Page
83	Analysis of the Nebular Hypothesis. Separation from the nebula
	??of the rings for the separate planets, etc.
84	Excessive heat attributed to the nebula erroneous and impossible
85	Centigrade thermometer to be used for temperatures
86	Temperature of the nebula not far from absolute zero
86	Erroneous ideas about glowing gases produced by collisions of their atoms,
	??or particles of cosmic matter in the form of vapours
87	Separation of ring for Neptune. It could not have been
	??thrown off in one mass, but in a sheet of cosmic matter
88	Thickness and dimensions of the ring
89	Uranian ring abandoned, and its dimensions
90	Saturnian ring abandoned, and its dimensions
91	Jovian ring abandoned, and its dimensions
93	Asteroidal ring abandoned, and its dimensions
94	Martian ring abandoned, and its dimensions
95	Earth ring abandoned, and its dimensions
96	Venus ring abandoned, and its dimensions
97	Mercurian ring abandoned, and its dimensions
98	Residual mass. Condensation of Solar Nebula to various
	??diameters, and relative temperatures and densities
100	Unaccountable confusion in the mode of counting absolute temperature examined and explained.
	??Negative 274 degrees of heat only equal 2 degrees of absolute temperature
103	The Centigrade thermometric scale no better than any other, and cannot be made decimal
104	The sun's account current with the Nebula drawn up and represented by Table III.

Analysis of the Nebular Hypothesis.

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

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

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

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

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

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

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

Separation of Ring for Neptune.

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

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

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

The Uranian Nebula.

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

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

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

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

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

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

Jovian Nebula.

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

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

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

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

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

Asteroidal Nebula.

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

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

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

Martian Nebula.

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

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

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

Earth Nebula.

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

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

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

Venus Nebula.

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

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

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

Mercurian Nebula.

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

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

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

Solar Nebula.

Lastly, as the volume of the nebula was

576,026,502,545,978,033⁶

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

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 102,176,129,412¹² cubic miles, and its density 1/274th of an atmosphere—about one-ninth inch of mercury—which would, in consequence, make its absolute mean heat equal to one degree of 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 372,905,560,345⁹ cubic 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 absolute temperature.

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 482,167¹² cubic miles, and mean heat 775°, including the 2° acquired in condensing it to the pressure of 1 atmosphere, as is plainly shown in Table III.

Before going any further we must enter into a digression to examine into the process of thought by which the absolute zero 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 accompanying Table 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 this usage has 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 from getting 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 called latent heat, which in the case of ice and water may be a fraction of -1° or -80°, or minus almost 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 hydrogen has 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 from
the Calculations made in Chapter V.

— NebulÆ —			Volume of the Mass of each Separate System at Density of Water	Times less Dense than Water.	Increase of Density	VolumesatDensities ofRespectiveNebulÆ
Name.	Diameter (Miles).	Explanations.	(Cubic Miles).		in times.	(Cubic Miles).
Neptunian	6,600,000,000			311,754,100,720
		Volume of Neptune's Ring	29,107,964,680,925	311,754,100,720		150,532,847,222,000,000,000,000,000,000
		Volume of Nebula less Ring				9,074,530,000,000,000,000,000,000
Uranian	4,580,000,000	CondensedfromNeptunianNebula			2.9923	150,523,772,692,000,000,000,000,000,000
		Volume of Uranus' Ring	25,876,388,977,000	104,184,535,721		50,303,255,814,000,000,000,000,000,000
		Volume of Nebula less Ring				2,695,918,851,000,000,000,000,000
Saturnian	2,672,000,000	Condensed from Uranian Nebula			5.0357	50,300,559,895,149,000,000,000,000,000
		Volume of Saturn's Ring	154,370,734,774,315	20,689,000,000		9,988,700,000,000,000,000,000,000,000
		Volume of Nebula less ring				3,193,775,478,000,000,000,000,000
Jovian	1,370,800,000	Condensed from Saturnian Nebula			7.4037	9,985,506,224,522,000,000,000,000,000
		Volume of Jupiter's Ring	479,368,921,317,000	2,794,417,420		1,348,720,186,335,000,000,000,000,000
		Volume of Nebula less ring				1,339,557,155,000,000,000,000,000
Asteroidal	744,000,000	Condensed from Jovian Nebula			6.2484	1,347,380,629,180,000,000,000,000,000
		Volume of Asteroidal Ring	367,792,000,000	447,218,905		215,634,925,373,133,820,000,000,000
		Volume of Nebula less ring				164,482,717,200,000,000,000
Martian	402,000,000	Condensed from Asteroidal Nebula			6.3392	215,634,760,890,416,620,000,000,000
		Volume of Martian Ring	160,728,460,000	70,547,110		34,015,582,677,165,354,000,000,000
		Volume of Nebula less ring				11,338,927,154,000,000,000
Earth	234,620,000	Condensed from Martian Nebula			5.0302	34,015,571,338,237,200,000,000,000
		Volume of Earth Ring	1,489,310,236,000	14,024,781		6,762,303,076,923,031,000,000,000
		Volume of Nebula less ring				20,887,249,553,000,000,000
Venus	160,210,000	Condensed from Earth Nebula			3.1410	6,762,282,189,673,478,000,000,000
		Volume of Venus Ring	1,131,960,000,000	4,465,512		2,153,120,792,079,207,921,000,000
		Volume of Nebula less ring				5,054,780,604,651,000,000
Mercurian	103,232,000	Condensed from Venus Nebula			3.7379	2,153,115,737,298,603,270,000,000
		Volume of Mercurian Ring	92,735,000,000	1,194,666		576,026,613,333,333,333,000,000
		Volume of Nebula less ring				110,787,355,300,000,000
Solar	63,232,000	Condensed from Mercurian Nebula		274,546	4.3514	576,026,502,545,978,033,000,000
	58,002,920	Volume at 1/274 of 1 atmosphere.		211,911	1.2956	132,376,310,975,609,756,000,000
	8,930,309	Volumeatdensityof1atmosphere.			274.0000	102,176,129,412,000,000,000,000
	972,895	Volume at density of water.			773.3950	372,905,560,345,000,000,000

TABLE III.—Continued.

			AtDensityofWater Dimensions of Rings.			AtAirDensity Space to Grain of Matter.
Name.	Times less Dense than Air.	Absolute Temperature (Degrees).	Breadth (Miles).	Thickness (Miles).	Avg. Thickness (Miles).	Cubic Feet.	Sideof Cube (Feet).	Inches
Neptunian	403,000,000	0·00000068				713,223	89·327
			1,010,000,000	511,794	341,196
Uranian	134,710,620	0·000002034	954,000,000	252,193	100,553	238,357	61·994
Saturnian	26,750,876	0·00001024	650,600,000	881,037	238,000	47,313	36·168
Jovian	3,613,182	0·00007583	313,400,000	1,406,771	450,282	6,303	18·472
Asteroidal	578,254	0·00047384	171,000,000	588	185	1,023	10·075
Martian	91,259	0·00300244	83,690,000	152	61	161	5·445
Earth	18,134	0·0151097	37,205,000	961	612	32	3·178
Venus	5,774	0·047454	28,489,000	420	225	10·2	2·170
Mercurian	1,545	0·1773463	20,000,000	25	11	2·734	1·398
Solar
	355	0·771831				0·6283	0·8565	10·28
	274	0·99635				0·4848	0·7856	9·43
	0	2·0000				0·00177	0·121	1·452

Returning now to page 84, we see that the volume of the sun alone was considered to be 482,169¹² cubic miles, which corresponds to a diameter of 972,869 miles. Comparing this with the volume 482,167¹² cubic 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 miles less than 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 to Table 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 482,860,744⁹ cubic 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 miles more than 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 results are 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 compiled Table 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.

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