We have seen that the sun is dissipating and wasting almost inconceivable amounts of heat every year: 3.8. 10³³ gramme-calories, corresponding to 2 gramme-calories for each gramme of its mass. We have also obtained an idea as to how the enormous storage of heat energy in the sun may endure this loss for ages. Finally, however, the time must come when the sun will cool down and when it will cover itself with a solid crust, as the earth and the other planets—so far, probably, in a gaseous state—have done long since or will do before long. No living being will be able to watch this extinction of the sun despairingly from one of the wandering planets; for, in spite of all our inventions, all life will long before have ceased on the satellites of the sun for want of heat and light.

The further development of the cold sun will recall the actual progress of our earth, except in so far as the sun will have no life-spending, central source of light and heat near it. In the beginning the thin, solid crust will again and again be burst by gases, and streams of lava will rush out from the interior of the sun. After a while these powerful discharges will stop, the lava will freeze, and the fragments will close up more firmly than before. Only on some of the old fissures volcanoes will rise and allow the gases to escape from the interior—water vapor and, to a less extent, carbonic acid, liberated by the cooling.

Then water will be condensed. Oceans will flood the sun, and for a short period it will resemble the earth in its present condition, though with the one important difference. The extinct sun, unlike our earth, will not receive life-giving heat from the outside, excepting the small amount of radiation from universal space and the heat generated by the fall of meteorites. The temperature fall will therefore be rapid, and the vanishing clouds of the attenuated atmosphere will not long check radiation. The ocean will become covered with a crust of ice. Then the carbonic acid will commence to condense, and will be precipitated as a light snow in the solar atmosphere. Finally, at a temperature of about -200° Cent., the gases of the atmosphere will be condensed, and new oceans, now principally of nitrogen, will be produced. Let the temperature sink another 20°, and the energy of the inrushing meteorites will just suffice to balance a further loss of heat by radiation. The solar atmosphere will then consist essentially of helium and hydrogen—the two gases which are most difficult to condense—and of some nitrogen.

In this stage the heat loss of the sun will be almost imperceptible. Owing to the low thermal conductive power of the earth’s crust, there escapes through each square mile of this crust scarcely one-thousand-millionth part of the heat which the sun is radiating from an equal area of its surface. In future days, when the solar crust will have attained a thickness of 60 km. (40 miles), its loss of heat will be diminished to the same degree. The temperature on the surface of the sun may then still be some 50° or 60° above absolute zero, and volcanic eruptions will raise the temperature only for short periods and over small areas. Yet in the interior the temperature will still be at nearly the same actual intensity, something like several million degrees, and the compounds of infinite explosive energy will be stored up there as today. Like an immense dynamite magazine, the dark sun will float about in universal space without wasting much of its energy in the course of billions of years. Immutable, like a spore, it will retain its immense store of force until it is awakened by external forces into a new span of life similar to the old life. A slow shrinkage of the surface, due to the progressive loss of heat of the core and to the consequent contraction, will in the meanwhile have covered the sun with the wrinkles of old age.

Let us suppose that the crusts of the sun and the earth have the same thermal conductivity—namely, that of granite. According to Homén, a slab of granite one centimetre in thickness, whose two surfaces are at a temperature difference of 1° Cent., will permit 0.582 calorie to pass per minute per square centimetre of surface. By analogy, the earth’s crust, with an increase of temperature of 30° per kilometre, as we penetrate inward, would allow 1.75 .10^-4 calorie to pass per minute and per square centimetre (this is 1/3580 of the mean heat supply of the earth, 0.625 calorie per minute per square centimetre); while the sun, with a crust of the same thickness as the earth, but with a diameter 108.6 times larger, would lose 3.3 times more heat per minute than the earth receives from it at the present time. At present the sun loses 2260 million times more heat than the earth receives; consequently, the loss of heat would be reduced to 1/686,000,000 of the present amount. If the thickness of the solar crust amounted to 1/140 of the solar radius—that is to say, to the same fraction that the thickness of the earth’s crust represents of the terrestrial radius—the sun would in 74,500 million years not lose any more heat than it does now in a single year. This number has to be diminished, on account of the colder surface which the sun would have by that time, to about 60,000 million years. Considering that the mean temperature of the sun may be as high as 5 million degrees Celsius, the cooling down to the freezing-point of water might occupy 150,000 billion years, assuming that its mean specific heat is as great as that of water. During this time the crust of the sun would increase in thickness and the cooling would, of course, proceed at a decreasing rate. In any case, the total loss of energy during a period of a thousand billion years could, under these circumstances, only constitute a very small fraction of the total stored energy.

When an extinct star moves forward through infinite spaces of time, it will ultimately meet another luminous or likewise extinct star. The probability of such a collision is proportional to the angle under which the star appears—which, though very small, is not of zero magnitude—and to the velocity of the sun. The probability is increased by the deflection which these celestial bodies will undergo in their orbits on approaching each other. Our nearest neighbors in the stellar universe are so far removed from us that light, the light of our sun, requires, on an average, perhaps ten years to reach them. In order that the sun, with its actual dimensions and its actual velocity in space—20 km. (13 miles) per second—should collide with another star of similar kind, we should require something like a hundred thousand billion years. Suppose that there are a hundred times more extinct than luminous stars—an assumption which is not unjustifiable—the probable interval up to the next collision may be something like a thousand billion years. The time during which the sun would be luminous would represent perhaps one-hundredth of this—that is to say, ten billion years. This conclusion does not look unreasonable. For life has only been existing on the earth for about a thousand million years, and this age represents only a small fraction of the time during which the sun has emitted light and will continue to emit light. The probability of a collision between the sun and a nebula is, of course, much greater; for the nebulæ extend over very large spaces. In such a case, however, we need not apprehend any more serious consequences than result when a comet is passing through the corona of the sun. Owing to the very small amount of matter in the corona, we have not perceived any noteworthy effects in these instances. Nevertheless, the entrance of the sun into a nebula would increase the chance of a collision with another sun; for we shall see below that dark and luminous celestial bodies appear to be aggregated in the nebulæ.

From time to time we see new stars suddenly flash up in the sky, rapidly decrease in splendor again, to become extinguished or, at any rate, to dwindle down to faint visibility once more. The most remarkable of these exceedingly interesting events occurred in February, 1901, when a star of the first magnitude appeared in the constellation of Perseus. This star was discovered by Anderson, a Scotchman, on the morning of February 22, 1901. It was then a star of the third magnitude.[12] On a photograph which had been taken only twenty-eight hours previous to the discovery of this star, the star was not visible at all, although the plate marked stars down to the twelfth magnitude. The light intensity of this new star would hence appear to have increased more than five-thousand-fold within that short space of time. On February 23d the new star surpassed all other stars except Sirius in intensity. By February 25th it was of the first magnitude, by February 27th of the second, by March 6th of the third, and by March 18th of the fourth magnitude. Then its brightness began to fluctuate periodically up to June 22d, with a period first of three, then of five days, while the average light intensity decreased. By June 23d it was of the sixth magnitude. The light intensity diminished then more uniformly. By October, 1901, it was a star of the seventh magnitude; by February, 1902, of the eighth magnitude; by July, 1902, of the ninth magnitude; by December, 1902, of the tenth magnitude; and since then it has gradually dwindled to the twelfth magnitude. When this star was at its highest intensity it shone with a bluish-white light. The shade then changed into yellow, and by the beginning of March, 1901, into reddish. During its periodical fluctuations the hue was whitish yellow at its maximum and reddish at its minimum intensity. Since then the color has gradually passed into pure white.

The spectrum of this star shows the greatest similarity to that of the new star in the constellation Auriga (Nova Aurigæ) of the year 1892 (Fig. 45).

On the whole, it is characteristic of new stars that the spectrum lines appear double—dark on the violet and bright on the red side. In the spectrum of Nova Aurigæ this peculiarity is, among others, striking in the three hydrogen lines C, F, and H, in the sodium line, in the nebula lines, and also in the magnesium line. In the spectrum of Nova Persei the displacement of the hydrogen lines towards the violet is so great that, according to Doppler’s principle,[13] the hydrogen gas which absorbed the light must have been moving towards us with a velocity of 700 or more kilometres (450 miles) per second. Some calcium lines show a similar displacement, which is less noticeable in the case of the other metals. This would appear to indicate that relatively cold masses of gas are issuing from the stars and streaming with enormous velocities towards the earth. The luminous parts of the stars were either at a stand-still or they were moving away from us. The simplest explanation of these phenomena would be that a star when flashing up by virtue of its high temperature and high pressure shows enhanced (widened) spectral lines, whose violet portion is absorbed by the strongly cooled masses of gas which are moving towards us and are cooled by their own strong expansion. These gases stream, of course, in all directions from the star, but we only become aware of those gases which absorb the light of the stars—that is to say, those situated between the star and the earth, and streaming in our direction.

Gradually the light of the metallic lines and of the continuous spectrum on which they were superposed began to fade, first in the violet, while the hydrogen lines and nebular lines still remained distinct; like other new stars, this star showed, after a while, the nebular spectrum. This interesting fact was first noticed by H. C. Vogel in the new star in the Swan (Nova Cygni, 1876). The star P in the Swan, which flashed up in the year 1600, still offers us a spectrum which indicates the emission of hydrogen gas. It is not impossible that this "new" star has not yet reached its equilibrium, and is still continuing to emit cold streams of gases. Insignificant quantities of gas suffice for the formation of an absorption spectrum; thus the emission of gas might continue for long periods without exhausting the supply.

We have already mentioned (page 116) the peculiar clouds of light which were observed around Nova Persei. Two annular clouds moved away from this star with velocities of 1.4 and 2.8 seconds of arc per day between March 29, 1901, and February, 1902. If we calculate backward from these dates the time which must have elapsed since those gases left the star, we arrive at the date of the week—February 8 to 16, 1901—in satisfactory agreement with the period of greatest luminosity of the star of February 23d. It would, therefore, appear that these emanations came from the star and were ejected by the radiation pressure. Their light did not mark any noticeable polarization, and could not be reflected light for this reason. We may suppose that the dust particles discharged their electric charges, and that the gases became thereby luminous.

In this case we were evidently witnesses of the grand finale of the independent existence of a celestial body by collision with some other body of equal kind. The two colliding bodies were both dark, or they emitted so little light that their combined light intensities did not equal that of a star of the twelfth magnitude. As, now, their splendor after the collision was greater than that of a star of the first magnitude, although their distance has been estimated to be at least 120 light years,[14] their radiation intensity must have exceeded that of the sun several thousand times. Under these circumstances the mechanical radiation pressure must also have been many times more powerful than on the surface of the sun, and the masses of dust which were ejected by the new star must have possessed a velocity very much greater than that of solar dust. Yet this velocity must have been smaller than that of light, which, indeed, the effect of the radiation pressure can never equal.

It is not difficult to picture to ourselves the enormous violence with which this "collision" must have taken place. A strange body—for instance, a meteorite—which rushes from the infinite universe into the sun has at its collision a velocity of 600 km. (400 miles) per second, and the velocity of the two colliding suns must have been of approximately that order. The impact will in general be oblique, and, although part of the energy will of course be transformed into heat, the rest of the kinetic energy must have produced a rotational velocity of hundreds of kilometres per second. By comparison with this number the actual circumferential speed of the sun, about 2 km. (1-1/4 miles) per second on the equator, would vanish altogether; and the difference is still more striking for the earth, with its 0.465 km. per second at the equator. We shall, therefore, not commit an error of any consequence if we presume the two bodies to have been practically devoid of circumferential speeds before their collision. At the collision, matter will have been ejected from both these celestial bodies at right angles to the relative directions of their motion in two powerful torrents, which would be situated in the plane in which the two bodies were approaching each other (compare Fig. 46). The rotational speed of the double star, which will be diminished by this ejection of matter, will have contributed to increase the energy of ejection. We remember, now, that when matter is brought up from the interior to the surface of the sun it will behave like an explosive of enormous power. The ejected gases will be hurled in terrific flight about the rapidly revolving central portions. We obtain an idea (though a very imperfect one) of these features when we look at a revolving pinwheel in a fireworks display. Two pinwheels have been attached to the ends of a diameter and belch forth fire in radial lines. The farther removed from the wheel, the smaller will be the actual velocity and also the angular velocity of these torrents of fire. Similarly with the star. The streams are rapidly cooled, owing to the rapid expansion of the gas. They will also contain fine dust, largely consisting of carbon, probably, which had been bound by the explosive materials. The clouds of fine dust will obscure the new star more and more, and will gradually change its white brilliancy into yellow and reddish, because the fine dust weakens blue-and-green rays more than it does yellow-and-red rays. At first the clouds were so near to the star that they possessed a high angular velocity of their own; they then appeared to surround the star completely. But after March 22, 1901, the outer particles of the streams attained greater distances and assumed longer periods of revolution (six days); the star then became more obscured when the extreme dust clouds of the streams covering it happened to get between us and the star. As the streams of particles were moving farther away, their rotational periods increased gradually to ten days. The star, therefore, became periodical with a slowly growing length of period, and its glow turned more reddish at its minimum than at its maximum of intensity. At the same time, the absorptive power of the marginal particles decreased, partly owing to their increasing expansion, partly because the dust was slowly aggregating to coarser particles; possibly, also, because the finest particles were being driven away by the radiation pressure. The sifting influence which the dust exercised upon the light, and owing to which the red-and-yellow rays were more readily transmitted than the blue-and-green, gradually became impaired; hence the color of the light turned more gray, and after a certain time the star appeared once more of a whitish hue. This white color indicates that the star must still have a very high temperature. By the continued ejection of dust-charged masses of gas, probably with gradually decreasing violence, the light intensity of the star must slowly diminish (as seen from the earth) and the distribution of the layers of dust around the luminous core will more and more become uniform. How violent the explosion must have been, we recognize from the observation that the first ejected masses of hydrogen rushed out with an apparent velocity of at least 700 km. per second. This velocity is of the same order as that of the most remarkable prominences of the sun.

It will be admitted that these arguments present us with a faithful simile even of the details of the observed course of events, and it is therefore highly probable that our view is in the main correct. But what has meanwhile become of the new star? Spectrum analysis tells us that it has been converted into a stellar nebula like other new stars. The continuous light of the central body has more and more been weakened by the surrounding masses of dust. By the radiation pressure these masses are driven towards the outer particles of the surrounding gaseous envelope consisting principally of hydrogen, helium, and "nebular matter." There the dust discharges its negative electricity, and thus calls forth a luminescence which equals that of the nebulæ.

We have to consider next that owing to the incredibly rapid rotation, the central main mass of the two stars will, in its outer portions, be exposed to centrifugal forces of extraordinary intensity, and will therefore become flattened out to a large revolving disk.[15] As the pressure in the outer portions will be relatively small, the density of the gases will likewise be diminished there. The energetic expansion and, more still, the great heat radiation will lower the temperature at a rapid rate. We have thus to deal with a central body whose inner portion will possess a high density, and which will resemble the mass of the sun, while the outer portion will be attenuated and nebular. Distributed about the central body we shall find the rest of the two streams of gases which were ejected immediately after the violent collision between the two celestial bodies. A not inconsiderable portion of the matter of these spirally arranged outer parts will probably travel farther away into infinite space, finally to join some other celestial body or to form parts of the great irregular spots of nebular matter which are collected around the star clusters. Another portion, not able to leave the central body, will remain in circular movement about it. In consequence of this circular movement, which will be extremely slow, the outlines of the two spirals will gradually become obliterated, and the spirals will themselves more and more assume the shape of nebular rings about the central mass.

This spiral form (Figs. 47 and 48) of the outer portions of the nebulæ has for a long time excited the greatest attention. In almost all the investigated instances it has been observed that two spiral branches are coiling about the central body. This would indicate that the matter is in a revolving movement about the central axis of the spiral, and that it has streamed away from the axis in two opposite directions. Sometimes the matter appears arranged as in a coil; of this type the great nebula of Andromeda is the best-known example (Fig. 49). A closer inspection of this nebula with more powerful instruments indicates, however, that it is also spiral and that it appears coiled, because we are looking at it from the side. The late famous American astronomer Keeler, who has studied these nebulæ with greater success than any one else, has catalogued a great many of them in all the divisions of the heavens which were accessible to his instruments, and he has found that these formations are predominatingly of a spiral nature.

Some nebulæ, like the so-called planetary nebulæ, offer rather the appearance of luminous spheres. We may assume in these cases that the explosions were less violent, and that the spirals, therefore, are situated so closely together that they seem to merge into one another. Possibly the inequalities in their development have become equalized in the course of time. A few nebulæ are ring-shaped, as the well-known nebula of Lyra (see Fig. 50). These rings may, again, have been formed out of spiral nebulæ, and the spirals may have gradually been obliterated by rotation, while the central nebulous matter may have been concentrated on the planets travelling round the central star. Schaeberle, an eminent American astronomer, has discovered traces of spiral shape also in the Lyra nebula.

Another kind of nebula is the ordinary nebula of vast extension and irregular shape, evidently formed out of most extremely attenuated matter; well-known characteristic examples are found in Orion, about the Pleiades, and in the Swan (Figs. 51, 52, and 53). In these nebulæ portions of a spiral structure have likewise often been discerned.

We have said that the collision between two celestial bodies would result in the formation of a spiral with two wings. If the impact is such that the two centres of the celestial bodies move straight towards each other, a disk will arise, and not a spiral; or if one star is much smaller than the other, possibly a cone, because the gases will uniformly be spread in all directions about the line of impact. A perfectly central impact is obviously very rare; but there may be cases which approach this limiting condition more or less, especially when the relative velocity of the two bodies is small. By slow diffusion a feebly developed spiral may also be converted into a rotating disklike structure. The extension of these nebular structures will depend upon the ratio between the mass of the system and the velocity of ejection of the gases. If, for example, two extinct suns of nearly equal dimensions and mass, like our sun, should collide, some gas masses would travel into infinite space, being hurled out with a velocity of more than 900 km. (550 miles) per second; while other particles, moving at a slower rate, would remain in the neighborhood of the central body. The nearer to that body, the smaller was their velocity. From their position they might fall back into the central body, to be reincorporated in it, if two circumstances did not prevent this. The one circumstance is the enormous radiation pressure of the glowing central mass. That pressure keeps masses of dust particles floating, which by friction will carry the surrounding masses of gas with them. Owing to the absorption of the radiation by the dust particles, only the finer particles will be supported farther outside, and at the extreme margin of the nebula even the very finest dust will no longer be maintained in suspension by the greatly weakened radiation pressure. Thus we arrive at an outer limit for the nebula. The other circumstance is the violent rotation which is set up by the impact of the central bodies. The rotation and the centrifugal forces will produce a disk-shaped expansion of the whole central mass. Owing to molecular collisions and to tidal effects, the angular velocity will in the denser portions tend to become uniform, so that the whole will rotate like a flattened-out ball filled with gas, and the spiral structure will gradually disappear in those parts. In the more remote particles the velocity will only increase to such an extent as to equal that of a planet moving at the same distance—that is to say, the gravitation towards the central body will be balanced by the centrifugal force, and at the very greatest distances the molecular bombardments, as well as gravitation towards the centre, will become so insignificant that any masses collected there will retain their shape for an almost unlimited space of time.

In the centre of this system the main bulk of the matter would be concentrated in a sun of extreme brightness, whose light intensity would, however, owing to strong radiation, diminish with comparative rapidity.

Such an extensive nebular system, in which gravitation, on account of the enormous distances, would act feebly and very slowly, would yet, in spite of the extraordinary attenuation of matter in its outer portions, and just on account of its vast extension, be able to stop the movement of the particles of dust penetrating into it. If the gases of the nebula are not to escape into space, notwithstanding the infinitesimal gravitation, their molecules must be assumed to be almost at a stand-still, and their temperature must not rise by more than 50° or 60° Cent. above absolute zero. At such low temperatures the so-called adsorption plays an enormously important part (Dewar). The small dust particles form centres about which the gases are condensed to a remarkable degree. The extremely low density of these gases does not prevent their condensation; for the adsorption phenomenon follows a law according to which the mass of condensed gas will only be reduced by about one-tenth when the density of the surrounding gas has been decreased by one-ten-thousandth. The mass of dust particles or dust grains will thus be augmented, and when they collide they will be cemented together by the semiliquid films condensed upon them. There must, hence, be a relatively energetic formation of meteorites in the nebulæ, and especially in their interiors. Then stars and their satellites, migrating through space, will stray into these swarms of gases and meteorites within the nebulæ. The larger and more rapidly moving celestial bodies will crush through this relatively less dense matter; but thousands of years may yet be occupied in their passing through nebulæ of vast dimensions.

An extraordinarily interesting photograph obtained by the celebrated Professor Max Wolf, of Heidelberg, shows us a part of the nebula in the Swan into which a star has penetrated from outside. The intruder has collected about it the nebulous matter it met on its way, and has thus left an empty channel behind it marking its track. Similar spots of vast extent, relatively devoid of nebulous matter, occur very frequently in the irregular nebulæ; they are frequently called "fissures," or by the specifically English term "rifts," because they have generally a long-drawn-out appearance. The presumption that these rifts represent the tracks of large celestial bodies which have cut their way through widely expanded nebular masses (Fig. 54) has been entertained for a long time.

The smaller and more slowly moving immigrants, on the other hand, are stopped by the particles of the nebulæ. We therefore see the stars more sparsely distributed in the immediate neighborhood of the nebulæ, while in the nebulæ themselves they appear more densely crowded. This fact had struck Herschel in his observations of nebulæ; in recent days it has been investigated by Courvoisier and M. Wolf. In this way several centres of attraction are created in a nebula; they condense the gases surrounding the nebula, and catch, so to say, any stray meteorites and collect them especially in the inner portions of the nebula. We frequently observe, further, how the nebular matter appears attenuated at a certain distance from the luminous bright stars (compare Figs. 52 and 55). Finally, the nebulæ change into star clusters which still retain the characteristic shapes of the nebulæ; of these the spiral is the most usual, while we also meet with conical shapes, originating from conical nebulæ, and spherical shapes (compare Figs. 56, 57, and 58).

This is, broadly, the type of evolution through which Herschel, relying upon his observations, presumed a nebula to pass. He was, however, under the impression that the nebulous matter would directly be condensed into star clusters without the aid of strange celestial immigrants.

It has been known since the most ancient times, and has been confirmed by the observations of Herschel and others in a most convincing manner, that the stars are strongly concentrated about the middle line of the Milky Way. It is not improbable that there was originally a nebula of enormous dimensions in the plane of the Milky Way, produced possibly by the collision of two such giant suns as Arcturus. This gigantic nebula has gathered up the smaller migrating celestial bodies which, in their turn, have condensed upon themselves nebular matter, and have thereby become incandescent, if they were not so before. The rotational movement in those parts which were far removed from the centre of the Milky Way may be neglected. At a later period collisions succeeded between the single stars which had been gathered up, and it is for this reason that gaseous nebulæ, as well as new stars, are comparatively frequent phenomena in the plane of the Milky Way. This view may some day receive confirmation, when we succeed in proving the existence of a central body in the Milky Way, evidence of which might possibly be deduced from the curvature of the orbits of the sun or of other stars.

As regards the ring-shaped nebula in the Lyre (Fig. 50), the most recent measurements made by Newkirk point to the result that the star visible in its centre is distant from us about thirty-two light-years. As it appears probable that this star really forms the central core of the nebula, the distance of the nebula itself must be thirty-two light-years. From the diameter of the ring-shaped nebula which Newkirk estimates at one minute of arc, this astronomer has calculated that the distance of the ring from its central body is equal to about three hundred times the radius of the earth’s orbit—that is to say, the ring is about ten times as far from its sun as Neptune is from our sun. There is a faint luminescence within this ring. The nebular matter may originally have been more concentrated at this spot than in the outer portions of the ring itself. But this mass was probably condensed on meteors which immigrated from outside, and when these meteors coalesced dark planets were produced which move about the central body, and which have gathered about them most of the gases. If that central body were as heavy as our sun, the matter in the ring should revolve about it in five thousand years. That rotation would suffice to wipe out the original spiral shape, enough of which has yet been left to permit of our distinctly discerning the two wings of the spiral. The central body of this ring-shaped nebula gives a continuous spectrum of bright lines which is particularly developed on the violet side. The star would therefore appear to be much younger and much hotter than our sun, and its radiation pressure would therefore be much more intense. The period of rotation of the nebula may, for this reason, have to be estimated at a considerably higher figure.

The eminent Dutch astronomer Kapteyn has deduced from the proper motions of 168 nebulæ that their average distance from the earth is about seven hundred light-years and equal to that of stars of the tenth magnitude. The old idea, that the nebulæ must be infinitely farther removed from us than the fainter stars, would therefore appear to be erroneous. According to the measurements of Professor Bohlin, the nebula in Andromeda may indeed be at a distance of not more than forty light-years.

The "new stars" form a group among the peculiar celestial bodies which on account of their variable light intensity have been designated as "variable stars," and of which a few typical cases should be mentioned, because a great scientific interest attaches to these problems. The star Eta, in Argus, may be said to illustrate the strange fate that a star has to pass through when it has drifted into a nebula filled with immigrated celestial bodies. It is one of the most peculiar variable stars. The star shines through one of the largest nebular clouds in the heavens. Whether it stands in any physical connection with its surroundings cannot be stated without further examination. The star might, for instance, be at a considerable distance in front of the nebula, between the latter and ourselves. Its frequent change in light intensity suggests, however, a series of collisions, which do not appear unnatural to us when we suppose that the star is within a nebula into which many celestial bodies have drifted.

As this star belongs to the southern hemisphere, it was not observed before our astronomers commenced to visit that hemisphere. In 1677 it was classed as a star of the fourth magnitude; ten years later it was of the second magnitude; the same in 1751. In 1827 it was of the first magnitude, and it was found to be variable—that is to say, it shone with variable brightness. Herschel observed that it fluctuated between the first and second magnitudes, and that it increased in brightness after 1837, so that it was by 1838 of magnitude 0.2. After that it began to decrease in intensity up to April, 1839, when it had the magnitude 1.1. It remained for four years approximately at this intensity; then it increased rapidly again in 1843, and surpassed all stars except Sirius (magnitude -1.7).[16] Afterwards its intensity slowly diminished once more, so that it remained just visible to the naked eye (sixth magnitude); by 1869 it had become invisible. Since then it has been fluctuating between the sixth and seventh magnitudes.

The last changes in the intensity of this star strongly recall the behavior of the new star in Perseus, only that the latter has been passing through its phases at a much more rapid rate. It appears to be certain, however, that Eta, in Argus, was from the very beginning far brighter than Nova Persei, and that at least once before the great collision in 1843 (after which it was surrounded by obscuring clouds of increasing opacity)—namely, in January, 1838, it had been exposed to a slight collision of quickly vanishing effect. This lesser collision was probably of the kind which Mayer imagined for the earth and sun. It would give rise to heat development corresponding to the heat expenditure of the sun in about a hundred years. As it had been observed that the star was variable in an irregular manner before that, we may, perhaps, presume that it had already undergone another collision.

According to the observations of Borisiak, a student in Kief, the new star in Perseus would have been, on the evening of February 21, 1901, of 1.5 magnitude, while a few hours previously it had been of magnitude 12, and the following evening of magnitude 2.7; afterwards its intensity increased up to the following evening, when it outshone all the other stars in the northern sky. If this statement is not based on erroneous observations, the new star must have been in collision with another celestial body two days before its great collision, perhaps with a small planet in the neighborhood of the sun, with which it later collided. That would account for its temporary brilliancy.

New stars are by no means so rare as one might perhaps assume. Almost every year some new star is discovered. By far most of these are seen in the neighborhood of the Milky Way, where the visible stars are unusually crowded, so that a collision which would become visible to us may easily occur.

For similar reasons we find there also most of the gaseous nebulæ.

Most of the star clusters are also in the neighborhood of the Milky Way. This is in consequence of the facts just alluded to. The nebulæ which are produced by collisions between two suns are soon crossed by migrating celestial bodies such as meteorites or comets, which there occur in large numbers; by the condensing action of these intruders they are then transformed into star clusters. In parts of the heavens where stars are relatively sparse (as at a great distance from the Milky Way), most of the nebulæ observed exhibit stellar spectra. They are nothing but star clusters, so far removed from us that the separate stars can no longer be distinguished. That single stars and gaseous nebulæ are so rarely perceived in these regions is, no doubt, due to their great distance.

Among the variable stars we find quite a number which display considerable irregularity in their fluctuations of brightness, and which remind us of the new stars. To this class belongs the just-mentioned star Eta, in Argus. Another example (the first one which was recognized as "variable") is Mira Ceti, which may be translated, "The Wonderful Star in the Constellation of the Whale." This mysterious body was discovered by the Frisian priest Fabricius, on August 12, 1596, as a star of the second magnitude. The priest, an experienced astronomer, had not previously noticed this star, and he looked for it in vain in October, 1597. In the years 1638 and 1639 the variability of the star was recognized, and it was soon ascertained to be irregular. The period has a length of about eleven months, but it fluctuates irregularly about this figure as a mean value. At its greatest intensity the star ranks with those of the first or second order. Sometimes it is weaker, but it is always of more than the fifth magnitude. Ten weeks after a maximum the star is no longer visible, and its brightness may diminish to magnitude 9.5. In other words, its intensity varies about in the ratio of 1: 1000 (or possibly more). After a minimum the brightness once more increases, the star becomes visible again—that is to say, it attains the sixth magnitude—and after another six weeks it will once more be at its maximum. We have evidently to deal with several superposed periods.

The spectrum of this star is rather peculiar. It belongs to the red stars with a band spectrum which is crossed by bright hydrogen lines. The star is receding from us with a velocity of not less than 63 km. (39 miles) per second. The bright hydrogen lines which correspond to the spectrum of the nebula may sometimes be resolved into three components, of which the middle one corresponds to a mean velocity of 60 km., and the two others have variable receding velocities of 35 and 82 km.—that is to say, velocities of 25 or 22 km. less or more than the mean velocity. Evidently the star is surrounded by three nebulæ; one is concentrated about its centre; the two others lie on a ring the matter of which has been concentrated on two opposite sides. The ring, which recalls the ring nebula in the Lyre, seems to move about the star with a velocity of 23.5 km. per second. As this revolution is accomplished within eleven—or, more correctly, within twenty-two months, since there must be two maxima and two minima during one revolution—the total circumference of the ring will be 23.5 × 86,400 × 670—1361 millions, and the radius of its orbit 217 million km., which is 1.45 times greater than the radius of the earth’s orbit. Now the velocity of the earth in its orbit is 29.5 km. (18.3 miles) per second. A planet at 1.45 times that distance from the sun would have the (1.203 times smaller) velocity of 24.5 km. per second, which is approximately that of the hypothetical ring of Mira Ceti. We conclude, therefore, that the mass of the central sun in Mira Ceti will nearly equal the mass of our sun. The calculation really suggests that Mira would be about eight per cent. smaller; but the difference lies within the range of the probable error.

Chandler has directed attention to a striking regularity in these stars. The longer the period of their variation, the redder in general their color. This is easily comprehended. The denser the original atmosphere, the more widely the gases will have extended outward from the star, and the more dust will have been caught or secreted by it. We have seen that the limb of the sun has a reddish light because of the quantities of dust in the solar atmosphere. The effect is chiefly to be ascribed to the absorption of the blue rays by the dust; but it may partly be explained on the assumption that the solar radiations render the dust incandescent, though its temperature may be lower than that of the photosphere, because the dust lies outside the sun, and that it will therefore emit a relatively reddish light. The more dust there is in a nebula, the redder will be its luminescence; and as the quantity of dust increases in general with the extension of the nebula, that star which is surrounded by wider rings of nebulæ will in general be more red; but the greater the radius of the ring, the longer also will in general be its period.

The so-called red stars show, in addition to the bright hydrogen lines, banded spectra which indicate the presence of chemical compounds. On this account such stars were formerly credited with a lower temperature. But the same peculiarity is also observed in sun-spots, although the latter, on account of their position, must have a higher temperature than the surrounding photosphere. The presence of bands in the spectrum certainly suggests high pressure, however. The red stars are evidently surrounded by a very extensive atmosphere of gases, in the inner portions of which the pressure is so high that the atoms enter into combination. The spectra of the red stars display, on the whole, a striking resemblance to those of the sun-spots. The violet portion of the spectrum is weakened, because the masses of dust have extinguished this light. Owing to the large masses of dust which lie in our line of sight, the spectrum lines are in both cases markedly widened and sometimes accompanied by bright lines.

Another class of stars, distinguished by bright lines, comprises those studied by Wolf and Rayet, and named after them. These stars are characterized by a hydrogen atmosphere of enormous extension, large enough in some cases, it has been calculated, to fill up the orbit of Neptune. These stars are evidently either hotter and more strongly radiating than the red stars, or there is not so much dust in their neighborhood—the dust may possibly have been expelled by the strong radiating pressure. They are, therefore, classed with the yellow, and not with the red stars. Although there is every reason to suppose that their central bodies are at least as hot as those of the white stars, the dust is yet able to reduce the color to yellow, owing to the vast extensions of their atmospheres.

The unequal periods in stars like Mira may be explained by the supposition that there are several rings of dust moving about them, as in the case of the planet Saturn. In the case of the inner rings which have a short period, there has probably been sufficient time during the uncounted number of revolutions to effect a uniform distribution of the dust. Hence we do not discern any noteworthy nuclei in them, such as we observe in the tails of comets; the dust rings only help to impart to the star a uniform reddish hue. In the outer rings the distribution of dust will, however, not be uniform. One of the rings may be responsible for the chief proper period. By the co-operation of other less important dust rings, the maximum or minimum, we shall easily understand, may be displaced, and thus the time interval between the maxima and minima be altered. This alteration of the period is so strong for some stars that we have not yet succeeded in establishing any simple periodicity. The best-known star of this type is the bright-red star Betelgeuse in the constellation of Orion. The brightness of this star fluctuates irregularly between the magnitudes 1.0 and 1.4.

By far the largest number of variable stars belong to the type of Mira. Others resemble the variable star Beta in the constellation of the Lyre, and thus belong to the Lyre type. The variability of the spectra of a great many of these stars indicates that they must be moving about a dark star as companion, or rather that they both move about a common centre of gravity. The change in the light intensity is, as a rule, explained by the supposition that the bright star is partially obscured at times by its dark companion. Many irregularities, however, in their periods and other circumstances prove that this explanation is not sufficient. The assumption of rings of dust circulating about the star and of larger condensation centres affords a better elucidation of the variability of these stars. They are grouped with the white or yellow stars, in whose surroundings the dust does not play so large a part as in that of Mira Ceti. The period of their variability is, as a rule, very short, moreover—generally only a few days (the shortest known, only four hours)—while the period of the Mira stars amounts to at least sixty-five days, and may attain two years. There may be still longer periods so far not investigated.

Nearly related to the Lyre stars are the Algol stars, whose variability can be explained by the assumption that another bright or dark star is moving within their vicinity, partially cutting off their light. There is no dust in these cases, and the spectrum characterizes these stars as stars of the first class—that is, as white stars—so far as they have been studied up to the present.

We must presume for all the variable stars that the line of sight from the observer to the star falls in the plane of their dust rings or of their companions. If this were not so, they would appear to us like a nebula with a central condensation nucleus, or, so far as Algol stars are concerned, like the so-called spectroscopic doubles whose motion about each other is recognized from the displacement of their spectral lines.

The evolution of stars from the nebulous state has been depicted by the famous chief of the Lick Observatory, in California, W. W. Campbell, as follows (compare the spectra of the stars of the 2d, 3d, and 4th class, Figs. 59 and 60):