Recent Progress in Solar Research

I

IF we notice with the naked eye the appearance of the Sun in the heavens, we see that it presents the aspect of a round disk of nearly uniform brightness. When passing clouds or fog of the proper density give the disk a dull lustre, so that it may be directly and easily studied with the naked eye, we sometimes see sunspots, as dull, dark blotches upon the brilliant background. And if the intervening layer of clouds be of uniform density, so that we can examine the Sun more closely, we shall see that the disk is brightest at the centre, and fades away slightly toward the edges. The comparative faintness near the limb is due to absorption of part of the emitted light in the Sun’s atmosphere. This effect is naturally greatest near the edges, where the escaping rays traverse the greatest depth of the overlying gases. The slight darkness near the limb is thus an indication of the globular form of the Sun; and yet it was not noticed by the ancients, most of whom supposed the Sun to have the form of a flat disk, such as it presents to the naked eye, though a few of the Greek philosophers understood it to be an immense globe of fire.

When Galileo invented the telescope, in 1610, he discovered the spots on the Sun, and found that they move slowly in the same direction in which the Earth revolves in its orbit, the period of the Sun’s rotation being about twenty-eight, days. Subsequent researches of astronomers have shown many wonderful things about the Sun’s constitution, but it is remarkable that the most refined modern measurements do not indicate any deviation from a perfectly globular figure. This perfect roundness of the Sun’s figure is explained by the intensity of solar gravity (about twenty-eight times more powerful than that of the Earth), and by the slowness of the Sun’s rotation, which makes the solar centrifugal force relatively small and the resulting oblateness wholly insensible. As the Sun’s globe is at an enormously high temperature, it cannot be either a solid or a liquid body, but must be a sphere of gas, compressed and held in equilibrium by the tremendous power of its own gravitation.

What, then, are the most recent results of scientific research as to the constitution of the Sun ? What are the laws of its internal density, pressure,and temperature ? How much heat is now stored up in the Sun’s globe; — and how are these results obtained ? These are some of the questions which the general reader will naturally ask, and which we shall endeavor to answer in this paper.

The recent advancement of our knowledge of the Sun, in respect to mathematical theory as well as photographic and experimental measurement, is one of the most notable results of our time. In addition to the fascination of the problem in its purely scientific aspects, a summary of the principal achievements of the past forty years seems likely to be of interest in illuminating the great philosophical question of man’s ability to explore the innermost secrets of physical phenomena, and discover the permanent laws of nature.

This fundamental problem was much debated by the Greeks of the age of Socrates, Plato, and Aristotle, and doubtless will abide with us always; but naturally it comes to the front with great prominence in this modern epoch which has passed in rapid succession from the molecular to the atomic theory, and from the theory of atoms to that of their smallest known components, now called corpuscles or electrons, of which some 800 are shown to compose the simplest atom of hydrogen.

Indeed, when we read in contemporaneous scientific literature of the atoms and electrons making up the various molecules, we are naturally carried back in thought to the age of Democritus and Lucretius, who founded the atomistic theories among the Greeks; and are led to wonder whether modern science, like the philosophy of the Greeks, will eventually pass from these materialistic conceptions to a kind of spiritualism corresponding to that of the Neoplatonists. This recognized tendency in the history of Greek philosophy may be as significant of the trend of the human mind as the atomistic theories which we see revived and extended in our own age, and playing a conspicuous part in the theories of the Sun and stars. Though science is generally supposed to be materialistic, it is really less so than is often imagined, and it may some day lead us to a spiritualism much deeper and more abiding than that of Plato.

To judge correctly of the tendencies of modern progress, we may recall that the learned among the Greeks and Romans considered the Sun to be an immense globe of fire. As fire was one of the four fundamental constituents of the physical universe recognized by the ancients, namely, air, water, fire, and earth, the theory that self-luminous bodies are made up of fire was a very natural one, and it remained current until long after the Middle Ages.

Descartes, in his Principia Philosophiae, published in 1644, described the universe as made up of three kinds of matter. The first is composed of bright spherical particles like ordinary fire, and makes luminous bodies, as the Sun and stars; the second goes to make up the transparent substances, such as water, glass, crystals, diamond, and the skies; the third is the material of opaque bodies, as the Earth, non-luminous planets, and comets. Descartes supposes that the motion of matter is in the form of circular currents or vortices, and that the particles are necessarily ground by friction into a spherical form; the corners thus rubbed off, like sawdust or filings, producing the second or more subtile matter, seen in transparent bodies; the coarser parts, less fitted for motion, give the third kind of matter, as found in ordinary opaque substances, like stones and metals, which make up the planets. These curious views of Descartes are interesting chiefly as forming a connecting link between the atomic speculations of the Greeks and the more highly developed theories of modern times.

After Priestley’s discovery of oxygen in 1772, and Lavoisier’s demonstration some fifteen years later that fire is not an element, but only a process, a combination of the elements of oxygen and carbon, thus liberating molecular and atomic energy, the light of the Sun and stars doubtless appeared in a new aspect. Instead of being made up of the element fire, the stars were now considered to be burning bodies.

Yet all the various attempts to explain the light and heat of the stars by chemical processes largely failed; and in 1854 Helmholtz showed that a great and steady supply of energy becomes available from the gravitational potential of the Sun’s mass, converted into light and heat by slow shrinkage and subsidence of the particles toward the centre.

To make it quite clear how this takes place, we need only recall Joule’s experiments on the mechanical equivalent of heat. About sixty years ago this eminent British physicist showed experimentally that if a mass with a weight of one pound be allowed to fall through a space of 772 feet, the heat given up by the falling body would be adequate to raise the temperature of one pound of water one degree Fahrenheit. Larger bodies would produce more heat in proportion to their masses; and where the force of gravity is larger than on the Earth, as in the Sun, this would give still more heat in proportion to the intensity of gravity. Now at the surface of the Sun the force of gravity is about 28 times what it is upon the Earth; and moreover, the Sun’s mass is about 332,750 times that of the Earth. If, therefore, the Sun’s force of gravity is so much larger, and it has a so much larger quantity of matter to fall under the action of this force, it follows that the heat developed in the condensation of the Sun must be enormous. To calculate the exact amount of heat developed, we have to make use of the higher mathematics, and also know the law of density within the Sun’s globe, which we shall discuss more fully hereafter.

On the supposition that the Sun is homogeneous, or of uniform density throughout, and the heat and light radiated away as fast as produced, a contraction in the radius of 110 feet per annum was found by Helmholtz to be adequate to furnish our enormous supply of light and heat.¹ We shall see in the course of this paper that this theory of Helmholtz is only the beginning of our present theories of the Sun; yet it has the great advantage over the old theories of assigning a true cause based on established physical laws, and therefore will remain of interest throughout all time.

The work of Helmholtz thus marks an epoch in our theories of the Sun, and has been the starting-point of nearly all subsequent researches on the subject. But it can hardly be said that the theory of Helmholtz was more fundamental than that of Lane, who treated of the Sun’s constitution on the hypothesis that it is a sphere of gas kept in equilibrium under the temperature, pressure, and attraction of its parts. For Helmholtz had only considered the gravitational condensation of a homogeneous Sun of given size and mean density, without inquiring whether it was solid, liquid, or gaseous. He supposed it to have formed according to the nebular hypothesis of Laplace, and therefore, no doubt, assumed that it was originally a gaseous nebula, of which the high temperature might have arisen from the falling together of cold matter, in accordance with Joule’s experiments. Lane took up the consideration of the Sun as it is to-day, and worked out some of the most important laws for its internal constitution, showing that the mass must be essentially gaseous throughout, although already of considerable density.

Jonathan Homer Lane was a native of western New York, for many years connected with the Patent Office and U. S. Coast and Geodetic Survey in Washington, and a member of the National Academy of Sciences. He was a man of retiring disposition, and, although he did no vast amount of scientific work, what he did was of high quality, and bears unmistakable marks of genius. His paper on the Sun is probably his most famous effort, and has since become classic and justly celebrated. Frequently cited by astronomers of other nations, it is perhaps the most important single contribution since that of Helmholtz in 1854. Lane’s paper “On the Theoretical Temperature of the Sun, under the Hypothesis of a Gaseous Mass maintaining the volume by its internal Heat, and depending on the Laws of Gases as known to Terrestrial Experiment,” was read to the National Academy of Sciences at the Washington meeting of April 13-16, 1869, and published in the American Journal of Science for July, 1870. This is the famous paper so much quoted by Lord Kelvin, Ball, Newcomb, Perry, and others, who have discussed the mathematical theory of the Sun’s heat.

Lane describes the inception of his paper as follows: —

“ Some years ago the question occurred to me, in connection with this theory of Helmholtz, whether the entire mass of the sun might not be a mixture of transparent gases, and whether Herschel’s clouds might not arise from the precipitation of some of these gases, say carbon, near the surface, with their revaporization when fallen or carried into the hotter subjacent layers of atmosphere beneath; the circulation necessary for the play of this Espian theory being of course maintained by the constant disturbance of equilibrium due to the loss of heat by radiation from the precipitated clouds. Professor Espy’s theory of storms I first became acquainted with more than twenty years ago from lectures delivered by himself; and, original as I suppose it to be, and well supported as it is in the phenomena of terrestrial meteorology, I have long thought that Professor Espy’s labors deserve a more general recognition than they have received abroad. It is not surprising, therefore, in a time when the constitution of the sun was exciting so much discussion, that the above suggestion should have occurred to myself before I became aware of the very similar, and in the main identical, views of Professor Faye, put forth in the Comptes Rendus. I sought to determine how far such a supposed constitution of the sun could be made to connect with the laws of gases as known to us in terrestrial experiments at common temperatures.”

Although Lane’s treatment of the Sun’s internal constitution was considered highly satisfactory, his mathematical processes were so difficult that very few later investigators have ever worked out his results independently. The subject of the Sun’s internal condition was next treated by the German physicist Ritter, of Aixla-Chapelle, in 1878, and a few years later by Lord Kelvin. In 1899 this problem was also treated by Professor John Perry of London, who followed the same general methods as Lane, Ritter, and Kelvin.

An outline of these researches, and of the considerable extension very recently made of them by the writer, is all that would be of interest to the general reader. Before taking up the details of this treatment, however, it is necessary to remark that, while in these calculations full account is taken of the energy of gravitation arising from the mutual approach of the particles under gravity, no attention is given to the energy arising from such substances as radium. At present it is not known whether radium exists in the stars, but, as it exists in the Earth, it has been held that it must also exist in the Sun, or will develop there some time in the future when our star cools down to a stage corresponding to that now occupied by the Earth. We shall recur to this subject again toward the end of this paper.

Assuming that the only energy given out by a condensing body is that derived from the gravitational attraction of the particles, Helmholtz in 1854 showed that the total heat produced up to the present time in the condensation of the Sun would raise the temperature of an equal mass of water about 27,000,000° Centigrade. As Pouillet found by experiment that the annual radiation of the Sun was adequate to cool an equal mass of water 1.25° Centigrade, it followed that the total duration of the Sun’s activity at this uniform rate of radiation could not exceed some twenty million years, which very markedly curtailed the past duration of the Earth as inferred by geologists from the study of phenomena of the Earth’s surface.

Helmholtz’s theory was somewhat defective, in assuming the density of the Sun’s globe to be uniform throughout; but as a first approximation to the laws of nature it met all requirements, and, indeed, marked an important epoch in the history of scientific thought during the nineteenth century.

In Lane’s paper the conclusion was reached that the Sun is really quite heterogeneous, the central density being some 20 times the mean. This result was based upon the hypothesis that the solar gases are like oxygen, hydrogen, nitrogen, and common air, in which the ratio of the specific heat of the matter under constant pressure to that under constant volume is k=l.4. The value of k always plays an important part in the theory of the Sun; for upon this physical constant depend the laws of internal density, and therefore, also, the total heat developed up to the present time, as well as the pressure and temperature throughout the Sun’s globe.

II

The writer has recently carried out the most elaborate investigation of the mathematical theory of the Sun yet attempted, and published the results in the Astronomische Nachrichten, noumber 4053. On carefully examining the work of Lane, Kelvin, and Ritter, it was found that they could all be reconciled quite perfectly among themselves by correcting a misconception in the paper of Lane.

This was to the effect that the Sun’s atmosphere extends above the photosphere by one twenty-second part of the radius. Though it is now known that this assumption is not justifiable, the misconception misled Lord Kelvin, and caused him and other eminent writers to conclude that the central density of the Sun, conceived as made up of biatomic gases, should be about 20 times the mean density, whereas it should be a little over 23 times the mean. By a different process Lord Kelvin concluded that the central density should be 22.5 times the mean density, while from certain equations of the celebrated French mathematician, Poisson, Ritter found 23 to be the proper number.

When it was found by the writer’s recent researches that Lane’s theory, correctly interpreted, made the central density about 23.4 times the mean, instead of 20 times, as given in the published paper of 1869, it was seen that all three determinations of the internal laws of the Sun’s density ware essentially in perfect agreement. The rigor of the gaseous theory of the Sun’s constitution was thus confirmed by the accordant results reached by three independent processes, and there can be no doubt of the accuracy of the final value.

These investigations, however, in which the ratio of the specific heat of the gas under constant pressure to that under constant volume is k=1.4, as in biatomic gases like oxygen, nitrogen, hydrogen, air, do not correspond to the conditions in nature, where the temperature is enormously high, and we shall consider more particularly the case in which k=1⅔. This corresponds to a monatomic gas, or a gas in which the molecules are identical with the atoms, and may be viewed as single spheres without mutual connections of any kind. Ordinary gases, such as oxygen, hydrogen, nitrogen, have two atoms in a molecule, probably joined together like the two ends of a dumb-bell, while the more complex gases have molecules made up of many atoms grouped together in various ways.

Now when the molecules are very complex, made up of many atoms variously arranged, the group thus formed frequently becomes unstable. The parts are always in rapid motion, and a molecule may be likened to a political convention, which is made up of many individuals, and has correspondingly unsteady qualities.

It is found by experiment that all complex gases are decomposable at some temperature not enormously high. Vapor of water and ammonia are dissociated into their constituent atoms at temperatures less than 1000° Centigrade, and probably all the chemical bodies we know of would be dissociated at temperatures less than 10,000° Centigrade, or 18,000° Fahrenheit. At all higher temperatures chemical compounds probably cease to exist, and the molecules of the substances are reduced to the state of single atoms, and hence called monatomic.

Such we conceive to be the state of the matter in the Sun. For it is shown by observation and calculation that the fixed stars and the Sun have internal temperatures of many millions of degrees, while at their surface the temperatures will seldom fall short of 10,000° Centigrade. We may, therefore, take the whole interior of the Sun and stars as monatomic gas; and suppose that even at their surfaces few compounds can form, so that, in general, the body of stars composing the visible universe are flaming globes of monatomic gas, in which all the elements are reduced to their simplest form of single atoms.

No doubt our Sun is a globe of this kind, but it has usually been treated as made up of compound gases, like air, hydrogen, oxygen, nitrogen. What, then, is the arrangement of its internal density when the gases are monatomic ?

Lane began to consider this question as far back as 1869, treating the Sun’s globe as possibly made up throughout of monatomic gas; and the mathematical methods employed by him have recently been much extended and improved by the writer of this paper. These processes depend on the development of certain series based on methods of the higher mathematics, of which an account here would be out of place. Suffice it to say that the investigation as thus carried out involved the calculation of numbers running up into the hundreds of sextillions, that is, numbers expressed by twenty-four places of figures. These numbers are so stupendous as to be almost unmanageable, and the work had to be done by the oldfashioned direct processes, without the use of logarithms, which are no longer available. This vastly increased the labor of calculation, and also the liability to error, so that all the work had to be repeated three or four times to insure accuracy in the final result. At length the process was made sufficiently accurate, and led to some of the most beautiful results yet attained in any branch of physical science, because apparently applicable to the great body of the fixed stars.

One of these results of great interest is that the central density in a star made up of layers of monatomic gas is exactly six times the mean density. This appears to be a general law of nature. In the case of our Sun, for example, the mean density is 1.4 times that of water; and the density at the centre thus becomes 8.40; which exceeds the density of steel (7.816) and even brass (8.383), and proves to be practically midway between that and German silver (8.432).

An examination of the table on page 769 shows the following facts: —

1. The outer layers of the Sun are of the same order of density as our atmosphere, becoming only 153 times the density of air one tenth of the way to the centre, where the pressure is 21,636,565 atmospheres, or 7 times greater than it is at the centre of the earth.

2. The rise of pressure and temperature downward is very rapid. At the centre the pressure is over 11,215,000,000 atmospheres, equivalent to that exerted by a vertical column of quicksilver about one tenth as long as from the earth to the sun if all parts of the column were under the uniform acceleration of terrestrial mean gravity.

3. The temperature at the centre of the Sun is about 50,000,000 degrees Centigrade.

TABLE SHOWING THE INTERNAL DENSITY, PRESSURE, AND TEMPERATURE OF THE SUN CALCULATED BY THE MONATOMIC THEORY

4. In the outer layers of the Sun the density rises steadily, the temperature somewhat more rapidly, and the pressure most rapidly of all. The result is that at a moderate depth the pressure becomes so great that circulation under this great strain on the atoms is impossible, on account of the friction of the fluid against itself. Currents observed near the surface of the Sun, therefore, do not extend to any considerable depth, and the matter in the Sun’s interior is always kept highly rigid from pressure.

Heretofore astronomers have very generally supposed that the circulation extended throughout the Sun’s body.

We shall first examine the effects of this arrangement of the density on the total amount of heat developed in the condensation of the Sun. It will be seen from what is said above that when k=1.4, as imagined by Lane, Ritter, Lord Kelvin, and Perry, the central density is 23 times the average for the whole sphere, but when k=1⅔, as in gases reduced to the monatomic state by intense heat, the central density is only six times the mean density. Now, in the theory of the Sun’s heat considered by Helmholtz, the density was taken to be uniform throughout. As a heterogeneous Sun can be imagined to result from a homogeneous one by the descent of many of the particles toward the centre, so as to increase the density in that region, we see that when the particles have fallen inward in a certain way the arrangement corresponds to the monatomic sphere, and when still more of them have fallen downward, and nearer the centre, the arrangement corresponds to 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. 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 immortality 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 slowly 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=1⅔, 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 + γ per cent of the heat of condensation, γ 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 γ 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 γ 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 γ 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, γ 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 into its component parts, and afterwards to reunite them into atoms of gold. Although even the dissociative stage of the alchemistic problem still lies far beyond the power of the chemist, yet modern researches seem to furnish a sufficiently clear idea of the structure of atoms to enable us to see what would have to be done to effect a transformation of elements. Indeed, in the complex changes which are found to occur spontaneously in uranium, radium, and the allied metals we are probably watching a spontaneous dissociation and transmutation of elements.

“Natural selection may seem, at first sight, as remote as the poles asunder from the ideas of the alchemist; yet dissociation and transmutation depend on the instability and regained stability of the atom, and the survival of the stable atom depends on the principle of natural selection.

“Until some ten years ago the essential diversity of the chemical elements was accepted by the chemist as an ultimate fact, and indeed, the very name of atom, or that which cannot be cut, was given to what was supposed to be the final indivisible portion of matter. The chemist thus proceeded in much the same way as the biologist, who, in discussing evolution, accepts the species as his working unit. Accordingly, until recently the chemist discussed working models of matter of atomic structure, and the vast edifice of modern chemistry has been built with atomic bricks.

“But within the last few years the electrical researches of Lenard, Roentgen, Becquerel, the Curies, of my colleagues Larmor and Thomson, and of a host of others, have shown that the atom is not indivisible, and a flood of light has been thrown on the ultimate constitution of matter. Amongst all these fertile investigators it seems to me that Thomson stands preëminent, because it is principally through him that we are to-day in a better position for picturing the structure of an atom than was ever the case before.”

Sir George Darwin then describes the type of mechanical atom conceived by Thomson, and the conditions and limits of its stability, and the physical causes of the slow transmutation through exchanges of electrons. The bearing of these researches on the type of atoms existing in the Sun is obvious, and we merely note the results of recent experiments. It appears from announcements made several years ago that Ramsay found radium slowly evolving helium. Rutherford has since reported it breaking up into helium and lead; and Strutt announces that uranium has been experimentally proved to be decomposing into radium. If uranium is passing into radium, and radium in turn passing into lead and helium, the heavier atomic weights would seem to be breaking up into lighter ones. Our so-called atoms are thus not generally ultimate and stable, but compounds of ephemeral type, which in time break up; and the Sun and stars may be viewed as made up internally of atoms of the lighter sort, so that the monatomic theory seems to be confirmed by the tendency of recent physical experiments.

While much will always remain to be discovered, and the theory of dissociation and transmutation is still in its infancy, yet the lines of thought already opened up to philosophical inquiry promise a rich harvest, and assure us that we are just beginning the exploration of the constitution of the Sun and stars.