When the nebula was 6,600,000,000 miles in diameter its volume would
be 150,533^{24} cubic miles--as we have seen at page 87--the half
of which is 75,266^{24} cubic miles, corresponding to a diameter of
5,238,332,000 miles, or radius of 2,619,166,000 miles. Now, according
to our theory, it would be at this distance from the centre that the
greatest density and activity of the nebulous matter would be, where we
have just been showing how a movement of rotation could be generated,
and where, in consequence, its motive power, so to speak, originated
and existed. Here we find by dividing 5,238,332,000 by 6,600,000,000
that the region of greatest density in such a nebula would be at 0·7937
of its diameter. In our calculations about the earth, as it is, the
proportion was found to be 0·7939, but the densities of the outer
layers were empirically arranged by us; and, besides, almost the whole
of the mass was supposed to be solid matter, so that no accurate result
could be expected from that operation. There also we found that the
inner surface of the hollow shell was at 0·5479 of the whole diameter,
which we may adopt for the nebula we are about to deal with, as that
dimension may be varied considerably--so may the other also--without in
any way vitiating our theory.
Having found these proportions, which can only be considered as
distantly approximate, let us go back to the 9 nebulæ--excluding the
final solar one--into which we supposed the original nebula to have
been divided--in the analysis just alluded to--and see how the regions
of greatest density in them would correspond to the orbits of the
planets formed out of them. This examination requires a good deal of
calculation and accompanying description, which it might be found
tiresome to follow, and would really answer no good end were it written
out; so we shall suppose it to be made and the results obtained from
the calculations to be represented in the form of Table IX., where they
can be seen at a glance almost, and compared without much trouble. This
arrangement will also furnish a readier means of reference for the
remarks we shall have to make on, and the information obtained from,
the examination. And we have still to add that the extreme diameters of
the 9 nebulæ are the same as those we used for the analysis; as also,
that we make use of only the first of the proportions just cited, viz.,
0·7937, it being the only one required for determining the positions of
the regions of greatest density in the nebulæ.
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