the gaseous sphere, with k=1.4, which has the central density 23 times the average. The monatomic Sun thus occupies a position intermediate between the homogeneous Sun considered by Helmholtz and that of Lane's gaseous sphere with k=1.4.

There is every reason to believe that the monatomic sphere is that which occurs in nature, and yet it has received heretofore scarcely any attention from investigators. One of the most important results deduced from the theory of the monatomic sphere is that it gives up about forty-three per cent more heat in condensation than Helmholtz's homogeneous sphere, and the effect is to multiply Helmholtz's values by 1.43 as a factor. Instead of raising an equivalent mass of water through about 27,000,000 degrees Centigrade, the total heat of condensation of such a sphere of monatomic gas would raise an equal mass of water through nearly 40,000,000 degrees Centigrade. This considerably increases the past duration of the Sun's activity; and as the calculation is very accurate, we are enabled to speculate with great confidence on the duration of the solar system, so far as it depends on the energy of gravitation.

Now, it is found by the finest modern measurements that the heat annually radiated by the Sun would raise an equal mass of water through perhaps 2° Centigrade. And it will be shown below that exactly one half of all the heat developed in the condensation of the Sun regarded as a sphere of monatomic gas is radiated away, and the other half stored up in the Sun's globe for elevating the temperature, and thus made available for radiation through future ages. Thus 20,000,000 years of uniform radiation is the part of the Sun's heat already expended, and at the rate of 2° per annum, it would last 10,000,000 years. If the loss of energy in the past was not uniform, but smaller than at present, the duration of the Sun's past activity would be correspondingly increased. Professor Perry of the Royal College of Science, London, has

expressed the opinion that over long periods the radiation may have been only one-tenth what it is at present. Thus the Sun may have existed from 10,000,000 to 100,000,000 years in the past, according to the rate employed in dispensing with its gravitational energy.

Astronomers are pretty generally agreed that the Sun will eventually cease to shrink, and then cool down, darken, and go out, but this stage will not arrive until the molecular forces exert sufficient repulsion to counteract the shrinkage now going on. If we imagine the Sun's globe contracted to one half of its present diameter, it is evident that the average density would thus be increased eight fold, and the average amount of space available for each molecule will be only one eighth what it is now. Molecular forces in some cases are supposed to vary inversely as the fifth power of the distance, and hence, when their mutual distance is reduced one half, the repulsion will be increased thirty-two fold. thirty-two fold. This rapid growth of molecular repulsion as the sun shrinks, will finally check the contraction; and it is generally supposed that the Sun's shrinkage will terminate when the diameter has diminished to about one half of its present dimensions.

From the considerations advanced in the next section, the writer has shown that one half of all the heat thus far developed in the condensation of the solar nebula is still stored up in the Sun's globe. The future contraction, giving a radius only one half of the present one, will double the heat already developed, since the total heat of condensation is inversely as the radius. As the future supply of heat, the Sun will give out all that may be produced by future contraction, as well as that now stored up in its body. Thus, on the hypothesis that the Sun will shrink to one half of its present diameter before contraction ceases, we see that the gravitational energy in store for the Sun's future activity will be three times that of the past.

If we imagine the rate of future radiation to be the same as in former ages, we

may say that the future duration of the Sun's activity will be three times that of the past; and therefore we have not yet approached the middle, but are only at the first quarter of the Sun's career. Thus the zenith of the Sun's glory lies in the future.

It has been stated by such authorities as Lord Kelvin, Newcomb, and Ball that the future of the Sun's activity will be comparatively short, not more than 10,000,000 years, and some have even suggested that the Sun's activity already shows signs of waning. So far is this from being the case that only one fourth of our supply of energy has been expended, and three fourths are yet in store for the future life of the planetary system. This opens up to our contemplation a decidedly refreshing view of the future, and will give renewed hope to all who believe that the end of mundane progress is not yet in sight. Not only should the future possibilities of scientific progress be vastly extended, but there will in all probability be the most ample time for the further development of the races of beings inhabiting this planet. According to this view, the evolution of our earth is still in its infancy, with the zenith of its splendor far in the future.

If we cannot subscribe to Professor Sir G. H. Darwin's recent estimate of 1,000,000,000 years for the past life of the Solar System, this period being based on the assumed existence of radium throughout all nature, we may yet be sure that the future duration, depending on the energy of gravitation, will be three times that of the past, and that this period may perhaps be as great as 300,000,000 years, or one third of the period estimated by Darwin. On the basis of uniform radiation at the present rate, a future of 30,000,000 years seems absolutely assured. This result illustrates the folly of concluding that the end of discovery is yet in sight. Scientific progress appears to be still in its infancy, and the time will not soon arrive when we can adopt any final philosophy of the Universe. All the

attempts thus far made in this direction have been doomed to failure, and the pulling down of the idols of the past warns us to beware of expecting inmortality in those now erected in their places.

Indeed, it may be said that scientific progress in the widest sense does not consist of the solution of a mathematical problem, but of a series of successive approximations to the laws of the world, each improvement extending beyond the former, and leading to results of greater and greater generality. The goal is not and never will be in sight! But the twinkling of the stars constantly beckons the astronomer on to renewed effort. Labor of mind and body is a part of the great process of cosmical evolution, and the explanation of the heavens is one of nature's ways of effecting the development of the powers of the mind in the race of beings who inhabit this planet.

III

We now come to one of the most interesting results of recent science. It is shown by the writer in Astronomische Nachrichten, number 4053, that there is a certain ratio between the amount of heat developed in a gaseous mass condensing under gravity, and that radiated away, the exact percentage in any given case depending on the value of k, which is determined by experiment. In very complex substances, such as the vapor of oil of turpentine, which has 26 atoms in a molecule, k=1.03; while in monatomic gas

the value of k is 1.66. This last value of k has been confirmed experimentally for the following monatomic gases: vapor of mercury, argon, helium, neon, xenon, crypton. Now for gases made up of single atoms, it is a very remarkable fact that exactly so much of the heat of condensation is retained in the gas, for raising the temperature, as is radiated away into space. This means that bodies like the stars and our Sun, if they are really made up of gases composed of single atoms, have one half of all their

heat from eternity still stored up in their

masses.

This theorem appears extremely remarkable, and yet the laborious calculations made by the writer seem to prove that this law is applicable to most of the fixed stars which stud our firmament. That there must be some law which causes the heat to accumulate within the bodies of the stars, so as to raise their temperatures, is evident from the naked-eye aspect of the celestial sphere. For without such a law the brilliant light of the stars would never develop, so as to give luminosity to the visible universe. On the contrary, the heat and light would be radiated away as fast as developed, so that the bodies of the stars would never rise in temperature. The result would be that, although heat might be developed and radiated away in the condensation of matter into large masses, yet none of the masses would become brilliantly selfluminous, as at present, but we should have a universe made up of dark bodies accumulating no sensible amount of heat. Such a universe of invisible bodies would seem very strange to us, accustomed as we are to the light of the stars at night. Yet how many of us ever thought a law existed, according to which one half of all the heat of condensation accumulated within the flaming globes of the stars, and thus caused their luminosity? It is evident on general principles that some very important law lies at the basis of the brilliant light of the stars, and thus gives rise to the luminosity of these bodies, all of which resemble our Sun in constitution.

Not only do the isolated stars shine brightly, but the prevailing principle of luminosity is exemplified by great masses of these objects of various ages, seen in clusters, and especially in the stupendous arch of the Milky Way, which spans the firmament with unspeakable grandeur on a clear night. Accordingly it appears that there is a law of heat accumulation applying in general to the life of every star, the heat steadily increasing while the body is gaseous, and then slow

ly dying down by secular cooling, when consolidation sets in, and the light begins to wane. The lucid phenomena exhibited to our naked-eye contemplation are thus products of a law of unexampled grandeur operating throughout all space.

But how does this law change with respect to the time, when the stars pass from the youngest types to the oldest, in periods to be reckoned in the hundreds of millions of years? It is found that when the star is composed of common gases, such as hydrogen, oxygen, nitrogen, air, made up of two atoms in a molecule, the ratio of the specific heat under constant pressure to that under constant volume is k=1.4, and 81.3 per cent of the heat developed is retained in the star for raising the temperature; and when the temperature becomes high, say more than 10,000° Centigrade, the gases are decomposed into single atoms, so that k=13, and only 50 per cent of the heat developed is retained for raising the temperature of the mass. Thus, as a star develops from a cold nebula, it has at first more than half of its heat stored up, but later on exactly one half. For the whole period of the star's development, therefore, there is stored up 50+7 per cent of the heat of condensation, 7 being a small percentage depending on the length of time and the rate of condensation when the mass is composed of compound gases, compared to that in which it is rendered monatomic by the development of great internal temperature.

Now all our knowledge tends to show that a star soon rises in temperature, so that the first stage of condensation would be short compared to the second; and the period during which the mass is made up of compound gases is short compared to that in which the gases are monatomic. The first period may be only a hundredth, or at most a tenth, of the second; and we may, therefore, be sure that it is only a short time, comparatively, during which the star is storing up 81.3 per cent; so that is generally small, of the order of two or three per cent, and probably never

much exceeding ten per cent, for stars of any considerable size. It would appear that is relatively larger for small stars, and smaller for large stars; because small stars are slow in acquiring high temperatures, while large ones acquire such temperatures very rapidly. If the mass were very small, like a satellite, the temperature would never become high, and thus T would become large, about 31.2 per cent, because the body would never become sufficiently heated to disintegrate into monatomic gas. Such a body could hardly be considered a star in the usual sense of that word, because all the stars are of the same order of magnitude as our Sun. Among the stars, therefore, 7 is a small percentage, and our law of heat accumulation applicable to the luminous bodies composing the sidereal universe takes the following form:

A little over one half of all the heat developed in the condensation of the stars is stored up in their flaming globes, and this storage of heat is what gives luminosity to the visible Universe.

When we look out upon the vault of the sky at night, and admire the brightness of the starry heavens, we are paying an unconscious tribute to this law of heat accumulation, on which the beauty of the nocturnal heavens depends. It is remarkable that this law of heat accumulation should have been so recently discovered. In considering scientific progress, however, we have to remember that few investigators are looking for general laws of nature, because many persons suppose that all the great laws have already been discovered. Moreover, many scientific inquiries are very special, and a very limited trend of thought seldom leads to anything of general and universal interest.

There will naturally be differences of opinion as to the degree of rigor attaching to this law, in its application to the whole life history of a star, but the mathematical soundness of the demonstration is beyond dispute; and in its application to actual masses it will evidently hold true so long as the bodies obey the laws of

gaseous matter. Thus it will include in its scope the larger part of the history of the stellar universe; and even when the masses become so much condensed that the gaseous laws begin to fail, owing to increase of density and pressure within the globes of the stars, it will still hold true approximately.

The law of heat accumulation thus enables us to explain the slow decline in a star's temperature, after the maximum temperature has been attained, and assures us that the heavens must have an abundance of stars slowly advancing in decrepitude.

All in all, it is difficult to overrate the philosophical interest attaching to this law, yet the poetical interest excited by its application to the naked-eye aspect of the stars, as we behold them from night to night illuminating the vault of the firmament, is fully as keen and abiding. The researches of science have thus made known the law upon which the nocturnal beauty of the world depends, and thus we may view science itself as contributing to the poetry of the starry heavens.

IV

One other remarkable result of recent researches as to the Sun is that the theory long held by men of science regarding the internal circulation of the Sun is shown to be of doubtful validity. For nearly a century it has been held that convective currents are at work in the Sun's globe to bring hot matter from the interior up to the surface, and dispose of that cooled by radiation by the descent of corresponding cool currents. This theory has had the support of many eminent men, but they probably have not examined the important question of the pressure operative within the Sun, and their conclusions, therefore, seem wholly inadmissible. A system of opposing currents so directly antagonistic to one another as is here imagined evidently would not work. Some of the views of these gentlemen, however, are as follows.

Lane says: "The heat emitted each minute would therefore be fully half of all that a layer ten miles thick would give out in cooling down to zero, and a circulation that would dispose of volumes of cooled atmosphere at such a rate seems inconceivable."

Lord Kelvin expresses himself as follows: "Gigantic currents throughout the Sun's liquid mass are continually maintained by fluid, slightly cooled by radiation, falling down from the surface, and hot fluid rushing up to take its place."

Young says: "From the under surface of this cloud shell (the photosphere), if it really exists, there must necessarily be a continual precipitation into the gaseous nucleus below, with a corresponding ascent of vapors from beneath, a vertical circulation of great activity and violence, one effect of which must be a constricting pressure upon the nucleus much like that of the liquid skin of a bubble upon the enclosed air. With this difference, however, that the photospheric cloud shell is not a continuous sheet, but 'porous,' so to speak, and permeated by vents through which the ascending vapors and gases can force their way into the regions above."

Newcomb describes the Sun's radiation thus: "It follows that the heat radiated from the surface must be continually supplied by the rising up of hot material from the interior, which again falls back as it cools off. It is difficult to suppose that even a liquid could rise and fall back rapidly enough to keep up the supply of heat constantly radiated. We therefore conclude that the photosphere is really a mass of gas, in which, however, solid particles of very refractory substances may be suspended."

In Astronomische Nachrichten, number 4053, the writer has exhaustively studied the internal constitution of the Sun, showing that the outer layers are of the same order of density as the Earth's atmosphere; and that the light and heat from beneath are not supplied by a system of antagonistic convection currents, one set ascending, and the other descending, but

by direct radiation, the energy going through the overlying layers of rare gases like sunlight through the Earth's atmosphere. This new conception will be extremely useful in the future studies of the spots, faculæ, prominences, and other phenomena observed on the Sun's surface. But it is only after a long study of the photographs now being taken that we can expect to establish and verify the processes involved in the surface radiation. That they will be of the general character here described admits of no reasonable doubt, though there will naturally be great commotion in the surface layers, and the real movements very difficult to disentangle.

In his recent presidential address to the British Association, at the meeting in South Africa, Professor Sir G. H. Darwin dwelt on the general theme of the instability of matter. This line of thought has been uppermost in the minds of the Cambridge Physicists for several years; and Rayleigh, Strutt, Soddy, Thomson, Larmor, Rutherford, and others have established the slow transmutation of the elements for some particular cases. Thus the dreams of the alchemists of the Middle Ages are already partially realized; and the whole trend of recent thought has been toward the problem of the ultimate constitution of matter, and especially its slow transmutation.

Professor Sir George Darwin says: "The fascinating idea that matter of all kinds has a common substratum is of remote antiquity. In the Middle Ages the alchemists, inspired by this idea, conceived the possibility of transforming the baser metals into gold. The sole difficulty seemed to them the discovery of an appropriate series of chemical operations. We now know that they were always indefinitely far from the goal of their search, yet we must accord to them the honour of having been the pioneers of modern chemistry.

"The object of alchemy, as stated in modern language, was to break up or dissociate the atoms of one chemical element