We will now proceed to a more intimate consideration of the chemical and physical conditions which probably characterize the nebulæ in distinction from the suns. These properties differ in many respects essentially from those which we are accustomed to associate with matter as investigated by us, which may, from this point of view, be styled relatively concentrated.

The differences must be fundamental. For the motto of Clausius, which comprises the sum of our knowledge of the nature of heat, cannot apply to nebulæ. This motto reads:

Everybody understands what is meant by energy. We know energy in many forms. The most important are: energy of position (a heavy body has larger energy by virtue of its having been raised to a certain height above the surface of the earth than when it is lying on the surface); energy of motion (a discharged rifle-bullet has an energy which is proportional to the mass of the bullet and to the square of its velocity); energy of heat, which is regarded as the energy of the motion of the smallest particles of a body; electrical energy, such as can, for instance, be stored in an accumulator battery, and which, like all other modifications of energy, may be converted into energy of heat; and chemical energy, such as is displayed by a mixture of eight grammes of oxygen with one gramme of hydrogen, which can be transformed into water under a strong evolution of heat. When we say that the energy of a system to which energy is not imparted from outside is constant, we merely mean that the different forms of energy of the separate parts of this system may be transformed into other forms of energy, but that the sum total of all the energies must always remain unchanged. According to Clausius this law is valid throughout the infinite space of the universe.

By entropy we understand the quantity of heat of a body divided by its absolute temperature. If a quantity of heat, of Q calories, of a body at a temperature of 100° (absolute temperature, 373°) passes over to another body of 0° (absolute temperature, 273°), the total entropy of the two will have been decreased by Q/373, and increased by Q/273. As the latter quantity is the greater, the entropy of the whole will have increased. By itself, we know, heat always passes, either by radiation or by conduction, from bodies of higher temperature to bodies of lower temperature. That evidently implies an increase in entropy, and it is in agreement with the law of Clausius that entropy tends to increase.

The most simple case of heat equilibrium is that in which we place a number of bodies of unequal temperatures in an enclosure which neither receives heat from outside nor communicates heat to the outside. In some way or other, usually by conduction or radiation, the heat will pass from the warmer to the colder bodies, until at last equilibrium ensues and all the bodies have the same temperature. According to Clausius, the universe tends to that thermal equilibrium. If it be ever attained, all sources of motion, and hence of light, will have been exhausted. The so-called "heat-death" (Wärmetod) will have come.

If Clausius were right, however, this heat-death, we may object, should already have occurred in the infinitely long space of time that the universe has been in existence. Or we might argue that the world has not yet been in existence sufficiently long, but that, anyhow, it had a beginning. That would contradict the first part of the law of Clausius, that the energy of the universe is constant; for in that case all the energy would have originated in the moment of creation. That is quite inconceivable, and we must hence look for conditions for which the entropy law of Clausius does not hold.

The famous Scotch physicist Clerk-Maxwell has conceived of such a case. Imagine a vessel which is divided by a partition into two halves, both charged with a gas of perfectly uniform temperature. Let the partition be provided with a number of small holes which would not allow more than one gas molecule to pass at a time. In each hole Maxwell places a small, intelligent being (one of his "demons"), which directs all the molecules which enter into the hole, and which have a greater velocity than the mean velocity of all the molecules, to the one side, and which sends to the other side all the molecules of a smaller velocity than the average.[19] All the undesirable molecules the demon bars by means of a little flap. In this way all the molecules of a velocity greater than the average may be collected in the one compartment, and all the molecules of a lesser velocity in the other compartment. In other words, heat—for heat consists in the movements of molecules—will pass from the one constantly cooling side to the other, which is constantly raising its temperature, and which must therefore become warmer than the former.

In this instance heat would therefore pass from a colder to a warmer body, and the entropy would diminish.

Nature, of course, does not know any such intelligent beings. Nevertheless, similar conditions may occur in celestial bodies in the gaseous state. When the molecules of gas in the atmosphere of a celestial body have a sufficient velocity—which in the case of the earth would be 11 km. (7 miles) per second—and when they travel outward into the most extreme strata, they may pass from the range of attraction out into infinite space, after the manner of a comet, which, if endowed with sufficient velocity when near the sun, must escape from the solar system. According to Stoney, it is in this way that the moon has lost its original atmosphere. This loss of gas is certainly imperceptible in the case of our sun and of large planets like the earth. But it may play an important part in the household of the nebulæ, where all the radiation from the hot celestial bodies is stored up, and where, owing to the enormous distances, the restraining force of gravity is exceedingly feeble. Thus the nebulæ will lose their most rapid molecules from their outer portions, and they will therefore be cooling in these outer strata. This loss of heat is compensated by the radiation from the stars. If, now, there were only nebulæ of one kind in the whole universe, those escaped molecules would finally land on some other nebula, heat equilibrium would thus be established between the different nebulæ, and the "heat-death" be realized. But we have already remarked that the nebulæ enclose many immigrated celestial bodies, which are able to condense the gases from their neighborhood, and which thereby assume a higher temperature.

The lost molecules of gases may also stray into the vast atmosphere of these growing stars, and the condensation will then be hastened under a continuous lowering of the entropy. By such processes the clock-work of the universe may be maintained in motion without running down.

About the bodies which have drifted into nebulæ, and about the remnants of new stars which lie inside the nebulæ, the gases will thus collect which had formerly been scattered through the outer portions of the nebula. These gases originate from the explosive compounds which had been stored in the interior of the new stars. Hydrogen and helium are, most likely, the most important of these; for they are the most difficult to be condensed, and can exist in notable quantities at extremely low temperatures, such as must prevail in the outermost portions of the nebulæ, in which gases of other substances would be liquefied. Even if the nebulæ had an absolute temperature of 50° (-223° C.), the vapor of the most volatile of all the metals, mercury, would even in the saturated state be present in such a small quantity that a single gramme would occupy the space of a cube whose side would correspond to about two thousand light-years—that is to say, to 450 times the distance of the earth from the nearest fixed star. One gramme of sodium, likewise a very volatile metal, and of a comparatively high importance in the constitution of the fixed stars, would fill the side of a cube that would be a thousand million times as large. Still more inconceivable numbers result for magnesium and iron, which are very frequent constituents of fixed stars, and which are less volatile than the just-mentioned metals. We thus recognize the strongly selective action of the low temperatures upon all the substances which are less difficult to condense than helium and hydrogen. As we now know that there is another substance in the nebulæ, which has been designated nebulium, and which is characterized by two spectral lines not found in any terrestrial substance, we must conclude that this otherwise unknown element nebulium must be almost as difficult to condense as hydrogen and helium. Its boiling-point will probably lie below 50° absolute, like that of those gases.

That hydrogen and helium, together with nebulium, alone seem to occur in the vastly extended nebulæ is probably to be ascribed to their low boiling-points. We need not look for any other explanation. The supposition of Lockyer that all the other elements would be transformed into hydrogen and helium at extreme rarefaction is quite unsupported.

In somewhat lower strata of the nebula, where its shape resembles a disk, other not easily condensable substances, such as nitrogen, hydrocarbons of simple composition, carbon monoxide, further, at deeper levels, cyanogen and carbon dioxide, and, near the centre, sodium, magnesium, and even iron may occur in the gaseous state. These less volatile constituents may exist as dust in the outermost strata. This dust would not be revealed to us by the spectroscope. In the strongly developed spiral nebulæ, however, the extreme layers, which seem to hide the central body, appear to be so attenuated that the dust floating in them is not able to obscure the spectrum of the metallic gases. The spectrum of the nebula then resembles a star spectrum, because the deepest strata contain incandescent layers of dust clouds, whose light is sifted by the surrounding masses of gases.

It has been observed that the lines of the different elements are not uniformly distributed in the nebulæ. Thus Campbell observed, for instance, when investigating a small planetary nebula in the neighborhood of the great Orion nebula, that the nebulium had not the same distribution as the hydrogen. The nebulium, which was concentrated in the centre of the nebula, probably has a higher boiling-point than hydrogen, therefore, and occurs in noticeable quantities in the inner, hotter parts of the nebula. Systematic investigations of this kind may help us to a more perfect knowledge of the temperature relations in these peculiar celestial objects.

Ritter and Lane have made some interesting calculations on the equilibrium in a gaseous celestial body of so low a density that the law of gases may be applied to it. That is only permissive for gases or for mixtures of gases whose density does not exceed one-tenth of that of water or one-fourteenth of the actual density of the sun. The pressure in the central portions of such a mass of gas would, of course, be greater than the pressure in the outer portions, just as the pressure rises as we penetrate from above downward into our terrestrial atmosphere. If we imagine a mass of the air of our atmosphere transferred one thousand metres higher up, its volume will increase and its temperature will fall by 9.8° C. (18° F.). If there were extremely violent vertical convection currents in the air, its temperature would diminish in this manner with increasing altitude; but internal radiation tends to equalize these temperature differences. The following calculation by Schuster concerning the conditions of a mass of gas of the size of the sun is based on Ritter’s investigation. It has been made under the hypothesis that the thermal properties of this mass of gas are influenced only by the movements in it, and not by radiation. The calculation is applied to a star which has the same mass as the sun (1.9 × 10³³ grammes, or 324,000 times the mass of the earth), and a radius of about ten times that of the sun (10 × 690,000 km.), whose mean density would thus be 1000 times smaller than that of the sun, or 0.0014 times the density of water at 4° C. In the following table the first column gives the distance of a point from the centre of the star as a fraction of its radius; the density (second column) is expressed in the usual scale, water being the unit; pressures are stated in thousands of atmospheres, temperatures in thousands of degrees Centigrade. The temperature will vary proportionately to the molecular weight of the gas of which the star consists; the temperatures, in the fourth column of the table, concern a gas of molecular weight 1—that is to say, hydrogen gas dissociated into atoms, as it will be undoubtedly on the sun and on the star. If the star should consist of iron, we should have to multiply these latter numbers by 56, the molecular weight of iron; the corresponding figures will be found in the fifth column.

Schuster’s calculation was really made for the sun—that is to say, for a celestial body whose diameter is ten times smaller, and whose specific gravity is therefore a thousand times greater than the above-assumed values. According to the laws of gravitation and of gases, the pressure must there be 10,000 times greater, and the temperature ten times higher, than those in our table. The density of the interior portions would, however, become far too large to admit of the application of the gas laws. I have therefore modified the calculations so as to render them applicable to a celestial body of ten times the radius of the sun or of 1080 times the radius of the earth; the radius would then represent one-twenty-second of the distance from the centre of the sun to the earth’s orbit, and the respective celestial body would have very small dimensions indeed if compared to a nebula.

The extraordinarily high pressure in the interior portions of the celestial body is striking; this is due to the great mass and to the small distances. In the centre of the sun the pressure would amount to 8520 million atmospheres, since the pressure increases inversely as the fourth power of the radius. The pressure near the centre of the sun is, indeed, almost of that order. If the sun were to expand to a spherical planetary nebula of a thousand times its actual linear dimensions (when it would almost fill the orbit of Jupiter), the specific gravity at its centre would be diminished to one-millionth of the above-mentioned value—that is to say, matter in this nebula would not, even at the point of greatest concentration, be any denser than in the highly rarefied vacuum tubes which we can prepare at ordinary temperatures. The pressure would likewise be greatly diminished—namely, to about six millimetres only, near the centre of the gaseous mass. The temperature, however, would be rather high near the centre—namely, 24,600° C., if the nebula should consist of atomatic hydrogen, and fifty-six times as high again if consisting of iron gas. Such a nebula would restrain gases with 1.63 times the force which the earth exerts. Molecules of gases moving outward with a velocity of about 18 km. (11 miles) per second would forever depart from this atmosphere.

The estimation of the temperature in such masses of gases is certainly somewhat unreliable. We have to presume that neither radiation nor conduction exert any considerable influence. That might be permitted for conduction; but we are hardly justified in neglecting radiation. The temperatures within the interior of the nebula will, therefore, be lower than our calculated values. It is, however, difficult to make any definite allowance for this factor.

If the mass of the celestial body should not be as presumed—for instance, twice as large—we should only have to alter the pressure and the density of each layer in the same proportion, and thus to double the above values. The temperature would remain unchanged. We are hence in a position to picture to ourselves the state of a nebula of whatever dimensions and mass.

Lane has proved, what the above calculations also indicate, that the temperature of such nebula will rise when it contracts in consequence of its losing heat. If heat were introduced from outside, the nebula would expand under cooling. A nebula of this kind presumably loses heat and gradually raises its own temperature until it has changed into a star, which will at first have an atmosphere of helium and of hydrogen like that of the youngest stars (with white light). By-and-by, under a further rise of temperature, the extremely energetic chemical compounds will be formed which characterize the interior of the sun, because helium and hydrogen—which were liberated when the nebula was re-formed and which dashed out into space—will diffuse back into the interior of the star, where they will be bound under the formation of the compounds mentioned. The atmosphere of hydrogen and of helium will disappear (helium first), the star will contract more and more, and the pressure and the convection currents in the gases will become enormous. There will be a strong formation of clouds in the atmosphere of the star, which will gradually become endowed with the properties which characterize our sun. The sun behaves very differently from the gaseous nebulæ for which the calculations of Lane, Ritter, and Schuster hold. For when the contraction of a gas shall have proceeded to a certain limit, the pressure will increase in the ratio 1: 16, while the volume will decrease in the ratio 8: 1, provided there be no change in the temperature. When the gas has reached this point and is still further compressed, the temperature will remain in steady equilibrium. At still higher pressures, however, the temperature must fall if equilibrium is to be maintained. According to Amagat, this will occur at 17° C. (290° absolute) in gases like hydrogen and nitrogen, which at this temperature are far above their critical points, and at a pressure of 300 or 250 atmospheres. When the temperature is twice as high on the absolute scale, or at 307° C., twice the pressure will be required.

We can now calculate when our nebula will pass through this critical stage, to which a lowering of the temperature must succeed. Accepting the above figures, we find that half the mass of the nebula will fill a sphere of a radius 0.53 of that of the nebula. If the mass were everywhere of the same density, half of it would fill a sphere of 0.84 of this radius. When will the interior mass cross the boundary of the above stage, while the exterior portions still remain below this stage? That will be at about the time when the nebula in its totality will pass through its maximum temperature. We will now base our calculations on the temperatures which apply to iron in the gaseous state; for in the interior of the nebula the mean molecular weight will at least be 56 (that of iron). We shall find that the pressure at the distance 0.53 will be about 177,000 atmospheres, and the temperature approximately 71 million degrees—i.e., 245,000 times higher than the absolute temperature in the experiments of Amagat. The specified stage will then be reached when the pressure will be 245,000 times as large as 250 atmospheres—viz., 61 million atmospheres. As, now, the pressure is only 177,000 atmospheres, our nebula will yet be far removed from that stage at which cooling will set in. We can easily calculate that this will take place when the nebula has contracted to a volume about three times that of our sun. The assertion which is so often made that the sun might possibly attain higher temperatures in the future is unwarranted. This celestial body has long since passed through the culminating-point of its thermal evolution, and is now cooling. As the temperatures which Schuster deduced were no doubt much too high, the cooling must, indeed, have set in already in an earlier stage. But stars like Sirius, whose density is probably not more than one per cent, of the solar density, are probably still in a rising-temperature stage. Their condition approximates that of the mass of gas of our example.

The planetary nebulæ are vastly more voluminous. The immense space which these celestial bodies may occupy will be understood from the fact that the largest among them, No. 5 in Herschel’s catalogue, situated near the star B in the Great Bear, has a diameter of 2.67 seconds of arc. If it were as near to us as our nearest star neighbor, its diameter would yet be more than three times that of the orbit of Neptune; doubtless it is many hundreds of times larger. This consideration furnishes us with an idea of the infinite attenuation in such structures. In their very densest portions the density cannot be more than one-billionth of the density of the air. In the outer portions of such nebulæ the temperature must also be exceedingly low; else the particles of the nebula could not be kept together, and only hydrogen and helium can occur in them in the gaseous state.

Yet we may regard the density and temperature of such celestial bodies as gigantic by comparison with those of the gases in the spirals of the nebulæ. There never is equilibrium in these spirals, and it is only because the forces in action are so extraordinarily small that these structures can retain their shapes for long periods without noticeable changes. It is, probably, chiefly in those parts in which the cosmical dust is stopped in its motion that meteorites and comets are produced. The dust particles wander into the more central portions of the nebulæ, into which they penetrate deeply, owing to their relatively large mass, to form the nuclei for the growth of planets and moons. By their collisions with the masses of gases which they encounter, they gradually assume a circular movement about the axis of rotation of the nebula. In this rotation they condense portions of the gases on their surface, and hence acquire a high temperature—which they soon lose again, however, owing to the comparatively rapid radiation.

So far as we know, spiral nebulæ are characterized by continuous spectra. The splendor of the stars within them completely outshines the feeble luminosity of the nebula. The stars in them are condensation products and undoubtedly in an early stage of their existence; they may therefore be likened to the white stars, like the new star in Perseus and the central star in the ring nebula of the Lyre. Nevertheless, it has been ascertained that the spectrum of the Andromeda nebula has about the same length as that of the yellow stars. That may be due to the fact that the light of the stars in this nebula, which we only seem to see from the side, is partly extinguished by dust particles in its outer portion, as was the case with the light of the new star in Perseus during the period of its variability.

Our considerations lead to the conclusion that there is rotating about the central body of the nebula an immense mass of gas, and that outside this mass there are other centres of condensation moving about the central body together with the masses of gas concentrated about them. Owing to the friction between the immigrated masses and the original mass of gas which circulated in the equatorial plane of the central body, all these masses will keep near the equatorial plane, which will therefore deviate little from the ecliptic. We thus obtain a proper planetary system, in which the planets are surrounded by colossal spheres of gas like the stars in the Pleiades (Fig. 52). If, now, the planets have very small mass by comparison with the central body—as in our solar system—they will be cooled at an infinitely faster rate than the sun. The gaseous masses will soon shrink, and the periods of rotation will be shortened; but for those planets, at least, which are situated near the centre, these periods will originally differ little from the rotation of the central body. The dimensions of the central body will always be very large, and the planets circulating about it will produce very strong tidal effects in its mass. Its period of rotation will be shortened, while the orbital rotation of the planets will tend to become lengthened. Thus the equilibrium is disturbed; it is re-established again, because the planet is, so to say, lifted away from the sun, as G. H. Darwin has so ingeniously shown with regard to the moon and the earth. Similar relations will prevail in the neighborhood of those planets which will thus become provided with moons. Hence we understand the peculiar fact that all the planets move almost in the same plane, the so-called ecliptic, and in approximately circular orbits; that they all move in the same direction, and that they have the same direction of rotation in common with their moons and with the central body, the sun. It is only the outermost planets, like Uranus and Neptune, in whose cases the tidal effects were not of much consequence, that form exceptions to this rule.

In explanation of these phenomena various philosophers and astronomers have advanced a theory which is known as the Kant-Laplace theory, after its most eminent advocates. Suggestions pointing in the same direction we find in Swedenborg (1734). Swedenborg assumed that our planetary system had been evolved under the formation of vortices from a kind of "chaos solare," which had acquired a more and more energetic circulating motion about the sun under the influence of internal forces, possibly akin to magnetic forces. Finally a ring had been thrown off from the equator, and had separated into fragments, out of which the planets had been formed.

Buffon introduced gravitation as the conservational principle. In an ingenious essay, "Formation des Planètes" (1745), he suggests that the planets may have been formed from a "stream" of matter which was ejected by the sun when a comet rushed into it.

Kant started from an original chaos of stationary dust, which under the influence of gravitation arranged itself as a central body, with rings of dust turning around it; the rings, later on, formed themselves into planets. The laws of mechanics teach, however, that no rotation can be set up in a central body, which is originally stationary, by the influence of a central force like gravitation. Laplace, therefore, assumed with Swedenborg that the primeval nebula from which our solar system was evolved had been rotating about the central axis. According to Laplace, rings like those of Saturn would split off, as such a system contracted, and planets and their moons and rings would afterwards be formed out of those rings. It is generally believed at present, however, that only meteorites and small planets, but not the larger planets, could have originated in this way. We have, indeed, such rings of dust rotating about Saturn, the innermost more rapidly, the outer rings more slowly, just as they would if they were crowds of little moons.

Many further objections have later been raised against the hypothesis of Laplace, first by Babinet, later especially by Moulton and Chamberlin. In its original shape this hypothesis would certainly not appear to be tenable. I have therefore replaced it by the evolution thesis outlined above. It is rather striking that the moons of the outermost planets, Neptune and Uranus, do not move in the plane of the ecliptic, and that their moons further describe a "retrograde" movement—that is to say, they move in the direction opposite to that conforming to the theory of Laplace. The same seems to hold for the moon of Saturn, which was discovered in 1898 by Pickering. All these facts were, of course, unknown to Laplace in 1776; and if he had known them he would scarcely have advanced his thesis in the garb in which he offered it. The explanation of these facts does not cause any difficulty. We may assume that the matter in the outer portions of the primeval nebula was so strongly attenuated that the immigrating planet did not attain a sufficient volume to have the large common rotation in the equatorial plane of the sun impressed upon it by the tidal effects. Charged only with the small mass of matter which they met on their road, the planet and its moon, on the contrary, remained victorious in the limited districts in which they were rotating. Only the slow orbital movement about the central body was influenced, and that adapted itself to the common direction and the circular orbit. It is not inconceivable that there may be, farther out in space, planets of our solar system, unknown to us, moving in irregular paths like the comets. The comets, Laplace assumed, probably immigrated at a later period into our solar system when the condensation had already advanced so far that the chief mass of the nebular matter had disappeared from interplanetary space.

Chamberlin and Moulton have attempted to show that the difficulties of the hypothesis of Laplace may be obviated by the assumption that the solar system has evolved from a spiral nebula, into which strange bodies intruded which condensed the nebular mass of their surroundings upon themselves. We have pointed out examples of how the nebula seems to vanish in the vicinity of the stars, which would correspond to growing planets, located in nebulæ.

In concluding this consideration, we may draw a comparison between the views which were still entertained a short time ago and the views and prospects which the discoveries of modern days open to our eyes.

Up to the beginning of this century the gravitation of Newton seemed to rule supreme over the motions and over the development of the material universe. By virtue of this gravitation the celestial bodies should tend to draw together, to unite in ever-growing masses. In the infinite space of past time the evolution should have proceeded so far that some large suns, bright or extinct, could alone persist. All life would be impossible under such conditions.

And yet we discern in the neighborhood of the sun quite a number of dark bodies, our planets, and we may surmise that similar dark companions or satellites exist in the vicinity of other suns and stars; for we could not understand the peculiar to-and-fro motions of those stars on any other view. We further observe that quite a number of small celestial bodies rush through space in the shapes of meteorites or shooting-stars which must have come to us from the most remote portions of the universe.

The explanation of these apparent deviations from what we may regard as a necessary consequence of the exclusive action of gravity will be found under two heads—in the action of the mechanical radiation pressure of light, and in the collisions between celestial bodies. The latter produce enormous vortices of gases about nebular structures in the gaseous condition; the radiation pressure carries cosmical dust into the vortices, and the dust collects into meteorites and comets and forms, together with the condensation products of the gaseous envelope, the planets and the moons accompanying them.

The scattering influence of the radiation pressure therefore balances the tendency of gravitation to concentrate matter. The vortices of gases in the nebulæ only serve to fix the position of the dust, which is ejected from the suns through the action of the radiation pressure.

The masses of gas within the nebulæ form the most important centres of concentration of the dust which is ejected from the sun and stars. If the world were limited, as people used to fancy—that is to say, if the stars were crowded together in a huge heap, and only infinite, empty space outside of this heap, the dust particles ejected from the suns during past ages by the action of the radiating pressure would have been lost in infinite space, just as we imagined that the radiated energy of the sun was lost.

If that were so, the development of the universe would long since have come to an end, to an annihilation of all matter and of all energy. Herbert Spencer, among others, has explained how thoroughly unsatisfactory this view is. There must be cycles in the evolution of the universe, he has emphasized. That is manifestly indispensable if the system is to last. In the more rarefied, gaseous, cold portions of the nebulæ we find that part of the machinery of the universe which checks the waste of matter and, still more, the waste of force from the suns. The immigrating dust particles have absorbed the radiation of the sun and impart their heat to the separate particles of the gases with which they collide. The total mass of gas expands, owing to this absorption of heat, and cools in consequence. The most energetic molecules travel away, and are replaced by new particles coming from the inner portions of the nebulæ, which are in their turn cooled by expansion. Thus every ray emitted by a sun is absorbed, and its energy is transferred, through the gaseous particles of the nebulæ, to suns that are being formed and which are in the neighborhood of the nebula or in its interior portions. The heat is hence concentrated about centres of attraction that have drifted into the nebula or about the remnants of the celestial bodies which once collided there. Thanks to the low temperature of the nebula, the matter can again accumulate, while the radiation pressure, as Poynting has shown, will suffice to keep bodies apart if their temperature is 15° C., their diameter 3.4 cm., and their specific gravity as large as that of the earth, 5.5. At the distance of the orbit of Neptune, where the temperature is about 50° absolute and approximates, therefore, that of a nebula, this limit of size is reduced to nearly one millimetre. It has already been suggested (compare page 153) that capillary forces, which would prevail under the co-operation of the gases condensed upon the dust grains, rather than gravity, play a chief part in the accumulation and coalescence of the small particles. In the same manner as matter is concentrated about centres of attraction energy may be accumulated there in contradiction to the law of the constant increase of entropy.

During this conservational activity the layers of gas are rapidly rarefied, to be replaced by new masses from the inner parts of the nebula, until this centre is depleted, and the nebula has been converted into a star cluster or a planetary system which circulates about one or several suns. When the suns collide once more new nebulæ are created.

The explosive substances, consisting probably of hydrogen and helium (and possibly of nebulium), in combination with carbon and metals, play a chief part in the evolution from the nebular to the stellar state, and in the formation of new nebulæ after collisions between two dark or bright celestial bodies. The chief laws of thermodynamics lead to the assumption that these explosive substances are formed during the evolution of the suns and are destroyed during their collisions. The enormous stores of energy concentrated in these bodies perform, in a certain sense, the duty of powerfully acting fly-wheels interposed in the machinery of the universe in order to regulate its movements and to make certain that the cyclic transition from the nebular to the star stage, and vice versa, will occur in a regular rhythm during the immeasurable epochs which we must concede for the evolution of the universe.

By virtue of this compensating co-operation of gravity and of the radiation pressure of light, as well as of temperature equalization and heat concentration, the evolution of the world can continue in an eternal cycle, in which there is neither beginning nor end, and in which life may exist and continue forever and undiminished.