# In the High Heavens/Chapter 9

CHAPTER IX.
THE BOUNDARIES OF ASTRONOMY.
T is proposed in the following chapter to trace some parts of the boundary line which divides the truths that have been established in astronomy from those parts of the science which must be regarded as more or less hypothetical. We intend therefore to select certain prominent questions, and to discuss those questions with such fulness as the circumstances will admit. It is desirable to commence with that great doctrine in astronomy which is often regarded as almost universally established. The doctrine to which we refer is known as the law of universal gravitation. It is customary to enunciate this law in the proposition that every particle of matter attracts every other particle with a force which varies directly as the product of the masses and inversely as the square of their distance. It is no doubt convenient to enunciate the great law in this very simple manner. It might seem awkward to have to specify all the qualifications which would be necessary if that enunciation is to assert no more than what we ​absolutely know. Perhaps many people believe, or think they believe, the law to be true in its general form; yet the assertion that the law of gravitation is universally true is an enormous, indeed, an infinite, exaggeration of the actual extent of our information.
To make this clear, let us contrast the law of gravitation as generally stated with the proposition which asserts that the earth rotates on its axis. No one who is capable of understanding the evidence on the question can doubt that the earth really does rotate upon its axis. I purposely set aside any difficulties of a quasi-metaphysical character, and speak merely of words in their ordinary acceptation. In stating that the earth rotates upon its axis we assert merely a definite proposition as regards one body, all the facts which the assertion involves are present to our minds, and we know that the assertion must be true. Equally conclusive is the evidence for the statement that the earth revolves around the sun. Concrete truths of this kind could be multiplied indefinitely. We can make similar assertions with regard to the planets. We can assert that the planets rotate upon their axes, and that the planets revolve around the sun. But the law of gravitation is a proposition of quite a different nature. Let us examine briefly the evidence by which this law has been established.
The science of dynamics is founded upon certain principles known as the laws of motion. The simplest of these principles asserts that a body once set moving in a straight line will continue to move on uniformly for ever in the same straight line, unless some force be permitted to act upon that body. For nature as we know it, this law seems to be fully proved. It has been tested in every ​way that we have been able to devise. All these tests have tended to confirm that law. The law is therefore believed to be true, at all events throughout the regions of space accessible to us and to our telescopes.
Assuming this law and the other principles analogous to it, we can apply them to the case of the revolution of the earth around the sun. As the earth is not moving in a straight line, it must be acted upon by some force. It can be shown that this force must be directed towards the sun. It will further appear that the intensity of this force will vary inversely as the square of the distance between the earth and the sun. The movements of the planets can be made to yield the same conclusions. All these movements can be accounted for on the supposition that each planet is attracted by the sun with a force which varies directly as the product of the masses, and inversely as the square of the distance between the two bodies. When more careful observations are introduced it is seen that the planets exhibit some slight deviations from the movements which they would have were each planet only acted upon by the attraction of the sun. These deviations do not invalidate the principle of attraction. They have been shown to arise from the mutual attractions of the planets themselves. Each of the planets is thus seen to attract each of the other planets. The intensity of this attraction between any pair of the planets is proportional to the masses of these planets and varies inversely as the square of the distance between them. We may use similar language with regard to the satellites by which so many of the planets are attended. Each satellite revolves around its primary. The movements of each satellite are mainly due to the preponderating attraction of the ​primary. Irregularities in the movements of the satellites are well known to astronomers, but these irregularities can be accounted for by the attraction of other bodies of the system.
The law of attraction thus seems to prevail among the small bodies of the system as well as among the large bodies. It is true that there are still a few outstanding discrepancies which cannot yet be said to have been completely accounted for by the principle of gravitation. This is probably due to the difficulties of the subject. The calculations which are involved are among the most difficult on which the mind of man has ever been engaged. We may practically assume that the law of gravitation is universal between the sun, the planets, and the satellites; and we may suppose that the few difficulties still outstanding will be finally cleared away, as has been the case with so many other seeming discrepancies.
But even when these admissions have been made, are we in a position to assert that the law of gravitation is universal throughout the solar system? We are here confronted with a very celebrated difficulty. Do those erratic objects known as comets acknowledge the law of gravitation? There can be no doubt that in one sense the comets do obey the law of gravitation in a most signal and emphatic manner. A comet usually moves in an orbit of very great eccentricity; and it is one of the most remarkable triumphs of Newton's discovery, that we were by its means able to render account of how the movements of a comet could be produced by the attraction of the sun. As a whole, the comet is very amenable to gravitation, but what are we to say as to the tails of comets, which ​certainly do not appear to follow the law of universal gravitation? The tails of comets, so far from being attracted towards the sun, seem actually to be repelled from the sun. Nor is even this an adequate statement of the case. The repulsive force by which the tails of the comets are driven from the sun is sometimes a very much more intense force than the attraction of gravitation.
I have no intention to discuss here the vexed question as to the origin of the tails of comets. I do not now inquire whether the repulsion by which the tail is produced be due to the intense radiation from the sun, or to electricity, or to some other agent. It is sufficient for our present purpose to note that, even if the tails of comets do gravitate towards the sun, the attraction is obscured by a more powerful repulsive force.
The solar system is a very small object when viewed in comparison with the dimensions of the sidereal system. The planets form a group nestled up closely around the sun. This little group is separated from its nearest visible neighbours in space by the most appalling distances. A vessel in the middle of the Atlantic Ocean is not more completely isolated from the shores of Europe and America than is our solar system from the stars and other bodies which surround it in space. Our knowledge of gravitation has been almost entirely obtained from the study of the bodies in the solar system. Let us inquire what can be ascertained as to the existence of this law in other parts of the universe. Newton knew nothing of the existence of the law of gravitation beyond the confines of the solar system. A little more is known now.
Our actual knowledge of the existence of gravitation in the celestial spaces outside the solar system depends ​exclusively upon those interesting objects known as binary stars. There are in the heavens many cases of two stars occurring quite close together. A well-known instance is presented in the star Epsilon Lyræ, where two pairs of stars are such near neighbours that it is a fair test of good vision to be able to separate them. But there are many cases in which the two stars are so close together that they cannot be seen separately without the aid of a telescope. We may take, for instance, the very celebrated double star Castor, well known as one of the Twins. Viewed by the unaided eye, the two stars look like a single star, but in a moderately good telescope it is seen that the object is really two separate stars quite close together. The question now comes as to whether the propinquity of the two stars is apparent or real. It might be explained by the supposition that the two stars are indeed close together compared with the distance by which they are separated from us; or it could be equally explained by supposing that the two stars, though really far apart, yet appear so nearly in the same line of vision that when projected on the surface of the heavens they seem close together. It cannot be doubted that in the case of many of the double stars, especially those in which the components appear tolerably distinct, the propinquity is only apparent, and arises from the two stars being near the same line of vision. But it is, also, undoubtedly true that in the case of very many of the double stars, especially among those belonging to the class which includes Castor, the two stars are really at about the same distance from us, and, therefore, as compared with that distance, they are really close together.
Among the splendid achievements of Sir W. Herschel, ​one of the greatest was his discovery of the movements of the binary stars. It was shown by Herschel that in some of the double stars one star of the pair was moving around the other, and that their apparent distances were changing. The discoveries inaugurated by Herschel have been widely extended by other astronomers. One of the more rapidly moving of the double stars lies in the constellation of Coma Berenices. The revolution of one component around the other requires a period of 25·7 years. The two bodies forming this composite star are very close together, the greatest distance being about one second of arc. There is very great difficulty in making accurate measurements of a double star of which the components are so close. More reliance may consequently be placed upon the determination of the orbits of other binary stars of which the components are further apart. Among these we may mention a remarkable binary star in Ursæ Majoris. The distance between the two components of this star varies from one second of arc to three seconds. The first recorded measurement of this object was by Sir W. Herschel in 1781, and since that date it has been repeatedly observed. From a comparison of all the measurements which have been made it appears that the periodic time of the revolution of one of these components around the other is about sixty years. This star has thus been followed through more than one entire revolution.
The importance of these discoveries became manifest when an attempt was made to explain the movements. It was soon shown that the movements of the stars were such as could be explained if the two stars attracted each other in conformity with the law of gravitation. It would, however, be hardly correct to assert that the discovery of the ​binary stars proved that the two stars attracted each other with a force which varies inversely as the square of their distance. Even under the most favourable circumstances the observations are very difficult; they cannot be made with the same accuracy as is attained in observing the movements of the planets; they have not even the value which antiquity will often confer on an observation which has not much else in its favour. There are probably many different suppositions which would explain all that has yet been observed as to the motions of the binary stars. Gravitation is but one of those suppositions. Gravitation will no doubt carry with it the prestige acquired by its success in explaining phenomena in the solar system. I do not know that any one has ever seriously put forward any other explanation except gravitation to account for the movements of the binary stars, nor is any one likely to do so while gravitation can continue to render an account of the observed facts; but all this is very different from saying that the discovery of the binary stars has proved that the law of gravitation extends to the stellar regions.
Except for what the binary stars tell us, we should know nothing as to the existence or the non-existence of the law of gravitation beyond the confines of the solar system. Does Sirius, for instance, attract the pole star? We really do not know. Nor can we ever expect to know. If Sirius and the pole star do attract each other, and if the law of their attraction be the same as the law of attraction in the solar system, it will then be easy to show that the effect of this attraction is so minute that it would be entirely outside the range of our instruments even to detect it. Observation in such a matter is hopeless. If ​we cannot detect any attraction between a star in one constellation and a star in another, no more can we detect any attraction between our sun and the stars. Such attractions may exist, or they may not exist: we have no means of knowing. Should any one assert that there is absolutely no gravitation between two bodies more than a billion miles apart there are no facts by which he can be contradicted.
If we know so little about the existence of gravitation in the space accessible to our telescopes, what are we to say of those distant regions of space to which our view can never penetrate? Let a vast sphere be described of such mighty dimensions that it embraces not only all the objects visible to the unaided eye, not only all the objects visible in our most powerful telescopes, but even every object that the most fertile imagination can conceive, what relation must this stupendous sphere bear to the whole of space? The mighty sphere can only be an infinitely small part of space. Are we then entitled to assert that every particle in the universe attracts every other particle with a force which is proportional to the product of their masses, and which varies inversely as the square of their distance? We have, indeed, but a slender basis of fact on which to rest a proposition so universal. Let us attempt to enunciate the law of gravitation so as to commit ourselves to no assertion not absolutely proved. The statement would then run somewhat as follows:—
Of the whole contents of space we know nothing except within that infinitely small region which contains the bodies visible in our telescopes. Nor can we assert that gravitation pervades the entire of even this infinitely small region. It is true that in one very minute part ​of this infinitely small region the law of gravitation appears to reign supreme. This minute part is of course the solar system. There are also a few binary stars in this infinitely small region whose movements would admit of being explained by gravitation, though as yet they can hardly be held absolutely to prove its existence.
It must then be admitted that when the law of gravitation is spoken of as being universal, we are using language infinitely more general than the facts absolutely warrant. At the present moment we only know that gravitation exists to a very small extent in a certain indefinitely small portion of space. Our knowledge would have to be enormously increased before we could assert that gravitation was in operation throughout this very limited region; and even when we have proved this, we should only have made an infinitesimal advance to a proof that gravitation is absolutely universal.
I do not for a moment assert that our ordinary statement of the law of gravitation is untrue. I merely say that it has not been proved, and we may also add that it does not seem as if it ever could be proved. Most people who have considered the matter will probably believe that gravitation is universal. Nor is this belief unnatural. If we set aside comets' tails, and perhaps one or two other slightly doubtful matters, we may assert that we always find the law of gravitation to be true whenever we have an opportunity of testing it. These opportunities are very limited, so that we have but very slender supports for the induction that gravitation is universal. But it must be admitted that an hypothesis which has practically borne every test that can be applied has very strong grounds for our acceptance: such, then, are the claims of ​the law of gravitation to be admitted to a place among the laws of Nature.
The series of spectroscopic researches by which Sir William Huggins has so vastly extended our knowledge should be referred to. Sir William Huggins has shown that many of the substances most abundant on earth are widely spread through the universe. Take, for instance, the metal iron and the gas hydrogen. We can detect the existence of these elements in objects enormously distant. Both iron and hydrogen exist in many stars, and hydrogen has been shown, in all probability, to be an important constituent of the nebulæ. That the rest of the sidereal system should thus be composed of materials known to be to a large extent identical with the materials in the solar system is a presumption in favour of the universality of gravitation.
In what has hitherto been said, we have attempted to give an outline of the facts so far as they are certainly known to us. Into mere speculations we have no desire to enter. We may, however, sketch out a brief chapter in modern sidereal astronomy, which seems to throw a ray of light into the constituents of the vast abyss of space which lies beyond the range of our telescopes. The ray of light is no doubt but a feeble one, but we must take whatever information we can obtain, even though it may fall far short of that which an intellectual curiosity will desire. The question now before us may be simply stated. Are we entitled to suppose that the part of the universe accessible to our telescopes is fairly typical of the other parts of the universe, or are we to believe that the system we know is altogether exceptional; that there are stars in other parts quite unlike our stars, composed of different ​materials, acted upon by different laws, of which we have no conception? The presumption is that the materials of which our system is composed are representative of the materials elsewhere. This presumption is strengthened by the very important considerations now to be adduced.
In the first place, let us distinctly understand what is meant by our sidereal system. We have already dwelt on the isolated position of the sun and the attendant planets. The grandest truth in the whole of astronomy is that which asserts that our sun is only a star separated by the most gigantic distances from the other stars around. Our sun, indeed, appears to be but one of the vast host of stars which form the Milky Way. We need not here enter into the often discussed question as to whether the nebulæ are, generally speaking, at distances of the same order as the stars. There seems to be no doubt that some of the nebulæ are quite as near to us as some of the stars. At all events, for our present purpose, we may group the Milky Way, the nebulæ, the stars, and the clusters, all into one whole which we call our sidereal system. Is this sidereal system as thus defined an isolated object in space? Are its members all so bound together by the law of universal gravitation that each body, whatever be its movements, can only describe a certain path such that it can never depart finally from the system? This is a question of no small importance. It presents features analogous to certain very interesting problems in biology which the labours of Mr. Wallace have done so much to elucidate. We are told that the fauna and flora of an oceanic island, cut off from the perpetual immigration of new forms, often assume a very remarkable type. The evolution of life under such circumstances proceeds ​in a very different manner to the corresponding evolution in an equal area of land which is connected with the great continental masses. Is our sidereal system to be regarded as an oceanic island in space, or is it in such connection with the systems in other parts of space as might lead us to infer that the various systems had a common character?
The evidence seems to show that the stars in our system are probably not permanently associated together, but that in the course of time some stars enter our system and other stars leave it, in such a manner as to suggest that the bodies visible to us are fairly typical of the general contents of the universe. The strongest evidence that can be presented on this subject is met with in the peculiar circumstances of one particular star. The star in question is known as number 1830 of Groombridge's catalogue. It is a small star, not to be seen without the aid of a telescope. This star is endowed with a very large proper motion. It would not be correct to say that its proper motion exceeds that of any other known star, but it certainly has the largest visible proper motion of any star of which the distance is known. The proper motion of 1830 Groombridge amounts to over seven seconds annually. It would take between two and three centuries to move over about eighteen hundred seconds, a distance in the heavens equal to the apparent diameter of the moon. The distance of this star is much greater than might have been anticipated from its very large proper motion. The estimates of the distance present some irregularities, but we shall probably be quite correct in assuming that the distance is not less than two hundred billions of miles. This star is indeed ten times as far from us as Alpha Centauri, which is generally ​considered to be the sun's nearest neighbour in our sidereal system.
The proper motion and the distance of 1830 Groombridge being both assumed, it is easy to calculate the velocity with which the star must be moving. The velocity is indeed stupendous and worthy of a majestic sun; it is no less than 200 miles a second. It would seem that the velocity may even be much larger than this. The proper motion of the star which we see is merely the true proper motion of the star foreshortened by projection on the surface of the heavens. In adopting 200 miles a second as the velocity of 1830 Groombridge, we therefore make a most moderate assumption, which may and probably does fall considerably short of the truth. But even with this very moderate assumption, it will be easy to show that 1830 Groombridge seems in all probability to be merely travelling through our system, and not permanently attached thereto.
The star sweeps along through our system with this stupendous velocity. Now there can be no doubt that if the star were permanently to retain this velocity, it would in the course of time travel right across our system, and after leaving our system would retreat into the depths of infinite space. Is there any power adequate to recall this star from the voyage to infinity? We know of none, unless it be the attraction of the stars or other bodies of our sidereal system. It therefore becomes a matter of calculation to determine whether the attraction of all the material bodies of our sidereal system could be adequate, even with universal gravitation, to recall a body which seems bent on leaving that system with a velocity of 200 miles per second.
​This interesting problem has been discussed by Professor Newcomb, whose calculations we shall here follow. In the first place we require to make some estimate of the dimensions of the sidereal system, in order to see whether it seems likely that this star can ever be recalled. The number of stars may be taken at one hundred millions, which is probably double as many as the number we can see with our best telescopes. The masses of the stars may be taken as on the average five times as great as the mass of the sun. The distribution of the stars is suggested by the constitution of the Milky Way. One hundred million stars are presumed to be disposed in a flat circular layer of such dimensions that a ray of light would require thirty thousand years to traverse one diameter. Assuming the ordinary law of gravitation, it is now easy to compute the efficiency of such an arrangement in attempting to recall a moving star. The whole question turns on a certain critical velocity of twenty-five miles a second. If a star darted through the system we have just been considering with a velocity less than twenty-five miles a second, then, after that star had moved for a certain distance, the attractive power of the system would gradually bend the path of the star round, and force the star to return to the system. If, therefore, the velocities of the stars were under no circumstances more than twenty-five miles a second, then, supposing the system to have the character we have described, that system might be always the same. The stars might be in incessant motion, but they must always remain in the vicinity of our present system, and our whole sidereal system might be an isolated object in space, just as our solar system is an isolated object in the extent of the sidereal system.
​We have, however, seen that for one star at all events the velocity is no less than 200 miles a second. If this star dash through the system, then the attractions of all the bodies in the system will unite in one grand effort to recall the wanderer. This attraction must, to some extent, be acknowledged; the speed of the wanderer must gradually diminish as he recedes into space; but that speed will never be lessened sufficiently to bring the star back again. As the star retreats further and further, the potency of the attraction will decrease; but, owing to the velocity of the star being over twenty-five miles a second, the attraction can never overcome the velocity; so that the star seems destined to escape.
This calculation is of course founded on our assumption as to the total mass of the stars and other bodies which form our sidereal system. That estimate was founded on a liberal, indeed a very liberal interpretation of the evidence which our telescopes have afforded. But it must probably fall short of the truth on account of the myriads of dark stars. There may be more than a hundred million stars in our system; the average weight may be more than five times the weight of our sun. But unless the assumption we have made is enormously short of the truth, our inference cannot be challenged. If the stars are sixty-four times as numerous, or if the whole mass of the system be sixty-four times as great as we have supposed, then the critical velocity would be 200 miles a second instead of twenty-five miles a second. Our estimate of the system would therefore have to be enlarged sixty-four fold, if the attraction of that system is to be adequate to recall 1830 Groombridge. It should also be recollected that our assumption of the velocity of the star is very ​moderate, so that it is not at all unlikely that a system at least 100 times as massive as the system we have supposed would be required if this star was to be recalled.
The result of this inquiry is to be stated as an alternative: either our sidereal system is not an entirely isolated object, or its bodies must be vastly more numerous or more massive than a liberal interpretation of observations would seem to warrant. If we adopt the first alternative, then we see that 1830 Groombridge, having travelled from an indefinitely great distance on one side of the heavens, is now passing through our system for the first and the only time. After leaving our neighbourhood it will retreat again into the depths of space, to a distance which, for anything we can tell, may be practically regarded as infinite. Although we have only used this one star as an illustration, yet it is not to be supposed that the peculiarities which it presents are absolutely unique. It seems more likely that there may be many other stars which are at present passing through our system. In fact, considering that most or all of the stars are actually in motion, it can be shown that in the course of ages, the whole face of the heavens is gradually changing. We are thus led to the conclusion that our system may not be an absolutely isolated group of bodies in the abyss of space, but that we are visited by other bodies coming from the remotest regions of space. The whole range of astronomy presents no speculations which have attracted more attention than the celebrated nebular hypotheses of Herschel and of Laplace. We shall first enunciate these speculations, and then we shall attempt to indicate how far they seem to be warranted by the actual state of scientific knowledge. In one of his ​most memorable papers, Sir W. Herschel presents us with a summary of his observations on the nebulæ arranged in such a manner as to suggest his theory of the gradual transmutation of nebulæ into stars. He first shows us that there are regions in the heavens where a faint diffused nebulosity is all that can be detected by the telescope. There are other nebulæ in which a nucleus can be just discerned; others again in which the nucleus is easily seen; and still others where the nucleus is a brilliant starlike point. The transition from an object of this kind to a nebulous star is very natural, while the nebulous stars pass into the ordinary stars by a few graduated stages. It is thus possible to enumerate a series of objects, beginning at one end with the most diffused nebulosity, and ending at the other with an ordinary fixed star or group of stars. Each object in the series differs but slightly from the object just before it and just after it.
It seemed to Herschel that he was thus able to view the actual changes by which masses of phosphorescent or glowing vapour became actually condensed down into stars. The condensation of a nebula could be followed in the same manner as we can study the growth of the trees in a forest by comparing the trees of various ages which the forest contains at the same time. In attempting to pronounce upon the positive evidence available in the discussion of Herschel's theory, we encounter a well-known difficulty. To establish this theory, it would be necessary to watch the actual condensation of one single nebula from the primitive gaseous condition down to the stellar points. It may easily be conceived that such a process would require a vast lapse of time, perhaps enormously greater than the period between the invention of the telescope and the ​sent moment. It may at all events be confidently asserted that the condensation of a nebula into a star is a process which has never been witnessed. Whether any stages in that process can be said to have been witnessed is a different matter, on which it is not easy to speak with precision. Drawings of the same nebula made at different dates often exhibit great discrepancies. In comparing these drawings, it must be remembered that a nebula is an object usually devoid of distinct outline, and varying greatly in appearance with different telescopic apertures. Take, for instance, the very splendid nebula in Orion, which is one of the most glorious objects that can be seen in a telescope. There can be no doubt that the drawings made at different times do exhibit most marked differences. Indeed, the differences are sometimes so great that it is hard to believe that the same object is depicted. It is well to look also at drawings made of the same object at the same time, but by different observers and with different telescopes. Where we find contemporary drawings at variance and they are often widely at variance it seems hard to draw any conclusion from drawings as to the presence or the absence of change in the shape of the nebula.
There are, however, good grounds for believing that nebulæ really do undergo some changes, at least as regards brightness; but whether these changes are such as Herschel's theory would seem to require is quite another question. Perhaps the best authenticated instance is that of the variable nebula in the constellation of Taurus, discovered by Mr. Hind in 1852. At the time of its discovery this object was a small nebula about one minute in diameter, with a central condensation of light. D'Arrest, ​the distinguished astronomer of Copenhagen, found in 1861 that this nebula had vanished. On the 29th of December, 1861, the nebula was again seen in the powerful refractor at Pulkova, but on December 12, 1863, Mr. Hind failed to detect it with the telescope by which it had been originally discovered. This instrument had, however, only half the aperture of the Pulkova telescope. In 1868, O. Struve, observing at Pulkova, detected another nebulous spot in the vicinity of the place of the missing object, but this also has now vanished. Struve does not, however, consider that the nebula of 1868 is distinct from Hind's nebula, but he says—
"What I see is certainly the variable nebula itself, only in altered brightness and spread over a larger space. Some traces of nebulosity are still to be seen exactly on the spot where Hind and D'Arrest placed the variable nebula. It is a remarkable circumstance that this nebula is in the vicinity of a variable star, which changes somewhat irregularly from the ninth to the twelfth magnitude. At the time of the discovery in 1861, both the star and the nebula were brighter than they have since become."
This is the best authenticated history of observed change in any nebula. It must be admitted that the changes are such as would not be expected if Herschel's theory were universally true.
Another remarkable occurrence in modern astronomy may be cited as having some bearing on the question as to the actual evidence for or against Herschel's theory. On November 24, 1876, Dr. Schmidt noticed a new star of the third magnitude in the constellation Cygnus. The discoverer was confident that no corresponding object existed on the evening of the 20th of November. The ​brilliancy of the new star gradually declined until on the 13th of December Mr. Hind found it of the sixth magnitude. The spectrum of this star was carefully studied by many observers, and it exhibited several bright lines, which indicated that the star differed from other stars by the possession of vast masses of glowing gaseous material. The star was observed by the late Dr. Copeland at the Earl of Crawford's observatory on September 2, 1877. It was then below the tenth magnitude, and of a decidedly bluish tint. Viewed through the spectroscope, its light was almost completely monochromatic, and appeared to be indistinguishable from that which is often found to come from nebulæ. Dr. Copeland thus concludes:—
"Bearing in mind the history of this star from the time of its discovery by Schmidt, it would seem certain that we have an instance before us in which a star has changed into a planetary nebula of small angular diameter. At least it may be safely affirmed that no astronomer discovering the object in its present state would, after viewing it through a prism, hesitate to pronounce as to its present nebulous character."
It should, however, be added that Professor Pickering has since found slight traces of a continuous spectrum, but the object has now become so extremely faint that such observations are very difficult. This remarkable history might be adduced if we wished to procure evidence of the conversion of stars into nebulæ, but for the nebular theory we require evidence of the conversion of nebulæ into stars.
Care must be taken not to exaggerate the inferences to be drawn from the two instances I have quoted—viz., the variable nebula in Taurus and the new star in Cygnus. I ​think it more likely that both of these are to be regarded as exceptional phenomena. It is certainly true that they are perhaps the most remarkable instances in which changes in nebulæ have actually been witnessed; but the probability is that the only reason why they have been witnessed is because they were very exceptional. Those who have observed the nebulæ for many years are well assured of the general permanence of their appearance. The nebulæ we have referred to are chosen out of thousands. The ordinary nebulæ appear just as constant as the ordinary bright stars. Every one expects to see Vega in the constellation Lyra; and with equal confidence every astronomer counts on seeing the celebrated annular nebula when he directs his telescope to the same constellation. This permanence is very probably merely due to the stupendous distances at which these objects are placed. Only gigantic changes could be detected, and for these gigantic periods of time would be required. We are bound to believe that heated bodies radiate their heat; and if so they must contract. This general law, which pervades all nature, so far as we know it, seems to be the real basis indeed, the only basis on which the nebular theory of Herschel can be maintained. Up to the present, it must be admitted that this theory has received no direct telescopic confirmation.
The nebular theory by which Laplace sought to account for the origin of the solar system seems, from the nature of the case, to be almost incapable of receiving any direct testimony. We shall here enunciate the theory in the language of Professor Newcomb:—
"The remarkable uniformity among the directions of the revolutions of the planets being something which ​could not have been the result of chance, Laplace sought to investigate its probable cause. This cause, he thought, could be nothing else than the atmosphere of the sun, which once extended so far out as to fill all the space now occupied by the planets. He conceives the immense vaporous mass forming the sun and his atmosphere to have had a slow rotation on its axis. The mass, being intensely hot, would slowly cool off, and as it did so, would contract towards the centre. As it contracted its velocity would, in obedience to one of the fundamental laws of mechanics, constantly increase, so that a time would arrive when, at the outer boundary of the mass, the centrifugal force due to the rotation would counterbalance the attractive force of the central mass. Then those outer portions would be left behind as a revolving ring, while the next inner portions would continue to contract, until at their boundary the centrifugal and attractive forces would be again balanced, when a second ring would be left behind; and so on. Thus, instead of a continuous atmosphere, the sun would be surrounded by a series of concentric revolving rings of vapour.
"Now, how would these rings of vapour behave? As they cooled off, their denser materials would condense first, and thus the ring would be composed of a mixed mass, partly solid and partly vaporous, the quantity of solid matter constantly increasing and that of vapour diminishing. If the ring were perfectly uniform this condensing process would take place equally all around it, and the ring would thus be broken up into a group of small planets like that which we see between Mars and Jupiter. But we should expect that, in general, some portions of the ring would be much denser than others, ​and the denser portion would gradually attract the rarer portions around it, until instead of a ring we should have a single mass, composed of a nearly solid centre, surrounded by an immense atmosphere of fiery vapour. This condensation of the ring of vapour around a single point would have produced no change in the amount of rotary motion originally existing in the ring; the planet surrounded by its fiery atmosphere would therefore be in rotation, and would be, in miniature, a reproduction of the case of the sun surrounded by his atmosphere with which we set out. In the same way that the solar atmosphere formed itself first into rings, and then these rings condensed into planets, so, if the planetary atmosphere were sufficiently extensive, they would form themselves into rings, and these rings would condense into satellites. In the case of Saturn, however, one of the rings was so perfectly uniform that there could be no denser portion to draw the rest of the ring around it, and thus we have the well-known rings of Saturn."
It will thus be seen that one of the principal features in the solar system for which the nebular theory has been invoked is the fact that the planets all revolve round the sun in the same direction. It will therefore be natural to take up first the discussion of this subject, and to inquire how far the common motion of the planets can be claimed in support of Laplace's nebular theory. The value of this argument is very materially influenced by another consideration of a somewhat peculiar character. If it were quite immaterial to the welfare of the planetary system whether all the planets moved the same way, or whether some moved one way and some another, then the nebular hypothesis would be entitled to all the support which ​could be derived from the circumstances of the case. Take, for instance, the eight principal planets Mercury, Venus, the Earth, Mars, Jupiter, Saturn, Uranus, Neptune. All these planets move in the same way around the sun. The chances against such an occurrence are 127 to 1. The probability that the system of eight planets has been guided to move in the same direction by some cause may be taken to be 127 to 1. If we include the two hundred minor planets the probability would be enormously enhanced. The nebular theory seems a reasonable explanation of how this uniformity of movements could arise, and therefore the advocates of the nebular theory may seem entitled to claim all this high degree of probability in their favour. There is, however, quite a different point of view from which the question may be regarded. There are reasons which imperatively demand that the planets (at all events the large planets) shall revolve in uniform directions, which lie quite outside the view taken in the nebular theory. If the big planets did not all revolve in the same direction, the system would have perished long ago, and we should not now be here to discuss the nebular or any other hypothesis.
It is well known that in consequence of the gravitation which pervades the solar system, each of the planets has its movements mainly subordinated to the attraction of the sun. But each of the planets attracts every other planet. In consequence of these attractions, the orbits of the planets are to some extent affected. The mutual actions of the planets present many problems of the highest interest, and, it should be added, of the greatest difficulty. Many of these difficulties have been overcome. It is the great glory of the French mathematicians to ​have invented the methods by which the nature of the solar system could be studied. The results at which they arrived are not a little remarkable. They have computed how much the planets act and react upon each other, and they have shown that in consequence of these actions the orbit of each planet gradually changes its shape and its position. But the crowning feature of these discoveries is the demonstration that these changes in the orbits of the planets are all periodic. The orbits may fluctuate, but those fluctuations are confined within very narrow limits. In the course of ages the system gradually becomes deformed, but it will gradually return again to its original position, and again depart therefrom. These changes are comparatively so small that our system may be regarded as substantially the same even when its fluctuations have attained their greatest amplitude. These splendid discoveries are founded upon the actual circumstances of the system, as we see that system to be constituted.
Take, for instance, the eccentricities of the orbits of the planets around the sun. Those eccentricities can never change much; they are now small quantities, and small quantities those eccentricities must for ever remain. The proof of this remarkable theorem partly depends upon the fact that the planets are all revolving around the sun in the same direction. If one of the planets we have named were revolving in an opposite direction to the rest, the mathematical theory would break down. We should have no guarantee that the eccentricities would for ever remain small, as they are at present. In a similar manner, the planets all move in orbits whose planes are inclined to each other at very small angles. The positions of ​those planes fluctuate, but these fluctuations are confined within very narrow limits. The proof of this theorem, like the proof of the corresponding theorem about the eccentricities, depends upon the actual conditions of the planetary system as we find it. If one of the planets were to be stopped, turned round, and started off again in the opposite direction, our guarantee for the preservation of the planes would be gone. It therefore follows that if the system is to be permanently maintained, all the planets must revolve in the same direction.
In this connection it is impossible not to notice the peculiar circumstances presented by the comets. By a sort of convention the planets have adopted, or, at all events, they possess, movements which fulfil the conditions necessary if the planets are to live and let live; but the comets do not obey any of the conditions which are imposed by the planetary convention. The orbits of the comets are not nearly circles. They are sometimes ellipses with a very high degree of eccentricity; they are often so very eccentric that we are unable to distinguish the parts of their orbits which we see from actual parabolas. Nor do the directions in which the comets move exhibit any uniformity; some move round the sun in one direction, some move in the opposite direction. Even the planes which contain the orbits of the comets are totally different from each other. Instead of being inclined at only a very few degrees to their mean position, the planes of the comets hardly follow any common law; they are inclined at all sorts of directions. In no respect do the comets obey those principles which are necessary to prevent constitutional disorder in the planetary system.
The consequences of this are obvious, and unfortunate in ​the highest degree—for the comets. A comet possesses no security for the undisturbed enjoyment of its orbit. Not to mention the risk of actual collision with the planets, there are other ways in which the path of a comet may experience enormously great changes by the disturbances which the planets are capable of producing. How is it that the system has been able to tolerate the vagaries of comets for so many ages? Solely because the comets, though capable of suffering from perturbations, are practically incapable of producing any perturbations on the planets. The efficiency of a body in producing perturbations depends upon the mass of the body. Now all we have hitherto seen with regard to comets tends to show that the masses of comets are extremely small. Attempts have been made to measure them, but have always failed, because the scales in which we have attempted to weigh them have been too coarse to weigh anything of the almost spiritual texture of a comet. It is unnecessary to go as far as some have done, and to say that the weight of a large comet may be only a few pounds or a few ounces. It might be more reasonable to suppose that the weight of a large comet was thousands of tons, though even thousands of tons would be far too small a weight to admit of being measured by the very coarse balance which is at our disposal.
The enduring stability of the planetary system is thus seen to be compatible with the existence of comets solely because comets fulfil the condition of being almost imponderable in comparison with the mighty masses of the planetary system. The very existence of our planetary system is a proof of the doctrine that the masses of the comets are but small. Indeed, to those who will duly ​weigh the matter, it will probably appear that, this negative evidence as to the mass of the comets is more satisfactory than the results of any of the more direct attempts to place the comets in the weighing scales. If we restate the circumstances of the solar system, and if we include the comets in our view, it will appear how seriously the existence of the comets affects the validity of the argument in favour of the nebular hypothesis which is derived from the uniformity in the directions of the planetary movements. If we include the whole host of minor planets, we have for the population of the solar system something under three hundred planets, and an enormous multitude of comets. It will probably not be an overestimate if we suppose that the comets are ten times as numerous as the planets. The case, then, stands thus:
The solar system consists of some thousands of different bodies; these bodies move in orbits of the most varied degrees of eccentricity; they have no common direction; their planes are situated in all conceivable positions, save only that each of these planes must pass through the sun. Stated in this way, the present condition of the solar system is surely no argument for the nebular theory. It might rather be said that it is inconceivable on the nebular theory how a system of this form could be constructed at all. Nine-tenths of the bodies in the solar system do not exhibit movements which would suggest that they were produced from a nebula: the remaining tenth do no doubt exhibit movements which seem to admit of explanation by the nebular theory: but, had that tenth not obeyed the group of laws referred to, they would not now be there to tell the tale. The planetary system now lives because it was an organism fitted for survival.
​It is often alleged that the comets are not indigenous to the solar system. It has been supposed that the comets have been imported from other systems. It has also been urged with considerable probability that perhaps many comets may have had their origin in our sun, and have been actually ejected therefrom. I do not now attempt to enter into the discussion of these views, which are at present problematical; let me pass from this part of the subject, with the remark that until the nature and origin of comets is better understood, it will be impossible to appraise with accuracy the value of the argument for the nebular hypothesis which has been based on the uniformity of the directions in which the planets revolve around the sun.
There are, however, other circumstances in the solar system which admit of explanation by the nebular theory. It is a remarkable fact that the Earth, Mars, Jupiter, and Saturn are all known to rotate upon their axes in the same direction as their revolutions around the sun. The nebular theory offers an explanation of this circumstance. It does not appear that this common rotation of the planets is absolutely necessary for the stability of the system. Should it further be proved that there is no other agency at work which would force the planets to rotate in the same direction, then it must be admitted that the nebular theory receives very substantial support.
There is another way in which we can examine the evidence on behalf of the nebular hypothesis. There are certain actions going on at present in the solar system; and by reasoning backwards from these present actions we are led to believe that in extremely early times the condition of things may have resembled that which is supposed ​by the nebular hypothesis. Let us begin with the consideration of our sun, which is, as we know, daily radiating off light and heat into space. This heat is poured off in all directions; a small portion of it is intercepted by the earth, but this portion is less than one two-thousand-millionth part of the whole; the planets also, no doubt, each intercept a small portion of the solar radiation; but the great mass of radiated heat from the sun entirely escapes. This heat is supposed not to be restored to the sun. The sun certainly must receive some heat by the radiation from the stars; but this is quite infinitesimal in comparison with its own stupendous radiation. We therefore conclude that the sun's heat is being squandered with prodigal liberality. We also know that the store of heat which the sun can possess, though no doubt enormously great, is still limited in amount. It is, indeed, a question of very great interest to decide what are the probable sources by which the sun is able to maintain its present rate of expenditure. It must have some source of heat in addition to that which it would possess in virtue of its temperature as an incandescent body. If we suppose the sun to be a vast incandescent body, formed of materials which possess the same specific heat as the materials of which our earth is composed, the sun would then cool at the rate of from 5° to 10° per annum. At this rate the sun could not have lasted for more than a few thousand years before it cooled down. We are therefore compelled to inquire whether the sun may not have some other source of heat to supply its radiation beyond that which arises merely from the temperature.
Of the various sources which have been suggested, it will here only be necessary to mention two. It has been ​supposed that the heat of the sun may be recruited by the incessant falling of meteoric matter upon the sun's surface. If that matter had been drawn only by the sun's attraction from the remote depths of space, it would fall upon the sun with an enormously great velocity, amounting to about 300 miles a second. It follows from the principle of the equivalence between heat and mechanical energy that a body entering the sun with this velocity would contribute to the sun a considerable quantity of heat. It is known that small meteoroids abound in the solar system; they are constantly seen in the form of shooting stars when they dash into our atmosphere, and it can hardly be doubted that myriads of such bodies must fall into the sun. It does not, however, seem likely that enough matter of this kind can enter the sun to account for its mighty radiation of heat. It can be shown that the quantity of matter necessary for this purpose is so large that a mass equal in the aggregate to the mass of the earth would have to fall into the sun every century if the radiation of the sun were to be defrayed from this source. That so large a stream of matter should be perennially drawn into the sun is, to say the least, highly improbable.
But it is quite possible to account for the radiation of the sun on strictly scientific principles, even if we discard entirely the contributions due to meteoric matter. As the sun parts with its heat it must contract, in virtue of the general law that all bodies contract when cooling; but in the act of contraction an amount of heat is produced. By this the process of cooling is greatly retarded. It can, indeed, be shown that, if the sun contracts so that his diameter decreases one mile every twenty-five years, the amount of heat necessary to supply his radiation would ​be amply accounted for. At this rate many thousands of years must elapse before the diminution in the sun's diameter would be large enough to be appreciable by our measurements.
Looking back into the remote ages, we thus see that the sun was larger and larger the further back we project our view. If we go sufficiently far back, we seem to come to a time when the sun, in a more or less completely gaseous state, filled up the surrounding space out to the orbit of Mercury, or, earlier still, out to the orbit of the remotest planet. If we admit that the present laws of nature have been acting during the past ages to which we refer, then it does not seem possible to escape the conclusion that the sun was once a nebulous mass of gas such as the nebular theory of Laplace would require.
It will also throw some light upon this retrospective argument for the nebular theory if we briefly consider the probable history of the earth. It is known that the interior of the earth is hotter than the exterior. It has been suggested that this interior heat may arise from certain chemical actions which are at present going on. If this were universally the case, the argument now to be brought forward could not be entertained. I believe, however, most physicists will agree in thinking that the interior heat of the earth is an indication that it is cooling down from some former condition in which it was hotter than it is at present. The surface has cooled already, and the interior is cooling as quickly as the badly conducting materials of the crust will permit. We are thus led to think of the earth as having been hotter in past time than at present. The further we look back the greater must the earth's heat have been. We cannot stop ​till the earth was once red-hot or white-hot, till it was molten or a mass of fiery vapour. I have endeavoured to set forth a popular account of the nebular theory in a volume entitled "The Earth's Beginning."
The verdict of science on the whole subject cannot be expressed better than in the words of Newcomb:—
"At the present time we can only say that the nebular hypothesis is indicated by the general tendencies of the laws of nature; that it has not been proved to be inconsistent with any fact; that it is almost a necessary consequence of the only theory by which we can account for the origin and conservation of the sun's heat; but that it rests on the assumption that this conservation is to be explained by the laws of nature as we now see them in operation. Should any one be sceptical as to the sufficiency of these laws to account for the present state of things, science can furnish no evidence strong enough to overthrow his doubts until the sun shall be found growing smaller by actual measurement, or the nebulæ be actually seen to condense into stars and systems."