From the Jovian nebula of 1,370,800,000 miles in diameter, volume of
1,348,720,186,335^{15} 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 1,339,557,155^{15} cubic miles for his system at the
same density as the nebula; therefore, substracting this amount from
1,348,720,186,335^{15} we get 1,347,380,629,180^{15} 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. 1,339,557,155^{15}
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.
Public-domain text, read in full here on John Shaqi.
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