NEW THEORIES IN
ASTRONOMY

BY

WILLIAM STIRLING

CIVIL ENGINEER

London:

E. & F. N. SPON, Limited, 57 HAYMARKET

New York:

SPON & CHAMBERLAIN, 123 LIBERTY STREET

1906

[TO THE READER.]

Mr. William Stirling, Civil Engineer, who devoted the last years of his life to writing this work, was born in Kilmarnock, Scotland, his father being the Rev. Robert Stirling, D.D., of that city, and his brothers, the late Mr. Patrick Stirling and Mr. James Stirling, the well known engineers and designers of Locomotive Engines for the Great Northern and South Eastern Railways respectively.

After completing his studies in Scotland he settled in South America, and was engaged as manager and constructing engineer in important railway enterprises on the west coast, besides other concerns both in Peru and Chile; his last work being the designing and construction of the railway from the port of Tocopilla on the Pacific Ocean to the Nitrate Fields of Toco in the interior, the property of the Anglo-Chilian and Nitrate Railway Company.

He died in Lima, Peru, on the 7th October, 1900, much esteemed and respected, leaving the MS. of the present work behind him, which is now published as a tribute to his memory, and wish to put before those who are interested in the Science of Astronomy his theories to which he devoted so much thought.

CONTENTS

NEW
Theories in Astronomy.

INTRODUCTION.

That a little knowledge is a dangerous thing to the possessor, has been pointed out often enough, probably with the idea of keeping him quiet, but it is very certain that the warning has not always had the desired effect; and in some respects it is perhaps much better that it has not, for it is sometimes the case that a little knowledge exhibited on an inappropriate occasion, or even wrongly applied, throws light upon some subject that was previously not very well understood. It sometimes happens that unconscious error leads to the discovery of what is right. The fact is, all knowledge is at first little, so that if the first possessor of it is kept quiet there is little chance of its ever increasing. On the other hand, much knowledge seems to be quite as ready to become dangerous on occasion, for it has sometimes led its possessor to fall into errors that can be easily pointed out, even by the possessor of little, if it is combined with ordinary intelligence. The possessor of much knowledge is apt to forget, in his keen desire to acquire more, that he has not examined with sufficient care all the steps by which he has attained to what he has got, and that by placing reliance on one false step he has erected for himself a structure that cannot stand; or, what is worse perhaps, has prevented those who have followed him in implicit dependence on his attainments and fame from finding out the truth. If, then, both of these classes are liable to fall into error, there appears to be no good reason why one belonging to the first mentioned of them should absolutely refrain from making his ideas known, especially as he may thus induce someone of the second to re-examine the foundations on which he has built up his knowledge.

These reflections are in greater or lesser degree applicable to all knowledge and science of all kinds, even theological, in all their individual branches, and can be very easily shown to be both reasonable and true. And it may be added, or rather it is necessary to add, that every one of all the branches of all of them has a very manifest tendency towards despotism; to impose its sway and way of thinking upon the whole world.

At various intervals during the present century speculation has been indulged in, and more or less lively discussion has taken place about the great benefit it would confer on universal humanity, were all the weights and measures of the whole earth arranged on the same standard. The universal standard proposed has been, of course, the metrical system, which had been elaborated by French savants who most probably thought they had arrived at such a state of knowledge that they were able to establish the foundations of all science of all kinds and for all time, upon the most sure and most durable principles. These periods of metrical fever, so to speak, seem to come on without any apparent immediately exciting cause, and some people succumb to the disease, others do not, just the same as in the cases of cholera, influenza, plague, etc. Whether some species of inoculation for it may be discovered, or whether it will be found that an unlimited attack is really perfect health, will most probably be found out in the course of time, although it may be some centuries hence. What is of interest to understand at the present time is, what are the benefits to be derived from the proposed universal standard of weights and measures, and how they are to be attained.

The principal and most imposing reason for its adoption is that it would be of immense service to scientific men all over the world, who would thus be able to understand the discourses, writings, discoveries, etc. of each other without the necessity of having to enter into calculations of any kind in order to be able to comprehend the arithmetical part of what they have listened to or read. Another argument brought forward in favour is, that it would greatly facilitate commercial transactions with foreign countries; and it has been lately advanced that great loss is suffered by one country selling its goods, manufactured according to its own measures, in countries where the metrical system has been adopted. Yet another advantage held out is the convenience it would be to travellers in money matters; but as this argument cannot be admitted without taking into consideration the necessity for one universal language all over the world, it has practically no place in any discussion on the subject, until the evil caused by the building of the Tower of Babel has been remedied.

Not long after one of the periodical attacks of metric fever we came upon an essay written by J. J. Jeans on "England's Supremacy," and published in New York by Harper and Brothers, in 1886, in which we found the following:—

Numerical relation of occupations in England and Wales in 1881:

This statement shows that 43 per cent. of the whole population are occupied in some business or work of some kind, and leads us reasonably to suppose that the remaining 57 per cent. consist of women, children, and people who—to put it short—are non-producers; the whole of whom can hardly be considered as much interested in the making of any alterations in the weights and measures of their country, rather the contrary, for they cannot expect to be much benefited by any change.

The professional class naturally comprehends Theology, Law, Medicine, and Science generally, so that the 2·5 per cent. ascribed to it would be seriously reduced, if the advantage derived from the desired change were reckoned by the number really benefited by it. A similar reduction would have to be made on the 3·7 per cent. stated to be occupied in Commerce, as it is not to be supposed that the whole of the number are engaged in foreign trade. Thus the number of people in these two classes who might really reap some advantage from the change, may be reduced by at least one half; and if we consider that one person in ten of those occupied in the Agricultural and Industrial classes is a scientist—we may pardon the Domestic class—a very liberal allowance indeed, we arrive at the conclusion that 6 per cent. of the whole population might find, some more, some less, interest in the introduction into our country of the French metric system.

The above statement refers only to England and Wales, but if Scotland and Ireland are added to them, the 6 per cent. proportion could not be very greatly altered: perhaps it would be less favourable to the change. Thus 94 per cent., or something like 37 millions, of the whole population of the United Kingdom would be called upon to change their whole system of weights and measures, in order that 6 per cent., or somewhere between 2 and 2½ millions, should find some little alleviation in a part of their labours; and surely 2 to 2½ millions of scientists and merchants engaged in foreign trade is a very liberal allowance for the population of our country. If this does not show a tendency towards despotism, it would be hard to tell what it does show.

Of course, it would not be fair to assume that the whole of the 6 per cent. would desire to see the proposed change carried into effect. In all likelihood, a very considerable portion of the number would be disposed to count the cost of erecting such a structure before actually laying its foundations, and would refrain from beginning the work on considering by what means it was to be brought to a conclusion; even without going so far as to find out that 94 per cent. of it at least would have to be done by forced labour. They might even go the length of speculating on how long it would take to coerce the 94 per cent. into furnishing the forced labour, and on the hopelessness of the task. On the other hand, they might think it more natural to lay hold of the alternative of adopting a special system of weights and measures for the use of Science and Foreign Commerce alone, and leave the 94 per cent. to follow their own national and natural customs, which they would be very likely to do whatever might be determined, if we may judge by the progress made in France a century after the system was thought to be established. Very little opposition could be made to such a course, and if the best possible system were not adopted, the scientists would be the only parties put to inconvenience. They could improve and reform it, should they find it not to be perfect, without the necessity of coercing the 94 per cent. into furnishing another contingent of forced labour. But little is to be gained by saying any more about it. Should the metrical system be adopted some day by Act of Parliament, Science will have obtained what it has so long coveted, will be quite satisfied, and will trouble itself very little about how it affects the rest of the population. It will perhaps never even think of how India will be brought to buy and sell through the medium of the French Metrical System.

And now we have only one step to take on this subject. We may say that the project of establishing one standard of weights and measures for the whole world has a most unpleasant resemblance to the object proposed by the builders of the Tower of Babel; the only thing that can be said in its favour being that it points towards an endeavour to do away with the bad results produced by that enterprise and to bring matters back to the state the world was in before the foundations of that celebrated edifice were laid.

The foregoing is only one instance of the many that could be cited where science has schemed projects for universal progress without due thought, and has come to the conclusion that they could be easily carried out. There are as many examples of this jumping at conclusions as would fill many books, which of course it is not our purpose to do; but there is one that it is necessary to have brought forward for examination, because of its having, through a most incomprehensible want of thought, a tendency to establish Natural Religion on the very bases upon which the Christian Religion is established.

The one referred to is that by which some of the most eminent scientists of the present century, following up what was done in former times, have been able by deep study and experiment, unfortunately coupled with unaccountable blindness or preconceived erroneous ideas, to formulate processes by which the whole universe may have elaborated itself from protyle and protoplasm, or some such substances which, without any foundation to build upon, they suppose to have existed from all eternity. This advance in science has been called the Theory of Evolution, and has been very generally considered to be new, or of comparatively very recent conception; but it is only a piece of the evidence of a very general propensity in those who come to acquire a little more knowledge, to flatter themselves that they have power to seize hold of the Unknown.

The theory may be new, but evolution most assuredly is not, as any one may convince himself who will take the trouble to read the first chapter of the Book of Genesis and to think. There he will find it stated that the earth and all things in it and on it were created and made in six days, or periods of time, showing him distinctly, if he does not shut his eyes wilfully, that two operations were employed in the process, one of creation and the other of making, which last can mean nothing but evolution. It does not matter a straw whether the latter operation was carried on personally by the Creator and Maker, or under the power of laws ordained by Him for the purpose; it was evolution all the same, and just the kind of evolution the scientists above alluded to would have us believe to be new, not far from 3500 years after the account of the creation and making of the world was written by Moses.

It will do no harm to take special notice of the work that was done in each of the six periods, as it will help to fix attention on the subject during examination and judgment; and may even tend to open the eyes of any one who had made up his mind to keep them shut.

In the first period the heavens and the earth were created, but the earth was without form and void, inanis et vacuus, according to The Vulgate—(does that mean empty and hollow?)—and darkness was upon the face of the deep; but light was let shine upon the earth to alternate with darkness, and between the two to establish day and night. It is therefore evident that after the earth was created it had to be reduced to something like its present form, a globe of some kind, and to rotate on an axis, otherwise there could have been no alternations of light and darkness, of day and night. Where did the light come from? Some people seem to think that Moses should have included a treatise on the creation and evolution of the universe, in his account of the work done in the first period of creation. For all that can be truly said to the contrary, he seems to have been quite as able to do so as any scientist of the present day; but it is evident he thought it best to limit himself to writing only of the earth, as being of most interest to its inhabitants, and enough for them as a first lesson. The literature of science, however, of the present day, will tell them that long ages after the earth was evolved into a globe, it must have been in a molten, liquid state, surrounded by an atmosphere of vapours of some of the chemical elements so dense that no light from without could shine through it, and could only be penetrated by light after the cooling of the earth had dispelled a sufficient portion of that dense atmosphere. With this explanation, which they had at hand for the looking for, they might have been so far satisfied, and have left Moses to tell his story in his own way.

In passing, it may not be out of place to say that, after the cooling of the earth had proceeded so far that the vapours of matter had been condensed and precipitated on its surface, all boiling of water whether in the seas or on its surface must soon have ceased, so that no inconceivably enormous volumes of steam could be thrown upwards to maintain an atmosphere impenetrable to light; and that when dense volumes of steam ceased to be thrown up, the condensation of what was already in the atmosphere would be so rapid, and its density so soon reduced sufficiently to admit of the passage of light through it, that one can almost fancy himself present on the occasion and appreciate the sublimity of the language. "And God said, Let there be light, and there was light"; more especially if he had ever stood by the side of the cylinder of a large steam engine, and understood what he heard when the steam rushed from it into the condenser, and noted how instantaneous it seemed to be. Any one who has watched a pot of water boiling on the fire and emitting clouds of steam, will have noticed how immediately the boiling ceased whenever the pot was removed from the fire; but he will also have noticed that the water still continued to emit a considerable quantity of vapour, and will be able to understand how it was that the cloudy atmosphere of the earth, at the time we are dealing with, could allow light to pass through it but still keep the source of light from being visible. He experiences daily how thin a cloud will hide the sun from his sight. But there is more to be said about this when the time comes for taking note of the actual appearance on the scene of the sun, moon, and stars.

To obtain some rude idea of the time to be disposed of for evolution during the first period, let it be supposed that the whole of the time consumed in the creation and development of the earth was 300 million years, as demanded by some geologists, the first period of the six would naturally be somewhere about 50 millions of years, a period which would allow, probably, very liberal time for evolution, but could never have been consumed in creation, seeing that creation has always been looked upon as an almost instantaneous act. And if anyone is still capable of exacting that the period was a day of twenty-four hours, he has to acknowledge that at least twenty-three of them were dedicated to the work of evolution.

The second period was evidently one solely of evolution, as all that was done during it was confined to making the firmament which divides the waters from the waters; an operation which could never be confounded with creation, being probably brought about solely by the cooling of the earth, which was the only means by which a separation between the waters covering the earth, and those held in suspension above it by the atmosphere, could be brought about, and must have been purely the work of evolution.

The third period was begun by collecting the waters under the firmament into one place and letting the dry land appear; which, it may be well to note, gives it to be understood that the surface of the solid part of the earth had come to be uneven either by the elevation or depression, perhaps both, of some parts of it, and next the earth was let bring forth grass and trees, and in general vegetation of all kinds. These cannot be considered otherwise than as operations of evolution: there was no creation going on beyond what may have been necessary to help evolution, and of that not a word is said. Here it is well to notice that until the waters were gathered together into one place and the dry land appeared there could be no alluvial deposits made in the sea, and that till well on into this third period, that is well on for 150 million years from the beginning, there could be no geological strata deposited in it containing vegetable matter, for the very good reason that although rains and rivers may have swept earthy matter into the sea, the rivers could not carry along in their flow any vegetable matter until it had time to grow.

Should evolutionists think they have discovered something new in spontaneous generation, we refer them to the 11th verse of the chapter, where they will see—"And God said, Let the earth bring forth grass, the herb yielding seed, and the fruit-tree yielding fruit after his kind, whose seed is in itself, upon the earth." The conclusion of this passage asserts plainly that the seed was already in the earth, somehow or other, ready to germinate and sprout when the necessary accompanying conditions were prepared. The words are very few, and they can have no other meaning.

In the first period "God made two great lights: the greater light to rule the day and the lesser light to rule the night; he made the stars also." This passage has been "a stumbling block and rock of offence" to some people possessed of much knowledge and to some possessed of little; the one party professing to disbelieve all because the sun was made four days after there was light, and the other party, supposing that there might have been light proceeding from some other source during the first four days. Both parties seem to have forgotten that the earth was created without form and void, and that being so the same would naturally be the case with the sun and the moon; all of them had to be made into form after their creation. By what means? By evolution, of course, or whatever else anyone chooses to call it; that will make no difference.

As far as it can penetrate into the mysteries of creation, Physical Astronomy has endeavoured to show how the solar system may have been formed out of a mass of nebulous matter. Furthermore, as has already been adduced in evidence, that at one time the earth must have been a molten, liquid globe surrounded by vapours of metals, metalloids, gases, and finally by water; and even goes the length of supposing that the planets were evolved to something approaching their present state, long before the sun attained its present form. Following up this hypothesis, it is more than probable that the sun had not attained that form when this fourth period began, and, although capable of emitting light early in the first period, still required a vast amount of evolution to reduce it to the brilliant globe now seen in the heavens. Everybody knows that plants grow without sunshine, and it is generally believed that the primary forests of the earth grew most rapidly in a moist, stifling atmosphere, which neither admitted of animal life, nor could be penetrated by sunshine. Thus Physical Astronomy cannot say that the sun could not have been made into its present state until near the end of this fourth period. It may have been as bright as it is now, though very probably not, as we shall see in due time; but it could not shine upon the earth, neither could the earth, nor anything thereon, see it. It is not necessary to say anything about the moon, as it only reflects sunlight, and the reflection could not reach the earth if the light could not.

In the fifth period the waters were let "bring forth the moving creature that hath life, and fowl that may fly above the earth in the open firmament of heaven." Here again spontaneous generation may have been provided for beforehand, the same as in the case of vegetation. Also it is said "God created great whales," and it is to be observed that this is only the second time that creation has been mentioned in the book, and would seem to teach that making, or evolution, was the most active agent at work in the construction of the earth—and, we may add, of the universe.

The sixth period was one almost exclusively of evolution, unless it should be considered that spontaneous generation is a different, and newly discovered process. In it God made the beast of the earth, cattle, and everything that creepeth upon the earth, after his kind. Last of all: "God said, let us make man in our image, after our likeness." Thus it appears that the only work of creation done in this period was that of creating man, and even that after some length of time and work had been expended in making or evolution, which may have extended over a very considerable portion of the fifty millions of years corresponding to it.

We have supposed the work of creation to have extended over three hundred million years to satisfy some geologists, but our arguments would not be affected in any way by the time being reduced to the limit given by Lord Kelvin to the heat-giving power of the sun in the past, which he has made out to be between fifteen and twenty million years. That would only limit our periods of evolution to two and a half or three million years each; each of them quite long enough to be totally inconsistent with our ideas of creation, which conceive of this as an instantaneous act. But although Lord Kelvin has in rather strong terms placed this limit, he at the same time says that it could by no means exceed four hundred million years, which is one-third more than we have calculated upon. Neither can our arguments be affected in any serious way by our dividing the periods into fifty million years each; these may have varied much in length, but whatever was taken from one would have to be added to the others.

Furthermore, we may be allowed to say that fifteen to twenty millions of years of the sun's heat at the rate it is now being expended, can be no reliable measure of the time required for the operations of geology, for the reason that its heat must have been emitted in proportion to the quantity it possessed at any time. When it was created without form and void as no doubt it was, the same as the earth, it would have no heat to emit, but that does not mean that it possessed no heat until it was formed into the brilliant globe that we cannot now bear to turn our eyes upon. Even when it became hot enough to show light sufficient to penetrate the "darkness that was upon the face of the deep," it may still have been an almost shapeless mass, and have continued more or less so until it was formed into the body of the fourth period, which may even then have been very different from what it is now. Thus geology would have not far from one hundred and fifty million years in which a very small fractional part of the sun's emission of heat would suffice for its operations. But we shall have more to say on this subject when the time comes.

It being, therefore, a matter beyond all question—to people possessed of the faculty of thinking, and of candour to confess that they cannot help seeing what has been set plainly before their sight and understanding—that the opening chapter of the book of Genesis plainly teaches that making—evolution—had a very large and active part to perform in the creation of the universe and—much more within our grasp—of the earth; we can come to the conclusion that the theory of evolution, instead of being new and wonderful, comes to be almost infinitely older than the everlasting hills, without losing any of its power of inspiring inexpressible wonder.

Looking back over the examination into the first chapter of the book of Genesis we have just concluded, we cannot conceive how it could ever have entered into the thoughts of man, that the state of vegetable and animal life on the earth, at the present day, must have been brought about by continual and unceasing acts of creation, when creation has been mentioned only on three occasions during the whole process described in the chapter we have analysed, that is, 3 out of 31 verses; and while the other processes which we have brought forward—making and spontaneous generation—have never been alluded to, perhaps not even thought of.

We have no desire, neither are we qualified, to follow up this subject any further, but we have still one or two things to bring into remembrance.

One of the most illustrious of the founders of the Theory of Evolution has based his dissertations on the Descent of Man, on the Variation of Animals and Plants under Domestication, and on their wonderful plasticity under the care of man. Here there is an explicit acknowledgment of the necessity for the direction of an intelligent guiding power to produce such variations; these never having any useful or progressive results except under such care. If, then, there is a necessity of such directing and guiding power in the case of variations of such inferior importance, the superintendence of some similar power must have assuredly been much more necessary for the creation and evolution of matter, of life, and of man himself. This is what, one would think, common sense and reason would point, and what the Theory of Evolution seems to think—evidently without studying the subject far enough; but all that it has been able to do has been to substitute Nature for the Creator to whom Moses has ascribed not only Creation but the Making—Evolution—of the universe.

This naturally leads us to speculate on what Evolutionists consider Nature to be, and as none of them—nor anyone else—as far as we know, has ever thought it necessary to define Nature, we have to endeavour to draw from their writings what, in some measure and some way, they would like us to believe it to be. We find, then, that the base of their operations seems to be Natural Selection, which can hardly be interpreted in any other way than by calling it the Selection of Nature. Thus, then, they apparently want us to look upon Nature as the First Cause. But, if Nature can select, it must be a being, an entity, a something, that can distinguish one particle of matter from another, and be able to choose such pieces of it, be they protyle or protoplasm, and to make them unite, so as to form some special body, organic or inorganic. It is plain, also, that Selection can only be performed by such a being, or something, such as just so far described, that can distinguish, choose, and arrange the particles of matter destined to form the very smallest body or the universe. Thus we see that in whatever way the basis of the Theory of Evolution is looked upon—even for its own evolution—there is required a being of some kind that has knowledge and power to evolve or make all things that are "in heaven above, or in the earth beneath, or in the waters under the earth." So we see that, if the theory of evolution dethrones the Creator and Evolver of the first chapter of Genesis, it has to enthrone another god which it calls Nature; and has to get rid of that god, and any number of others, before it can be what it pretends to be.

We are all very voluble in talking of Nature, and enthusiastic in admiring its beauties, wonders, and wisdom, but it seldom occurs to us that we are really doing so without thinking of whence come the beauty, wonders, and wisdom. We must, therefore, not be too hard on evolutionists, as they have only done what we all do every day of our lives; but if the theory of evolution is to be looked upon as a branch of science, we would recommend its students to open their eyes and think of it as a process which has been in existence from the beginning of things at least, and not as one of their invention or discovery. They may be able some day, through more accurate study and more convincing argumentation than they generally use, to lay claim to having discovered, as far as it is possible for man to do, the modus operandi of evolution, but that is all, and we would also warn some of them to think that, when we see them in their highest flights of science, genius, and self-sufficiency, we can

"Conceive the bard the hero of the story."

We have read a good deal of what has been called the War of Science, without having been able to see that there ever was any cause for such a war, with the exception of ignorance.

If Theology had been able, or rather had taken the trouble, to study thoroughly the first chapter of Genesis, and thus to comprehend that, if the earth was created without form and void, a great deal of work had to be done, after creation, in forming it into its present condition, there was no call upon it to find fault with Copernicus or persecute Galileus, because they said the earth revolved round the sun; more especially as they do not appear to have ever said anything against religion or revelation. Neither was there any necessity for opposing the so-called new science of evolution, because it (Theology) ought to have seen that the work expended in reducing the earth into form could hardly be conceived of otherwise than as a process of evolution; and would thus have been in a position to tell the authors of the new science that they had only discovered what had existed before the beginning of time.

On the other hand, there was no occasion for Science to take up the war. If it, in its turn, had taken the trouble to study and understand the first chapter of Genesis, it could have shown Theology that it did not comprehend, and could not give a true account of what religion and revelation are; whereas it (Science) seems to have had a strong tendency to demonstrate that religion and revelation are altogether false, and that the great work it has to perform is to dethrone Theology, and set itself up it in its stead.

It is not worth while even to think of who or which was the aggressor, seeing that the war originated from ignorance caused by want of thought and study on both sides. All that has to be said on the subject reduces itself to the fact that both Religion and Science have been coming, and are at present going, through the process of evolution. Can anyone say that Science has been truly scientific, without ever incurring in error, from the beginning of history up to the present day? Will any one venture to maintain that there has been no evolution, no progress, no softening of the spirit of Religion, from the institution of Christianity up to the end of the nineteenth century? If such there be, let the one look back to the time of Aristotle, and the other to the establishment of the Church under Constantine.

There has been for long an opinion, which goes on increasing in strength, that Science will ultimately reform Theology and put Religion in its right place; but if such is to be the case, Science has to begin by reforming itself and putting an end to error it has been, in many cases, teaching for generations; and by ceasing to formulate new theories, or bases of progress, which can be in many cases exploded by suppressing some of the error just alluded to. Little advance is made in science by forming hypotheses and theories, however brilliant they may appear, unless they are carefully studied and thought out to the very uttermost; because, if published abroad on the authority of some celebrated or even well-known name, they have a tendency to stop further investigation, and prevent students from exercising their own judgment and perhaps discovering what they might possibly find out were they to study them to the very end for their own satisfaction. This is in some measure the case even with respect to the solar system. We believe it can be shown that a more complete knowledge and comprehension of it, and even of the universe, has been kept back by the unquestioning acceptation by successive astronomers of the ideas and conceptions of their predecessors.

We have to acknowledge, at the same time, that Astronomy could not start into perfection at once, any more than any other science, and it is not to be wondered at that in times past ideas relating to it should have been formed without being properly thought out; even ideas that could not be properly thought out to the end for want of the requisite knowledge. But it is much to be regretted that such ideas should continue to be published at the present day as trustworthy instruction for readers who may look upon it as strictly correct. Among those who read text-books even on Astronomy, there must be a very considerable number who are rather surprised when they see statements made which do not agree with what they were taught at school, or with what they have practised in other sciences in their own professions or trades. It may be said that any person of ordinary intelligence will easily be able to correct such errors, but the evil does not stop here. If he can really correct them he will most probably find as well, that his instructors have been led into more serious errors, perhaps in more important matters, founded on the ideas which they had not fully studied out before giving them a place in their books. He may also find sometimes, in his reading, such ideas brought forward to substantiate some theory, just as far as they are required and then dropped, while a step or two further forward in the examination of these same ideas, would have exploded the theory altogether; because, although founded to a certain extent on one law of nature, they are in contradiction with what is laid down in some other law.

The above will be looked upon as an unwarrantably bold assertion; but a careful study of, or attention to, what is taught in the most advanced works on the solar system, even in science generally, will show it to be perfectly true. It is not only true, but the consequences of its being true have been much more serious than will be readily believed. In our own endeavours to understand what we had been reading, we have seen that some of the notions presented to us were only half formed, and that they have led to theories being founded which could never have been entertained at all had they been thoroughly studied out. More than that, they have prevented the truth from being arrived at in the fundamental conceptions of the construction of the earth, and, as a natural consequence, of the whole solar system, perhaps even of the whole universe.

There are probably many, even a great many, people who have arrived at the same conclusions as we have, but as far as it has been in our power to search into the matter, we have met with no attempt from any quarter to put an end to this defect in the literature of science; perhaps because the work has the appearance of being too great to be readily undertaken, and also because it may be thought that there is little to be gained by it—as all is sure to be set right through time. But, as we believe that it will be beneficial immediately, in the case of the earth and solar system at least, we shall first attempt to show what are some of the defects alluded to, and then what knowledge may be acquired through their removal.

[CHAPTER I.]

Before astronomers could begin to determine the relative distances from each other, and the relative dimensions and masses of the various members of the solar system, they had to establish scales of measurements appropriate to their undertaking. This entailed upon them, of course, the necessity of determining the form, the different circumferences and diameters, and the weight of the whole earth, as any other scales derived from the only available source, the earth, would have been too small to give even an approximate value of the measures and masses to be sought for.

History tells us that at least one attempt had been made, over two thousand years ago, to find the circumference and necessarily the diameter of the earth, but it says nothing of any to ascertain its weight. There may have been many to determine both diameter and mass, but we know nothing of them; and when we think seriously about this, we cannot help feeling somewhat surprised that no attempt had been made to find out the density and mass till more than a century after Sir Isaac Newton's discovery of the law of Attraction, or Gravitation, as it is more usually called. But perhaps this is an idea that could only occur to one who has been spoilt by witnessing, in great measure, the immense strides in advance that have been made during the nineteenth century in science of all kinds, and does not duly take into account the immense labour, and the incessant meeting with almost insurmountable difficulties, that astronomers have had to encounter and overcome between the birth of modern astronomy and the end of the eighteenth century. Indeed, the difficulties can hardly be looked upon as altogether overcome even yet, as efforts are still being made to find out the exact distance of the sun, and it is not impossible that some small difference may be found, plus or minus, in the density at present adopted for the earth of 5·66 times the weight of water.

The geometer who, more than two thousand years ago, set himself the task of measuring the circumference of the earth, is supposed to have made use of very much the same kind of implements as those employed by modern astronomers. He must have had a very fair instrument for measuring angles, and have known very well how to use it, seeing he was able to determine a value for the obliquity of the ecliptic which agrees so well with that established by modern science, its variations being, for what we know, taken into account; and for length or distance he would doubtless have some implement analogous to the metre, chain, foot-rule, or something called by other name that would, in those days, present facilities for selling a yard of calico. His operations would probably be as plain and simple as those applied to the measuring of a village green—for we are not told that he had any idea of there being any difference between the length of a degree of the meridian at the equator and one nearer either of the poles—and involved no hypotheses or theories, any more than modern operations have done.

When the time came for making efforts to ascertain the density of the earth, science seems to have employed the very simplest means it had at its disposal for attaining its object, and to have gone on refining its implements and operations in conformity with the lessons it went on learning while pursuing its self-imposed task. Every one who, even for recreation, has read a fair amount of the multitude of works and writings that have been published on Popular Astronomy—not to speak of text-books—knows that the first attempts were made by measuring the attraction of steep, or precipitous, mountains for plummets suspended in appropriate positions in their neighbourhood; then—evidently from knowledge acquired during these operations—by the attraction for each other of large and small leaden balls suspended on frames and torsion balances, which go under the name of the Cavendish Experiment; and afterwards by a refinement on this in using the Chemical Balance, where only one large and one small ball of metal are required. All these operations and their results are to be found described in works of various kinds, and are generally reduced to something like the following tubular form, which we reproduce in order to make more intelligible what we have just said, and that we may make a few remarks upon them.

There is no hypothesis, no theory, connected with any of the operations, unless it was the supposition that a plummet—which was naturally believed to point to the centre of the earth—should be pulled to one side by the attraction for it of a mountain in its neighbourhood, and that was found to be a fact.

Methods Employed for Finding the Density of the Earth,
And their Results.

In the case of the plummet deviating from its absolutely straight direction towards the centre of the earth, caused by their attraction, not only the mountains themselves had to be measured and virtually weighed as far as they were measurable, but the weight of the wedge or pyramid between that measurable point, in each case, and the centre of the earth had to be estimated in some way; then the centre of gravity of the whole of this mass had to be ascertained, as well as the respective distances from the centre of the earth of this centre of gravity and that of the plummet, and only after all this and a deep study of the mutual attractions of this mass and the plummet could an estimate be formed of the mass of the earth. It will thus be seen that such measurements and estimates could never be looked upon as very exact and reliable; and nevertheless they have come very near the density of 5·66 finally adopted for the earth.

In the case of the Torsion Balance experiments a very considerable advance was made in consequence, most undoubtedly, of the knowledge acquired from what had been done by Maskelyne. When it was found that the attraction of Schiehallien for the plummets was such a measurable quantity, Cavendish evidently saw that the attraction of manageable leaden balls for each other would be measurable also, and that as no calculations of any kind whatever were necessary to find the masses of the balls, the mutual attraction of large and small balls would furnish a more exact means of measuring the density of the earth, than the roundabout way of having to calculate the weight of a mountain as a beginning; and with the requisite ingenuity, invention, and labour, he found the means of applying the torsion balance, to make the experiments.

After these experiments were revised by Reich and Baily—and the density of 5·66 adopted, we believe—still another set were undertaken by J. H. Pointing, with the Chemical Balance, in which only two metal balls, one large and one small were required, which gave a density of 5·690 as shown opposite, and from its extreme simplicity may perhaps have been the most exact of all.

We have said, we think with truth, that there is no hypothesis or theory involved in any of these experiments, but only the simplest form of—we might almost say—arithmetical calculation. But there is a theory built up on hypothesis which has no foundation whatever, and about which most people, who take the trouble to study it out to the very end, will come to the conclusion that "the less said the better." This, at all events, is our opinion, and we would not have taken any notice whatever of it had it not been that up to the present day, it is published in many works on Popular Astronomy, and even in some text-books, and is looked upon in them, apparently, as an example of the transcendent height to which human science can reach.

We allude, of course, to the theory that the deeper we go down into the earth—at least to an undefined and undefinable depth—the greater is its attraction for the bob of a pendulum at that depth, and the greater the number of vibrations the pendulum is caused to make in a given time. The explanation of the theory is, that were the earth homogeneous throughout its whole volume, the pendulum ought to make the fewer vibrations, the deeper down in the earth it is placed; but as the earth is not homogeneous, it actually makes a greater number of vibrations in a given time, because the attractive force of the earth increases—up to the undefined and undefinable depth—on account of the denser matter beneath the pendulum bob more than overbalancing the loss of attraction from the lighter matter left above it. The author of the theory was the late Astronomer Royal, Sir George B. Airy, who from it endeavoured to calculate the mean density of the earth, and with that view made two experiments which are thus described by Professor C. Piazzi Smythe in his work on the Great Pyramid:—

"Another species of experiment. . . was tried in 1826 by Mr. (now Sir) George B. Airy, Astronomer Royal, Dr. Whewell, and the Rev. Richard Sheepshanks, by means of pendulum observations at the top and bottom of a deep mine in Cornwall; but the proceedings at that time failed. Subsequently, in 1855, the case was taken up again by Sir George B. Airy and his Greenwich assistants, in a mine near Newcastle. They were reinforced by the new invention of sympathetic electric control between clocks at the top and bottom of a mine, and had much better, though still unexpectedly large results—the mean density of the earth coming out, for them, 6·565."

From other sources we have also found that the pit, or mine, was at the Harton Colliery and 1260 feet deep, that the pendulum at the bottom of it gained 2¼ seconds on the similar one at the top, in 24 hours; and that the surrounding country had to be extensively surveyed, the strata had to be studied, and their specific gravities ascertained.

A little unbiassed thought bestowed on this theory will at once show that it begins by violating the law of attraction discovered by Newton, when he showed that the mutually attractive forces of several bodies are the same as if they were resident in the centres of gravity of the bodies. In the case in point this means, that the attraction of the earth for the bob of the pendulum at the top of the mine was the same as if all its force was collected at its (the earth's) centre. In that position the force of the earth's attraction comprehended, most undeniably, the whole of its attractive power, including whatever might be imagined to be derived from the non-homogeneity of the earth, due to its density increasing towards the centre; and we are called upon to believe that when, virtually, the same pendulum was removed to the bottom of the mine, and a segment 1260 feet thick, at the centre as good as cut off from the earth and—as far as the pendulum was concerned—hung up on a peg in a laboratory, the diminished quantity of its matter had a greater attractive force, a very little beyond the centre—non-homogeneity again included—than the whole when the sphere was intact. This we cannot do, because all that we can see in the placing of the pendulum at the bottom of the mine, is that the position of the bob has divided the earth into two sections, one of which has a tendency to pull it up towards the surface, and the other to pull it down towards its centre of gravity; and because the mass of the smaller segment is so insignificant that its entire removal to the laboratory peg, not only could not produce the reverse action, on which the theory is based, but could not be measured by any stretch of human invention or ingenuity; it is far beyond the reach of mathematics and human comprehension of quantity.

The difficulty of belief is increased when we reflect that, were the pendulum taken down towards the centre of the earth, the number of its vibrations in a given time ought gradually to decrease as it approached the centre, and would cease altogether when that point was reached. And we feel confident that no mathematician could calculate where the theoretical acceleration of the vibrations would cease, and the inevitable retardation commence; where the theory would come to an end and the law of attraction begin to assert its rights, simply because he does not know how the non-homogeneity is distributed in the earth. No man can tell, even yet, how the mean density of 5·66 is made up throughout the earth, and without that any theory founded on its non-homogeneity is out of place.

But to follow up our assertion of non-commensurability. Taking the diameter of the earth at 8000 miles, and its mean specific gravity at 5·66, its mass would be represented by 1,517,391,000,000 cubic miles of water. On the other hand, supposing the earth to be a true sphere, the volume of a segment of it cut off from one side, at one quarter of a mile deep—not 1260, but 1320 feet—would be 785·35 cubic miles in volume, and if we suppose its specific gravity to be 2·5—greater most probably than the average of all the strata in the neighbourhood of the Harton Colliery—its mass would be represented by 1963·38 cubic miles of water. Then, if we divide the mass of the section below the pendulum, that is, 1,517,391,000,000 minus the mass of the one above it, 1963·38, viz. 1,517,390,998,036·62 by the mass of 1963·38 just mentioned, we find that the proportion they bear to each other is as 1 to 772,846,315. This being so, we are asked to believe that by removing 1/772,846,315th part of the mass of the earth from one side of it, its force of attraction at the centre will not only not be decreased, but will be so increased that it will cause a pendulum, suspended at the centre of the flat left by the removal of the segment, to vibrate 86,402·25 times in twenty-four hours instead of 86,400 times as it did when suspended at the surface before the segment was removed; that is, that the vibrations will be increased by 1/38,400th part. Again we cannot do so. Had we been asked to believe that the removal of so small a fraction as 1/772,846,315th had decreased the earth's attraction at its centre, so much as to produce a diminution of 1/38,400th part in the number of vibrations of the pendulum, we could not have done so; how much less then can we believe that the central attractive force had increased so much as to produce an augmentation of the vibrations in the same proportions? But more in this strain presently.

We have no doubt whatever that Sir George B. Airy and his assistants satisfied themselves that the pendulum at the bottom of the mine gained 2¼ seconds in twenty-four hours over the one at the top, but they may have been deceived by their over-enthusiastic adoption of what seemed to be a very grandly scientific theory, or by some unperceived changes in the temperature in the pendulums, caused by varying ventilation in the mine or the varying weather outside of it, or by the insidious manifestations of the "sympathetic electric control between clocks at the top and bottom of a mine," called in to assist at the experiments. An error of 1/38,400th part of the time the sympathetic electricity would take to travel from the top to the bottom of the shaft would be sufficient to make the experiments of no value whatever; not to speak of the small errors that may have been made in surveying the surrounding country, calculating the specific gravities of the strata—for we are told that all this had to be done-and applying the elements thus obtained to the solution of the problem they had in hand. We have read of the difficulties met with by Mr. Francis Baily when he began to revise the Cavendish Experiment—some twelve or fifteen years before the final Harton Colliery experiments were made, and suppose it possible that they met with similar difficulties without being aware of it. And 1/38,400th part is such a very small fractional difference in the vibrations in twenty-four hours, of the pendulums of the two separate clocks, that—taking into consideration the circumstances under which it was found—it would hardly be looked upon as reliable at the present day, when the clocks of astronomical observatories are placed in the deepest cellars or even caves available, so as to free them as much as possible from variations of temperature.

Having referred to the difficulties met with by Mr. Baily, we believe it worth while to transcribe Professor C. Piazzi Smythe's account of them, given in his work already referred to at page 22; because it not only has a very direct bearing on what we have been saying of changes of temperature, but is exceedingly interesting, and probably very rarely to be met with in other works. It is as follows:—

"Nearly forty years after Cavendish's great work, his experiment was repeated by Professor Reich of Freyberg, in Saxony, with a result of 5·44; and then came the grander repetition of the late Mr. Francis Baily, representing therein the Royal Astronomical Society, and, in fact, the British Government and the British Nation.

"With exquisite care did that well-versed and methodical observer proceed to his task, and yet his observations did not prosper.

"Week after week, and month after month, unceasing measures were recorded; but only to show that some disturbing element was at work, overpowering the attraction of the larger on the smaller balls.

"What could it be?

"Professor Reich was applied to, and requested to state how he had continued to get the much greater degree of accordance with each other, that his published observations showed.

"'Ah!' he explained, 'he had to reject all his earlier observations until he had guarded against variations of temperature by putting the whole apparatus into a cellar, and only looking at it with a telescope through a small hole in the door.'

"Then it was remembered that a very similar plan had been adopted by Cavendish, who had furthermore left this note behind him for his successor's attention—'that even still or after all the precautions which he did take, minute variations and small changes of temperature between the large and small balls were the chief obstacles to full accuracy.'

"Mr. Baily therefore adopted yet further, and very peculiar, means to prevent sudden changes of temperature in his observing room, and then only did the anomalies vanish and the real observations begin.

"The full history of them, and all the particulars of every numerical entry, and the whole of the steps of calculation, are to be found in the Memoirs of the Royal Astronomical Society, and constitute one of the most interesting volumes (the Fourteenth) of that important series; and its final result for the earth's mean density was announced as 5·675, probable error ± 0·0038."

After reading this story of Baily's experiments with care, one cannot help feeling something stronger than want of confidence in those made at the Harton Colliery, especially after what has been shown of the smallness of the fraction of the earth that was dealt with, and due consideration is given to the insignificant difference of effect that the non-homogeneity of the earth could produce on the remainder after the supposed removal of such a small fraction; and here we might let the theory drop. Perhaps it may be thought that now there is nothing to be gained by spending time and work in showing it to be more truly erroneous than we have yet made it out to be; but if there is error, it cannot be too clearly exposed, and the sooner it is put an end to, the better; more especially as it has been accepted as true by some authors of text-books, and by some competent astronomers who, in trying to explain the anomaly of the increase instead of decrease in the force of attraction at the bottom of a mine compared with the top, have used arguments which are not consistent with the law of gravitation, or rather attraction.

Messrs. Newcomb and Holden in their work, entitled "Astronomy for High Schools and Colleges," sixth edition, 1889, apparently accept the theory, and proceed to explain and support it by showing what would be the action of a hollow spherical shell of any substance on a particle of it, say the bob of a pendulum, placed on the outside and also on the inside of the shell; and give us two theorems which are supposed to comprehend both cases. These are:—

(1) "If the particle be outside of the shell, it will be attracted as if the whole mass of the shell were concentrated at its centre."

(2) "If it be inside the shell, the opposite attractions in every direction will neutralise each other, no matter whereabouts in the interior the particles may be, and the resultant attraction of the shell will therefore be zero."

To the first theorem no objection can be made: The particle on the outside of the shell will undoubtedly be attracted by every particle in the shell, with the same force as if the attractive power of all the particles composing it were concentrated in the centre. Not so with the second theorem: for it can be objected that it altogether ignores the Law of Attraction laid down by Sir Isaac Newton, where it asserts that the resultant attraction of the shell for the particle will be zero, when it is placed anywhere on the inside. In fact the theorem supposes a case impossible for the Harton Colliery experiments, in order to demonstrate their accuracy; for it makes use of the bob of the pendulum—a particle of matter—as if it were transferable to any part of the interior of the earth instead of being confined within the bounds of its swing. That the attraction of the shell—1260 feet thick all round the earth—on the pendulum bob inside of it continues in all its force, and is only divided into two opposing parts, is made plain by Fig. 1. Supposing O to represent the bob of the pendulum at the bottom of the mine, and the space between the two circles the shell of the earth. Then the line B C will show where the attraction of the shell for the bob is divided into two parts acting in opposite directions. Supposing these two parts to be separated from each other, only far enough to admit the bob—a particle to all intents and purposes—between them; the part B A C will attract the bob as if its whole attractive force were collected at its centre of gravity, and the part B D C as if the whole of its attractive force were collected, not at the centre B of the shell, but at its centre of gravity, a very little distance from B in the direction towards D. This is an incontrovertible fact, because it is in strict accordance with Newton's Law of Attraction, which is: Every particle of matter in the universe attracts every other particle with a force directly as their masses, and inversely as the square of the distance which separates them.

Fig. 1.

If we now suppose the interior of the shell to be filled up solid, that will make no difference, because the mass of the part B D C will only be increased vastly thereby, while the mass of A B C will remain the same; the two parts only increasing their proportion to each other, and thus coming to be for the earth—in the Harton Colliery experiments—what we represented them to be at [page 24]; and we can now proceed to find the attractive force of each of the two masses for the bob of the pendulum which is as the inverse square of their distances from it. These distances may be taken, without any very great stretch of conscience, as one-tenth of a mile and 3999·75 miles; because the centre of gravity of the segment A B C will be about that distance from O, and that of B D C cannot be adequately represented by a greater sum than 3999·75, always supposing the diameter of the earth to be 8000 miles. Thus the squares of these two distances will be 0·01 and 15,898,000 miles respectively, and the relative force of attraction for the pendulum of the two segments A B C and B D C will be as 1 × 0·01 and 772,846,315, and 772,846,315 × 15,898,000; that is as 1 is to 1,228,671,000,000,000,000. Here then we get confirmed the unbelief in the theory we expressed at pages [23 and 24]. Surely no one will be bold enough to assert that by decreasing the total attractive force of the earth by a little less than a 1¼ trillionth part cut off from one side of it, the want of homogeneity in what remains will not only not decrease its attractive force at the centre, but increase it so as to make a pendulum be lessened by 1/38,400th part of its time in beating one second. This fraction of time is quite small enough to inspire doubt of any theory founded upon it; and if there ever is a quantity in mathematics that can be called negligible, the fraction of attractive force found above ought to be included in the same category. We may therefore assert that no human measurements could find a true difference between the beats of a seconds pendulum at the top and bottom of the pit at the Harton Colliery. If all the people who have puzzled themselves with this theory had spent an hour or two in making the above calculations before they began them, there would have been no experiments made, and the theory would have died almost ere it was born. Those who believed in it may have looked upon a particle as a negligible quantity, but as the whole earth is made up of particles a little thought would have put an end to such a notion. What puzzles us is how such a theory could be formed by people who knew nothing whatever of the nature of the interior of the earth at a depth of even one mile, and how they could speculate on its want of homogeneity without knowing anything of how the density of 5·66 is made up in it? To suppose that the earth is made up of strata of different densities, and that each is in some degree elliptical—the ellipticity of one stratum being different from another, as the French mathematician Clairaut did—is all very allowable; but to build up any theory on any such suppositions is to build upon shifting sands without examining the foundations. For anything that is known up to the present time, the density of the earth may go on increasing gradually from the surface to the centre, or it may attain nearly its greatest density at a few miles from the surface, and continue homogeneous or nearly so from there to the centre.

To go further now: it is not true that the attraction of a hollow shell of a sphere for any particle within it, is the same "no matter whereabouts in the interior the particle may be." The only place where the attraction will be the same is when the particle is at the centre. In that position a particle would be in a state of very unstable equilibrium, and a little greater thickness of the shell on one side than the others, would pull it a little, perhaps a great, distance from the centre towards that side; and if we extend our ideas to a plurality of particles within the shell of a sphere, we are led to speculate on how they would be distributed, and to see the possibility of there not being any at all at the centre. This is a point which has never been mooted, as far as we have been able to learn, and we shall have to return to it when the proper time comes.

It is difficult to understand how any man could conceive the notion that a shell of a sphere, such as that shown at [Fig. 1], could have no attraction for each separate one of all the particles which make up the mass of the whole solid sphere within it; for that is the truth of the matter if properly looked into, when it is asserted, as has been done by Messrs. Newcomb and Holden, that "the resultant attraction of the shell will therefore be zero." If such a notion could be carried out in a supposed formation of the earth, an infinity of particles would carry off the whole of the interior, and leave the earth as only a shell of 1260 feet thick, as per the Hartley Colliery experiment; only we are told, or left to understand, that that process could not go on for ever, but would have to come to an end somehow and somewhere; and then we are left to speculate on how the unattracted particles could come back to take part in the composition of the earth. Left to ourselves we can only liken the process to that followed by a man who peels off the outer layer of an onion, eats the interior part, and when he is satisfied throws down the outer layer and thinks no more of it; not even that he might be asked what had become of the interior part.

Curiously enough, there is a way of explaining how, or rather why, the notion was formed—not unlike the one just given—to be found in the third of Sir George B. Airy's lectures on Popular Astronomy, delivered at Ipswich several years before the final experiments were made at the Harton Colliery. In that lecture, while describing how the Greek Astronomers accounted for the motions of the sun and planets round the stationary earth, he says, "It does appear strange that any reasonable man could entertain such a theory as this. It is, however, certain that they did entertain such a notion; and there is one thing which seems to me to give something of a clue to it. In speaking to-day and yesterday of the faults of education, I said that we take things for granted without evidence; mankind in general adopts things instilled into them in early youth as truths, without sufficient examination; and I now add that philosophers are much influenced by the common belief of the common people."

We can agree with Sir George B. Airy in his ideas about education, and now conclude by saying that he has given us a very clear and notable example of a theory being accepted very generally, without being thoroughly examined to the very end, and of how easy it is for such theories to be handed down to future generations for their admiration.

[CHAPTER II.]

A good deal of theorising has been expended in accounting for the absence of all but traces of an atmosphere and water on the moon, which might have been avoided had astronomers not caught up the notion, and stuck to it, that it rotates on its axis once for every revolution that it makes round the earth. It might be difficult to find out with whom the notion originated; but perhaps it was first conceived to be the case by some celebrated astronomer, and has been accepted by almost all his successors without being properly looked into. Any one who chose to take the trouble to study the matter thoroughly, would have easily discovered that the moon can have no rotation of any kind on its axis, and immediately afterwards have found out the reason why nothing beyond traces of air and water were to be seen on the side of it constantly turned towards the earth. This is another example we can give of erroneous ideas leading to erroneous and impossible conclusions, and preventing the truth from being discovered. That the rotation of the moon on its axis is stated to be a fact, by recognised and celebrated astronomers, will be seen from the following quotations.

(1) Sir John Herschel, in his "Treatise on Astronomy," new edition of 1835, says at page 230: "The lunar summer and winter arise, in fact, from the rotation of the moon on its own axis, the period of which rotation is exactly equal to its sidereal revolution about the earth, and is performed in a plane 1° 31´ 11´´ inclined to the ecliptic, and therefore nearly coincident with her own orbit. This is the cause why we always see the same face of the moon, and have no knowledge of the other side."

(2) In his "Poetry of Astronomy," page 187, Mr. Proctor says: "For my own part, though I cannot doubt that the substance of the moon once formed a ring around the earth, I think there is good reason for believing that when the earth's vaporous mass, receding, left the moon's mass behind, this mass must have been already gathered up into a single vaporous globe. My chief reason for thinking this is, that I cannot on any other supposition find a sufficient explanation of one of the most singular characteristics of our satellite—her revolution on her axis in the same mean time, exactly, as she circuits around the earth."

(3) Professor Newcomb, in his "Popular Astronomy," 5th edition, 1884, at page 313, has what follows: "The most remarkable feature in the motion of the moon is, that she makes one revolution on her axis in the same time that she revolves around the earth, and so always presents the same face to us. In consequence, the other side of the moon must remain for ever invisible to human eyes. The reason for this peculiarity is to be found in the ellipticity of her globe." Then he enlarges upon and confirms the fact of her rotation.

(4) Mr. George F. Chambers, in his "Handbook of Astronomy," 4th edition, 1889, says at page 119, Vol. I.: "In order that the same hemisphere should be continually turned towards us, it would be necessary not only that the time of the moon's rotation on its axis should be precisely equal to the time of the revolution in its orbit, but that the angular velocity in its orbit should, in every part of its course, exactly equal its angular velocity on its axis."

It may be necessary, to avoid misconception, to note that angular velocity on its axis confirms rotation; and what is more extraordinary, that Chambers must have thought that its angular velocity on its axis must have increased and diminished in order to agree with its increased and diminished velocities in its elliptic orbit at its perigee, apogee, and quadratures. A rather strange notion in mechanics where there is no provision made for acceleration or retardation of rotation.

(5) Dr. Samuel Kinns, in "Moses and Geology," twelfth thousand, 1889, says at page 208, "the same side of its (the moon's) sphere is always towards us. This could only happen by its having an axial rotation equal in period to its orbital revolution, which is 27d. 7h. 43m. 11s."

(6) In the "Story of the Heavens," Sir Robert S. Ball informs us, in the fifteenth thousand, 1890, page 530, "That the moon should bend the same face to the earth depends immediately on the condition that the moon should rotate on its axis in precisely the same period as that which it requires to revolve around the earth. The tides are a regulating power of the most unremitting efficiency to ensure that this condition should be observed."

(7) And finally we have what follows from Messrs. Newcomb and Holden, at page 164 of their work already referred to at page 27, "The moon rotates on her axis in the same time and in the same direction in which she moves around the earth. In consequence, she always presents very nearly the same face to the earth." And in a footnote to this consequence, add: "This conclusion is often a pons asinorum to some who conceive that, if the same face of the moon is always presented to the earth, she cannot rotate at all. The difficulty arises from a misunderstanding of the difference between a relative and an absolute rotation. It is true that she does not rotate relatively to a line drawn from the earth to her centre, but she must rotate relative to a fixed line, or a line drawn to a fixed star."

In six of the above cases it is distinctly maintained that the moon rotates once on its axis in the same time that it makes one revolution round the earth, and that it is in consequence of this rotation that it always presents the same side to the earth. Thus we feel authorised to conclude that their authors did either believe that it does so rotate, or that they entertained some confused idea on the subject, which they did not take the trouble to examine properly, but accepted as a dogma, because some predecessor, with a great name, had stated that such rotation was necessary in order that its same side should be always turned towards the earth. In the seventh case the authors, while actually making the same assertion, try to persuade those who they acknowledge can see that the moon does not rotate on its axis in any sense, that their difficulty in comprehending what is meant by rotation, arises from the misunderstanding of the difference between an absolute rotation and one relative to a line drawn to a fixed star. But they do not attempt to show how this relative rotation has anything to do with or has any effect in causing the moon to present always the same side to the earth; and leave the story in the same confused state, out of which nobody can draw any satisfactory conclusion. Also, though they distinctly recognise that it does not rotate relatively to a line drawn from the surface of the earth to its centre, they do not include in their general description of the moon anything in any way connected with what would be the consequences of its not really rotating on its axis relatively to the earth. So they leave us the problem in much the same state as they found it, and it is still necessary to show that there can be no actual rotation of any kind on its axis; and the worst of it is that it is a thing that will have to be done in such very plain language that it will compel people to think of the absurdity of the idea so generally accepted.

To begin, it is very difficult to comprehend what the authors, above alluded to, meant by saying that the moon "must rotate relative to a fixed line, or a line drawn to a fixed star." It may mean relative to the line itself or to the star to which it is drawn. If it is to the line itself we cannot form any notion of what direction the rotation will have, direct, retrograde, or otherwise; and if it is relative to the star itself, then we can see that the relative rotation must depend on what is the position of the star. Should it be placed in the "milky way," we can understand how the moon could show every side it has—almost, not quite—to the star during every revolution it makes round the earth, and how they may look upon it as a relative rotation. But if we draw the line to the pole star we cannot see how the moon can show every side it has to it in every revolution round the earth, so there can be no relative rotation in that case—and the "almost, not quite," applies to every star between the pole and the ecliptic. The moon shows only the northern hemisphere, or a little more due to libration of its own kind, to that star, and would have to remove its poles to the equator, and make a new departure, in order to show the whole of its surface to that star in every revolution round the earth. Thus it is clear that the explanation given us of the relative rotation, is evidently one of the kind not properly thought out to the end.

No one has ever said, or perhaps even thought, that a gin-horse makes one rotation on his vertical axis, in the same time as he makes a circuit round his ring, but, all the same, he keeps his same side always towards the gin, or mill, he is giving motion to. The proof that he does not make any such rotation is easy—no proof is really required. But, suppose he is giving motion to a whim for raising ores from a mine, and that his motion is what is called direct. When the cage containing the ore is brought to bank, is emptied, and has to be lowered into the mine again, the horse has then to reverse his motion to retrograde, in doing which he has to make a half rotation on his vertical axis, and turn his other side to the whim. When again the cage has to be raised to bank, he has to resume his direct motion, for which he has to make another half rotation on his vertical axis, but it is this time in the opposite direction. Thus it is shown that he can only make half rotations, under any circumstances, on his axis, and these in opposite directions, when he changes his motion from direct to retrograde, or vice versâ; and that, when he moves in only one direction he cannot make even one rotation on his vertical axis, however long he may travel round the mill. In the same manner the moon which never turns back in its orbit can never make even one half rotation on its axis, which is all that we have had to prove. It is hardly necessary to observe that its axis is nearly parallel to the earth's, just the same as the horse's is to that of the whim. Neither could any one say that the relative rotation of the horse to a star, or tower, or, say, a bridge, outside of his ring, could have any effect on his revolution round the mill, or his always keeping his same side to it, there being no mechanical connection between them, nor any law of attraction; and the same is the case between the moon and a fixed star.

Now, we may begin to consider what effects must be produced by the moon not rotating on its axis, and we can do so most easily by continuing to work with our gin horse, or some equivalent substitute. It would not cost a great deal of ingenuity to plant a steam engine in the centre of the mill he is supposed to be driving, and to drive with it not only the mill but the horse also at the end of his lever. There might be some dissipation—Professor Tate would call it degradation—of energy in such an experiment, but we could get over that by making divina Palladis arte a wooden horse. We might arrange the steam-engine so as to cause the mill to make 27-1/3 revolutions for one made by our wooden horse, and so have a sort of a model of the earth and moon performing their most important relative motions. Then, having got our model ready for action, instead of filling it armato milite we might fill it half full of water. We fill it only half full, because the armed soldiers could not lie on the top of each other in the other horse, and there would be a vacant space above them for air, thus making the resemblance between the two the more similar; and also because it suits our purpose better, as will soon be seen. We have still to propose that a lot of holes should be supposed to be made in the sides of our horse all round, just a little higher than between wind and water. Pallas did not order any holes to be made in hers as far as we know, even for ventilation, though we think it would have been an advantage; but that will not spoil the experiment we are now prepared for. Let the steam-engine be started now and we shall soon see what will happen to the water. As the speed increases it will not be long till it begins to be thrown out, not from the side turned towards the mill but from the one furthest from it; and if it is increased sufficiently the whole of it will be very soon thrown out. If we could now close up the holes on the side of the horse turned towards the mill, it would so happen that a good deal of the air would be expelled also; and if the speed of the horse were brought up so as to equal that of the moon in its orbit, there would be nothing more, at the most, than traces of air left even in it. The expelling agent in this experiment would, of course, be centrifugal force, and we do not need to exercise our mental faculties very greatly, to comprehend that it is the same force that has driven both air and water away from the side of the moon always turned towards the earth. All the difficulty we have to contend with will be to make sure that the orbital velocity of the moon is sufficient to produce the force required. That the force is exceedingly greater than what is required is proved by the fact, that the velocity with which the moon travels in its orbit is a little more than 38 miles per minute, whereas the velocity of the circumference of a centrifugal machine, used for clarifying sugar, drying clothes, or any other similar industrial purpose, does not require a greater velocity than about one mile per minute, in order to throw everything in the form of water out of the material to be dried, and out of the centrifugal machine itself; and we know that air would be expelled more easily than water, were none re-admitted to supply the place of what was expelled.

Here the idea very naturally occurs to any one, that so great a velocity would drive both air and water away, even from the far off side of the moon, into space, but in order to do so the velocity would have to be 120, not 38, miles per minute. Our authority for this statement will be found in "The Nineteenth Century," for August 1896, in an article written by Prince Kropotkin, in which he says: "But it appears from Dr. Johnstone Stoney's investigations that even if the moon was surrounded at some time of its existence with a gaseous envelope consisting of oxygen, nitrogen and water vapour, it would not have retained much of it. The gases, as is known, consist of molecules rushing in all directions at immense speeds; and the moment that the speed of a molecule which moves near the outer boundary of the atmosphere exceeds a certain limit (which would be about 10,600 feet in a second for the moon) it can escape from the sphere of attraction of the planet. Molecule by molecule the gas must wander off into interplanetary space; and the smaller the mass of the molecule of a given gas, the feebler the planet's attraction, and this is why no free hydrogen could be retained in the earth's atmosphere, and why the moon could retain no air or water vapour."

A velocity of 10,600 feet per second is as near 120 miles per minute as there is any use for, which is more than three times as great as the velocity of the moon in its orbit, so there is no possibility whatever of air and water having been swept away from the far off side of it by centrifugal force; more especially as it ought to be well known that that force is always counteracted by the attractive force of the satellite for these or any other elements.

We do not want to discuss the point of whether the mutual collisions of the molecules of a gas could get up such a velocity as would enable them to free themselves from the attraction of the moon, for it looks to us too much like one of those notions that are got up to account for something that does not exist; but we do want to state our dissent to the conclusion—evidently jumped at—that because there are hardly any signs of there being air or water on our side of the moon, there can be none on the other. No astronomer, physicist, scientist of any kind, can prove that there is none, simply because he has never been round there to see or make experiments to prove it; and if there is any one bold enough to make such an assertion, it is only an example of how stupendous a jump to a conclusion can be made.

When we first read, many years ago, some of the reasons given for there being no water visible on the side of the moon constantly turned to the earth, one of which was that if there ever had been any it must have been absorbed into its body during the process of cooling and consolidation; and when we had convinced ourselves, by placing two oranges on two ends of a wire and revolving the one round the other, that the moon did not rotate on its axis in any sense whatever, we came to the conclusion that both water and air could be removed to the far off hemisphere by centrifugal force. We thought this so simple, so self-evident, and so indisputable an explanation, that every one who had read what we had read must have come to the same conclusion; so that we were not a little surprised when we saw it stated by "The Times" of September 15, 1893, in its first report of the meeting of the British Association for that year, that Sir Robert Ball had suggested, some time previously, that the "absence of any atmosphere investing the moon is a simple and necessary consequence of the kinetic theory of gases." This at once made us suspect that the theory—our theory—must have been new, but we could not altogether believe it. It seemed to us passing strange that it should not have occurred to astronomers, from the moment they discovered that they could not find any, or hardly any, traces of air or water on the only hemisphere they could examine; but it would appear from Sir Robert Ball's suggestion, being even discussed at that meeting, that the notion of their having been removed simply by centrifugal force to the unseen hemisphere, had never been entertained by, to say the least, any one who was present at that discussion.

Not satisfied with this conclusion, we proceeded to examine all the books, journals, magazines, and papers we could get hold of, to see whether we could find any indication of such a conception having been published previously, and the nearest approach to anything of the kind having been conceived of by anyone, we found in Chambers's work—already referred to—at page 134, Vol. I., where we read, "Professor Hansen has recently started a curious theory from which he concludes that the hemisphere of the moon which is turned away from the earth may possess an atmosphere. Having discovered certain irregularities in the moon's motion, which he was unable to reconcile with theory, he was led to suspect that they might arise from the centre of gravity of the moon not coinciding with the centre of figure. Pursuing this idea, he found upon actual investigation that the irregularities could be almost wholly accounted for by supposing the centre of gravity to be at a distance of 33½ miles beyond the centre of figure. Assuming this hypothesis to be well founded, Professor Hansen remarks that the hemisphere of the moon, which is turned towards the earth, is in the condition of a high mountain, and that consequently we need not be surprised that (little or) no trace of an atmosphere exists; but that on the opposite hemisphere, the surface of which is situated beneath the mean level, we have no reason to suppose that there may not exist an atmosphere and consequently both animal and vegetable life. Professor Newcomb has disputed these conclusions of Hansen, which it is obvious must be very difficult of either proof or disproof."

What Professor Newcomb's objections to the conclusions of Hansen were we do not know, but we do know that Mr. Proctor also objected to the "curious theory," as it is called by Mr. Chambers. In his "Poetry on Astronomy," he discusses pretty fully the withdrawal of water from the surface of the moon during the process of cooling and condensation, ascribing the conception of it to four independent authors, namely, Seeman, a German geologist, Frankland in England, Stanislas Mennier in France, and Sterry Hunt in America; and in a footnote, at page 163, says of Hansen's theory: "The idea was that the moon, though nearly spherical, is sometimes egg-shaped, the smaller end of the egg-shaped figure being directed towards the earth. Now, while it is perfectly clear that on this supposition the greater part of the moon's visible half would be of the nature of a gigantic elevation above the mean level, and would, therefore, be denuded (or might be denuded) of its seas and denser parts of the air covering it, yet it is equally clear that all around the base of this monstrous lunar elevation, the seas would be gathered together, and the air would be at its densest. But it is precisely round the base of this part of the moon or, in other words, round the border of the lunar hemisphere, that we should have the best chance of perceiving the effects of air and seas, if any really existed; and it is because of the absolute absence of all evidence of the kind, that astronomers regard the moon as having no seas and very little air."

Had the idea of centrifugal force ever occurred to Mr. Proctor, he could not have written this last sentence; for he could not have failed to see that "the border of the visible lunar hemisphere" would be the very place, from which it could most easily remove air and water, after they had got so far down the monstrous elevation; because there it—the centrifugal force—would be acting at right angles to the moon's attraction, instead of having to contend against it, as it would have to do in a constantly increasing degree until it arrived at its maximum, just in proportion to the distance the air and water got down to the similar monstrous depression on the other hemisphere, down which the gradient would start off under the most favourable circumstances possible.

From what has been said, it is very evident that neither Hansen, Chambers, Proctor, nor any of those whose names have been mentioned by the last, in connexion with the withdrawal of water into the body of the moon by absorption, while cooling and condensing, had ever thought of the possibility of air and water having been removed by centrifugal force from the side of the moon turned towards the earth. That it should not have occurred to Hansen seems passing strange, seeing that he had conceived the idea of their possible existence on the hemisphere turned away from the earth, which could hardly fail to make him think of how they got there, and could exist only there; and the only explanation of his not having perceived the true cause seems to be, that his thoughts were hampered by a sort of confused notion that the moon actually rotates on its axis once for every revolution it makes around the earth, that being, as it were, one of the dogmas of astronomic belief, handed down from some great authority of times past, and never properly inquired into.

We do not want to question the suggestion, that the absence of any atmosphere investing the moon is a simple and necessary consequence of the kinetic theory of gases—though we see that a good deal could be argued against it—as we do not consider it to be necessary—neither the questioning nor the theory. We have demonstrated clearly, how both air and water could be removed from the side of the moon constantly shown to us, and that is sufficient for our purpose both now and later on; besides it would appear that the moon really has some sort of an atmosphere somewhere.

Following up the quotation, made at page 39, from Prince Kropotkin's article in the "Nineteenth Century" as being the latest information we have on the subject, we are told that "a feeble twilight is seen on our satellite, and twilight is due, as is known, to the reflection of light within the gaseous envelope; besides it has been remarked long since at Greenwich that the stars which are covered by the moon during its movements in its orbit remain visible for a couple of seconds longer than they ought to be visible if their rays were not slightly broken as they pass near the moon's surface. Consequently it was concluded that the moon must have an atmosphere" ... and:

"The observations made at Lick, Paris, and Arequipa, fully confirm this view. A twilight is decidedly visible at the cusps of the crescent-moon, especially near the first and last quarters. It prolongs the cusps as a faint glow over the dark shadowed part, for a distance of about 70 miles (60"), and this indicates the existence of an atmosphere having on the surface of the moon the same density as our atmosphere has at a height of about forty miles."

What is of interest for us to know is where that "feeble twilight," or, "reflection of light within the gaseous envelope," is seen. Whether it is at what Mr. Proctor calls "the border of the visible lunar hemisphere," on this side of it, or beyond it. It cannot be a difficult matter to decide. It must be beyond it, for the following reasons: If the atmosphere has been driven away to the far-off hemisphere of the moon by centrifugal force, its natural tendency would be to spread out immediately after it had passed the visible border where we have said the centrifugal force would be acting most effectively. Also, if all the air at one time belonging to our side of the moon has been driven away to the other, that side must have a double allowance of atmosphere, which, though it does not increase its density at the surface, on account of the centrifugal force, will double its volume, and enable it to extend to a greater proportionate distance in all directions from the border and from the far-off hemisphere. In this way there must be a considerable wedge of atmosphere illuminated by the sun, and visible past the edge of the moon's disc, to reflect a feeble twilight—perhaps something stronger—towards the earth, and to intercept the light of a star before its edge and that of the moon come into actual apparent contact. But before the wedge becomes thick enough to reflect that light, the reflecting part must be far beyond the edge of the moon's disc. Perhaps the feeble light might be seen more clearly when looked for in the proper place; quite possibly hundreds of miles beyond the disc.

In order to make more clear the truth of what we have said about water and air—and more especially the latter—being thrown away to the far-off side of the moon by centrifugal force, we may add the following details: If the force of gravity at its surface is one-sixth part of what it is at the surface of the earth, the pressure of an atmosphere there would be 2·5 lb. per square inch, if it rotated on its axis; but as it does not so rotate and is subjected to centrifugal force, the pressure of an atmosphere will vary according to the part of it over which it exists. On the nearest part of the side turned towards the earth, gravity, which we have just seen must be equal to 2·5 lb., would be acting in the same direction as centrifugal force, which in its turn is equal to 0·7 lb. or thereby, and the whole would be 3·2 lb. per square inch tending to drive off air and water to the far-off hemisphere. But from that place, gravity would gradually diminish its aid till it came to be nil at the disc separating the two hemispheres, where it would have no effect whatever as it would be acting at right angles to centrifugal force, and this would be reduced to 0·7 lb. per square inch. Then, from the edges of the disc forward, on the far-off hemisphere, gravity would begin to act against centrifugal force, or rather vice versâ, until it, gravity, got reduced to 1·8 lb. per square inch. Also, as that hemisphere must have a double portion of air or atmosphere on it, and as its pressure on any part of it cannot be greater than the 1·8 lb. just mentioned, we can imagine that the double quantity will hang closer to the surface than if there was only one portion. Such being the case the atmosphere would spread out much more rapidly than would be represented by the extension of a triangle starting from the earth and reaching beyond the moon's disc to the farthest limit of the atmosphere; and thus the wedge, which we have supposed to be visible beyond the edges of the disc may come to have a very considerable thickness. What that thickness may be, and up to what distance beyond the disc the density of the wedge would be sufficient to reflect the light of the sun, it would be very difficult to calculate, but we think it might possibly extend even as far as one-fourth of the radius of the moon—because at that point the force of gravity pulling it towards the centre, or the axis, would be very small, and its distance from the axis would be little less than the radius, not over 33 miles—and cause it to project over the edges as far, to appearance, as the 70 miles (60") that have been observed at Greenwich. This reflected light must be all round the moon—not at the cusps only of the crescent-moon—and it has occurred to us that it may, most probably does, account for the appearance of what we call "the old moon in the young moon's arms." We know what effect the "earth-shine" has upon the moon at its change, and the brighter ring-shine just outside of it, may very well be caused by the sunlight reflected from the atmosphere far beyond the visible limit of the hemisphere turned to us.

In support of this suggestion we may refer to Professor C. A. Young's description, in his "Sun," p. 213, of one particular feature observed at the time of a total eclipse of the sun. He says:—"On such an occasion, if the sky is clear, the moon appears of almost inky darkness, with just a sufficient illumination at the edge of the disc to bring out its rotundity in a striking manner. It looks not like a flat screen, but like a huge black ball, as it really is. From behind it stream out on all sides radiant filaments, beams, and sheets of pearly light, which reach to a distance sometimes of several degrees from the solar surface, forming an irregular stellate halo, with the black globe of the moon in its apparent centre."

There can be little doubt, we think, from what is said here, that Professor Young looks upon this "illumination of the edge of the disc" as pertaining to the moon, and upon the "radiant filaments, beams," etc. behind it as belonging to the sun. And in that case the illumination can only be caused by the light of the sun, refracted by the atmosphere belonging to the hemisphere of the moon that is never seen from the earth.

We have taken it for granted in what we have been doing, that the moon has really rotated on its axis, and to some purpose, at some former period of its existence. Some people think otherwise, or that there is at least a doubt about it; we cannot see even the shadow of a doubt. All that we need to say in support of our opinion is, that there is no other conceivable way of accounting for its perfectly circular form. All the planets are circular, or spheroidal—to speak more correctly—in form, admittedly in consequence of rotation on their axes; and if one or two of Jupiter's satellites are not completely circular or spheroidal, it does not stretch our conscience very much to suppose that it is because they have not yet been rotated into form. Saturn apparently has satellites still in the form of rings, and there can be nothing out of the way in supposing that all of Jupiter's are not yet licked into shape. The fact that there is no appearance of compression on the moon makes us think of why there is none, and the only explanation that occurs to us is, that, as its rotation must have come to an end gradually, the compression it must have had when rotating must have disappeared gradually also, by reason of the differences of force in the equatorial and polar attractions, drawing in the bulged out, and thus forcing out the compressed parts. This is a notion that will be scoffed at by those who have always thought, and maintained, that the earth acquired its present form when in a liquid state; but they have not thought this supposition—for it is nothing else—out to the very end. Several reasons could easily be given against their opinion, among others the variations in rate of rotation we so frequently see used in favour of other notions; but we shall content ourselves with the best one of all, which is this: The pressures in the interior of the earth must be so enormous that they are quite sufficient to compress steel, or adamant if that is supposed to be more resistant, into any shape whatever, almost as if it were dough, and there can be no doubt—mathematics notwithstanding—that the earth has the form, to-day, due to its present rate of rotation. We shall have to return to this subject some time hence, if we live to complete what we have taken in hand.

How many things there are, in what is considered to be astronomical science, that have not been properly thought out to the end, and to what strange notions they have given rise! This one of the rotation of the moon which we have been discussing, has evidently given occasion for the conception of the theory that the absence of atmosphere and seas from the moon is the natural consequence of the kinetic theory of gases; and the author of the theory, and its supporters, have never, apparently, taken the trouble to think whether their absence from the near hemisphere is a satisfactory and convincing proof of there not being any air or water on the far-off one. In what we have proposed to write many similar examples of want of study will be met with, but we do not intend to call special attention to them, unless it be in cases where we consider it to be of some importance to do so. In fact we have already been working on that plan.

[CHAPTER III.]

We have thought it worth while to dedicate this chapter to some remarks on cosmogonies in general, and examination into a very few conceived by eminent men; these forming in our opinion the most attractive matter for those readers who do not pretend to make a study of astronomy, but are very desirous to have some knowledge of the most plausible ideas which have been conceived by astronomers, of how the universe, and more particularly the solar system, were brought into existence; while, at the same time, they are the subjects on which more crude conceptions, more limited study, and more fanciful unexamined thought have been expended, than any others we have met with. Some readers will, no doubt, be able to reject what is erroneous, to speak mildly, but there will be, equally surely, some who cannot do so; and it must be confessed there are a good many to whom the most complicated conceptions, and the most difficult of comprehension, are the most attractive.

A great many centuries ago, astronomers and philosophers had already conceived the idea that the sun and stars had been formed into spherical bodies by the condensation of celestial vapours; but when the telescope was invented, and the nature of nebulæ in some measure understood, it was not long till it came to be thought that the matter, out of which the sun and stars were formed, must have been much more substantial in its nature than celestial vapours. Being visible, they were naturally considered to be self-luminous, and consequently endowed with great heat, because the self-luminous sun was felt to be so endowed, though perhaps not with the same degree. Accordingly, astronomers began to form theories, or hypotheses, on the construction of the solar system out of a nebula, which, like everything else, went on each one improving on its predecessor as, through continued observation and study, more knowledge was acquired of the nature of nebulæ. The most notable of these cosmogonists were Descartes, Newton, Kant, and Laplace, each of whom contributed valuable contingents to the general work; which may be said to have culminated about a century ago in the Nebular Hypothesis of the last-named; for the many attempts that have been made to improve upon it, or to supplant it altogether, have been very far from successful.

The hypothesis is about a century old, as we have said, and there may still be many people who can remember having heard it denounced as a profane, impious, atheistic speculation, for it is not over half a century since the ban begun to be taken off it. Sir David Brewster, in his "Life of Newton," said of it, "That the nebular hypothesis, that dull and dangerous heresy of the age, is incompatible with the established laws of the material universe, and that an omnipotent arm was required to give the planets their positions and motions in space, and a presiding intelligence to assign to them the different functions they had to perform." With others, its chief defect was that the time required to form even the earth in the manner prescribed by it, must have been infinitely greater than six days of twenty-four hours each. In the meantime, geologists had also discovered that, for the formation of the strata of the earth, which they had been examining and studying, the time required for their being deposited must have been, not days of twenty-four hours, but periods of many millions of years each; and the evidence adduced by them that such must have been the case was so overwhelming, that Theology had to acknowledge its force, and gradually to recognise that the days must have been periods of undefinable length. Thus relieved from the charge of heresy, the hypothesis rose rapidly into favour, and came to be generally accepted by the most eminent astronomers, subject always to certain modifications, which modifications have never been clearly defined, if at all. It was not, however, allowed to enjoy long the exalted station to which it had attained.

Astronomers had begun to consider from whence the sun had acquired the enormous quantity of heat it had been expending ever since the world began, and, after long discussion, had come to the conclusion that by far the greatest source must have been the condensation from the nebulous state of the matter of which it is composed. Having settled this point, it was calculated that the amount of heat derived from that and all other sources could not have kept up its expenditure, at the present rate of consumption, for more than twenty million years, and could not maintain it for more than from six to eight million years in the time to come. Owing in good part to this great difference between the calculations of astronomers and geologists about the age of the earth, the hypothesis began again to suffer in repute, and then all its faults and shortcomings were sought out and arrayed against it.

The chief defects attributed to it were: The retrograde motion of rotation of Uranus and Neptune and revolution of their satellites—that fault in the former having been noted by Sir John Herschel, in his Treatise on Astronomy already cited; the discovery of the satellites of Mars which exposed the facts, that the inner one revolves round the planet in less than one-third of the time that it ought to, and that the outer one is too small to have been thrown off by Mars, in accordance with the terms of the hypothesis; the exclusion from it of comets, some of which at least have been proved, in the most irrefutable manner, to form part of the solar system; and what can only be called speculations, on the formation of a lens-shaped nebula brought about by the acceleration of rotation—caused by condensation according to the areolar theory—which it is supposed would be enormously in excess of the actual revolution of the inner planets, and of the rotation of the sun. Here we must protest against retrograde motion of rotation in any of the members of the solar system being considered as militating against the theory, because Laplace states distinctly, while explaining his hypothesis, that the rotation of the earth might just as well have been retrograde as direct: a fact that some eminent astronomers have not noticed, simply because they have not paid proper attention to what they were reading. We shall have to return to this statement again, and to present the proof of its being true.

An idea of how far the hypothesis had fallen into disrepute may be formed from the following extract, from "Nature" of August 4, 1887, of a Review of a "New Cosmogony," by A. M. Clerke, in which it is said: "But now the reiterated blows of objectors may fairly be said to have shattered the symmetrical mould in which Laplace cast his ideas. What remains of it is summed up in the statement that the solar system did originate somehow, by the condensation of a primitive nebula. The rest is irrecoverably gone, and the field is open for ingenious theorising. It has not been wanting.... The newer cosmogonists are divided into two schools by the more or less radical tendencies of the reforms they propose. Some seek wholly to abolish, others merely to renovate the Kant Laplace scheme. The first class is best represented by M. Faye, the second by Mr. Wolfe and Dr. Braun"—the author of the "New Cosmogony."

We cannot pass this quotation without remarking "How glibly some people can write!" More we do not want to say about it, except that it gave us the notion to examine closely some of the new cosmogonies, which have not been wanting, to see whether they are better than Laplace's.

We have not had the opportunity of knowing what are Mr. Wolfe's amendments, but the Review, just cited, gives us a pretty good notion of those of Dr. Braun, and we have been able to study carefully M. Faye's "Origine du Monde," in which he considers the solar system to have been evolved from cosmic matter partially endowed with motion in the form of eddies, whirlwinds, vortices, or tourbillons, which last may comprehend all of them, and even more. We have also studied, with some surprise, in "Climate and Cosmology" Dr. Croll's Impact, or Collision, Theory, and will confine our examination to the three of which we know something, beginning with Dr. Croll's, which we believe to be the oldest of the three.

We understand that Dr. Croll accepts the nebular hypothesis in all its main features, including the intense heat in which the original nebula is supposed to have existed from the beginning; and has only invented the collision theory in order to increase its quantity, to suit the demands of geologists for unlimited time, by showing how an unlimited supply of both heat and time may be obtained. But he has incurred an oversight in not taking into consideration the kind of matter in which that unlimited supply of heat was to be stored up—whether it would hold it. He wrote in times when something was really known about heat, and we cannot suppose him to have believed that heat could exist independent of matter, or that a gas or vapour could be heated to a high temperature except under corresponding pressure; but he has evidently overlooked this point, his thoughts recurring to old notions; and he has fallen, probably for the same reason, into other oversights equally as grave.

When showing how a supply of fifty millions of years of sun-heat could be produced from the collision of two half-suns colliding with velocities of 476 miles per second, Dr. Croll says in his "Discussions on Climate and Cosmology," of 1885, at page 301: "The whole mass would be converted into an incandescent gas" (the handmaid of the period), "with a temperature of which we can have no adequate conception. If we assume the specific heat of the gaseous mass to be equal to that of air (viz. 0·2374), the mass would have a temperature of about 300,000,000° C., or more than 140,000 times that of the voltaic arc."

Now, let us suppose the whole mass of the whole solar system to be converted into a gas, or vapour, at the pressure of our atmosphere, and temperature of 0° C., its volume would be equal to that of a sphere of not quite 9,000,000 miles in diameter. Suppose, then, this volume to be heated to 300,000,000° C. in a close vessel, as would necessarily have to be the case, the pressure corresponding to that temperature would be 1,094,480 atmospheres, according to the theory on which the absolute zero of temperature is founded. Without stopping to consider whether air or any gas could be heated to the temperature mentioned; or the strength of the vessel 9,000,000 miles in diameter required to retain it at the equivalent pressure; if we increase the diameter of the containing sphere to a little more than that of the orbit of Neptune, or, say 6,000,000,000 miles, and allow the air or gas or vapour to expand into it; then, as the volume of the new sphere will be greater than the former one in the proportion of 9,000,000 cubed to 6,000,000,000 cubed, or as 1 is to 296,296,296, the pressure of the gas will be reduced to 296,296,296 divided by 1,094,980, that is just over the 270th part of an atmosphere; which, in its turn would correspond to a temperature of a very little more than -273°, or what is considered to be[A] 273° C. above absolute zero of temperature; or, at all events, to the temperature of space, whatever that may be.

Dr. Croll goes on to say at page 302: "It may be objected that enormous as would be such a temperature, it would nevertheless be insufficient to expand the mass against gravity so as to occupy the entire space included within the orbit of Neptune. To this objection it might be replied, that if the temperature in question were not sufficient to produce the required expansion, it might readily have been so if the two bodies before encounter be assumed to possess a higher velocity, which of course might have been the case. But without making any such assumption, the necessary expansion of the mass can be accounted for on very simple principles. It follows in fact from the theory, that the expansion of the gaseous mass must have been far greater than could have resulted simply from the temperature produced by the concussion. This will be obvious by considering what must take place immediately after the encounter of the two bodies, and before the mass has had sufficient time to pass completely into the gaseous condition. The two bodies coming into collision with such enormous velocities would not rebound like two elastic balls, neither would they instantly be converted into vapour by the encounter. The first effect of the blow would be to shiver them into fragments, small indeed as compared with the size of the bodies themselves, but still into what might be called in ordinary language immense blocks. Before the motion of the two bodies could be stopped, they would undoubtedly interpenetrate each other; and this of course would break them up into fragments. But this would only be the work of a few minutes. Here then we should have all the energy of the lost motion existing in the blocks as heat (molecular motion), while they were still in the solid state; for as yet they would not have had time to assume the gaseous condition. It is obvious, however, that the greater part of the heat would exist on the surface of the blocks (the place receiving the greatest concussion), and would continue there while the blocks retained their solid condition. It is difficult in imagination to realize what the temperature of the surfaces would be at this moment. For supposing the heat were uniformly distributed through the entire mass, each pound, as we have already seen, would possess 100,000,000,000 foot-pounds of heat. But, as the greater part of the heat would at this instant be concentrated on the outer layers of the blocks, these layers would be at once transformed into the gaseous condition, thus enveloping the blocks and filling up the interstices. The temperature of the incandescent gas, owing to this enormous concentration of heat, would be excessive, and its expansive force inconceivably great. As a consequence the blocks would be separated from each other, and driven in all directions with a velocity far more than sufficient to carry them to an infinite distance against the force of gravity were no opposing obstacle in the way. The blocks, by their mutual impact, would be shivered into small fragments, each of which would consequently become enveloped in incandescent gas. These smaller fragments would in a similar manner break up into smaller pieces, and so on until the whole came to assume the gaseous state. The general effect of the explosion would be to disperse the blocks in all directions, radiating from the centre of the mass. Those towards the circumference of the mass, meeting with little or no obstruction to their outward progress, would pass outwards into space to indefinite distances, leaving in this manner a free path for the layers of blocks behind them to follow in their track. Thus eventually a space, perhaps twice or even thrice that included within the orbit of Neptune, might be filled with fragments by the time the whole had assumed the gaseous condition.

"It would be the suddenness and almost instantaneity with which the mass would receive the entire store of energy before it had time even to assume the molten, far less the gaseous condition, which would lead to such fearful explosions and dispersion of the materials. If the heat had been gradually applied, no explosions, and consequently no dispersion of the materials would have taken place. There would first have been a gradual melting; and then the mass would pass by slow degrees in vapour, after which the vapour would rise in temperature as the heat continued, until it became possessed of the entire amount. But the space thus occupied by the gaseous mass would necessarily be very much smaller than in the case we have been considering, where the shattered materials were first dispersed in space before the gaseous condition could be assumed."

We have made this very long quotation; first, because we have not been able to condense it without running the risk of not placing sufficiently clearly the whole of the argumentations employed in it; secondly, because the purport of the whole explanation set forth is evidently to demonstrate that, by means of the explosions of gases produced by the collision, the matter of the whole mass would be more extensively distributed into space—bearing heat along with it—than were it gradually melted and converted into vapour; and thirdly, because every argument advanced in favour of the theory of explosions, if carefully looked into, brings along with it its testimony that it has not been studied thoroughly out to the end. Thus the quotation in a great measure saves us that labour.

Dr. Croll seems sometimes to demand more from the laws of nature than they can give. He says, at p. 42 of the work cited, that the expansion of the gaseous mass, produced by the collision of the two bodies, must have been far greater than could have resulted simply from the temperature produced by the concussion; and goes on to show how it—the expansion—might be caused by explosions of gases blowing out blocks of matter in all directions to indefinite distances. But he forgets that these explosions of gases would consume a great part of the heat they contained, that is, turn it into motion of the blocks, and so diminish the quantity produced by the collision, just in proportion to the velocities given to the masses of all the blocks blown out; so that what was gained in expansion would be lost in heat, and the object aimed at—of producing heat for the expenditure of the sun—so far lost. Also, that, were the thing feasible, the blocks could not carry with them any of the heat of the exploded gases that might not be used up, and that the heat contained in them derived from the concussion would have time in their flight—about two hours at 476 miles per second—to melt the matter composing them and turn it into vapour, long before even the orbit of Neptune was reached. The heat produced by the explosion of powder in a cannon gives the projectile all the impulse it can, and disappears; it is converted into motion. It does not cluster round the projectile, nor follow it up in its flight, nor push it through an armour plate when it pierces one. We cannot admit—for this reason—the possibility of a block of matter flying off into space, with a mass of heat clustering round it, like bees when swarming round a branch of a tree. Thermodynamics does not teach us anything about a mass of heat sticking to the surface of a block of matter of any kind.

If the heat were, at a given moment—that is, when motion was stopped—brought into existence uniformly throughout the entire mass, which, according to the law of conversion of motion into heat and vice versâ, would most assuredly be the case, and each pound of the mass possessed 100,000,000,000 foot-pounds of heat, it could not be heaped up on the outer layers of the blocks—it matters not whether this means the layers of the outside of the whole mass, or at the outsides of the blocks—for the energy of lost motion, converted into heat, must have existed at the centres of the blocks or masses just in as great force as it did at the surfaces when motion was stopped. If each pound of matter carried along with it 100,000,000,000 foot-pounds of heat, that given out by one pound at the centre of a block would be as great as that given out by one pound at its surface; and the pounds at the surface could not acquire any greater heat from a neighbouring pound, because its neighbour could have no greater quantity to give it. Pounds of matter would be melted and vaporized, or converted into gas, just as readily at the centre of the mass or block as at its surface; and storing up of heat in the interstices of the blocks is rather a strange notion, because we are not at liberty to stow away heat in a vacuum. Besides, it is impossible to conceive how anything in the shape of a block could exist in any part of the whole mass, long enough for it to be blown out into space as a block. But supposing that a block could exist, it would most notoriously be in a state of unstable equilibrium; and were it then to receive from an explosion of gas, an impulse sufficient to drive it off to the verge of the sun's power of attraction—or rather to a distance equal to what that is—which would imply a velocity of not less than 360 miles per second, the shock would be quite sufficient to blow it into its constituent atoms. Moreover, as already stated, the heat of the explosion of the gas required to give the impulse would be immediately converted into motion, and disappear; so that out of the heat produced by the stoppage of a motion of 476 miles per second, that required to produce a motion of 360 miles per second, in each one of the blocks blown out to the distance above mentioned, would be entirely lost to the stock of heat schemed for so boldly. Of course, the less the distance from the centre the blocks were blown the less would be the loss, but the fact remains that there would be a loss instead of a gain of heat, in dispersing the matter of two half suns into space by explosions of gas. In fine, a given amount of heat will raise the temperature of a given amount of matter to an easily calculable degree, and no more; and if part of that is expended in expanding the volume of the matter, the whole stock of heat will be diminished by exactly the quantity required to produce the expansions. So that we come back to what we have said at [page 54], viz., that when the matter and the heat of the collision of the two half suns were dispersed, under the most favourable circumstances, into a sphere of 6,000,000,000 miles in diameter, the mean density of the matter would be equal to about 1/270th part of an atmosphere, and its temperature—what is called—273° C. of absolute temperature, always considering the quantity of the heat to have been 300,000,000° C.

Dr. Croll says that if a velocity of 476 miles per second were not sufficient to produce the quantity of heat required, any other necessary velocity might be supposed, but when we consider that his supply of 300,000,000° C. would have to be increased to 82,000,000,000° C., in order to add 1° C. of heat to the matter dispersed through a sphere of 6,000,000,000 miles in diameter, it seems unnecessary to pursue the subject any farther.

We may now take a look at Dr. Braun's Impact Cosmogony, of which we know nothing beyond what is set forth in the Review in "Nature" already alluded to, but that is enough for our purpose. We understand that he extends his operations to the whole universe, which he conceives to have been formed out of almost unlimited, and almost imponderable, nebulous matter, not homogeneous, but with local irregularities in it, which "would lead to the breaking up of the nebula into a vast number of separate fragments." Out of one of these fragments he supposes the solar system to have been formed. This fragment would contain local irregularities also, which through condensation would lead to the formation of separate bodies, and these bodies are supposed to have been driven into their present forms, and gyrating movements of all kinds, by centric and eccentric collisions among themselves, caused by their mutual attractions. Of course anything can be supposed, but in a construction of this kind the idea is forced upon us of the necessity of the active superintendence of the Creator, to create in the proper places and bring in the matter at the exact moment required, and to see that the collisions were directed with the proper degree of energy and eccentricity, to construct the kind of machine that was proposed. To this idea we have no objections whatever, but we would like to see the necessity for it acknowledged. Perhaps Dr. Braun does acknowledge it, but the cosmogony is given to us, it would seem, to show what most probably was the original scheme of construction, and implying that no continual supervision and direction were required during the process. If Dr. Braun could show us some method of attraction, and suspension and variation of attraction, by which some of the separate bodies could be drawn towards each other so as to form a central mass, nebula, or sun, and to give it, by their impacts of collision, a rotary motion; and how others of the separate bodies could be formed and held in appropriate places, so as to be set in motion at the right moment; and how they were to be so set in motion without the direct action of the constructor, to revolve as planets around the central mass, we might be able to recognise that a mechanism such as that of the solar system might be brought into existence; but when we are left to discover all these requisites, and their modus operandi, we find that we might be as well employed in designing a cosmogony of our own.

Dr. Braun indulges in somewhat startling numbers in temperature and pressure. He considers that the temperature of the sun, at the surface, may be from 40,000° to 100,000° C., and that it may reach to from ten to thirty million degrees at the centre. In this he may be right for anything we know to the contrary. When riding over a sandy desert, under an unclouded vertical sun, we could easily have believed anything of the central heat of such a fire, especially when we considered that it was at a distance of ninety-three millions of miles from us. But when he tells us that in the depths of the sun's interior the pressure reaches a maximum of two thousand millions of atmospheres, we "pull in resolution and begin to doubt." Air at that pressure would have a density 2,585,984 times that of water, or 456,887 times the mean density of the earth, and we should have a species of matter to ponder over, of which no physicist has ever as yet dreamt.

We have been able to study M. Faye's cosmogony in his work on "L'Origine du Monde," second edition of 1885, and can give a better account of it than of Dr. Braun's.

(1) He repudiates almost all existence of heat in the cosmic matter he is about to deal with, recognising that its temperature must have been very near the point of absolute zero, and also that its tenuity must have been almost inconceivable; so tenuous that a cubic miriamètre of it would not contain more perhaps than 5·217 grammes in weight. And very properly, we think, he looks upon the solar systems as having, at one time, formed a part of the whole universe, all of which was brought into existence, created, more or less, about the same time. In this universe, he considers that the stars have been formed, as well as the sun, by the progressive concentration of primitive materials disseminated in space, which conception gives rise to a totally new notion of the most positive character: viz. that each star owes to its mode of formation a provision of heat essentially limited; that it is not permissible, as Laplace thought he could do, to endow a sun with an indefinite amount of heat; and that what it has expended and what it still possesses, depend upon its volume and actual mass. And also that the primitive materials of the solar system were, at the beginning, part of a universal chaos from which they were afterwards separated, in virtue of movements previously impressed on the whole of the matter; and sums up his first ideas in the following manner or theorem:

"At the beginning the universe consisted of a general chaos, of extreme tenuity, formed of all the elements of Chemistry more or less mixed and confounded together. These materials under the force of their mutual attractions were, from the beginning, endowed with diverse movements which brought about their separation into masses or clouds. These still retained their movements of rapid translation, and very gentle interior gyrations. These myriads of chaotic fragments have given birth, by means of progressive condensations, to the diverse worlds of the universe."

(2) So much for the formation of the universe, including, of course, the solar system, for which he acknowledges the necessity for the intervention of a creating power, because it is impossible to account for it simply by the laws of nature; and adds: It is unnecessary to say that the universe is an indefinite series of transformations, that what we see results logically from a previous condition, and thus necessary in the past as in the future; we cannot see how a previous condition could tend towards the immense diffusion of matter, to the chaos out of which the actual condition has arisen; and that it is, therefore, necessary to begin with a hypothesis, and postulate of God, as Descartes did, the disseminated matter and the forces which govern it.

(3) From dealing with the universe, M. Faye comes to the formation of an isolated star, and begins with an entirely ideal case, that of a spherical homogeneous mass, without interior movement of any kind, and concludes that the molecules would fall in straight lines towards the centre; that the mass would condense regularly without losing its homogeneity, and would end in producing an incandescent sphere perfectly immovable; and that that would be a star, but a star without satellites, without rotation, without proper movement. This not being what was wanted, he goes on to show how, previous to its separation and complete isolation from the universal chaos, such a mass would possess, and carry with it when separated, a considerable velocity of rotation, and would still retain the internal movements it had acquired from the attraction of the other masses with which it had been previously in contact; and how the molecules, drawn towards the centre in obedience to gravitation, would not fall in straight lines but in concentric ellipses.

(4) From this state of affairs, two very different results might arise. One, that the molecules might resolve themselves into a multitude of small masses without the centre acquiring a preponderating increase. The other, that the central condensation might greatly exceed the others, and there would be formed a central star accompanied by a crowd of small dark bodies. M. Faye accepts the second result, in which case the ellipses described by the small bodies, now become satellites, would, as the central mass increased in preponderance, have one of their centres at the centre of the preponderating mass, and their times of revolution would vary from one to another in conformity to the third law of Kepler.

(5) For the formation of the solar system M. Faye finds that it is of little importance whether the movements of bodies around the sun be very eccentric or almost circular; the first cause is always the same. They arise from the eddies, tourbillonnements, they have brought with them from their rectilinear movements in the primitive chaos. But the circle is such a particular case of the ellipse, that we ought not to expect to see it realized in any system. It is therefore necessary that, among the initial conditions of the chaotic mass, one should be found which would prevent the gyrations, eddies, from degenerating into elliptical movements, and which has at first made right, and afterwards firmly preserved, the form, more or less circular, in all its changes.

(6) For the formation of circular rings he gives us the following conceptions: In order that a star should have companions, great or small, circulating round the centre of gravity of the system, it is necessary that the partial chaos from whence it proceeded should have possessed, from the beginning, a gentle eddying movement affecting a part of its materials. Besides, if the partial chaos has been really round and homogeneous, we shall see that these gyrations must have taken up, and to some extent preserved, the circular form. He then requests the reader not to lose sight of the feeble density of the medium, in which a succession of mechanical changes are to be brought about; and not to conclude that that density was such that a cubic miriamètre of the space occupied by it might not contain 3250 grammes of matter, as he stated in the preceding chapter (we think he said 5217 grammes), but that it might contain only 3 grammes or even less. And adds that in such a medium, the small agglomerations of matter which would be formed all through it, would move as if they were in an absolute vacuum, and any changes in them would be produced extremely slowly.

(7) Then he goes on to say that the gyrating movements belonging to the chaotic mass, would have very little difficulty in transforming a part of a motion of that kind into a veritable rotation, if this last were compatible with the law of the internal gravitation; that it is the nature of that kind of masses to only permit, to the bodies moving in them, revolutions, elliptic or circular, concentric and of the same duration; that therefore notable portions of the gyrating matter could take the form and movements of a flat ring, turning around the centre with the same angular velocity, exactly as if this nebulous ring were a solid body; that all the particles which have the proper velocity in the plane of the gyrations, will arrange themselves under the influence of gravitation in a flat ring with a veritable rotation around the centre; that any other parts having velocities too great or too small, will move in the same plane, describing ellipses concentric to the ring; that if the ellipses are very elongated the materials composing them will approach the centre, where they will produce a progressive condensation, communicating to the central globe formed there a rotation in the same plane with the primitive gyrations; and finishes off the whole scheme by specifying the first results to be: (1) The formation of concentric rings turning in one piece, in the manner of a solid body, around a centre almost empty (d'abord vide); and (2) A rotation in the same direction, communicated to the condensation which would be produced, little by little, by means of matter coming in, partly, from regions affected by the internal eddyings (tourbillonnements).

(8) It is unnecessary to go any farther, and take note of his method of the formation of planets and satellites from rings, as it is much the same as what we have seen described by others who have written on the same subject; only interpreted by him in a way to suit his own purposes, and in which interpretation he does not do full justice to Laplace, through not having paid sufficient attention to his explanation of how planets could be formed out of rings. Except in so far as to note that all along he has considered that rings were formed, and even those nearest to the centre condensed into globes, long before the central condensation had attained any magnitude of importance, or assumed any distinctive shape, and that afterwards all the disposable matter of the rings and also all the exterior matter that had not formed part of what was separated from the original universal chaos, had fallen in towards the small central mass, and so completed the formation of the sun last of all.

We shall now proceed to make a few remarks with respect to this condensation of M. Faye's cosmogony, which we think we have made without adding to or omitting anything of importance that we have met with in his work, for which purpose we have numbered the paragraphs containing it, in the last six pages, in order to do away with the necessity of repeating the parts to which we refer.

No. 1. All those who believe that "the solar system did originate somehow, by the condensation of a primitive nebula," agree with M. Faye in considering that the density of the nebulous matter must have been extremely low, and some of them seem almost to vie with each other in showing how great must have been the degree of its tenuity; but M. Faye is one of the few who, paying due respect to the law of the interdependence of temperature and pressure in a gas or vapour, maintain that it must have been almost devoid of temperature, and we have to acknowledge that he is in the right. Then we believe that his assumption, that the whole universe of stars, including the sun, was created, humanly speaking, about the same time, is shared by the great majority of those who have thought at all seriously on the subject. Also, we agree with him firmly in his statement that each star—and we add planet, satellite, etc.—was originally supplied with an extremely limited quantity of heat, and that what it has expended and what it still retains has been derived entirely from the condensation of the original cosmic matter out of which it was made.

With regard to his theorem: we cannot follow him in his statement that the diverse movements caused by the mutual attractions of parts of the original universal mass of cosmic matter, have brought about its separation into myriads of fragments; nor how these fragments could carry with them a rapid movement of translation, unless the whole universal mass was endowed with a rapid movement of translation through space, in which case we think that such a motion would have had no greater particular effect in producing new forms of motion in the fragments, than if the whole had been created in a state of rest. Stray movements of translation might give rise to collisions among the multitude of fragments, and perhaps that was one of the modes of formation into suns through which they had to pass; but we cannot follow it out. Neither can we see clearly how translation could be effected of one mass into the space occupied by another mass—unless empty spaces were reserved for that purpose from the beginning. Without that, translation could not exist: it would be collision.

No. 2. We have nothing to object to what is said in this paragraph; except that a rotating sphere might have been postulated at once, in imitation of Laplace, instead of trying like Descartes to join fragments together, endowed with movements so adjusted that, among the whole of them, they would produce in the whole mass, when united, the kind of movement that was wanted.

No. 3. To the ideal case of the formation of an isolated sun from a homogeneous mass without interior movement of any kind, we cannot agree in any way. The molecules of matter would not, could not, fall in towards the centre in straight lines. Their mutual collisions would drive them generally in curved lines in all directions as they fell in, which would create new internal movements; and these movements would prevent the possibility of the formation of an immovable incandescent sphere such as is described. There could be no immobility in the interior of a sun, as long as its temperature was sufficient to keep the surface incandescent. But we cannot give our reasons here for this assertion—to most people they will, we think, occur at once—because we have a long road to travel before we can do so.

When M. Faye abandons the isolated case, he leaves us without giving us any help, to conceive for ourselves how the mass would possess and carry with it a considerable velocity of rotation, and still retain the internal movements it had acquired from the attraction of the other masses—of the universal chaos—with which it had been in contact; and also how the molecules drawn towards the centre would not fall in straight lines but in concentric ellipses. And this last we have to do without his giving us any reason why the molecules should fall in towards the centre at all; or rather in spite of the fact that one of his principal ideas would lead us to expect exactly the contrary, as we shall see presently.

No. 4. Here he places before us again, two cases in one of which the molecules might resolve themselves into a multitude of small masses, without the centre acquiring any preponderating increase; and the other where the central condensation might greatly exceed the others, and there would be formed a central star accompanied by a crowd of small dark bodies, now become satellites, describing ellipses around the central preponderating mass. This second case he seems, for the time being, to accept as the most probable; but it is strangely at variance with what he sets forth afterwards. He does not give us the least hint as to why or how the satellites acquired their various times of revolution, but only assumes that they did so; and we are very sure that it was not the third law of Kepler that was the agent in the case, however much it might suit his purpose.

No. 5. Although this part of his exposition is dedicated to the formation of the solar system, all that M. Faye says is that it is of little importance whether the movements of bodies around the sun be very eccentric or almost circular; and that among the initial conditions of the chaotic mass, all that we require is that one should be found which would prevent the gyrations from degenerating into elliptic movements, and which had first put right and afterwards firmly preserved the form, more or less circular, in all its changes. But he does not make any attempt to show what that one condition is, and allows us to find it out for ourselves.

No. 6. What M. Faye says about the formation of circular rings is more or less a repetition of what he has adduced, to explain all the other movements which he has derived from the universal chaos; and which he seems to think sufficient to account for such movements being nearly circular. For our part we do not think they are sufficient, and he does not show us how they influence each other to bring about the final movements he wants to present to us.

We duly take note of the tenuity of the cosmic matter on which he operates, which at 3 grammes in weight to 1 cubic miriamètre would correspond to one grain in weight to 771,947,719,300 cubic feet of space, or 1 grain to a cube of 9173 feet—more than 3000 yards—to the side. We do this in order to remind him of what he says at page 151 of his work, when dealing with the rotation of the Kant-Laplace nebula—namely, that it is impossible to comprehend how an immense chaos, of almost inconceivable tenuity, could possess such a rotation from the beginning, and that for want of that inadmissible supposition nothing remains to fall back upon but the mouvements tourbillonnaires of Descartes. Thus he wants us to believe that his tourbillons could move in straight or curved lines, have motions of translation, could attract, restrain, and drive each other into all sorts of movements with the tenuity he has indicated; but that Laplace's nebula, with a density of 1 grain to a cube of 90 feet—or at most 150 feet—to the side, could not be conceived to have the single movement of rotation. And lastly, we repeat that if the centre of the chaos was almost empty, we do not see what induced the cosmic matter to fall into it in elliptic orbits.

Nos. 7 & 8. In these paragraphs, the main features are repetitions of the simple assertions made in all the others, that certain movements possessed by matter in one state would produce other movements in another state, without attempting to show how they all came to so far coincide with each other and form one harmonious whole, with movements in almost one single direction. It is clear that one side of the separated chaos might have acquired motion in one direction from the universal chaos with which it had been in contact, and that the opposite side might have acquired motion in exactly the opposite direction from the original chaos with which it had been in contact; and we are left to find out how these came to agree with each other in the end. And, going back to the beginning, we are left to find out where the mass, out of which he constructs his solar system, was stowed away, after it was separated from the original universal chaos. We can conceive of its being separated by condensation, in obedience to the law of attraction, from the surrounding chaos, in which case it might fall towards a centre, or that some parts of it might come to revolve round each other, and that finally the whole of these parts might come to rotate about a common centre; but that is evidently very different from the mode of formation of the solar system which M. Faye has advocated. It comes to be by far too like the nebula which Laplace supposed to be endowed with rotary motion from the beginning, probably because he did not see, or did not take the trouble to see, how such a motion could be produced. In any case, Laplace did not consider that the primary motion of rotation was the most important part of his hypothesis; neither was it, as it seems to have been in the case we have been considering. And he did not go much further than M. Faye in postulating primary motion, only he did it in a more effectual and business-like manner. He drew on the bank at once for all the funds he required, instead of having to draw afresh every time he found himself in difficulties, as has been the lot of his critic and successor.

Finally, M. Faye tries to show that after all his rings, flat or otherwise, converted or not converted into globes, had been formed according to his ideas, the greater mass by far of the chaos had fallen into the centre, and had formed the sun there last of all. Now, if the preponderating mass of the chaos had been outside of the field of his operations, up to the period when all his planets, satellites, etc. were formed, or at least laid out, it is more natural to suppose that the matter inside of his structure, if there was any, would be drawn outwards by the attraction of the greatly preponderating mass outside, than that any portion of it should have fallen in, in elongated ellipses, towards the insignificant mass that he supposes to have been inside his structure. This, of course, would be nearly exactly the reverse of the mode of formation he was trying to demonstrate, and clearly shows that he was working on unsound principles from the beginning to the end of his cosmogony. It had never occurred to him that matter could be attracted outwards as well as inwards, most probably because it would seem to him ridiculous to imagine that anything in the universe could gravitate upwards.

There are other theories of the formation of the solar system from meteorites and meteors, giving us the idea of its being made out of manufactured articles instead of originally created raw material, which does not in any way simplify the process. In some of them, the inrush of meteor swarms is invoked as the cause of gyratory motion, which places them in much the same category as impact theories. We know that broadcloth is made out of woollen yarn, but we also know how the yarn is made out of wool, and how it is woven into the cloth, whereas we are not told by what process, or even out of what the meteors and meteorites are made, although some of them are said to have thumb-marks upon them.

All these theories and cosmogonies may be very appropriately classified as variations of the nebula hypothesis, and like variations in another science, may be very brilliant, scientific, imaginative, grand, but after all the flights of fancy exhibited by them are set before us, we feel in a measure relieved when a return is made to the original air. They all assume original motion, varied, accidental, opportune, more dependent upon the will of the cosmogonist than on the laws of nature, which tend to confound rather than enlighten any one who tries to understand and bring them, mentally, into actual operation. Laplace assumed rotary motion for the whole of his nebula, and was thus able to account at once for the relation which exists among the planets in respect of distance from, and period of revolution around the sun—arising from the original rotation of the whole mass in one piece—a result which, in any impact theory, has to be accounted for separately, and, in plain truth, empirically in each case, and at each step.

Seeing, then, that we have not been able to find any cosmogony, or speculation, that gives us a more plausible idea of how the solar system has been formed, we shall try whether from the original nebula as imagined by Laplace, it is possible to separate the various members, and form the system in the manner described in his celebrated hypothesis. In other words, we shall endeavour to analyse the hypothesis.

[CHAPTER IV.]

Preliminaries to Analysis of the Nebular Hypothesis.

It may be thought that there is little benefit to be derived from analysing an hypothesis which has been declared, by very eminent authorities in the matter treated of, to be erroneous in some points of very serious importance; but hypotheses are somewhat of the nature of inventions, and we know that it has often happened that many parties, aiming at the same invention, have altogether failed, while some other person using almost exactly the same means as his predecessors, has been entirely successful in his pursuit. How many times has it been pointed out to us, that if such a person had only gone one step further in the process he was following, or had only studied more deeply the matter he had in hand, he would have anticipated by many years one of the greatest discoveries of the age! In some cases the failure to take that one step was occasioned through want of knowledge acquired long years afterwards; whereas we think that in the case we have in hand, it can be shown that the want of knowledge acquired many years after he had formulated his hypothesis, or if otherwise, the want of faith in what he knew, enabled Laplace to construct an edifice which otherwise he could hardly have convinced himself could be built up in a practical form. We think also that if he had made the proper use of the knowledge he must have had of the law of attraction, he would have seen that no nebula could ever have existed such as the one he assumed, extending far beyond the orbit of the remotest planet. Furthermore, we think it can be shown that if he had thoroughly considered what must have been the interior construction of his nebula, he would have found one that would have suited his hypothesis in the main point, viz. condensation at the surface, at least equally as well as endowing it with excessive heat. But to be able to show these things our first step must be to analyse the hypothesis, to examine into it as minutely and deeply as lies in our power.

For this purpose it will be necessary to define what the hypothesis is. Many definitions have been given, more or less clear, and it would be only a waste of time to try to set forth Laplace's own exposition of it, with all its details, which he had no doubt studied very carefully. But in those definitions that have come under our observation, several of the conditions he has specified are wanting, or not made sufficiently prominent; so instead of adopting any one of them we will make a sort of condensation of the whole, adding the conditions that have been left out; because the want of them, has been the cause of mistaken conceptions of the evolution of the system having been formed by very eminent astronomers. Our definition will therefore be as follows:—

(1) It is supposed that before the solar system was formed the portion of space in which its planets and other bodies now perform their revolutions and other movements, was occupied by an immense nebula of cosmic matter in its most simple condition—of molecules or atoms—somewhat of a spherical form, extending far beyond its present utmost limits, and that it was endowed with excessive heat and a slow rotary motion round its centre; which means that while it made one revolution at the circumference it also made one at the centre. The excessive heat, by counteracting in a certain measure the force of gravitation, kept the molecules of matter apart from each other; but as the heat was gradually radiated into space, gravitation became more effective, and then began to condense and contract more rapidly, by which process its rotary motion was, in accordance with the areolar law, gradually increased at the surface, in the atmosphere of the sun, where the cooling took place, and condensation was most active; and the increase of rotation was propagated from there towards the centre.

(2) As the contraction and rotation increased a time or times arrived, when the centrifugal force produced by the rotation came to balance the force of gravitation, and a series of zones or rings were separated from the nebula, each one of them continuing to rotate—revolve now—around the central mass, with the same velocities they had at the times of their separation; until at last the nebula became so contracted that it could not abandon any more rings, and what of it remained condensed and contracted into a central mass which ultimately assumed the form of the actual sun.

(3) In the meantime, or following afterwards, each one of the rings which were abandoned by the nebula, acquired, through the friction of its molecules with each other, an equal movement of revolution throughout its entire mass, so that the real velocities of the molecules furthest removed from the centre of the nebula were greater than those of the molecules nearest to its centre, and the ring revolved as if it were in one solid piece. Arrived at this stage the rings broke up and formed themselves into smaller nebulæ, each of which condensed into a globe or planet, and continued to revolve around the central mass in the same time as its mass had done when in the form of a ring. And some of these sub-nebulæ, imitating the example of their common parent more perfectly than others, abandoned in space in their turn smaller rings which in the same manner condensed, broke up, and formed themselves into smaller globes or satellites; all, as far as we know, except the rings of Saturn, which have not as yet been converted into satellites.

[TABLE I.]

Elements and other Data of the Solar System Employed
in this Analysis.

Part I.—Sun and Planets.

Part II.—Satellites of Planets.

Name.	Mean Distance from Primary (Miles).	Equatorial Diameter (Miles).	Volume (Cubic Miles) Water=1.	Density. Water=1.	Volume at Density of Water (Cubic Miles).	Total Volume at Density of Water (Cubic Miles).
			Of the Earth.
Moon	238,833	2160	5,276,682,926	3·438	——	18,141,236,000
			Of Jupiter.
Jo	267,380	2252	5,980,050,000	1·132	6,769,416,600
Europa	425,160	2099	4,842,133,708	2·141	10,367,008,269
Ganymede	678,390	3436	21,240,229,268	1·868	39,676,748,273
Callisto	1,192,820	2929	13,157,027,273	1·472	19,367,144,146
						76,180,317,288
			Of Saturn.
Mimas	120,800	1000	523,600,000	—
Enceladus	155,000	- ? -	65,450,000	—
Tethys	191,000	500	65,450,000	—
Dione	246,000	500	65,450,000	—
Rhea	343,000	1200	904,780,417	—
Titan	796,000	3300	18,816,606,060	—	Total Volume
Hyperon	1,007,000	- ? -	3,053,634,965	—	(Cubic Miles).
Japetus	2,314,000	1800	3,053,634,965	0·736	26,548,606,407	19,539,774,315
			Of Uranus.
Ariel	123,000
Umbriel	171,000		Total mass taken at 1/15,000th of primary			1,724,977,600
Titania	281,000
Oberon	376,000
			Of Neptune.
———	220,000	Mass taken at 1/40,000th of primary				727,680,925

Part III.—Rings of Saturn.

Rings.		Diameter of Rings in Miles.		Areas of Rings in Square Miles.		Thickness of Rings in Miles.	Volume of Rings in Cubic Miles.	Density (Water=1).	Volume at Density of Water in Cubic Miles.
Outer		Outer	172,240		5,252,035,427
		Inner	151,590
Middle		Outer	148,100		6,919,075,757
		Inner	114,560
Dark		Outer	110,060		3,040,689,488
		Inner	90,993
		Total			15,211,800,672	90	1,369,062,060,480	.0001425	195,000,000

(4) All of these bodies, planets, satellites, and rings were supposed to revolve around their primaries, and to rotate on their axes, in the same direction viz., from right to left, in the opposite direction to the hands of a watch.

In addition to the above definition it is necessary to give some sort of description of the various parts of the machine or system which has to be made out of the nebula, with their positions, dimensions, and details. This we believe will be made plain enough, in the simplest manner, by [Table No. I]., taken and calculated from the elements of the solar system given in almost all astronomical works, from which we have selected what we believe to be the most modern data.

The construction of this table requires some explanation on account of its being made to show complete results from incomplete data. There has been no difficulty with the sun, the major planets, and the satellites of the earth and Jupiter, but for the minor planets, the satellites of the three outer planets, and the rings of Saturn, we have been obliged to exercise our judgment as best we could.

There being almost no data whatever of the dimensions and densities of the minor planets, to be found, we have been driven in order to assign some mass to them, to imagine the existence of one planet to represent the whole of them (in fact Olbers's planet before it exploded), which we have supposed to be placed at the mean distance of 260,300,000 miles from the centre of the sun; and we have given to it a mass equal to one-fourth of the mass of the earth, that being, in the opinion of some astronomers, the greatest mass which the whole of them put together could have. This assumption we shall explain more fully at a more suitable time.

In the case of Saturn the diameters of two of the satellites are wanting which we have assumed to be the same as those of the smallest of those nearest to them, and thus have been able to compute the volumes of the whole of them; but we have not been able to find any statement anywhere of their densities, and to get over this difficulty we have reasoned in the following manner.

The density of the moon is very little over two-thirds of that of the earth, while that of the satellites of Jupiter varies from a little more than the same to a little more than twice as much as the density of their primary. Why this difference? To account for it we appeal to the very general opinion of astronomers, that the four inner planets are in a more advanced stage of their development, or existence, than the four outer ones. In this way it is easy to conceive that the earth has arrived at the stage of being more dense than its satellite; while in the case of Jupiter, his satellites being of so very much less volume than their primary, have already arrived at a higher degree of development. Carrying this motion forward to Saturn, we have supposed that from his being considerably less dense than any other of the outer planets—quite possibly from having been formed out of material comparatively (perhaps not actually) less dense than the others—his satellites may not have condensed to a greater degree than his own mass, and we have, therefore assumed their density, that is the density of the volume of the whole of them, to be the same as that of their primary.

To determine some mass for the rings of Saturn, is a much more intricate matter than for his satellites, and presents to us some ideas—facts rather—which had never before crossed our imagination. The most natural way to look upon these rings is to suppose that they are destined to become satellites at some future time. All the modern cosmogonies that have come under our notice are founded upon the idea that rings are the seed, as it were, of planets and satellites, and if those of Saturn have been left, as it has been said, to show how the solar system has been evolved, it cannot be said that the supposition is not well founded. In this way we are led to speculate upon how many satellites are to be made out of the rings before us. Considering, then, that the nearest satellite is 120,800 miles from the centre of Saturn, leaving only 83,500 miles between his surface and that of Mimas, and also that the distances between satellites diminish rapidly as they come to be nearer to their primaries, there is not room to stow away a great number of satellites. On the other hand, seeing that there are at least three distinct rings, we cannot reasonably do less than conclude that three satellites are intended to be made out of them. But let the number be what it may, all that we have to do with them for our present purpose is to assign some mass to them. With this view, we have given, arbitrarily, to each one of the three we have supposed, a volume equal to that of one of the satellites of 500 miles in diameter, that is, about 65,000,000 cubic miles, and we have supposed their density to be the same as that of water, instead of that of the planet. Thus, in the table, we have assigned to the three a mass of 195,000,000 cubic miles at density of water, which would be more than sufficient to make four other satellites for the system of 500 miles in diameter each, and of the same density as the planet.

For the table referred to we have calculated the areas of the three rings to be 152,110,800,172 square miles, and we have assumed the thickness as 90 miles, that is about two-thirds of that estimated by Chambers in his handbook of Astronomy, but almost the same as that given by Edmund Dubois; nevertheless their total volume comes up to 1,369,062,060,480 cubic miles, which reduces their average density to 0·0001425 that of water, to make up the mass of 195,000,000 cubic miles at the density of water, which we have adopted for the three. This density corresponds to very nearly one-tenth of that of air, which, however strange it may appear to us, may be considered to be a very full allowance, seeing that we shall find, later on, that the planet itself was formed out of matter whose density could not have been more than one twenty-six millionth part of that of air. All the same, it is hardly matter that we could liken to brickbats. After being driven to this low estimate of density, which startled us, we referred to an article in "Nature" of Nov. 26, 1886, on Ten Years' Progress in Astronomy, where we find what follows:—"He (Newcomb) finds the mass of Titan to be about 1/12,000 that of Saturn. It may be noted, too, that Hall's observations of the motions of Mimas and Enceladus indicate for the rings a mass less than 1/10 that deduced by Bessel; instead of being 1/100 as large as the planet, they cannot be more than 1/1000, and are probably less than 1/10,000." (We make them 1/791514). Thinking over the numbers herein given we cannot help being surprised by them. If Titan be 1/12500 of the mass of Saturn, we cannot conceive how the mass of his rings can be so much greater than that of Titan. We cannot pretend to fit even one satellite of that size, mechanically, into a space of 83,500 miles wide, while Titan revels in an ample domain with a width of 332,000 miles. But we shall not pursue this part of our speculations any further. Astronomers may be able to demonstrate that the rings are of a totally different nature to those out of which the planets and their satellites are supposed to have been made, or that the nebular hypothesis or anything resembling it is no better than a foolish dream. All that we have pretended to do has been to give them their due place in the hypothesis we are attempting to analyze, and to look upon them in a practical and mechanical light, as an unfinished part of the solar system.

To determine masses for the satellites of the two outer planets, we have to be more empirical even than we have yet been. A little trouble will show that the whole mass of all the satellites and rings of Saturn put together is about 1/7820th of the mass of the planet, and we shall avail ourselves of this proportion to assign masses for the satellites of the remaining planets, the numbers and names of which are the only data we have been able to find. Considering then, that Uranus has only four satellites and no rings, we think if we give them 1/15,000th of the mass of their primary, it will be a very fair allowance; and with the same empiricism we have adopted for the solitary satellite of Neptune 1/40,000th of the mass of its primary.

However rude and crude these approximations may be, we have the satisfaction of thinking that the masses obtained by their means, can have no appreciable effect upon the operations into which they are to be introduced, whilst they enable us to deal with a complete system or machine. But for these we have another Table No. II. to present, a résumé of the foregoing one, for greater facility of reference.

[TABLE II.]

Volumes of the Various Members of the Solar System
at the Density of Water.

Dividing 482,169,000,000,000,000 by 691,966,535,445,840 makes the mass of the whole of the members to be 1/696·86th part of the mass of the sun, instead of 1/700th as generally stated by astronomers.

[CHAPTER V.]

Analysis of the Nebular Hypothesis.

We may now proceed to take the original nebula to pieces, by separating from it all the members of the solar system, in performing which operation we shall suppose the divisions between the nebula and each successive ring to have taken place at a little more or less than the half distances between the orbits of two neighbouring planets, because we have no other data to guide us in determining the proper places. These divisions have manifestly been brought about in obedience to some law, as is proved in great measure by what is called Bode's Law; although no one has as yet been able to explain the action of that law. It is no doubt certain that a division must have taken place much nearer to the outer than the inner planet in each case, if we think of what would be the limit to the sphere of attraction between the nebula and a ring just detached from it—for the attraction of the abandoned ring, and even of all those that were outside of it, would have very little influence in determining the line where gravitation and centrifugal force came to balance each other—but the data necessary for calculating what these would be are wanting. Even if they existed the calculations would become too complicated for our powers as the number of rings increased; and for our purpose it is really of very little importance where the divisions took place. The breadths of the rings would be practically the same, whether they were divided at the half distances between, or much nearer to, the outermost of two neighbouring planets; and although the extreme diameters of the consecutive residuary nebulæ would be somewhat greater, their densities and temperatures would not materially differ from those we shall find for them as we proceed in our operations. Their masses would be the same in all cases, which is the principal thing in which we are interested.

This premised, we shall first examine into the excessive heat attributed to the nebula, that being the first condition mentioned in our definition of the hypothesis.

The diameter of the sun being 867,000 miles, his volume is 341,238,000,000,000,000 cubic miles, and his density being 1·413 times that of water, his volume reduced to the density of water would be 482,169,000,000,000,000 cubic miles. Now, astronomers tell us that the whole of the planets, with their satellites and rings, do not form a mass of more than 1/700th part of the mass of the sun. If, then, we add 1/700th part to the above volume, we get a total volume, for the whole of the system, of 482,857,590,478,000,000 cubic miles at the density of water, which corresponds to a sphere of about 973,360 miles in diameter. On the other hand, the diameter of the orbit of Neptune being 5,588,000,000 miles, if we increase that diameter to 6,600,000,000 miles, so that the extreme boundary of the supposed nebula may be as far beyond his orbit, as half the distance between him and Uranus is within it, we shall still be far within the limit at which the process of separation from the nebula, of the matter out of which Neptune was made, must have begun. From these data we can form a very correct calculation of what the density—tenuity rather—of the nebula must have been. For, as the volumes of spheres are to each other as the cubes of their diameters, the cube 973,630 is easily found to be to the cube of 6,600,000,000, as 1 is to 311,754,100,720, or in other words, the density of the nebula turns out to have been 1/311,754,100,720th part of density of the whole solar system reduced to that of water.

Carrying the comparison a little further, we find that as water is 773·395 times more dense than air, and 11,173·184 times more dense than hydrogen, the density of the nebula could not have been more than 1/403,000,000th part that of air, and 1/27,894,734th that of hydrogen. But, confining the comparison to air, as it suits our purpose better, we see that it would take 403,000,000 cubic feet of the nebula to be equal in mass to 1 cubic foot of air at atmospheric pressure; and that were we to expand this cubic foot of air to this number of times its volume, the space occupied by it would be as nearly in the state of absolute vacuum as could be imagined, far beyond what could be produced by any human means. Now, were heat a material, imponderable substance, as it was at one time supposed to be, we could conceive of its being piled up in any place in space in any desired quantity; but it has been demonstrated not only not to be a substance at all, but that its very existence cannot be detected or made manifest, unless it is introduced by some known means—friction, hammering, combustion—into a real material substance. Therefore, we must conclude that if it existed at all in the nebula, it must have been in a degree corresponding to the tenuity of the medium, and the air thermometer will tell us what the temperature must have been if we only choose to apply it.

Applying, then, this theory of the air thermometer, if we divide[B] 274° by 403,000,000—the number of times the density of the nebula was less than that of air—we get 0·00000068°, as the absolute temperature of the nebula, something very different to excessive heat, incandescence, firemist, or any other name that has been given to its supposed state. Furthermore, as a cubic foot of air weighs 565·04 grains, 403,000,000 divided by 565·04, which is equal to 713,223, would be the number of cubic feet of the space occupied by the nebula, corresponding to each grain of matter in the whole solar system, which would be equal to a cube of very nearly 90 feet to the side. And as the only means by which the nebula could acquire heat would be by collision with each other of the particles of matter of which it was composed; to conceive that two particles weighing 1 grain each, butting each other from an average distance of 90 feet, could not only bring themselves, but all the space corresponding to both of them—which would be 1,426,446 cubic feet, of what?—up to the heat of incandescence, or excessive heat of any kind, is a thing which passes the wit of man. Consequently, neither by primitive piling up, nor by collisions among the particles, could there be any heat in the nebula at the dimensions we have specified, beyond what we have measured above.

Some people believe, at least they seem to say so, that meteors or meteorites colliding would knock gas out of each other, sufficient to fill up the empty space around them, and become incandescent, and so pile up heat in nebulæ sufficient to supply suns for any number of millions of years of expenditure. But they forget that gas is not a nothing. It possesses substance, matter, of some kind, however tenuous. Therefore, if the meteors knock matter out of each other in the form of gas, they must end by becoming gas themselves, and we come back to what we have said above; we have two grains, in weight, of gas abutting each other at an average distance of 30 yards, instead of two grains of granite or anything else, and things are not much improved thereby. And if we compare 30 yards with M. Faye's 3000, where are we?

The next thing to deal with is the formation of the planets.

Separation of Ring for Neptune.

When the nebula was 6,600,000,000 miles in diameter its volume would be 150,532,847,222¹⁸[C] cubic miles, and we have just seen that its density must have been 311,754,100,720 times less than that of water, or 403,000,000 less than air, and its temperature 0·00000068° above absolute zero. On the other hand, we find from [Table II]. that the volume of Neptune and his satellite is 29,107,964,680,925 cubic miles at the density of water. Multiplying, therefore, this volume by 311,754,100,720 we get 9,074,530¹⁸ cubic miles as the volume of the ring for the formation of Neptune's system at the same density as the nebula. Then, subtracting this volume from 150,532,847,222¹⁸, there remain 150,523,772,692¹⁸ cubic miles as the volume to which the nebula was reduced by the abandonment of the ring out of which Neptune and his satellite were formed.

Then the mean diameter of the orbit of Neptune being 5,588,000,000 miles, its circumference or length will be 17,555,261,000 miles, and if we divide the volume of his system as stated above, by this length, we get 516,912,620,000,000 square miles as the area of the cross section of the ring, which is equal to the area of a square of 22,735,123 miles to the side. Again, if we divide the circumference of the orbit by this length of side, we find that it is 1/772·165th part of it, and therefore about 28 minutes of arc. Also if we divide the diameter of the orbit by an arc of 22,735,123 miles in length, we find that it bears the proportion of 1 to 246 to the diameter of the orbit. Thus the cross section of the ring would bear the same ratio to its diameter that a ring of 1 foot square would bear to a globe of 246 feet in diameter. Here we find it difficult to believe that by rotating a ball of 246 feet in diameter of cosmic matter, meteorites, or brickbats, we could detach from it, mechanically, by centrifugal force a ring of 1 foot square, and the same difficulty presents itself to us with respect to the nebula. We cannot conceive how a ring of that form could be separated by centrifugal force from a rotating nebula, and have therefore to suppose it to have had some different form, and to apply for that to the example of Saturn's rings—just the same as Laplace no doubt did. We cannot tell how the idea originated that the ring should be of the form we were looking for—perhaps it was naturally—but it seems to have been very general, and in some cases to have led to misconceptions. It is not difficult to show how a Saturnian or flat ring could be formed, but we shall have a better opportunity hereafter of doing so. We must try, nevertheless, to form some notion, however crude it may be, of what might be the thickness of a flat ring of the cross section and volume we have found for Neptune.

Let us suppose that the final separation of the ring took place somewhere near the half-distance between his orbit and that of Uranus, say, 2,290,000,000 miles from the centre of the nebula, the breadth of the ring would be the difference between the radius of the original nebula, i.e. 33,000,000,000 miles and the above sum, which is 1,010,000,000 miles. Then if we divide the area of the cross section of the ring by this breadth, that is, 516,912,620,000,000 by 1,010,000,000, we find that the thickness would be 511,794 miles; provided the ring did not contract from its outer edge inwards during the process of separation. This could not, of course, be the case, but, as we have no means of finding how much it would contract in that direction, we cannot assign any other breadth for it; and we shall proceed in the same manner in calculating the thicknesses of the rings for all the other planets as we go along. We can, however, make one small approach to greater accuracy. We shall see presently that the density of the ring would be increased threefold at its inner edge as compared with the outer during the process of separation, which would reduce its average thickness to somewhere about 341,196 miles at density of water, of course. The nebula remaining after Neptune's ring we may now call

The Uranian Nebula.

The volume of the nebula after abandoning the ring for the system of Neptune was found to be 150,523,772,692¹⁸ cubic miles at its original density, but during the separation it has been condensed into a sphere of 4,580,000,000 miles in diameter, whose volume would be 50,303,255,814¹⁸ cubic miles; so that if we divide the larger of these two volumes by the smaller, we find that the density of the Uranian nebula would be increased 2·9923 times, and therefore it would then be 311,754,100,720 divided by 2·9923, equal to 104,184,535,721 times less dense than water. Furthermore, if we compare it to the density of air, which we can do by dividing this last quantity by 773·395, we find it to have been 134,710,620 times less than that density; and if we apply the air thermometer to it, we shall find that its absolute temperature must have been 274 divided by 134,710,620 = 0·000002034° or -273·9999796.°

We can now separate the ring for the system of Uranus from the Uranian nebula, reduced as we have seen to 4,580,000,000 miles in diameter, volume of 50,303,255,814¹⁸ cubic miles, and density of 104,184,535,721 times less than water. Referring to [Table II]., we find the volume of the whole system of Uranus to have been 25,876,388,977,690 cubic miles at the density of water, but we have to multiply this volume by the new density of 104,184,535,721 times less than water in order to bring it to the same density as the nebula, which will make the volume of his system to be 2,695,918,851¹⁵ cubic miles at that density. Then, subtracting this volume from 50,303,255,814¹⁸, we find that the nebula has been reduced to 50,300,559,895,149¹⁵ cubic miles in volume.

Then the diameter of the orbit of Uranus being 3,566,766,000 miles, its circumference will be 11,205,352,065 miles, so that dividing the volume 2,695,918,851¹⁵ of his system by this length of circumference, the area of the cross section of the ring would be 240,592,061,166,666 square miles. If we now suppose the diameter of the nebula, after abandoning the ring for the whole system of Uranus, to have been 2,672,000,000 miles—dimension derived from nearly the half-distance between the orbits of Uranus and Saturn—we find that the breadth of the ring would be 954,000,000 miles, which would be the difference between the radii of the Uranian and Saturnian nebulæ, respectively 2,290,000,000 miles, and 1,336,000,000 miles; so that if we divide the area of cross section of Uranus' ring or 240,592,070,232,288 square miles by this breadth we find the thickness of the ring to have been 252,193 miles. But the density of the inner edge of the ring would be 5·036 times more dense than the outer edge, for the same reason as in the case of the Neptunian ring, which would make the average thickness to have been about 100,553 miles.

Saturnian Nebula.

We have seen that the volume of the nebula after the separation of the ring for Uranus' system would be 50,300,559,859,149¹⁵ cubic miles, but as we have reduced the diameter of the Saturnian nebula to 2,672,000,000 miles, its volume would also be reduced, or condensed to 9,988,700²¹ cubic miles, so that dividing the larger volume by the smaller we find that its density must have been increased 5·036 fold. Then dividing 104,184,535,721 by 5·036, we see that the density would be reduced, or increased rather, to 20,689,000,000 times less than that of water. This can be easily found to be 26,750,876 times less than the density of air, and the air-thermometer would show that the absolute temperature of the Saturnian nebula must have been 0·000010242° or -273·99998976°.

We have just seen that the Saturnian nebula has been condensed to 2,672,000,000 miles in diameter, to volume of 9,988,700²¹ cubic miles, and density of 20,689,000,000 times less than that of water. Then from [Table II]. we get the volume of the whole of the system of Saturn as 154,370,734,774,315 cubic miles at the density of water, and multiplying this by 20,689,000,000 will give 3,193,775,478¹⁵ as its volume at the same density as the nebula; and subtracting this from 9,988,700²¹ we find that the volume of the nebula had been reduced to 9,985,506,224,522¹⁵ cubic miles.

Then the diameter of the orbit of Saturn being 1,773,558,000 miles its circumference would be 5,571,809,813 miles in length, and if we divide the volume of his system, viz. 3,193,775,478¹⁵ cubic miles, by this length, we find the area of the cross section of the ring to have been 573,202,529,391,503 square miles. Now, supposing the diameter of the nebula, after abandoning the ring, to have contracted to 1,370,800,000 miles and radius consequently of 685,400,000 miles, the breadth of the ring would be 1,336,000,000 less 685,400,000 or 650,600,000 miles; and if we divide the area of the cross section of the ring, that is, 573,202,529,391,503 square miles, by this breadth, we get 881,037 miles for its thickness. But in the same way as before, the inner edge of the ring would be 7·4037 times more dense than the outer edge, which would reduce its average thickness to 238,000 miles.

Jovian Nebula.

The volume of the nebula after separation of the ring for Saturn's system having been 9,985,506,224,522¹⁵ cubic miles, this volume has to be condensed into the volume of the Jovian nebula of 1,370,800,000 miles in diameter, which would be 1,348,720,186,335¹⁵ cubic miles. Then if we divide the first of these two volumes by the second, we find the density of the Jovian nebula to have been increased 7·4037 fold over the previous one. But the density of the Saturnian nebula was 20,689,000,000 times less than water, dividing which by 7·4037 makes the Jovian nebula to have been 2,794,417,420 times less dense than water. Dividing this by 773·395 we get a density for it of 3,613,182 times less than that of air, which corresponds to the absolute temperature of 0·00007583° or -273·99992417°.

From the Jovian nebula of 1,370,800,000 miles in diameter, volume of 1,348,720,186,335¹⁵ cubic miles, and density of 2,794,417,420 times less than water, we have now to deduct the whole of the system of Jupiter, which, by [Table No. II]., is 479,368,921,317,000 cubic miles at density of water. Multiplying this by 2,794,417,420 we get the volume of 1,339,557,155¹⁵ cubic miles for his system at the same density as the nebula; therefore, substracting this amount from 1,348,720,186,335¹⁵ we get 1,347,380,629,180¹⁵ cubic miles as the volume to be condensed into the succeeding nebula which we shall call Asteroidal, the dimensions of which we can determine in the following manner, although only very approximately.

According to the nebula hypothesis, there must have been a ring detached from the nebula for the formation of the Asteroids, as well as the formation of the other planets. So, in order to be able to assign elements for that ring, corresponding to those we have found for the others, we shall suppose the whole of them to have been collected into one representative planet, at the mean distance from the centre of the nebula of 260,300,000 miles, more or less in the position denoted by the number 28 in Bode's Law; also its mass to have been one-fourth of that of the earth, or 367,792,000,000 cubic miles at density of water, which, in the opinion of probably most astronomers, is a considerably greater mass than would be made up by the whole of them put together—discovered and not yet discovered. With the above distance from the centre of the nebula, the divisionary line between the Jovian and the Asteroidal nebulæ would be 372,000,000 miles from the said centre, and the diameter of the latter 744,000,000 miles in consequence.

We know that some of the Asteroids move in their orbits beyond this supposed divisionary line, and it may be that when we come to determine the divisionary line between the supposed Asteroidal and the Martian nebulæ, some of them may revolve in their orbits nearer to Mars than that line, but that will not interfere in any way with our operations, because we are only dealing with the whole of them collected into one representative.

For finding the dimensions of the ring for Jupiter's system, we have the mean diameter of his orbit as 967,356,000 miles, which makes its circumference to be 3,039,045,610 miles in length. Therefore, dividing the volume of the ring as found above, viz. 1,339,557,155¹⁵ cubic miles by this length, the area of its cross-section comes to be 440,782,188,524,000 square miles, which divided in turn by the breadth of 313,400,000—the difference between the radii of the Jovian and Asteroidal nebulæ, or 685,400,000 less 372,000,000—makes the thickness of the ring to have been 1,406,771 miles. But, as before, the inner edge of the ring had become 6·2484 times more dense than the outer edge, so that the average thickness would be only 450,282 miles.

Asteroidal Nebula.

The volume of the nebula after the separation of the ring for the system of Jupiter having been 1,347,380,629,180¹⁵ cubic miles, this volume has to be condensed into the volume of the Asteroidal nebula of 744,000,000 miles in diameter and consequently of volume of 215,634,925,373,133,820⁹ cubic miles. Then if we divide the first of these volumes by the second, we find the density to have been increased 6·2484 fold, as used above for the average thickness of Jupiter's ring. But the density of the Jovian nebula was 2,794,417,420 times less than water, dividing which by 6·2484 makes the Asteroidal nebula to have been 447,218,905 times less dense than water. This again divided by 773·395 makes it 578,254 times less dense than air, which will give us 0·00047384° as its absolute temperature—or the same as -273·99952616°.

Next, from the Asteroidal nebula 774,000,000 miles in diameter, volume of 215,634,925,373,133,820⁹ cubic miles, and density 447,218,905 times less than water, we have to deduct the volume of the whole of the system which in [Table No. II]. we have supposed to have been 367,792,000,000 cubic miles at density of water. Multiplying this by 447,218,905 we get the volume to have been 164,482,717,200⁹ cubic miles for the ring at the same density as the nebula; so, deducting this quantity from 215,634,925,133,820⁹, we get 215,634,760,890,416,620⁹ cubic miles as the volume to which the nebula had been reduced by the separation of the ring.

For the dimensions of the ring we have the mean diameter of the orbit of the representative Asteroid as 520,600,000 miles, that is twice its distance from the centre of the nebula, which makes its circumference to be 1,635,516,960 miles in length. Dividing then the volume of the ring, which we found to have been 164,482,717,200⁹ cubic miles by this length, the area of its cross-section must have been 100,569,251,938 square miles, which divided by the breadth of 171,000,000 miles—the difference between the radii of the Asteroidal and Martian nebula, namely 372,000,000 less 201,000,000—makes the thickness of the ring to have been 588 miles. But the inner having been 6·339 times more than the outer edge, as we shall see presently, the average thickness would be 185 miles.

Martian Nebula.

The volume of the last nebula after the separation of the ring for the Asteroids was found to have been 215,634,760,890,416,620⁹ cubic miles, which had to be condensed into the volume of the Martian nebula of 402,000,000 miles in diameter, which would give a volume of 34,015,582,677,165,354⁹ cubic miles. Dividing then, the larger of these volumes by the smaller, we find that the density of the Martian nebula had been increased 6·339 times by the condensation. But we found the density of the Asteroidal nebula to have been 447,218,905 times less dense than water, dividing which by 6·339 makes the Martian nebula to have been 70,547,110 times less dense than water. This divided again by 773·395 makes it 91,259 times less dense than air, and consequently its absolute temperature to have been 0·00300243° or -273·99699757°.

From the Martian nebula of 402,000,000 miles in diameter, volume 34,015,582,677,165,354⁹ cubic miles, and density 70,547,110 times less than water, we have to deduct the volume of his ring, which by [Table II]., was estimated at 160,728,460,000 cubic miles at density of water. Multiplying this by 70,547,110 we find its volume to be 11,338,927,154⁹ cubic miles at the same density as the nebula, deducting which from its whole volume we get 34,015,571,338,237,20⁹ cubic miles as the volume after the separation of the ring.

For finding the dimensions of the ring we have 283,300,000 miles as the mean diameter of the orbit of Mars, which makes its circumference 890,015,280 miles in length. Then dividing the volume of the ring 11,338,927,154⁹ cubic miles by this length, the area of its cross-section comes to be 12,740,148,859 square miles, which, divided by the breadth of 83,690,000 miles—that is one-half of the difference between the diameters of the Martian and Earth nebula, respectively 402,000,000 and 234,620,000 miles—makes the thickness of the ring to have been 152 miles. But as before, the inner having become through condensation, 5·0302 times more dense than the outer edge, the average thickness would be 61 miles.

Earth Nebula.

As the volume of the nebula was 34,015,571,338,237,200⁹ cubic miles after the separation of the ring for Mars, we have to condense it into the volume of the earth nebula, which at 234,620,000 miles in diameter would be 6,762,303,076,923,031⁹ cubic miles. Dividing the larger of these volumes by the smaller we find that the density of the nebula has been increased 5·0302 times, as employed above. But we found the density of the Martian nebula to have been 70,547,110 times less than that of water, dividing which by 5·0302 makes the earth nebula to have been 14,024,781 times less dense than water. Dividing this again by 773·395 we find it to have been 18,134 times less dense than air, and 274° divided by this density of air—the same as in all the respective cases—gives 0·0151097° as the absolute temperature of the nebula and corresponds to -273·9848903°.

From the earth nebula 234,620,000 miles in diameter, 6,762,303,076,923,031⁹ cubic miles in volume, and 14,024,781 times less dense than water, we have to subtract the volume of the ring of the earth's system, which, in [Table II]., appears as 1,489,310,236,000 cubic miles at density of water. Multiplying this by 14,024,781 we find it to have been 20,887,249,553⁹ cubic miles at the same density as the nebula. And subtracting this quantity from 6,762,303,076,923,031⁹, we get 6,762,282,189,673,478⁹ cubic miles for the volume of the previous nebula after the separation of the ring for the system of the earth.

For finding the dimensions of the ring we have 185,930,000 miles for the mean diameter of the Earth's orbit, which makes the circumference 584,117,688 miles in length, and dividing the volume of the ring for the system, which was found to be 20,887,249,553⁹ cubic miles, by this length, the area of its cross section comes to be 35,760,344,109 square miles, which divided by the breadth of 37,205,000 miles—that is one-half of the difference between the diameters of the Earth and Venus nebulæ, respectively 234,620,000 and 160,210,000 miles—makes the thickness of the ring to have been 961 miles. But the inner will presently be seen to have been 3·141 times more dense than the outer edge when its separation was completed, so that the average thickness would be 612 miles.

Venus Nebula.

As the volume of the nebula was 6,762,282,189,673,478⁹ cubic miles after the separation of the ring for the system of the Earth, we have to condense it into the volume of the Venus nebula, which at 160,210,000 miles in diameter would be 2,153,120,792,079,208⁹ cubic miles. Then dividing the larger of these two volumes by the smaller, we find that the density of the Venus nebula had been increased to 3·141 times what that of the Earth nebula was. But we found the density of that nebula to have been 14,024,781 times less than that of water, dividing which by 3·141 makes the Venus nebula to have been 4,465,512 times less dense than water. Dividing this again by 773·395 we find it to have been 5,774 times less dense than air, which would make its absolute temperature to have been 0·04745486°, which corresponds to -273·9525459°.

From the Venus nebula of 160,210,000 miles in diameter, volume 2,153,120,792,079,207,921⁶ cubic miles, and density 4,465,512 times less than that of water, we have now to deduct the volume of her ring, which by [Table II]. is 1,131,960,000,000 cubic miles at the density of water. Multiplying this volume by 4,465,512 we find the volume of the ring to have been 5,054,780,604,651⁶ cubic miles at the same density as the nebula, and subtracting this amount from 2,153,120,792,079,207,921⁶ we get 2,153,115,737,298,603⁶ cubic miles for the volume to be condensed into the nebula following.

To find the dimensions of the ring we have 134,490,000 miles for the diameter of the orbit of Venus, which makes its circumference 422,513,784 miles in length. Then dividing the volume of the ring, i.e. 5,054,780,604,651⁶ cubic miles by this length, the area of its cross-section comes to be 11,963,821,788 square miles, which, divided by the breadth of 28,489,000 miles—that is one-half of the difference between the diameters of the Venus and Mercurian nebulæ, respectively 160,210,000 and 103,232,000 miles—makes the thickness of the ring to have been 420 miles. But the inner edge having become, in the process of separation, 3·738 times more dense than the outer one (see below) the average thickness would be reduced to 225 miles.

Mercurian Nebula.

As the volume of the nebula was 2,153,115,737,298,603,270⁶ cubic miles after the separation of the ring for Venus, we have to condense it into the volume of the Mercurian nebula, which at 103,232,000 miles in diameter would be 576,026,613,333,333,333⁶ cubic miles. Then, dividing the larger of these two volumes by the smaller, we find that the density of the Mercurian nebula must have been increased 3·738 fold over that of its predecessor. But we find the density of the Venus nebula to have been 4,465,512 times less than water, dividing which by 3·738 makes the Mercurian nebula to have been 1,194,666 times less dense than water. Dividing again this density by 773·395 we find it to have been 1545 times less than air, and 274° divided by this air density gives 0·1773463° as its absolute temperature, which corresponds to -273·8226537°.

From the Mercurian nebula 103,232,000 miles in diameter, volume of 576,026,613,333,333,333⁶ cubic miles, and density of 1,194,666 times less than water, we have to deduct the volume of his ring, which by [Table II]. is 92,735,000,000 cubic miles at density of water. Multiplying this volume by 1,194,666 makes the ring to have been 110,787,355,300⁶ cubic miles in volume at the density of the nebula, and subtracting this amount from 576,026,613,333,333,333⁶, we get 576,026,502,545,978,033⁶ cubic miles for the volume to be condensed into the nebula following.

To find the dimensions of the ring we have 71,974,000 miles for the mean diameter of the orbit of Mercury, which makes its circumference 226,113,518 miles in length. Then dividing the volume of his ring, i.e. 110,787,355,300⁶ cubic miles, as above, by this length, the area of its cross-section comes to be 489,963,459 square miles. Here we have to determine the breadth of the ring in a new way, that is empirically. Seeing that the breadth of the ring for the earth's system was 37,205,000 and of that for Venus 28,489,000 miles, we shall assume 20,000,000 miles for the breadth of the ring for Mercury. This will make the residuary, now the Solar nebula, to have been 31,616,000 miles in radius and 63,232,000 miles in diameter. Returning now to the area of the cross-section of the ring, that is, 489,963,459 square miles, and dividing it by the assumed breadth 20,000,000 miles, makes the thickness of the ring to have been 25 miles. But, as before, its inner edge having become 4·354 times more dense than the outer one during the process of separation (see below) the average thickness must have been only 11 miles.

Solar Nebula.

Lastly, as the volume of the nebula was

576,026,502,545,978,033⁶

cubic miles after the separation of the ring for Mercury, we have to condense it into the volume of the Solar nebula, which at 63,232,000 miles in diameter would be