We have seen that the volume of the nebula after the separation of the ring for Uranus' system would be 50,300,559,859,14915cubic 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 9,988,70021cubic 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 9,988,70021cubic miles, and density of 20,689,000,000 times less than that of water. Then fromTable 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 by20,689,000,000 will give 3,193,775,47815as its volume at the same density as the nebula; and subtracting this from 9,988,70021we find that the volume of the nebula had been reduced to 9,985,506,224,52215cubic 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. 3,193,775,47815cubic 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.
The volume of the nebula after separation of the ring for Saturn's system having been 9,985,506,224,52215cubic 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 1,348,720,186,33515cubic 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 1,348,720,186,33515cubic 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, byTable 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 1,339,557,15515cubic miles for his system at the same density as the nebula; therefore, substracting this amount from 1,348,720,186,33515we get 1,347,380,629,18015cubic 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. 1,339,557,15515cubic 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.
The volume of the nebula after the separation of the ring for the system of Jupiter having been 1,347,380,629,18015cubic 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 215,634,925,373,133,8209cubic 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 215,634,925,373,133,8209cubic miles, and density 447,218,905 times less than water, we have to deduct the volume of the whole of the system which inTable 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 164,482,717,2009cubic miles for the ring at the same density as the nebula; so, deducting this quantity from 215,634,925,133,8209, we get 215,634,760,890,416,6209cubic 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 164,482,717,2009cubic 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.
The volume of the last nebula after the separation of the ring for the Asteroids was found to have been 215,634,760,890,416,6209cubic 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 34,015,582,677,165,3549cubic 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 34,015,582,677,165,3549cubic miles, and density 70,547,110 times less than water, we have to deduct the volume of his ring, which byTable 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 11,338,927,1549cubic miles at the same density as the nebula, deductingwhich from its whole volume we get 34,015,571,338,237,209cubic 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 11,338,927,1549cubic 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.
As the volume of the nebula was 34,015,571,338,237,2009cubic 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 6,762,303,076,923,0319cubic 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, 6,762,303,076,923,0319cubic 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, inTable II., appears as 1,489,310,236,000 cubic miles at density of water. Multiplyingthis by 14,024,781 we find it to have been 20,887,249,5539cubic miles at the same density as the nebula. And subtracting this quantity from 6,762,303,076,923,0319, we get 6,762,282,189,673,4789cubic 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 20,887,249,5539cubic 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.
As the volume of the nebula was 6,762,282,189,673,4789cubic 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 2,153,120,792,079,2089cubic 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 2,153,120,792,079,207,9216cubic miles, and density 4,465,512 times less than that of water, we have now todeduct the volume of her ring, which byTable 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 5,054,780,604,6516cubic miles at the same density as the nebula, and subtracting this amount from 2,153,120,792,079,207,9216we get 2,153,115,737,298,6036cubic 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. 5,054,780,604,6516cubic 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.
As the volume of the nebula was 2,153,115,737,298,603,2706cubic 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 576,026,613,333,333,3336cubic 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 576,026,613,333,333,3336cubic miles, and density of 1,194,666 times less than water, we have to deduct the volume of his ring, which byTable 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 110,787,355,3006cubic miles in volume at the density of the nebula, and subtracting this amount from 576,026,613,333,333,3336, we get 576,026,502,545,978,0336cubic 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. 110,787,355,3006cubic 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.
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
132,376,310,975,609,7566
cubic miles. Then dividing the first of these two volumes by the second, we find that its density must have been increased 4·3514 fold. But we found that the density of the Mercurian nebula was 1,194,666 times less than that of water, dividing which by 4·3514 makes the Solar nebula to have been 274,546 times less dense than water. Dividing this in turn by 773·395 shows it to have been 355 times less dense than air, and, still further, dividing 274° by this air density makes its absolute temperature to have been 0·7718585° equal to -273·2281415°.
We might conclude our analysis here, but it will be more convenient to carry our calculations a few steps further, to save the additional trouble that might be occasioned by having to return to them later on.
First we shall condense the Solar nebula to 211,911 times less dense than water, and therefore 274 times less dense than air, which we may note will increase its density 1·2956 times. This supposed to be done, its diameter would be 58,002,920 miles, its volume 102,176,129,41212cubic miles, and its density 1/274th of an atmosphere—aboutone-ninthinch of mercury—which would, in consequence, make its absolute mean heat equal toone degreeof the ordinary Centigrade scale, or, in another way of expressing it, equal to -273°.
Second. Let us condense this same nebula to 773·395 times less dense than water, and consequently to the density of air at atmospheric pressure, then its diameter will be 8,930,309 miles, volume 372,905,560,3459cubic miles, and the mean heat 0°, or the heat of freezing water—which by some unexplained process of thought has hitherto been considered to be 274° of absolutetemperature.
Third. By again condensing the Solar nebula to the density of water, corresponding to a pressure of more than 773 atmospheres, its diameter becomes 972,285 miles, its volume 482,16712cubic miles, and mean heat 775°, including the 2° acquired in condensing it to the pressure of 1 atmosphere, as is plainly shown inTable III.
Before going any further we must enter into a digression to examine into the process of thought by which the absolutezero of heat has come to be called the absolute zero of temperature, and absolute temperature to be so many degrees of negative—less than 0° or nothing—heat counted from the lower or wrong end, to be called positive absolute temperature; thus making heat and temperature appear to be two very different things, without giving any explanation of what is the difference between them.
Science has, as it were, gone down a stair of 274 steps carrying along with it the laws of gases, and has found, most legitimately, with their assistance the total absence of even negative heat at the bottom of it; and, leaving these laws there, has jumped up to the top of the stair, thinking that it carried along with it 274° of absolute heat, which it now calls temperature; instead of bringing the said laws up with it and verifying, if not at every step at least at intervals, how much it brought up with it of what it had taken down. Had it done so it would have found that at the top of the stair it had got what was equal to only 2° of positive heat as measured by the Centigrade scale, as has been shown above, which might be called temperature, but that would not mend matters. Science seems to have forgotten, for the time being at least, all about the laws of gases; it had got something which it thought would enable it to mount much higher, and was satisfied. It will not be difficult to do away with the confusion of thought that is thus shown to have occurred.
The laws of gases are founded upon the fact that in gases there is a necessary interdependence between heat and pressure, and the starting points adopted by science for calculating this interdependence in them are 0° of heat and 1 atmosphere of pressure at 0° of heat. Obeying these laws, we have argued, from the beginning of our operations, that heat requires something to hold it in, and that the nebula from which the Solar system was formed—if it was so formed—could only contain heat in proportion to its density; that is being a gas, or vapour in the form of a gas, it could not contain, i.e. hold in it, more than 2° of positive heat when its density was equal to the pressure belonging to 1 atmosphere of a gas; all as shown in the most irrefragable manner in this chapter and in the accompanyingTable III.
A gas can be easily compressed in a close vessel to a pressure of 100 atmospheres, which would enable it to hold 100° of heat due to that compression; in fact, were it compressed to that degree by a piston in a cylinder, without any loss of heat, it would be raised to that heat by that act alone, but that would raise it to only 102° instead of 374° of what is called absolute temperature according to present usage; because as a gas it could not hold any more heat at that pressure. It is, therefore, evident that thisusagehas not been derived from the laws of gases. Neither has it been derived from the other two states of liquid and solid to which all gases can be reduced, as can be very easily demonstrated.
To cool steam at atmospheric pressure from its gaseous to its liquid state 519° of heat of one kind and another—as measured by the Centigrade thermometer—have to be abstracted from it, which leaves the liquid at its boiling point of 100°—a quantity that has been arbitrarily adopted to mark the difference between the freezing and boiling points of this liquid. In order, after this, to reduce the liquid, now water, to the freezing, or what is called 0° of heat, these 100 degrees of heat have to be extracted from it, which is not very difficult to do because the heat put into it arbitrarily can be extracted from it; but if it is now wanted to change the steam from its liquid to its solid state, the work, or operation assumes a very different character, because heat cannot be extracted from a substance which contains none at all. It is well known that 80° of heat are required to change one pound of ice at 0° into a pound of water also at 0° of heat; but it is equally well known that 80° of heat cannot be taken out of the pound of water which has none in it; how then, is the water to be changed into ice?
Even in cooling water to 0° it has to be put into a bath of some kind, either of cold water or some cold mixture of other substances at least as cold; because, otherwise, extraneous heat from any source might find its way into it, and prevent it from cooling down to zero of heat. In the same manner, to change the water into its solid state of ice it has to be put into a similar bath, not to extract heat from it, because it has not any to extract, but to prevent extraneous heat fromgetting into it. This being the case, it is evident that if water is put into a bath at what is called -1° of heat, or even a fraction of that amount, it will be converted into ice though very gradually, by keeping extraneous heat from getting to it to sustain the collisions, or vibrations, of its constituent atoms necessary to maintain it in its liquid state. All for the very same reason why a stone, a piece of metal, or of anything assumes the same degree of heat, or absence of heat, as the medium by which it is surrounded; be it derived from sun-heat, earth-heat, or heat produced chemically or mechanically, and is not cooled down to a lower degree than the surrounding bath, be it what it may.
The heat required to change a solid into a liquid is calledlatent heat, which in the case of ice and water may be a fraction of -1° or -80°, orminusalmost anything according to the time it is necessary for it to act; so that no quantity of what is called absolute temperature can be ascribed to ice without the element time being involved in it. The absolute temperature of water and ice, just changing from freezing to frozen, might be counted as the same, seeing that a fraction of a degree of heat may make all the difference between them; but no fixed absolute temperature can be applied to ice, as it, in conjunction with all solid bodies, may have any degree of absolute temperature between its melting point and the absolute zero of heat, as far as is at present known. The same, of course, must be the case with any gas or vapour, or nebulous matter changed into its liquid and then solid state; and this fact enables us to go a little further.
We have seen that what, according to present usage, is called the absolute temperature of solid hydrogen may be anything between -257° and -274° of heat, that is, between the absolute temperature of 0° and 17°, which, of course, is no measure at all; and, therefore, absolute temperature can only be looked upon as a conventional term, which, when added to positive Centigrade, or other, heat, conveys no clear idea to the mind, as it must always be mixed up with the concomitant idea of latent heat and its time of action. This leads us to think of what remains in the vessel, in which pure hydrogenhas been changed into its liquid and then solid state, after these operations have been performed; and our first conclusion comes to be that there can be nothing in it but a small piece of solid hydrogen; but from the limited accounts we have seen of these operations, there does appear to be something remaining, because it seems that by it the degree of negative heat in the vessel can be measured. What that remaining something may be can hardly be anything but a matter of conjecture. The first and most probable idea that occurs is that it may be some lighter gas mixed with the pure (?) hydrogen that was put into the vessel; the next is that it may be the vapour of solid hydrogen; and the last refuge for speculation is that it may be radiant matter, whatever that may turn out to be. At one time it was supposed to be impurities mixed with the gases operated upon, which in the case of common air, were found to be removed to a certain extent by means of absorbents; but the numerous components of common air discovered since that time, have gone far to throw light upon that supposition, and we are thus led to think of what a true gas really is. But we are not yet prepared to follow up this thought.
This is not an inappropriate place to say that when we adopted the Centigrade scale for our work, we thought that a special thermometer, decimal throughout and consequently more handy, might be arranged for science alone, leaving every man the free use of whatever scale he liked best; but our experience acquired in this chapter put an end to that thought, and has left us totally unable to see how any decimal scale can be contrived, which will start from absolute zero of heat and will admit of any combination with any existing scale, or will assist humanity in any of its operations in connection with heat and temperature, whichever science may choose to call it. We therefore see that no known thermometer scale is superior to another, and end where we began by saying that the Centigrade is the fashionable one at the present time. It is decimal as far as boiling water and resulting steam are concerned, but all the world is not boiling water; even steam has to be complicated with latent heat.
TABLE III.—Abstract of Measurements, etc., resulting fromthe Calculations made in Chapter V.
TABLE III.—Continued.
Returning now topage 84, we see that the volume of the sun alone was considered to be 482,16912cubic miles, which corresponds to a diameter of 972,869 miles. Comparing this with the volume 482,16712cubic miles, (see page 99), left after all the members of the Solar system have been separated from the original nebula, we find that there is a remainder of 2,000,000,000,000 cubic mileslessthan we ought to have. But it will be remembered that we added only 1/700th part to the mass of the sun for the mass of the whole Solar system, whereas it will be seen, by referring toTable II., that we ought to have added 1/696·86th part. Had we done so the sphere containing the whole Solar system at the density of water would have been 973,361·31 miles in diameter with volume of 482,860,7449cubic miles, which would have added 3,153,681,000,000 cubic miles to the volume we started with, and would have left us with 1,375,903,430,000 cubic milesmorethan we ought to have had. Besides, for the sake of round numbers, we made the diameter of the nebula containing the whole Solar system, at the density of water, to be 973,360 instead of 973,359·208 miles, and thereby really added more to the original volume than we should have; so that the defects in accuracy at the beginning of our work partially counterbalanced each other, which accounts so far for the difference noted at the end not being much more than half of what it should have been. Taking all this into consideration, and the really insignificant magnitudes of the differences that would result from the corrections that could be made, we have not thought it necessary to reform the whole of our calculations. Besides, the data we have been working upon are not so absolutely exact as to insure us that we should get nearer to the truth by making the revision. The whole error would be much more than obliterated were we to apply 5·67 instead of 5·66 for the mean density of the earth to the debit side of the sun's account.
To simply describe arithmetical operations conveys no really satisfactory meaning to the mind; of working them out in full there is no end; and to partially represent them as we have done in these pages, although showing how the resultsare arrived at, still leaves them so mixed up together that it is difficult to compare them with each other, and to note the sequences from the beginning to the end of the whole operation. For these reasons we have compiledTable III., where the whole of the principal and most important data, and results from them, may be followed out and examined.
We may now say that we have taken our nebula to pieces, with the exception of the parts belonging to the satellites of those planets which have them; which would only be a tiresome repetition of what we have done for each principal member of the system, provided we had the necessary data, which we have not; and have thus acquired a certain amount of knowledge of the primitive conditions of each one of them. But we have still to examine into and draw conclusions from what we have seen and learned during the operation; which in some points, differ very much from our notions, formed from what we had previously read on the subject.
WhenLaplace elaborated his hypothesis, heat was considered to be an imponderable material substance, and continued to be thought of as such—though perhaps not altogether believed to be so—for somewhere about half a century afterwards; so that it cannot be wondered at that he thought the nebula could have been endowed with excessive heat, more especially as it was looked upon as imponderable, and could in no way have any effect on the mass of the nebula. He only accepted the idea that was common to almost all astronomers of his time, that nebulæ were masses of cosmic matter of extremetenuity but self-luminous, and consequently possessed of intense heat; they saw the sun gave light and felt its heat, and very naturally thought the nebula must be hot also. Without this idea he could not have formed the hypothesis at all, because he could not have conceived that the condensation of the nebula could only take place at its surface, or, as he terms it, "in the atmosphere of the sun," as most assuredly would be the case with an excessively hot body. And in order that there may be no doubt about this being his idea, we quote his own words as guaranteed by M. Faye in "L'Origine du Monde": "La considération des mouvements planétaires nous conduit donc à penser qu'en vertu d'une chaleur excessive l'atmosphère du soleil s'est primitivement étendu au delà des orbes de toutes les planètes, et qu'elle s'est reserrée successivement jusqu'à ses limites actuelles." And again: "Mais comment l'atmosphère solaire a-t-elle déterminé les mouvements de rotation et de révolution des planètes et des satellites? Si ces corps avaient pénétré profondément dans cette atmosphère, sa résistance les aurait fait tomber sur le soleil. On peut donc conjecturer que les planètes ont été formées à ses limites successives par la condensation des zones de vapeurs qu'elle à dû, en se refroidissant, abandonner dans le plan de son équateur." Proceeding on these ideas Laplace was quite in order and logical in conceiving that successive rings could be abandoned by the hot nebula, through the centrifugal force of rotation, for the formation of planets, more or less just in the way we have separated them. Having obtained his end quite legitimately, as he thought, in this way, he had no occasion to look any deeper into the affair, and consequently was not under the necessity of taking any thought of what the interior construction of the nebula might be, any more than so many others have not done since his day.
That he should have conceived the nebula to have been endowed with intense heat was, as we have already said, a natural consequence of the mistaken notions of the nature of heat at that period; but that so many astronomers should, up to the present day, think that the nebula must have beenintensely hot, even to the degree required to dissociate the meteorites of which they conceive it to have consisted, seems to us to be almost inconceivable. We believe we have shown abundantly plainly, that there could have been almost no heat in the primitive nebula, because there was hardly any cosmic matter to hold it in. We have given as proof of this the laws of gases recognised and accepted by every scientist, according to which a gas cannot contain a stated amount of heat except it be at a pressure corresponding to that temperature, that is, unless it is subjected to conditions foreign to its natural state. Therefore we must either persist in maintaining that there was almost no heat in the original nebula, or we must throw the laws of gases to the winds, for they all depend one upon another. There may be nebulæ possessed of very high temperature, that of incandescence for example, but certainly the nebula out of which the solar system was made, could not have contained more heat than what we have shown it had at the various stages through which we have carried it. If there be nebulæ at the temperature of incandescence, they must be possessed of densities, or pressures, corresponding to that temperature. A few pages back we have spoken of the impossibility of two grains of matter 90 feet apart, raising, by mutual collisions, their temperature and that of the space occupied by each to the temperature of incandescence, and if we now substitute for them meteorites of a pound weight each, the space occupied by each of them will be a cube of 1670 feet to the side, which does not help us in any way to believe that the spaces occupied by them could be heated up by their collisions, so as to shine with the temperature of incandescence. So we get no help from meteorites.
Some people evidently seem to think that nebulæ can be incandescent and give the spectrum of incandescent gas, without their density or pressure being increased to the corresponding degree. Sir Robert Ball seems to be one of them, though at the same time he appears to be not altogether sure of it. When discussing the self-luminosity of the nebula in Orion, in his "Story of the Heavens," Ed. 1890, p. 465, he says:
"We have, fortunately, one or two very interesting observations on this point. On a particularly fine night, when the speculum of the great six-foot telescope of Parsonstown was in its finest order, the skilled eye of the late Earl of Rosse and of his assistant, Mr. Stoney, detected in the densest part of the nebula myriads of minute stars, which had never before been recognised by human eye. Unquestionably the commingled rays of these stars contribute not a little to the brilliancy of the nebula, but there still remains the question as to whether the entire luminosity of the great nebula can be explained, or whether the light thereof may not partly arise from some other source. The question is one which must necessarily be forced on the attention of any observer who has ever enjoyed the privilege of viewing the great nebula through a telescope of power really adequate to render justice to its beauty. It seems impossible to believe that the bluish light of such delicately graduated shades has really arisen merely from stellar points. The object is so soft and so continuous—might we not almost say ghost-like?—that it is impossible not to believe that we are really looking at some gaseous matter."
Here we see that his own belief about the matter is not very firm. He admits that the stars contribute not a little to the brilliancy of the nebula, and the most he can say in favour of its shining with its own light is, that it seems impossible to believe that the light has arisen merely from stellar points. He then goes on to show how the self-luminosity may be explained, as follows:—
"But here a difficulty may be suggested. The nebula is a luminous body, but ordinary gas is invisible. We do not see the gases which surround us and form the atmosphere in which we live. How, then, if the nebula consisted merely of gaseous matter, would we see it shining on the far distant heavens? A well-known experiment will at once explain this difficulty. We take a tube containing a very small quantity of some gas: for example hydrogen; this gas is usually invisible; no one could tell that there is any gas in the tube, or still less could the kind of gas be known; but pour a stream of electricity through the tube, and instantly the gasbegins to glow with a violet light. What has the electricity done for us in this experiment? Its sole effect has been to heat the gas. It is, indeed, merely a convenient means of heating the gas and making it glow. It is not the electricity which we see, it is rather the gas heated by the electricity. We infer, then, that if the gas be heated it becomes luminous. The gas does not burn in the ordinary sense of the word; no chemical change has taken place. The tube contains exactly the same amount of hydrogen after the experiment that it did before. It glows with the heat just as red-hot iron glows. If, then, we could believe that in the great nebula of Orion there were vast volumes of rarefied gas in the same physical condition as the gas in the tube while the electricity was passing, then we should expect to find that this gas would actually glow."
There is a great deal to be said about this explanation. We presume that a very small quantity of hydrogen gas means that it was considerably below atmospheric pressure. Even so we admit that by introducing sufficient heat into the tube by means of electricity or otherwise, the gas could be raised to the temperature of incandescence, but its pressure would, at the same time, be increased to the corresponding force measured in atmospheres; and we also admit that when the gas was allowed to cool down to its original temperature, the same quantity of hydrogen would be found in the tube; but how about the tube? When the gas came to be at the temperature of incandescence the tube would be the same, or very soon raised to it, and being made of glass would be sufficiently plastic to be distorted, or even burst by the pressure within, probably even before the gas reached the temperature of incandescence. We must not forget that the first appearance of incandescence begins with red heat whose temperature is not far from 500° in daylight, and that white heat rises to above 1000°. If the experiment was made in an almost capillary tube, sufficiently thick to prevent accidents, then it might appear to prove a foregone conclusion, but nothing else; it might keep the idea of pressure out of sight, but it could not prove that the gas inside was in a rarefied state when incandescent. That the gas glowed the same as ared-hot bar of iron has not been shown. The gas had to be shut up in a tube to make it glow, but the bar of iron could glow outside of the tube. Could a streak of hydrogen be put into a furnace along with a bar of iron and heated to incandescence by its side, there might be some fair comparison between them, as long as they were in the furnace together, but the moment they were taken out the glow would disappear from the gas, whereas the iron would glow for some time. On the other hand we mightsaythat a stream of incandescent gas might be made to heat a bar of iron in an oven to its own temperature, but the moment the stream of gas and the iron bar were removed from the oven, the former would disappear at once and the latter would continue to glow, simply because it was dense enough to contain a very considerable supply of heat compared to what the gas could, or rather, because the pressure of the gas, even did it correspond to the temperature, would disappear at once and the heat with it. So it is not always safe tosaythings. But it is quite safe to say that no gas—or substance such as we are accustomed to look upon as gas—can abide in a state of incandescence, and merely glow, unless its pressure, or density, corresponds to the temperature of incandescence; which for red heat (in the dark) would be 370° = 2·35 atmospheres, and for white heat at 1000° = 4·65 atmospheres, above absolute zero of pressure in both cases. And also, that if the self-luminosity of a nebula arises from incandescent gas, the pressure in the gas of that nebula must be somewhere between 2 and 5 atmospheres above absolute zero of pressure. Now we have shown, atpage 85, that the density and pressure in the solar nebula, at the stage there specified, could not have been more than the 403 millionth part of those of our atmosphere, and consequently were justified in asserting that in it there could be almost no heat whatever.
We have just been speaking of a streak of gas and a bar of iron being heated in an oven to a red or white heat side by side, but everybody knows that this could not be done; but everybody has not thought of why it could not be done, otherwise Sir Robert Ball would not have favoured us withhis laboratory experiment of a streak, or remnant, of hydrogen in a glass tube. We know that a plate, or bar, of iron can be heated up to the temperature of incandescence in an oven, but it has never occurred to anyone, who has seen the thing done, that the gas, air, or vapour which heats them must be at a pressure corresponding to that temperature. Multitudes of people may have thought of how the thing is done, but apparently very few have thought that it is not the gaseous part of the current of heated matter introduced into the oven, that heats it and the metal in it, but the solid part which is the distinctive and most important part of the constituents of the current. The solid part of the matter—let it be gas or any other element—is heated to incandescence in some furnace and carried along by the gaseous part—that is thestuffthat fills the empty spaces between the solid molecules—to give it out to the oven and iron. We are not sure that the gaseous part even glows. We see plainly enough that the walls of the oven glow, but with respect to the gas, or carrying agent, we are inclined to think that it rather dims the glow of the oven and iron than otherwise. In passing, we say it is not unreasonable to suppose that the solid matter which contained the heat till it was given out, consisted of the elements which were put into the furnace to raise the heat, and of those which were drawn in by the draught—in a word, the elements of combustion—but about the carrying constituent there is a great deal to be said after we know more about it. It seems to us from all this that the hydrogen gas in Sir Robert Ball's tube was not made to glow by heating up to the temperature of incandescence, but somehow by the electricity passing through it, if it did pass. We, therefore, come to the conclusion that the light of nebulæ does not come from gas—or what we call gas—heated up to be incandescent merely to make it glow, and that it might be as cold as the light that comes from the aurora, or as that of a glow-worm. Sir Robert Ball refers to stellar points seen through the nebula, and acknowledges that part of the glow may be due to them, which shows that the nebula must have been excessively tenuous; for we know how thin a cloud will hide Sirius from us,and we think that nobody will assert that two grains of matter dispersed in 1,426,445 cubic feet of space, as we have seen atpage 86, would hide Sirius from us. Therefore, we must acknowledge that the glow of nebula in Orion, observed by Sir Robert Ball, was caused either by the stellar points, or by some other thing that most assuredly could not be gas heated to the temperature of incandescence, or in part from both. For we believe that the glowing of nebulæ, fluorescence, phosphorescence, Will-o'-the-wisp, auroras, fire-flies, fire-on-the-wave, etc., etc., all, all proceed from the same cause.
We may now proceed to say a few words about the separation of the rings for the planets, brought about by the rotation of the nebula on its axis, and the centrifugal force produced throughout it thereby. We have shown, atpage 88, that a ring could not be detached from the nebula at once in one large annular mass, as it seems to have been the common notion was the mode of separation; and we shall now try to show with some detail what the process must have been, notwithstanding that it has been in a general way described by others; because, like everything else, there is something to be learnt from it. For this purpose we shall select what we have called the Jovian nebula, because we can suppose, for the present, it must have been more nearly in the form of a sphere than either the original or any of the exterior nebulæ, which may not have been properly licked into shape, as it were; and also because we have found that the thickness and mass of the ring for his, Jupiter's, system were vastly greater than those for any other one of the planets. We have made the Jovian nebula to have been 1,370,800,000 miles in diameter, and the greatest thickness of the ring detatched from it to have been 1,406,771 miles. Now in a circle of that diameter, a chord of the length of that thickness would subtend an arc of very little more than 7 minutes, one half of which we shall suppose to be measured on each side of the equatorial diameter of the nebula at right angles to the diameter; then, the middle ordinate of a chord of 1,406,771 miles long, would be 359 miles long. This length would be a very small fraction of the radius of the circle whichwould be 685,400,000 miles long, but in a rotating sphere of the same dimension, we must acknowledge that the centrifugal force at the middle of the arc would be greater—however small the difference—than at its ends, and would sooner come to balance the force of gravitation; therefore we must admit that the process of separation would begin there by abandoning a thin layer of matter, convex on the outer side and in a measure concave on the inner side, for the reason just given, much the same as a layer that could be peeled off from the equator of an orange—the poles and equator of an orange are easily distinguished. As the velocity of rotation increased another layer would be abandoned following the first, so far curved on both sides, i.e. convex and concave, and the same process would continue on and on, according as the centrifugal force continued to balance that of gravitation, till the whole of the matter for all the attendants of the sun was abandoned; so that in the process itself no such division of rings as we have been following could have taken place, but one continuous sheet, as it were, would be formed from first to last. Whether the thickness of the ring for Jupiter's system, or any other system or planet, was limited to the length of the chord we have been dealing with, or came to be many times greater or even less, makes no difference on our explanation. After being abandoned in a sheet, as we have shown it would be, the centrifugal force they had acquired would, for a time at least, keep the particles of the sheet near the radial positions they then occupied, and their mutual attraction would go on diminishing its thickness, till finally the radial attractions among the particles divided the sheet into entirely separate rings after the manner of those of Saturn; which would in due course break up and form themselves into the smaller nebulæ from which the planets were supposed to have been made.
M. Faye has made it a great point against the nebula hypothesis that when these rings broke up, the rotary motions of the planets resulting from them would be retrograde, because the outer parts of them would be travelling at a slower rate than the inner ones, and has taken the trouble toconstruct a diagram to show how this would be the case; but he himself has told us, in "L'Origine du Monde," that Laplace had duly considered this point, and had shown how the friction of the particles of the flat rings among themselves would, through course of time, retard and accelerate each other, so that a ring would come to revolve as if it were one solid piece, and consequently that the outer edge of the ring would come to be travelling faster than the inner one, which according to his (M. Faye's) own showing would produce, on breaking up, a planet with direct motion of rotation. Laplace's words, as cited by him, are:—
"Le frottement mutuel des molécules de chaque anneau a dû accélérer les unes et retarder les autres jusqu'à ce qu'elles aient acquis une même mouvement angulaire. Ainsi les vitesses réelles des molécules éloignées du centre de l'astre out été plus grandes. La cause suivante a dû contribuer encore à cette différence de vitesse: les molécules les plus distantes du soleil et qui, par les effets du refroidissement et de la condensation, s'en sont rapprochées pour former la partie supérieure de l'anneau out toujours décrit les aires proportionnelles aux temps, puisque la force centrale dont elles étaient animées a été constamment dirigée vers cet astre; or cette constance des airs exige un accroissement de vitesse à mesure qu'elles s'en sont rapprochées. On voit que la même cause a dû diminuer la vitesse des molécules qui se sont élevées vers l'anneau pour former sa partie inférieure."
In his method of bringing all the molecules of matter in a ring, to revolve round the centre as if they formed one sole piece, Laplace does not appeal to any accommodating force among them except friction, while he might have called in that of the collisions of the molecules amongst themselves. It is not to be supposed that each molecule would remain fixed in the position it occupied when separated from the nebulæ, and only went on rubbing against—and creating friction with—its neighbours, and only creeping closer to the centre or farther from it, as it was acted upon by the attraction of the other parts of the ring. The molecules would be rushing against each other in all directions, in spite of, although in themain obedient to, the law of attraction; and we could conceive the possibility of molecules gradually working their way from the extreme outer edge to the extreme inner edge of a ring, orvice versâ, which would be a much more effectual means of bringing about one period of revolution throughout the whole ring, than the simple force of rubbing against each other. When physicists get a gas shut up in a close vessel, they grant to its molecules the power of committing exactly the same kind of freaks; and a planetary ring is, to all intents and purposes, a closed vessel to our molecules; because they have been placed in it by the laws of attraction and centrifugal force, and there is no other force acting upon them sufficiently powerful to liberate them from it. Therefore there is no reason why a molecule in a ring should be always wedged up in one place, especially after we have shown that each molecule of matter, in any of the rings we have been dealing with, must have had a much greater free path to move about in, than a molecule of gas shut up in any of the vessels used by physicists.
We have no reason to look upon the rings of Saturn otherwise than as in process of being converted into one or more satellites, most probably more than one; because if the matter they are composed of has been separated from the planet in the form of a sheet, the same as we have seen must have been the case with the matter separated from the original nebula for the planets, the sheet has been already divided into at least three distinct parts, and surely that cannot have been done without some object. If these rings have been left, as has been said, in order to show us how the solar system has been formed, that does not authorise us to conclude that they will always remain in the form they have. There is no reason why the lesson should not be carried out to the very end, through the breaking up of the rings, formation of spherical nebiculæ, and finally satellites. It would be rash to assert that the matter of which any one of them is composed—be it atoms, molecules, meteorites, or brickbats—cannot, through friction and collisions of its particles among themselves, come to revolve around Saturn as if it were onesolid piece. But should anyone do so, and adopt M. Faye's condemnation of Laplace's mode of forming rings, he must confess that when Saturn's rings are converted into satellites, their rotations must be retrograde; and it might be, for him, an interesting inquiry to find out whether the rotations of the existing satellites are direct or retrograde.