[Footnote 11: _Cosmos._ (Seventh Edition.) Vol. i. pp. 79, 80.]
[Footnote 12: Since the publication of this essay the late Mr. R. A.
Proctor has given various further reasons for the conclusion that the
nebulae belong to our own sidereal system. The opposite conclusion,
contested throughout the foregoing section, has now been tacitly
abandoned.]
[Footnote 13: Any objection made to the extreme tenuity this involves,
is met by the calculation of Newton, who proved that were a spherical
inch of air removed four thousand miles from the Earth, it would expand
into a sphere more than filling the orbit of Saturn.]
[Footnote 14: A reference may fitly be made here to a reason given by
Mons. Babinet for rejection of the Nebular Hypothesis. He has calculated
that taking the existing Sun, with its observed angular velocity, its
substance, if expanded so as to fill the orbit of Neptune, would have
nothing approaching the angular velocity which the time of revolution of
that planet implies. The assumption he makes is inadmissible. He
supposes that all parts of the nebulous spheroid when it filled
Neptune's orbit, had the same angular velocities. But the process of
nebular condensation as indicated above, implies that the remoter
flocculi of nebulous matter, later in reaching the central mass, and
forming its peripheral portions, will acquire, during their longer
journeys towards it, greater velocities. An inspection of one of the
spiral nebulae, as 51st or 99th Messier, at once shows that the outlying
portions when they reach the nucleus, will form an equatorial belt
moving round the common centre more rapidly than the rest. Thus the
central parts will have small angular velocities, while there will be
increasing angular velocities of parts increasingly remote from the
centre. And while the density of the spheroid continues small, fluid
friction will scarcely at all change these differences.
A like criticism may, I think, be passed on an opinion expressed by
Prof. Newcomb. He says:--"When the contraction [of the nebulous
spheroid] had gone so far that the centrifugal and attracting forces
nearly balanced each other at the outer equatorial limit of the mass,
the result would have been that contraction in the direction of the
equator would cease entirely, and be confined to the polar regions, each
particle dropping, not towards the sun, but towards the plane of the
solar equator. Thus, we should have a constant flattening of the
spheroidal atmosphere until it was reduced to a thin flat disk. This
disk might then separate itself into rings, which would form planets in
much the same way that Laplace supposed. But there would probably be no
marked difference in the age of the planets." (_Popular Astronomy_,
p. 512.) Now this conclusion assumes, like that of M. Babinet, that all
parts of the nebulous spheroid had equal angular velocities. If, as
above contended, it is inferable from the process by which a nebulous
spheroid was formed, that its outer portions revolved with greater
angular velocities than its inner; then the inference which Prof.
Newcomb draws is not necessitated.]
[Footnote 15: It is true that since this essay was written reasons have
been given for concluding that comets consist of swarms of meteors
enveloped in aeriform matter. Very possibly this is the constitution of
the periodic comets which, approximating their orbits to the plane of
the Solar System, form established parts of the System, and which, as
will be hereafter indicated, have probably a quite different origin.]
[Footnote 16: Though this rule fails at the periphery of the Solar
System, yet it fails only where the axis of rotation, instead of being
almost perpendicular to the orbit-plane, is very little inclined to it;
and where, therefore, the forces tending to produce the congruity of
motions were but little operative.]
[Footnote 17: It is true that, as expressed by him, these propositions
of Laplace are not all beyond dispute. An astronomer of the highest
authority, who has favoured me with some criticisms on this essay,
alleges that instead of a nebulous ring rupturing at one point, and
collapsing into a single mass, "all probability would be in favour of
its breaking up into many masses." This alternative result certainly
seems the more likely. But granting that a nebulous ring would break up
into many masses, it may still be contended that, since the chances are
infinity to one against these being of equal sizes _and_ equidistant,
they could not remain evenly distributed round their orbit. This annular
chain of gaseous masses would break up into groups of masses; these
groups would eventually aggregate into larger groups; and the final
result would be the formation of a single mass. I have put the question
to an astronomer scarcely second in authority to the one above referred
to, and he agrees that this would probably be the process.]
[Footnote 18: The comparative statement here given differs, slightly in
most cases and in one case largely, from the statement included in this
essay as originally published in 1858. As then given the table ran
thus:--
Mercury. 1/362
Venus. 1/282
Earth. 1/289 1 Satellite.
Mars. 1/326
Jupiter. 1/14 4 Satellites.
Saturn. 1/6.2 8 Satellites, and three rings.
Uranus. 1/9 4 (or 6 according to Herschel).
The calculations ending with these figures were made while the Sun's
distance was still estimated at 95 millions of miles. Of course the
reduction afterwards established in the estimated distance, entailing,
as it did, changes in the factors which entered into the calculations,
affected the results; and, though it was unlikely that the relations
stated would be materially changed, it was needful to have the
calculations made afresh. Mr. Lynn has been good enough to undertake
this task, and the figures given in the text are his. In the case of
Mars a large error in my calculation had arisen from accepting Arago's
statement of his density (0.95), which proves to be something like
double what it should be. Here a curious incident may be named. When, in
1877, it was discovered that Mars has two satellites, though, according
to my hypothesis, it seemed that he should have none, my faith in it
received a shock; and since that time I have occasionally considered
whether the fact is in any way reconcilable with the hypothesis. But now
the proof afforded by Mr. Lynn that my calculation contained a wrong
factor, disposes of the difficulty--nay, changes the objection to a
verification. It turns out that, according to the hypothesis, Mars
_ought_ to have satellites; and, further, that he ought to have a number
intermediate between 1 and 4.]
[Footnote 19: Since this paragraph was first published, the discovery
that Mars has two satellites revolving round him in periods shorter than
that of his rotation, has shown that the implication on which Laplace
here insists is general only, and not absolute. Were it a necessary
assumption that all parts of a concentrating nebulous spheroid revolve
with the same angular velocities, the exception would appear an
inexplicable one; but if, as suggested in a preceding section, it is
inferable from the process of formation of a nebulous spheroid, that its
outer strata will move round the general axis with higher angular
velocities than the inner ones, there follows a possible interpretation.
Though, during the earlier stages of concentration, while the nebulous
matter, and especially its peripheral portions, are very rare, the
effects of fluid-friction will be too small to change greatly such
differences of angular velocities as exist; yet, when concentration has
reached its last stages, and the matter is passing from the gaseous into
the liquid and solid states, and when also the convection-currents have
become common to the whole mass (which they probably at first are not),
the angular velocity of the peripheral portion will gradually be
assimilated to that of the interior; and it becomes comprehensible that
in the case of Mars the peripheral portion, more and more dragged back
by the internal mass, lost part of its velocity during the interval
between the formation of the innermost satellite and the arrival at the
final form.]
[Footnote 20: I was about to suppress part of the above paragraph,
written before the science of solar physics had taken shape, because of
certain physical difficulties which stand in the way of its argument,
when, on looking into recent astronomical works, I found that the
hypothesis it sets forth respecting the Sun's structure has kinships to
the several hypotheses since set forth by Zoellner, Faye, and Young. I
have therefore decided to let it stand as it originally did.
The contemplated partial suppression just named, was prompted by
recognition of the truth that to effect mechanical stability the gaseous
interior of the Sun must have a density at least equal to that of the
molten shell (greater, indeed, at the centre); and this seems to imply a
specific gravity higher than that which he possesses. It may, indeed, be
that the unknown elements which spectrum analysis shows to exist in the
Sun, are metals of very low specific gravities, and that, existing in
large proportion with other of the lighter metals, they may form a
molten shell not denser than is implied by the facts. But this can be
regarded as nothing more than a possibility.
No need, however, has arisen for either relinquishing or holding but
loosely the associated conclusions respecting the constitution of the
photosphere and its envelope. Widely speculative as seemed these
suggested corollaries from the Nebular Hypothesis when set forth in
1858, and quite at variance with the beliefs then current, they proved
to be not ill-founded. At the close of 1859, there came the discoveries
of Kirchhoff, proving the existence of various metallic vapours in the
Sun's atmosphere.]