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.