial velocity measures of six of the component stars are in very satisfactory accord, giving 45.6 kilometers per second for the entire group.
We can get the transverse velocity, and therefrom the distances of the stars, which are among the best known in the heavens, because the proper motions are very accurately known. The mean parallax of the group by this indirect method comes out 0".025, agreeing almost exactly with the direct determination by photography, 0".023, by Kapteyn, De Sitter, and others.
Eddington concludes that this Taurus group is a globular cluster with a slight central condensation. Its entire diameter is about ten parsecs, and its known motion enables us to trace its past and future history. It was nearest the sun 800,000 years ago, when it was at about half its present distance. Boss calculated that in 65 million years, if the present motion is maintained, this group will have receded so far as to appear like an ordinary globular cluster 20' in diameter, its stars ranging from the ninth to the twelfth apparent magnitude. We may infer that the motion will likely continue undisturbed, because there are interspersed among the group many stars not belonging to it, and these have neither scattered its members nor sensibly interfered with the parallelism of their motion.
Another moving cluster, the similarity of proper motion of whose component stars was first pointed out by Proctor, is known as the Ursa Major system, which embraces primarily Beta, Gamma, Delta, Epsilon, and Zeta Ursæ Majoris, or five of the seven stars that mark the familiar Dipper. But as many as eight other stars widely scattered are thought to belong to the same system, including Sirius and Alpha Coronæ Borealis. The absolute motion amounts to 28.8 kilometers per second, and is approximately parallel to the Galaxy. Turner has made a model of the cluster, which has the form of a flat disk.
Among stars of the Orion type of spectrum are several examples of moving clusters. The Pleiades together with many fainter stars form another moving cluster; as also do the brighter stars of Orion, together with the faint cloudlike extensions of the great nebula in Orion, whose radial velocity agrees with that of the stars in the constellation. Still another very remarkable moving cluster is in Perseus, first detected by Eddington, and embracing eighteen stars, the brightest of which is Alpha Persei.
The further discovery of moving clusters is most important in the future development of stellar astronomy, because with their aid we can find out the relative distribution, luminosity, and distance of very remote stars. So far the stars found associated in groups are of early types of spectrum; but the Taurus cluster embraces several members equally advanced in evolution with the sun, and in the more scattered system of Ursæ Major there are three stars of Type F.
"Some of these systems," Eddington concludes, "would thus appear to have existed for a time comparable with the lifetime of an average star. They are wandering through a part of space in which are scattered stars not belonging to their system—interlopers penetrating right among the cluster stars. Nevertheless, the equality of motion has not been seriously disturbed. It is scarcely possible to avoid the conclusion that the chance attractions of stars passing in the vicinity have no appreciable effect on stellar motions; and that if the motions change in course of time (as it appears they must do) this change is due, not to the passage of individual stars, but to the central attraction of the whole stellar universe, which is sensibly constant over the volume of space occupied by a moving cluster."
CHAPTER LVI
THE TWO STAR STREAMS
Consider the ships on the Atlantic voyaging between Europe and America: at any one time there may be a hundred or more, all bound either east or west, some moving in interpenetrating groups, individuals frequently passing each other, but rarely or never colliding. We might say, there are two great streams of ships, one moving east and the other west.
Now in place of each ship, imagine a hundred ships, and magnify their distances from each other to the vast distances that the stars are from each other, and all in motion in two great streams as before. This will convey some idea of the relatively recent discovery, called by astronomers "star-streaming."
Early in this century the investigation of moving clusters began to reveal the fact that the motions of the stars were not at random throughout the universe, and about 1904 Kapteyn was the first to show that the stellar motions considered in great groups are very far from being haphazard, but that the stars tend to travel in two great streams, or favored directions. This was ascertained by analyzing the proper motions of stars in the sky, many thousands of them, and correcting all for the effect which the known motion of the sun would have upon them. The corrected motion, or part that is left over, is known as the star's own motion, or motus peculiaris.
This important investigation was very greatly facilitated by the general catalogue of 6,188 stars well distributed over the entire sky, the work of the late Professor Boss. It was published by the Carnegie Institution of Washington, and includes all stars down to the sixth magnitude. Boss was very critical in the matter of stellar positions and proper motions and his work is the most accurate at present available. Excluding stars of the Orion type and the known members of moving clusters, Kapteyn's investigation was based on 5,322 stars, which he divided into seventeen regions of the sky, each northern region having an antipodal one in the southern hemisphere.
Mathematical analysis of these regions showed them all in substantial agreement, with one exception, and enabled Kapteyn to draw the conclusion that the stars of one stream, called Drift I, move with a speed of thirty-two kilometers per second, while those of the other, Drift II, travel with a speed of eighteen kilometers per second. Their directions are not, like those of east and west bound ships, 180 degrees from each other, but are inclined at an angle of 100 degrees. Drift I embraces about three-fifths of the stars, and Drift II the remaining two-fifths. Quite as remarkable as the drifts themselves is the fact that the relative motion of the two is very closely parallel to the plane of the Milky Way.
This epochal research has very great significance in all investigations of stellar motions, and it has been verified in various ways, particularly by the Astronomer Royal, Sir Frank Dyson, who limited the stars under consideration to 1,924 in number, but all having very large proper motions. In this way the two streams are even more characteristically marked. But radial velocity determinations afford the ultimate and most satisfactory test, and Campbell has this investigation in hand, classifying the stars in their streaming according to the type.
Type A stars are so far found to be confirmatory. Turning to the question of physical differences between the stars of the two streams, Eddington inquires into the average magnitude of the stars in both drifts, and their spectral type. Also whether they are distributed at the same distance from the sun, and in the same proportion in all parts of the sky. His conclusion is that there is no important difference in the magnitudes of the stars constituting the two drifts. Regarding their spectra, stars of early and late types are found in both streams, with a somewhat higher proportion of late types among the stars of Drift II than those of Drift I. Campbell and Moore of the Lick Observatory have investigated seventy-three planetary nebulæ which exhibit the phenomena of star-streaming, and have motions which are characteristic of the stars.
Dealing with the very important question whether the two streams are actually intermingled in space, Eddington finds them nearly at the same mean distance and thoroughly intermingled, and there is no possible hypothesis of Drifts I and II passing one behind the other in the same line of sight. A third drift, to which all the Orion stars belong, is under investigation, together with comprehensive analysis of the drifts according to the spectral type of all the stars included.
The farther research on star-streaming is pushed, the more it becomes evident that a third stream, called Drift O, is necessary, especially to include B-type stars. The farther we recede from the sun, the more this drift is in evidence. At the average distances of B-type stars, the observed motions are almost completely represented by Drift O alone. Halm of Cape Town concludes from recent investigations that the double-drift phenomena (Drifts I and II) is of a distinctly local character, and concerns chiefly the stars in the vicinity of the solar system; while stars at the greatest distances from the sun belong preeminently to Drift O.
The 60-inch reflector on Mount Wilson gathers sufficient light so that the spectra of very faint stars can be photographed, and a discussion of velocities derived in this manner has shown that Kapteyn's two star streams extend into space much farther than it was possible to trace them with the nearer stars. Star-streaming, then, may be a phenomenon of the widest significance in reference to the entire universe.
As to the fundamental causes for the two opposite and nearly equal star streams, it is early perhaps to even theorize upon the subject. Eddington, however, finds a possible explanation in the spiral nebulæ, which are so numerous as to indicate the certainty of an almost universal law compelling matter to flow in these forms. Why it does so, we cannot be said to know; but obviously matter is either flowing into the nucleus from the branches of the spiral, or it is flowing out from the nucleus into the branches. Which of the two directions does not matter, because in either case there would be currents of matter in opposite directions at the points where the arms merge in the central aggregation. The currents continue through the center, because the stars do not interfere with one another's paths. As Eddington concludes: "There then we have an explanation of the prevalence of motions to and fro in a particular straight line; it is the line from which the spiral branches start out. The two star streams and the double-branched spirals arise from the same cause."
CHAPTER LVII
THE GALAXY OR MILKY WAY
Grandest of all the problems that have occupied the mind of man is the distribution of the stars throughout space. To the earliest astronomers who knew nothing about the distances of the stars, it was not much of a problem because they thought all the fixed stars were attached to a revolving sphere, and therefore all at essentially the same distance; a very moderate distance, too. Even Kepler held the idea that the distances of individual stars from each other are much less than their distances from our sun.
Thomas Wright, of Durham, England, seems to have been the first to suggest the modern theory of the structure of the stellar universe, about the middle of the eighteenth century. His idea was taken up by Kant who elaborated it more fully. It is founded on the Galaxy, the basal plane of stellar distribution, just as the ecliptic is the fundamental circle of reference in the solar system.
What is the Galaxy or Milky Way?
Here is a great poet's view of the most poetic object in all nature:
A broad and ample road, whose dust is gold,
And pavement stars, as stars to thee appear
Seen in the Galaxy, that Milky Way
Which nightly as a circling zone thou seest
Powder'd with stars.
Milton, P. L. vii, 580.
Were the earth transparent as crystal, so that we could see downward through it and outward in all directions to the celestial sphere, the Galaxy or Milky Way would appear as a belt or zone of cloudlike luminosity extending all the way round the heavens. As the horizon cuts the celestial sphere in two, we see at anyone time only one-half of the Milky Way, spanning the dome of the sky as a cloudlike arch.
As the general plane of the Galaxy makes a large angle with our equator, the Milky Way is continually changing its angle with the horizon, so that it rises at different elevations. One-half of the Milky Way will always be below our horizon, and a small region of it lies so near the south pole of the heavens that it can never be seen from medium northern latitudes.
Galileo was the first to explain the fundamental mystery of this belt, when he turned his telescope upon it and found that it was not a continuous sheet of faint light, as it seemed to be, but was made up of countless numbers of stars, individually too faint to be visible to the naked eye, but whose vast number, taken in the aggregate, gave the well-known effect which we see in the sky. In some regions, as Perseus, the stars are more numerous than in others, and they are gathered in close clusters. The larger the telescope we employ, the greater the number of stars that are seen as we approach the Galaxy on either side; and the farther we recede from the Galaxy and approach either of its poles fewer and fewer stars are found. Indeed, if all the stars visible in a 12-inch telescope could be conceived as blotted out, nearly all the stars that are left would be found in the Galaxy itself.
The naked eye readily notes the variations in breadth and brightness of the galactic zone. Nearly a third of it, from Scorpio to Cygnus, is split into two divisions nearly parallel. In many regions its light is interrupted, especially in Centaurus, where a dark starless region exists, known as the "coal sack." Sir John Herschel, who followed up the stellar researches of his father, Sir William, in great detail, places the north pole of the Galactic plane in declination 37 degrees N., and right ascension 12 h. 47 m. This makes the plane of the Milky Way lie at an angle of about 60 degrees with the ecliptic, which it intersects not far from the solstices.
Now Kant, in view of the two great facts about the Galaxy known in his time, (1) that it wholly encircles the heavens, and (2) that it is composed of countless stars too faint to be individually visible to the naked eye, drew the safe conclusions that the system of the stars must extend much farther in the direction of the Milky Way than in other directions.
This theory of Kant was next investigated from an observational standpoint by Sir William Herschel, the ultimate goal of whose researches was always a knowledge of the construction of the heavens. The present conclusion is that we may regard the stellar bodies of the sidereal universe as scattered, without much regard to uniformity, throughout a vast space having in general the shape of a thick watch, its thickness being perhaps one-tenth its diameter. On both sides of this disk of stars, and clustered about the poles of the sidereal system are the regions occupied by vast numbers of nebulæ. The entire visible universe, then, would be spheroidal in general shape. The plane of the Milky Way passes through the middle of this aggregation of stars and nebulæ, and the solar system is near the center of the Milky Way. Throughout the watch-form space the stars are clustered irregularly, in varied and sometimes fantastic forms, but without approach to order or system. If we except some of the star groups and star clusters and consider only the naked-eye stars, we find them scattered with fair approach to uniformity.
Star Clouds and Black Holes in Sagittarius. The dark rifts and lanes resemble those in the nearby Milky Way. (Photo, Yerkes Observatory.)
The Great Nebula of Andromeda, Largest (Apparently) of all the Spiral Nebulæ. This nebula can be seen very faintly with the naked eye, but no telescope has yet resolved it into separate stars. (Photo, Yerkes Observatory.)
The watch-shaped disk is not to be understood as representing the actual form of the stellar system, but only in general the limits within which it is for the most part contained.
A vigorous attack on the problem of the evolution and structure of the stellar universe as a whole is now being conducted by cooperation of many observatories in both hemispheres. It is known as the Kapteyn "Plan of Selected Areas," embracing 206 regions which are distributed regularly over the entire sky. Besides this a special plan includes forty-six additional regions, either very rich or extremely poor in stars, or to which other interest attaches.
Of all investigators Kapteyn has gone into the question of our precise location in the Milky Way most thoroughly, concluding that the solar system lies, not at the center in the exact plane, but somewhat to the north of the Galaxy. Discussing the Sirian stars he finds that if stars of equal brightness are compared, the Sirians average nearly three times more distance from the sun than those of the solar type. So, probably, the Sirians far exceed the Solars in intrinsic brightness. Farther, Kapteyn concludes that the Galaxy has no connection with our solar system, and is composed of a vast encircling annulus or ring of stars, far exceeding in number the stars of the great central solar cluster, and everywhere exceedingly remote from these stars, as well as differing from them in physical type and constitution. So it would be mainly the mere element of distance that makes them appear so faint and crowded thickly together into that gauzy girdle which we call the Galaxy.
The Milky Way reveals irregularities of stellar density and star clustering on a large scale, with deep rifts between great clouds of stars. Modern photographs, particularly those of Barnard in Sagittarius, make this very apparent. Within the Milky Way, nearly in its plane and almost central, is what Eddington terms the inner stellar system, near the center of which is the sun. Surrounding it and near its plane are the masses of star clouds which make up the Milky Way. Whether these star clouds are isolated from the inner system or continuous with it, is not yet ascertained.
The vast masses of the Milky Way stars are very faint, and we know nothing yet as to their proper motions, their radial motions, or their spectra. Probably a few stars as bright as the sixth magnitude are actually located in the midst of the Milky Way clusters, the fainter ninth magnitude stars certainly begin the Milky Way proper, while the stars of the twelfth or thirteenth magnitude carry us into the very depths of the Galaxy.
It is now pretty generally believed that many of the dark regions of the Milky Way are due not to actual absence of stars so much as to the absorption of light by intervening tracts of nebulous matter on the hither side of the Galactic aggregations and, probably in fact, within the oblate inner stellar system itself. Easton has made many hundred counts of stars in galactic regions of Cygnus and Aquila where the range of intensity of the light is very marked; in fact, the star density of the bright patches of the Galaxy is so far in excess of the density adjacent and just outside the Milky Way, that the conclusion is inevitable that this excess is due to the star clouds.
Of the distance of the Milky Way we have very little knowledge. It is certainly not less than 1,000 parsecs, and more likely 5,000 parsecs, a distance over which light would travel in about 16,000 years. Quite certainly all parts of the Galaxy are not at the same distance, and probably there are branches in some regions that lie behind one another. While the general regions of the nebulæ are remote from the Galactic plane, the large irregular nebulæ, as the Trifid, the Keyhole, and the Omega nebulæ, are found chiefly in the Milky Way.
In addition to the irregular nebulæ many types of stellar objects appear to be strongly condensed toward the Milky Way, but this may be due to the inner stellar system, rather than a real relation to Galactic formations. Quite different are the Magellanic clouds, which contain many gaseous nebulæ and are unique objects of the sky, having no resemblance to the true spiral nebulæ which, as a rule, avoid the Galactic regions. Worthy of note also is the theory of Easton that the Milky Way has itself the form of a double-branched spiral, which explains the visible features quite well, but is incapable of either disproof or verification. The central nucleus he locates in the rich Galactic region of Cygnus, with the sun well outside the nucleus itself. By combining the available photographs of the Galaxy, he has produced a chart which indicates in a general way how the stellar aggregations might all be arrayed so as to give the effect of the Galaxy as we see it.
Shapley, at Mount Wilson, has studied the structure of the Galactic system, in which he has been aided by Mrs. Shapley. An interesting part of this work relates to the distribution of the spiral nebulæ, and to certain properties of their systematic recessional motion, suggesting that the entire Galactic system may be rapidly moving through space. Apparently the spiral nebulæ are not distant stellar organizations or "island universes," but truly nebular structures of vast volume which in general are actively repelled from stellar systems. A tentative cosmogonic hypothesis has been formulated to account for the motions, distribution, and observed structure of clusters and spiral nebulæ.
An additional great problem of the Galaxy is a purely dynamical one. Doubtless it is in some sort of equilibrium, according to Eddington, that is to say, the individual stars do not oscillate to and fro across the stellar system in a period of 300 million years, but remain concentrated in clusters as at present. Poincaré has considered the entire Milky Way as in stately rotation, and on the assumption that the total mass of the inner stellar system is 1,000,000,000 times the sun's mass, and that the distance of the Milky Way is 2,000 parsecs, the angular velocity for equilibrium comes out 0".5 per century. That is to say, a complete revolution would take place in about 250 million years.
CHAPTER LVIII
STAR CLOUDS AND NEBULÆ
From star clusters to nebulæ, only a century ago, the transition was thought to be easy and immediate. Accuracy in determining the distances of stars was just beginning to be reached, the clusters were obviously of all degrees of closeness following to the verge of irresolvability, and it was but natural to jump to the conclusion that the mystery of the nebulæ consisted in nothing but their vaster distance than that of clusters, and it was believed that all nebulæ would prove resolvable into stars whenever telescopes of sufficiently great power could be constructed.
But the development of the spectroscope soon showed the error of this hypothesis, by revealing bright lines in the nebular spectra showing that many nebulæ emit light that comes from glowing incandescent gas, not from an infinitude of small stars.
In pre-telescope days nothing was known about the nebulæ. The great nebula in Andromeda, and possibly the great nebula in Orion, are alone visible to the naked eye, but as thus seen they are the merest wisps of light, the same as the larger clusters are. Galileo, Huygens and other early users of the telescope made observations of nebulæ, but long-focus telescopes were not well adapted to this work. Simon Mayer has left us the first drawing of a nebula, the Orion nebula as he saw it in 1612. The vast light-gathering power of the reflectors built by Sir William Herschel first afforded glimpses of the structure of the nebulæ, and if his drawings are critically compared with modern ones, no case of motion with reference to the stars or of change in the filaments of the nebulæ themselves has been satisfactorily made out.
Only very recently has the distance of a nebula been determined, and the few that have been measured seem to indicate that the nebulæ are at distances comparable with the stars. Of all celestial objects the nebulæ fill the greatest angles, so that we are forced to conclude, with regard to the actual size of the greater nebulæ as they exist in space, that they far surpass all other objects in bulk.
Photography invaded the realm of the nebulæ in 1880, when Dr. Henry Draper secured the first photograph of the nebula of Orion. Theoretically photography ought to help greatly in the study of the nebulæ, and enable us in the lapse of centuries to ascertain the exact nature of the changes which must be going on. The differences of photographic processes, of plates, of exposure and development produce in the finished photograph vastly greater differences than any actual changes that might be going on, so that we must rely rather on optical drawings made with the telescope, or on drawings made by expert artists from photographs with many lengths of exposure on the same object.
The great work on nebulæ and star clusters recently concluded by Bigourdan of the Paris Observatory and published in five volumes received the award of the gold medal of the Royal Astronomical Society. While D'Arrest measured about 2,000 nebulæ, and Sir John Herschel about double that number in both hemispheres, Bigourdan has measured about 7,000. His work forms an invaluable lexicon of information concerning the nebulæ.
Classification of the nebulæ is not very satisfactory, if made by their shapes alone. There are perhaps fifteen thousand nebulæ in all that have been catalogued, described, and photographed. Dreyer's new general catalogue (N.G.C.) is the best and most useful. Many of the nebulæ, especially the large ones, can only be classified as irregular nebulæ. The Orion nebula is the principal one of this class, revealing an enormous amount of complicated detail, with exceptional brilliancy of many regions and filaments. An extraordinary multiple star, Theta Orionis, occupies a very prominent position in the nebula, and photographs by Pickering have brought to light curved filaments, very faint and optically invisible, in the outlying regions which give the Orion nebula in part a spiral character. But the delicate optical wisps of this nebula are well seen, even in very small telescopes. Its spectrum yields hydrogen, helium and nitrogen. The Orion nebula is receding from the earth about eleven miles in every second. Keeler and Campbell have shown that nearly every line of the nebular spectrum is a counterpart of a prominent dark line in the spectrum of the brighter stars of the constellation of Orion. A recent investigator of the distribution of luminosity in the great nebula of Orion finds that radiations from nebulium are confined chiefly to the Huygenian region of the nebula and its immediate neighborhood.
Photography has revealed another extraordinary nebula or group of nebulæ surrounding the stars in the Pleiades, which the deft manipulation of Barnard has brought to light. All the stars and the nebula are so interrelated that they are obviously bound together physically, as the common proper motion of the stars also appears to show. Also in the constellation Cygnus, Barnard has discovered very extensive nebulosities of a delicate filmy cloudlike nature which are wholly invisible with telescopes, but very obvious on highly sensitive plates with long exposures.
Another class of these objects are the annular and elliptic nebulæ which are not very abundant. The southern constellation Grus, the crane, contains a fine one, but by far the best example is in the constellation Lyra. It is a nearly perfect ring, elliptic in figure, exceedingly faint in small telescopes; but large instruments reveal many stars within the annulus, one near the center which, although very faint to the eye, is always an easy object on the photographic plate, because it is rich in blue and violet rays. The parallax of the ring nebula in Lyra comes out only one-sixth of that of the planetary nebulæ, and the least greatest diameters of this huge continuous ring are 250 and 330 times the orbit of Neptune.
Planetary nebulæ and nebulous stars are yet another class of nebulæ, for the most part faint and small, resembling in some measure a planetary disk or a star with nebulous outline. Practically all are gaseous in composition, and have large radial velocities. Probably they are located within our own stellar system. The parallaxes of several of them have been measured by Van Maanen: one of the very small angle 0".023, which enables us to calculate the diameter of this faint but interesting object as equal to nineteen times the orbit of Neptune.
CHAPTER LIX
THE SPIRAL NEBULÆ
Last and most important of all are the spiral nebulæ. The finest example is in the constellation Canes Venatici, and its spiral configuration was first noted by Lord Rosse, an epoch-making discovery. The convolutions of its spiral are filled with numerous starlike condensations, themselves engulfed in nebulosity. Photography possesses a vast advantage over the eye in revealing the marvelous character of this object, an inconceivably vast celestial whirlpool. Naturally the central regions of the whorl would revolve most swiftly, but no comparison of drawings and photographs, separated by intervals of many years, has yet revealed even a trace of any such motion.
The number of large spiral nebulæ is not very great; the largest of all is the great nebula of Andromeda, whose length stretches over an arc of seven times the breadth of the moon, and its width about half as great. This nebula is a naked-eye object near Eta Andromedæ, and it is often mistaken for a comet. Optically it was always a puzzle, but photographs by Roberts of England first revealed the true spiral, with ringlike formations partially distinct, and knots of condensing nebulosity as of companion stars in the making. While its spectrum shows the nongaseous constitution of this nebula, no telescope has yet resolved it into component stars.
Systematic search for spiral nebulæ by Keeler, and later continued by Perrine, at the Lick Observatory, with the 36-inch Crossley reflector, disclosed the existence of vast numbers of these objects, in fact many hundreds of thousands by estimation; so that, next to the stars, the spiral nebulæ are by far the most abundant of all objects in the sky. They present every phase according to the angle of their plane with the line of sight, and the convolutions of the open ones are very perfectly marked. Many are filled with stars in all degrees of condensation, and the appearance is strongly as if stars are here caught in every step of the process of making.
The vast multitude of the spiral nebulæ indicates clearly their importance in the theory of the cosmogony, or science of the development of the material universe. Curtis of the Lick Observatory has lately extended the estimated number of these objects to 700,000. He has also photographed with the Crossley reflector many nebulæ with lanes or dark streaks crossing them longitudinally through or near the center. These remarkable streaks appear as if due to opaque matter between us and the luminous matter of the nebula beyond. Perhaps a dark ring of absorptive or occulting matter encircles the nebula in nearly the same plane with the luminous whorls. Duncan has employed the 60-inch Mount Wilson reflector in photographing bright nebulæ and star clusters in the very interesting regions of Sagittarius. One of these shows unmistakable dark rifts or lanes in all parts of the nebula, resembling the dark regions of the neighboring Milky Way.
Pease of Mount Wilson has recently employed the 60-inch and the 100-inch reflectors of the Mount Wilson Observatory to good advantage in photographing several hundred of the fainter nebulæ. Many of these are spirals, and others present very intricate and irregular forms. A search was made for additional spirals among the smaller nebulæ along the Galaxy, but without success. Several of the supposedly variable nebulæ are found to be unchanging. Many nights in each month when the moon is absent are devoted to a systematic survey of the smaller nebulæ and their spectra by photography. The visible spiral figure of all these objects is a double-branched curve, its two arms joining on the nucleus in opposing points, and coiling round in the same geometrical direction. The spiral nebulæ, as to their distribution, are remote from the Galaxy, and the north Galactic polar region contains a greater aggregation than the south. The distances of the spiral nebulæ are exceedingly great. They lie far beyond the planetary and irregular gaseous nebulæ, like that of Orion, which are closely related to the stars forming part of our own system. Possibly the spiral nebulæ are exterior or separate "island universes." If so, they must be inconceivably vast in size, and would develop, not into solar systems, but into stellar clusters. The enormous radial velocities of the spiral nebulæ, averaging 300 to 400 kilometers per second, or twenty-fold that of the stars, tend to sustain the view that they may be "island universes," each comparable in extent with the universe of stars to which our sun belongs.
Recent spectroscopic observations of the nebulæ applying the principle of Doppler have revealed high velocities of rotation. Slipher of the Lowell Observatory made the first discovery of this sort and Van Maanen of Mount Wilson has detected in the great Ursa Major spiral, No. 101 in Messier's catalogue, a speed of rotation at five minutes of arc from the center that would correspond to a complete period in 85,000 years. As was to be expected, the nebula does not rotate as a rigid body, but the nearer the center the greater the angular velocity, and Van Maanen finds evidence of motion along the arms and away from the center.
These great velocities appear to belong to the spiral nebulæ as a class, and not to other nebulæ. Thirteen nebulæ investigated by Keeler are as a whole almost at rest relatively to our system, as are the large irregular objects in Orion, and the Trifid nebula. This would seem to indicate that the spiral nebulæ form systems outside our own and independent of it.
Quite different from the spirals in their distribution through space are the planetary nebulæ. The spirals follow the early general law of nebulæ arrangement, that is, they are concentrated toward the poles of the Galaxy; but the planetary nebulæ, on the other hand, are very few near the poles and show a marked frequency toward the Galactic plane. Campbell and Moore have found spectroscopic evidence of internal rotatory motion in a large proportion of the planetary nebulæ.
The distribution of the nebulæ throughout space, like that of the stars, is still under critical investigation, but the location of vast numbers of the more compact nebulæ on the celestial sphere is very extraordinary. The Milky Way appears to be the determining plane in both cases; the nearer we approach it the more numerous the stars become, whereas this is the general region of fewest nebulæ and they increase in number outward in both directions from the Galaxy, and toward both poles of the Galactic circle. Obviously this relation, or contra-relation of stars and nebulæ on such a vast scale is not accidental, and it also must be duly accounted for in the true theory of the cosmogony. The nebulæ which are found principally in and near the Milky Way are the large irregular nebulæ, and vast nebulous backgrounds, like those photographed by Barnard in Scorpio, Taurus and elsewhere, as well as the Keyhole, Omega, and Trifid nebulæ. Allied to these backgrounds are doubtless some of the dark Galactic spaces, radiating little or no intrinsic light, and absorbing the light of the fainter stars beyond them. A peculiar veiled or tinted appearance has been remarked in some cases visually, and examination of the photographs strongly confirms the existence of absorbing nebulosity.
The spiral nebulæ are so abundant, and so much attention is now being given to them, both by observers and mathematicians, that their precise relation to the stellar systems must soon be known; that is, whether they are comparatively small objects belonging to the stellar system, or independent systems on the borders of the stellar system, or as seems more likely, vast and exceedingly remote galaxies comparable with that of the Milky Way itself. Our knowledge of the motions of the spirals, both radial and angular, is increasing rapidly, and must soon permit accurate general conclusions to be drawn.
CHAPTER LX
COSMOGONY
Down to the middle of the last century and later, it was commonly believed that in the beginning the cosmos came into being by divine fiat substantially as it is. Previously the earth had been "without form and void," as in the Scripture. Had it not been for the growth and gradual acceptance of the doctrine of evolution, and its reactionary effect upon human thought, it is conceivable that the early view might have persisted to the present day; but now it is universally held that everything in the heavens above and the earth beneath is subject more or less to secular change, and is the result of an orderly development throughout indefinite past ages, a progressive evolution which will continue through indefinite aeons of the future.
In the writings of the Greek philosophers, and down through the Middle Ages we find the idea of an original "chaos" prevailing, with no indication whatever of the modern view of the process by which the cosmos came to be what they saw it and as it is to-day. If we go still farther back, there is no glimmer of any ideas that will bear investigation by scientific method, however interesting they may be as purely philosophical conceptions. Many ancient philosophers, among them Anaxagoras, Democritus, and Anaximenes, regarded the earth as the product of diffused matter in a state of the original chaos having fallen together haphazard, and they even presumed to predict its future career and ultimate destiny.
In Anaximander and Anaximenes alone do we find any conception of possible progress; their thought was that as the world had taken time to become what it is, so in time it would pass, and as the entire universe had undergone alternate renewal and destruction in the past, that would be its history in the future. Aristotle, Ptolemy, and others appear to have held the curious notion that although everything terrestrial is evanescent, nevertheless the cosmos beyond the orbit of the moon is imperishable and eternal.
By tracing the history of the intellectual development of Europe we may find why it was that scientific speculation on the cosmogony was delayed until the 18th century, and then undertaken quite independently by three philosophers in three different countries. Swedenborg, the theologian, set down in due form many of the principles that underlie the modern nebular hypothesis. Thomas Wright of Durham whose early theory of the arrangement of stars in the Galaxy we have already mentioned, speculated also on the origin and development of the universe, and his writings were known to Kant, who is now regarded as the author of the modern nebular hypothesis. This presents a definite mechanical explanation of the development and formation of the heavenly bodies, and in particular those composing the solar system.
Kant was illustrious as a metaphysician, but he was a great physicist or natural philosopher as well, and he set down his ideas regarding the cosmogony with precision. Learned in the philosophy of the ancients, he did not follow their speculative conceptions, but merely assumed that all the materials from which the bodies of the solar system have been fashioned were resolved into their original elements at the beginning, and filled all that part of space in which they now move. True, this is pretty near the chaos of the Greeks, but Kant knew of the operation of the Newtonian law of gravitation, which the Greeks did not.
As a natural result of gravitative processes, Kant inferred that the denser portions of the original mass would draw upon themselves the less dense portions, whirling motions would be everywhere set up, and the process would continue until many spherical bodies, each with a gaseous exterior in process of condensation, had taken the place of the original elements which filled space. In this manner Kant would explain the sameness in direction of motion, both orbital and axial, of all the planets and satellites of our system. But many philosophers are of the opinion that Kant's hypothesis would result, not in the formation of such a collection of bodies as the solar system is, but rather in a single central sun formed by common gravitation toward a single center.
From quite another viewpoint the work of the elder Herschel is important here. No one knew the nebulæ from actual observation better than he did; but, while his ideas about their composition were wrong, he nevertheless conceived of them as gradually condensing into stars or clusters of stars. And it was this speculative aspect of the nebulæ, not as a possible means of accounting for the birth and development of the solar system, which constitutes Herschel's chief contribution to the nebular hypothesis. Classifying the nebulæ which he had carefully studied with his great telescopes, it seemed obvious to him that they were actually in all the different stages of condensation, and subsequent research has strongly tended to substantiate the Herschelian view.
Then came Laplace, who took up the great hypothesis where Kant and Herschel had left it, added new and important conceptions in the light of his mature labors as mathematician and astronomer, and put the theory in definitive form, such that it has ever since been known under the name of Laplacian nebular hypothesis. For reasons like those that prevailed with Kant, he began the evolution of the solar system with the sun already formed as the center, but surrounded by a vast incandescent atmosphere that filled all the space which the sun's family of planets now occupy. This entire mass, sun, atmosphere, and all, he conceived to have a stately rotation about its axis. With rotation of the mass and slow reduction of temperature in its outer regions, there would be contraction toward the solar center, and an increase in velocity of rotation until the whole mass had been much reduced in diameter at its poles and proportionately expanded at its equator.
When the centrifugal force of the outer equatorial masses finally became equal to the gravitational forces of the central mass, then these conjoined outer portions would be left behind as a ring, still revolving at the velocity it had acquired when detached. The revolution of the entire inner mass goes on, its velocity accelerating until a similar equilibration of forces is again reached, when a second rotating ring is left behind. Laplace conceived the process as repeated until as many rings had been detached as there are individual planets, all central about the sun, or nearly so.
In all, then, we should have nine gaseous rings; the outer ones preceding the inner in formation, but not all existing as rings at the same time. Radiation from the ring on all sides would lead to rapid contraction of its mass, so that many nuclei of condensation would form, of various sizes, all revolving round the central sun in practically the same period. Laplace conceived the evolution of the ring to proceed still farther till the largest aggregation in it had drawn to itself all the other separate nuclei in the ring.
This, then, was the planet in embryo, in effect a diminutive sun, a secondary incandescent mass endowed with axial rotation in the same direction as the parent nebula. With reduction of temperature by radiation, polar contraction and equatorial expansion go on, and planetary rings are detached from this secondary mass in exactly the same way as from the original sun nebula. And these planetary rings are, in the Laplacian hypothesis, the embryo moons or planetary satellites, all revolving round their several planets in the same direction that the planets revolve about the sun.
In the case of one of the planetary rings, its formation was so nearly homogeneous throughout that no aggregation into a single satellite was possible; all portions of the ring being of equal density, there was no denser region to attract the less dense regions, and in this manner the rings of Saturn were formed, in lieu of condensation into a separate satellite. Similarly in the case of the primal solar ring that was detached next after the Jovian ring; there was such a nice balancing of masses and densities that, instead of a single major planet, we have the well-known asteroidal ring, composed of innumerable discrete minor planets.
This, then, in bare outline, is the Laplacian nebular hypothesis, and it accounted very well for the solar system as known in his day; the fairly regular progression of planetary distances; their orbits round the sun all nearly circular and approximately in a single plane; the planetary and satellite revolutions in orbit all in the same direction; the axial rotations of planets in the same direction as their orbital revolutions; and the plane of orbital revolution of the satellites practically coinciding with the plane of the planet's axial rotation. But the principle of conservation of energy was, of course, unknown to Laplace, nor had the mechanical equivalence of heat with other forms of energy been established in his day.
In 1870, Lane of Washington first demonstrated the remarkable law that a gaseous sphere, in process of losing heat by radiation and contraction because of its own gravity, actually grows hotter instead of cooler, as long as it continues to be gaseous, and not liquid or solid. So there is no need of postulating with Laplace an excessively high temperature of the original nebula. The chief objection to Laplace's hypothesis by modern theorists is that the detachment of rings, though possible, would likely be a rare occurrence; protuberances or lumps on the equatorial exterior of a swiftly revolving mass would be more likely, and it is much easier to see how such masses would ultimately become planets than it is to follow the disruption of a possible ring and the necessary steps of the process by which it would condense into a final planet. The continued progress of research in many departments of astronomy has had important bearing on the nebular hypothesis, and we may rest assured that this hypothesis in somewhat modified form can hardly fail of ultimate acceptance, though not in every essential as its great originator left it.
Lord Rosse's discovery of spiral nebulæ, followed up by Keeler's photographic search for these bodies, revealing their actual existence in the heavens by the hundreds of thousands, has led to another criticism of the Laplacian theory. Could Laplace have known of the existence of these objects in such vast numbers, his hypothesis would no doubt have been suitably modified to account for their formation and development. It is generally considered that the ring of Saturn suggested to Laplace the ring feature in his scheme of origin of planets and satellites; so far as we know, the Saturnian ring is unique, the only object of its kind in the heavens. Whereas, next to the star itself, the spiral nebula is the type object which occurs most frequently. A theory, therefore, which will satisfactorily account for the origin and development of spiral nebulæ must command recognition as of great importance in the cosmogony.
Such a theory has been set forth by Chamberlin and Moulton in their planetesimal hypothesis, according to which the genesis of spiral nebulæ happens when two giant suns approach each other so closely that tide-producing effects take place on a vast scale. These suns need not be luminous; they may perhaps belong to the class of dark or extinguished suns. The evidences of the existence of such in vast numbers throughout the universe is thought to be well established.
Now, on close approach, what happens? There will be huge tides, and the nearer the bodies come to each other, the vaster the scale on which tides will be formed. If the bodies are liquid or gaseous, they will be distorted by the force of gravitation, and the figure of both bodies will become ellipsoidal; and at last under greater stress, the restraining shell of both bodies will burst asunder on opposite sides in streams of matter from the interior. In this manner the arms of the spiral are formed.
As Chamberlin puts it: "If, with these potent forces thus nearly balanced, the sun closely approaches another sun, or body of like magnitude … the gravity which restrains this enormous elastic power will be reduced along the line of mutual attraction. At the same time the pressure transverse to this line of relief will be increased. Such localized relief and intensified pressure must bring into action corresponding portions of the sun's elastic potency, resulting in protuberances of corresponding mass and high velocity."
Only a fraction of one per cent of the sun's mass ejected in this fashion would be sufficient to generate the entire planetary system. Nuclei or knots in the arms of the spiral gradually grew by accretion, the four interior knots forming Mercury, Venus, the Earth, and Mars. The earth knot was a double one, which developed into the earth-moon system. The absence of a dominating nucleus beyond Mars accounts for the zone of the asteroids remaining in some sense in the original planetesimal condition. The vaster nuclei beyond Mars gradually condensed into Jupiter, Saturn, Uranus, and Neptune; and lesser nuclei related to the larger ones form the systems of moons or satellites.
The orbits of the planetesimals and the planetary and satellite nuclei would be very eccentric, forming a confusion of ellipses with frequently crossing paths. Collisions would occur, and the nuclei would inevitably grow by accretion. Each planet, then, would clear up the planetesimals of its zone; and Moulton shows that this process would give rise to axial revolution of the planet in the same direction as its orbital revolution. The eccentricities would finally disappear, and the entire mass would revolve in a nearly circular orbit.
Rotation twists the streams into the spiral form, and the huge amounts of wreckage from the near-collision are thrown into eddies. The fragments or particles (planetesimals) which have given the name to the theory, begin their motion round their central sun in elliptical paths as required by gravitation. The form of the spiral is preserved by the orbital motion of its particles. There is a gradual gathering together of the planetesimals at points or nodes of intersection, and these become aggregations of matter, nuclei that will perhaps become planets, though more likely other stars. The appulse or near approach is but one of the methods by which the spiral nebulæ may have come into existence. The planetesimal hypothesis would seem to account for the formation of many of these objects as we see them in the sky, though perhaps it is hardly competent to replace entirely the Laplacian hypothesis of the formation of the solar system, which would appear to be a special case by itself.
It will be observed that while the Laplacian hypothesis is concerned in the main with the progressive development of the solar system, and systems of a like order surrounding other stellar centers, whose existence is highly probable, the origin and development of the stellar universe is a vaster problem which can only be undertaken and completed in its broadest bearings when the structure of the stellar universe has been ascertained.
Darwin's important investigations in 1877-1878 on tidal friction may be here related. Before his day acceptance of the ring-theory of development of the moon from the earth had scarcely been questioned; but his recondite mathematical researches on the tidal reaction between a central yielding mass and a body revolving round it brought to light the unsuspected effect of tides raised upon both bodies by their mutual attraction. The type of tides here meant is not the usual rise and fall of the waters of the ocean, but primeval tides in the plastic material of which the earth in its early history was composed. The Newtonian law of gravitation afforded a complete explanation of the rise and fall of the waters of the oceans, but as applied to the motions of planets and satellites by the Lagrangian formulæ, it presupposed that all these bodies are rigid and unyielding. However, mutual tides of phenomenal height in their early plastic substances must have been a necessary consequence of the action of the Newtonian law, and they gradually drew upon the earth's rotational moment of momentum.
In its very early history, before there was any moon to produce tides, the earth rotated much more rapidly, that is, the day was very much shorter than now, probably about five or six hours long. And with the rapid whirling, it was not a Laplacian ring that was detached, but a huge globular mass was separated from the plastic earth's equator. Darwin shows that the gravitative interaction of the two bodies immediately began to raise tides of extraordinary height in both, therefore tending to slow down the rotational periods of both bodies. Action and reaction being equal, the reaction at once began driving the moon away from the earth and thereby lengthening its period of revolution. So small was the mass of the moon and so near was it to the earth, that its relative rotational energy was in time completely used up, and the moon has ever since turned her constant face toward us. Tides of sun and moon in the plastic earth, acting through the ages, slowed down the earth's rotation to its present period, or the length of the day.
Moulton, however, has investigated the tidal theory of the origin of the moon in the light of the planetesimal hypothesis, concluding that the moon never was part of the earth and separated therefrom by too rapid rotation of the earth, but that the distance of the two bodies has always been the same as now. The more massive earth has in its development throughout time robbed the less massive moon in the gradual process of accretion. So the moon has never acquired either an ocean or atmosphere, and this view is acceptable to geologists who have studied the sheer lunar surface, Shaler of Harvard among the first, and laid the foundations for a separate science of selenology.
Tidal friction has also been operant in producing sun-raised tides upon the early plastic substances which composed the planets: more powerfully in the case of planets nearer the sun; less rapidly if the planet's mass is large; also less completely if the planet has solidified earlier on account of its small dimensions. So Darwin would account for the present rotation periods of all the planets: both Mercury and Venus powerfully acted on by the sun on account of their nearness to him, and their rotational energy completely exhausted, so that they now and for all time turn a constant face toward him, as the moon does to the earth; earth and possibly Mars even yet undergoing a very slight lengthening of their day; Jupiter and Saturn, also Uranus and probably Neptune, still exhibiting relatively swift axial rotation, because of their great mass and great original moment of momentum, and also by reason of their vast distances from the central tide-raising body, the sun.
By applying to stellar systems the principles developed by Darwin, See accounted for the fact, to which he was the first to direct attention, that the great eccentricity of the binary orbits is a necessary result of the secular action of tidal friction. The double stars, then, were double nebulæ, originally single, but separated by a process allied to that known as "fission" in protozoans. Indeed, Poincaré proved mathematically that a swiftly revolving nebula, in consequence of contraction, first undergoes distortion into a pear-shaped or hour-glass figure, the two masses ultimately separating entirely; and the observations of the Herschels, Lord Rosse and others, with the recent photographic plates at the Lick and Mount Wilson observatories, afford immediate confirmation in a multitude of double nebulæ, widely scattered throughout the nebular regions of the heavens.
Jeans of Cambridge, England, among the most recent of mathematical investigators of the cosmogony, balances the advantages and disadvantages of the differing cosmogonic systems as follows, in his "Problems of Cosmogony and Stellar Dynamics": "Some hundreds of millions of years ago all the stars within our Galactic universe formed a single mass of excessively tenuous gas in slow rotation. As imagined by Laplace, this mass contracted owing to loss of energy by radiation, and so increased its angular velocity until it assumed a lenticular shape…. After this, further contraction was a sheer mathematical impossibility and the system had to expand. The mechanism of expansion was provided by matter being thrown off from the sharp edge of the lenticular figure, the lenticular center now forming the nucleus, and the thrown-off matter forming the arms, of a spiral nebula of the normal type. The long filaments of matter which constituted the arms, being gravitationally unstable, first formed into chains of condensation about nuclei, and ultimately formed detached masses of gas. With continued shrinkage, the temperature of these masses increased until they attained to incandescence, and shone as luminous stars. At the same time their velocity of rotation increased until a large proportion of them broke up by fission into binary systems. The majority of the stars broke away from their neighbors and so formed a cluster of irregularly moving stars—our present Galactic universe, in which the flattened shape of the original nebula may still be traced in the concentration about the Galactic plane, while the original motion along the nebular arms still persists in the form of 'star-streaming.' In some cases a pair or small group of stars failed to get clear of one another's gravitational attractions and remain describing orbits about one another as wide binaries or multiple stars. The stars which were formed last, the present B-type stars, have been unusually immune from disturbance by their neighbors, partly because they were born when adjacent stars had almost ceased to interfere with one another, partly because their exceptionally large mass minimized the effect of such interference as may have occurred; consequently they remain moving in the plane in which they were formed, many of them still constituting closely associated groups of stars—the moving star clusters.
"At intervals it must have happened that two stars passed relatively near to one another in their motion through the universe. We conjecture that something like 300 million years ago our sun experienced an encounter of this kind, a large star passing within a distance of about the sun's diameter from its surface. The effect of this, as we have seen, would be the ejection of a stream of gas toward the passing star. At this epoch the sun is supposed to have been dark and cold, its density being so low that its radius was perhaps comparable with the present radius of Neptune's orbit. The ejected stream of matter, becoming still colder by radiation, may have condensed into liquid near its ends and perhaps partially also near its middle. Such a jet of matter would be longitudinally unstable and would condense into detached nuclei which would ultimately form planets."
CHAPTER LXI
COSMOGONY IN TRANSITION
We have seen how Wright in 1750 initiated a theory of evolution, not only of the solar system, but of all the stars and nebulæ as well; how Kant in 1752 by elaborating this theory sought to develop the details of evolution of the solar system on the basis of the Newtonian law, though weakened, as we know, by serious errors in applying physical laws; how Laplace in 1796 put forward his nebular hypothesis of origin and development of the solar system, by contraction from an original gaseous nebula in accord with the Newtonian law; how Sir William Herschel in 1810 saw in all nebulæ merely the stuff that stars are made of; how Lord Rosse in 1845 discovered spiral nebulæ; how Helmholtz in 1854 put forward his contraction theory of maintenance of the solar heat, seemingly reinforcing the Laplacian theory; how Lane in 1870 proved that a contracting gaseous star might rise in temperature; how Roche in 1873 in attempting to modify the Laplacian hypothesis, pointed out the conditions under which a satellite would be broken up by tidal strains; how Darwin in 1879 showed that the theory of tidal evolution of non-rigid bodies might account for the formation of the moon, and binary stars might originate by fission; how Keeler in 1900 discovered the vast numbers of spiral nebulæ; how Chamberlin and Moulton in 1903 put forward the planetesimal hypothesis of formation of the spiral nebulæ, showing also how that hypothesis might account for the evolution of the solar system; and how Jeans in 1916 advocated the median ground in evolution of the arms of the spiral nebulæ, showing that they will break up into nuclei, if sufficiently massive.
In all these theories, truth and error, or lack of complete knowledge, appear to be intermingled in varying proportions. Is it not early yet to say, either that any one of them must be abandoned as totally wrong, or on the other hand that any one of them, or indeed any single hypothesis, can explain all the evolutionary processes of the universe?
Clearly the great problems cannot all be solved by the kinetic theory of gases and the law of gravitation alone. Recent physical researches into sub-atomic energy and the structure and properties of matter, appear to point in the direction where we must next look for more light on such questions as the origin and maintenance of the sun's heat, the complex phenomena of variable stars and the progressive evolution of the myriad bodies of the stellar universe. Because we have actually seen one star turn into a nebula we should not jump to the conclusion that all nebulæ are formed from stars, even if this might seem a direct inference from the high radial velocities of planetary nebulæ.
Quite as obviously many of the spiral nebulæ are in a stage of transition into local universes of stars—even more obvious from the marvelous photographs in our day than the evolution of stars from nebulæ of all types was to Herschel in his day.
The physicist must further investigate such questions as the building up of heavy atomic elements by gravitative condensation of such lighter ones as compose the nebulæ; and laboratory investigation must elucidate further the process of development of energy from atomic disintegration under very high pressures. This leads to a reclassification of the stars on a temperature basis.
Equally important is the inquiry into the mechanism of radiative equilibrium in sun and stars. Not impossibly the process of the earth's upper atmosphere in maintaining a terrestrial equilibrium may afford some clue. What this physical mechanism may be is very incompletely known, but it is now open to further research through recent progress of aeronautics, which will afford the investigator a "ceiling" of 50,000 feet and probably more. Beneath this level, perhaps even below 40,000 feet, lie all the strata, including the inversion layer, where the sun's heat is conserved and an equilibrium maintained.
Even ten years ago, had an astronomer been asked about the physical condition of the interior of the stars, he would have replied that information of this character could only be had on visiting the stars themselves—and perhaps not even then. But at the Cardiff meeting of the British Association in 1920, Eddington, the president of Section A, delivered an address on the internal constitution of the stars. He cites the recent investigations of Russell and others on truly gaseous stars, like Aldebaran, Arcturus, Antares and Canopus, which are in a diffuse state and are the most powerful light-givers, and thus are to be distinguished from the denser stars like our Sun. The term giants is applied to the former, and dwarfs to the latter, in accord with Russell's theory.
As density increases through contraction, these terms represent the progressive stages, from earlier to later, in a star's history. A red or M-type star begins its history as a giant of comparatively low temperature. Contracting, according to Lane's law, its temperature must rise until its density becomes such that it no longer behaves as a perfect gas. Much depends on the star's mass; but after its maximum temperature is attained, the star, which has shrunk to the proportions of a dwarf, goes on cooling and contracts still further.
Each temperature-level is reached and passed twice, once during the ascending stage and once again in descending—once as a giant, and once as a dwarf. Thus there are vast differences in luminosity: the huge giant, having a far larger surface than the shrunken dwarf, radiates an amount of light correspondingly greater.
The physicist recognizes heat in two forms—the energy of motion of material atoms, and the energy of ether waves. In hot bodies with which we are familiar, the second form is quite insignificant; but in the giant stars, the two forms are present in about equal proportions. The super-heated conditions of the interior of the stars can only be estimated in millions of degrees; and the problem is not one of convection currents, as formerly thought, bringing hot masses to the surface from the highly heated interior, but how can the heat of the interior be barred against leakage and reduced to the relatively small radiation emitted by the stars. "Smaller stars have to manufacture the radiant heat which they emit, living from hand to mouth; the giant stars merely leak radiant heat from their store."
So a radioactive type of equilibrium must be established, rather than a convective one. Laboratory investigations of the very short waves are now in progress, bearing on the transparency of stellar material to the radiation traversing it; and the penetrating power of the star's radiation is much like that of X-rays. The opacity is remarkably high, explaining why the star is so nearly "heat-tight."
Opacity being constant, the total radiation of a giant star depends on its mass only, and is quite independent of its temperature or state of diffuseness. So that the total radiation of a star which is measured roughly by its luminosity, may readily remain constant during the entire 'giant' stage of its history. As Russell originally pointed out, giant stars of every spectral type have nearly the same luminosity. From the range of luminosity of the giant stars, then, we may infer their range of masses: they come out much alike, agreeing well with results obtained by double-star investigation.
These studies of radiation and internal condition of the stars again bring up the question of the original source of that supply of radiant energy continually squandered by all self-luminous bodies. The giant stars are especially prodigal, and radiate at least a hundredfold faster than the sun.
"A star is drawing on some vast reservoir of energy," says Eddington, "by means unknown to us. This reservoir can scarcely be other than the sub-atomic energy which, it is known, exists abundantly in all matter; we sometimes dream that man will one day learn how to release it and use it for his service. The store is well-nigh inexhaustible, if only it could be tapped. There is sufficient in the sun to maintain its output of heat for fifteen billion years."