Fig. 1.
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 atpage 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 amile 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 pages23 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 eachis 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 atFig. 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 tospeculate 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.
A gooddeal 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 beyondtraces 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.: "Inorder 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 apons asinorumto 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 relativelyto 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 fixedstar." 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 thesein opposite directions, when he changes his motion from direct to retrograde, orvice 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 makingdivina Palladis artea 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 itarmato militewe 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 theotherhorse, 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 ofourhorse all round, just a little higher than between wind and water.Pallasdid not order any holes to be made inhersas 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 aboutonemile 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 articlewritten 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, andpaperswe 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 concludesthat 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 milesbeyondthe 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 situatedbeneaththe 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 thismonstrous 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 monstrousdepressionon 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 fromsome 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 bycentrifugal 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 actingat 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 rathervice 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 brighterring-shinejust 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 equatorialand 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.
Wehave 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, andthe 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 bythem 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 calledspeculations, on the formation of a lens-shaped nebula brought about by the acceleration of rotation—caused by condensation according to the areolartheory—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 evolvedfrom cosmic matter partially endowed with motion in the form of eddies, whirlwinds, vortices, ortourbillons, 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 haveresulted 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 smallfragments, 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 andvice 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 ofunstable 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 schemedfor 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 atpage 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 formationof 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 theirmodus 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 believedanything 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: