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rials of lava, aiding as he supposed, in giving mobility to the
more solid materials of the fluid mass. But, when advocating
this igneo-aqueous theory, he never dreamed of impugning the
Huttonian doctrine as to the intensity of heat which the produc-
tion of the unstratified rocks, those of the plutonic class espe-
cially, implies.

The exact nature of the chemical changes which hydrother-
mal action may effect in the earth's interior will long remain ob-
scure to us, because the regions where they take place are inac-
cessible to man ; but the manner in which volcanos have shifted
their position throughout a vast series of geological epochs — be-
coming extinct in one region and breaking out in another — may,
perhaps, explain the increase of heat as we descend toward the
interior, witnout the necessity of our appealing to an original
central heat, or the igneous fluidity of the eartlrs nucleus.

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D. Trowbridge on the Nebular Hypothesis. 25

Art. IV. — On the Nebular Hypothesis; by David
Trowbridge, A.M.

[CoDcladed from voL xxxriii, p. 860.]

1. The Breaking-up of the Rings,

84. The process of cooling would still continue after the rings
had separated. The loss of caloric from radiation would cause
the rings to contract their dimensions ; and this, the unequal
density of different parts, and the extraordinary perturbations to
which they would necessarily be subject in their motions, would
cause a separation of the rings in certain weak places. When
once broken into parts while the density of the ring was very
small, even if the parts were not many, the case would be extra-
ordinary in which the parts would be prevented from re-uniting
into a single planet, owing to the very great perturbations to
which their motions would be subject, as separate bodies. It is
impossible at present to tell just how a ring would be resolved
into a. planet. A system of waves would probably be developed,
owing to perturbations ; and by an accumulation in one part,
owing to tne nature of the disturbing force, such as calculation
shows might exist under certain conditions in the case of the
rings of Saturn, and thus a considerable portion of the matter
of the ring would be driven into one side, and this accumulation
would be the center of attraction around which the planet would
be formed.

35. We may now ask in what direction the planet thus
formed would rotate ? The direction of rotation would depend
on circumstances. Let us take the breadth of the ring from
which Uranus was formed, the same as the diameter of his
sphere of attraction in Kirkwood's Analogy. The diameter of
the sphere of attraction of Uranus, as given by Professor Kirk-
wooa," is 7'438. The inner radius is 2*558, and the outer one,
4*879. If we suppose the inner and the outer parts of the
ring each to have the velocity due it according to Kepler's third
law, then, the velocity of the inner part being callea 1, that of
. the outer will be 0*8287 ; and the angular velocities of the same
parts will be to each other as 1 to 04715. If every part of the
ring have the same angular velocity, and that of the inner part
be 1, the angular velocity of the outer part will be 1*457. If
the inn^r and the outer parts have the same velocity, the angu-
lar velocity of the inner part being called 1, that of the outer
part will be 0'6866. But none of these cases can obtain in any
of the rings, but one or another will be approximated to, accord-

^ This Journal, [2], xiv, ].. 218.
Am. Jour. Soi.— Second Series, Vol. XXXIX, No. 115.— Jan., 1866.

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26 D. Trowbridge on the Nebular Hypothesis.

ing to circumstances. The outer rings would approximate to
the first case, and the inner ones, to the second case ; while
intermediate rings would approximate more or less, according to
their position in the Sj'stem, to the last case. In confirmation
of this, we may refer to the case of Saturn's rings. It is demon-
strated by mathematicians that the stability of the motions of
those rings cannot exist unless the parts at different distances
from the center of Saturn, have different angular velocities.*'

But observation" shows that the stability of the motion of the
Rings exists. We hence conclude that those parts of the Kings
situated at different distances from the center of Saturn do have
difierent angular velocities. But it is concluded from observa-
tion that the rings of Saturn are liquid ;" we hence conclude
that there is still greater necessity for the different parts of a
gaseous ring situated at different distances from the center of at-
traction, to have different angular velocities; just as we have
concluded in speaking of the separation of the rings from the
equatorial parts of the great solar spheroid.

36. In the case of the first two or three rings abandoned by
the primitive spheroid, their density would be relatively so, small
that the velocity of the outer parts would be regulated approx-
imately by Kepler's third law. Such being the case, it is prob-
able that the velocity of the inner parts will exceed that of the
outer parts. When the rings break up to form planets,'the parts
will in a great measure retain the velocity which they had in the
complete rings, and the consequence will be that the rotation of
such planets will, at first, be performed in a direction opposite
to that of their motions around the central body." In conse-
quence of the great friction of the different strata of the fluid
planetary rings abandoned by the solar spheroid, the outer strata
would, in most cases, probably, have a greater absolute velocity
than the inner strata ; and the planets formed from them would
naturally at first take the direct motion of rotation, because the
external parts having a greater velocity than the inner parts, the
excess of velocity would give the planet a direct rotatory velocity.
Even if some of the outer planets should prove to have a retro-

** Maxwell, On the Stability of the Motion of SatvmU Ring%^ pp. 8 and 45 ;
Peirce in Gould's Astronomical Journal, ii. 17-18.

" Observation Beems to show that the Rings of Saturn are gradually approaching
the body of the planet ; but it by no means follows that they will ever come in
contact with the body of the planet They have existed too long for us to suppose^
there is any probability that the Rings are to be precipitated upon the body of the
planet before our eyes, as it were.

■* See Annual of Scientific Discover}/ for 1862, p. 377.

** Professor Kirkwood has pointed this out in his article in this Journal, [2],
xzxviii, 2-4 ; and he has alM> attempted to show that in certain cases the rota-
tion will become direct from the action of other members of the System. See also,
volume XXX vii, page 61, where Prof. Hinrichs has given a formula indicating the
same thing that we have arrived at in the text.

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2>. Trowbridge on the Nebular Hypotkesit. 37

grade rotatory motion, our reafioning would not lead us to con-
clude that such would be the case with many of them.

37. But are we certain that all the rings would break up ; or
if broken up, that each would form a single planet ? In this part
of our enquiry we cannot guess at it ; nor will it do to be guid-
ed by the phenomena of the Solar System ; for it is the phenom-
ena of such a system of which we are to render a rational ac-
count. We must here be guided by strictly mathematical and
philosophical deductions. Prof. Peirce, of Harvard University,
in his investigation of the problem of the stability of the mo-
tions of Saturn's Rings, arrived at the remarkable conclusion
that the dynamical equilibrium of the rings is preserved by the
sustaining effect of the satellites in the very act of perturbation.
He then makes the remark that the only place in the Solar Sys-
tem, among the primary planets, where we could, from the
above conclusions, expect a permanent ring, is just within the
powerful masses of Jupiter and Saturn." But even here, he
says, the ring could not exist, but must ultimately be destroyed.
He says, " But had there been a ring at this part of the system,
it must have been subject to such extraordinary perturbations
that It would, in the course of time, have been vibrated up
against the next inferior planet, Mars; and in this way have
been broken into the asteroids. The orbits of planets, formed
under such circumstances, must have been characterized by great
eccentricity." ,

The above view of the formation of the Asteroids, needs
some modification. According to Peirce's conclusions, drawn
from his investigation of the problem of Saturn's Rings, a fluid
ring miffht, perhaps, exist for some considerable length of time,
within the orbit of Jupiter. Granting this to be true, it is diffi-
cult to escape the conclusion that the process of cooling, to which
the ring would be subject, even if it were gaseous, would grad-
ually reduce it to a condition approximating to that of the rings
of Saturn at the present time ; tnat is, a liquid state. The vari-
ous conclusions, then, at which mathematicians have arrived,
respecting the perturbations of those rings, will apply with
greater or less force, according to circumstances, to the supposed
ring within the orbit of Jupiter. Prof. Maxwell," in his inves-
tigation of the problem ot the motion of Saturn's Rings, dis-
cussed the case of a solid ring, a ring of disconnected particles,
and a fluid (or more definitely a liquid,) ring. The first case he
found to be one of unstable equilibrium. In the last two cases
he found that if the perturbations to which the ring would be sub-

" Gould's Ast. Journal, vol. ii, p. 18. Also Annual of Scientific Discovery for
1S62. p. 879.

** On the stability of the motion of Saturn's rings. An essay vhich obtained tho
Adnms Prize for the year 1356, in the UuiTersity of Cambridge, Eng. By J. Clerk
Maxwell, M. A.

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28 D. Trowbridge on the Nebular Hypothesis.

ject could be propagated around the ring in the form of waves,
subject to particular conditions, the ring would be permanent ;
but if these particular conditions were not fulfilled, the ring
would be destroyed. In the case of a fluid ring, (incompres-
sible,) he found that in general a wide ring could not revolve
every part of which had the same angular velocity." In his
recapitulation" he says, " We next took tip the case of a flat-
tened ring, composed of incompressible fluid, and moving with
uniform angular velocity. The internal forces here arise partly
from attraction and partly from fluid pressure. We began by
taking the case of an infinite stratum of fluid afiected by regu-
lar waves. I found the accurate values of the forces in this
case. For long waves, the resultant force is in the same direc-
tion as the displacement, reaching a maximum for waves whose
length is about ten times the thickness of the stratum. For
waves about five times as long as the stratum is thick, there is
no resultant force; and for shorter waves, the force is in the op-
posite direction to the displacement.

39. *' Applying these results to the case of the ring, we find
that it will be destroyed by the long waves unless the fluid is
less than -^d of the density of the planet, and that in all
cases the short waves will break up the ring into small satellites.

40. '* Passing to the case of narrow rings, we should find a
somewhat larger maximum density, but we should still find that
very short waves produce forces in the direction opposite to the
displacement, and that therefore, as already explained, these
short undulations would increase in magnitude without being
propagated along the ring, till they had broken up the fluid fila-
ment into drops. These drops may or may not fulfill the condi-
tion formerly given [in the essay] for the stability of a ring of
equal satellites. If they fulfill the conditions, they will move as
a permanent ring. If they do not, short waves will arise and
be propagated among the satellites, with ever increasing magni-
tude, till a sufficient number of drops have been brought into
collision, so as to unite and form a smaller number of larger
drops, which may be capable of revolving as a permanent ring."

41. Basing our reasoning on the preceding results, we are led
to the conclusion that under certain conditions — such as prob-
ably exist within the orbits of Jupiter and Saturn in the Solar
System — the abandoned fluid ring may preserve its form for im-
mense ages, and thus have time to cool down somewhat and ap-
proximate to the condition of an incompressible fluid, and then,
with the changes already taken place, undergo the necessary
transformation, to convert it into small, separate bodies. These
bodies would continue to come into collision until the conditions
of dynamical equilibrium were fully established, and thus en-

•• MaxweU, p. 46. *» lb., p. 64.

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2>. Trowbridge on the Nebular Hypothesis. 29

able each body to move in its own independent orbit. Bodies
so formed must xary in size from the largest of them to bodies
too minute to be visible through our most powerful telescopes.**
The original ring would necessarily have considerable width, and
since it would be prevented from uniting into a single planet,
any such zone of small planets would also be of considerable
wiSth, and the planets would range in mean distance from one
limit of the broken ring to the opposite limit. The various dis-
turbing causes would verj probably cause the small planetary
bodies to move in very eccentric (planetary) orbits, and the
action of the short waves which would bVeak up the ring, might,
perhaps, cause the resulting planets to move in orbits consider-
ably inclined to each other, and to the plane of the ecliptic.

42. The heterogeneousness of the materials composing the
outer rings, and the great rarity of their physical condition,
would, perhaps, cause som0 of the less dense portions, at the
time of the breaking-up of the rings, owing to the action of the
great disturbing forces to which their motions would be subject,
to be projected to a considerable distance from either the outer
or the inner parts of the rings, and such detached portions-
might never return to the parent masses, but would move around
the central solar bodv in an elliptical orbit, having, perhaps, in
some cases, considerable inclination to the plane of tne equator
of the rings from which they were projected. Such bodies
would revolve around the sun as Comets. The theory of Central
Forces" shows us that, when the distances from the central body
and the initial velocity are given, the eccentricity is dependent on
the angle of projection ; that is, the angle formed by the radius-
vector and the line of projection. Supposing comets to have
been formed as we have just described, we see that the great
eccentricity of their orbits results from the direction with respect
to the radius- vector, in which the mass is thrown from the ring.
Such comets would very probably move around the sun in the
same direction as the planets. Those rings abandoned nearer
the centre of the solar spheroid, would, very likely, be more
symmetrical in the disposition of their materials, and conse-
quently less likely to have any large collection of rare materials
that could be projected from the rings. We hence conclude
that those comets which have a comparatively short period of
revolution, will not be very large and conspicuous objects when
they approach their perihelia. We may further conclude that
the last three or four rings would not throw off any comets.
We hence conclude that periodic comets having a direct motion
should be found in groups, perhaps, with periods of revolution
a little greater or a little less than the planets to which they

" 2dsij we not iti this way account for the existeDce of meteoric riDgs ?
'^ See Math. MoDthlj, ii, 160.

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80 D. Trowbridge on the Nebular Hypothesis.

nearest correspond in their motions. Eetrogra'le comets, and a
portion of those -vs hich have a direct motion, c^i^iot very well be
accounted for upcn this hypothesis of the breaking-up of the
rings, nor should we expect to find retrograde comets with short
periods. If, as Laplace supposed, and which, according to our
hypothesis, is not improbable, comparatively small quantities of
nebulous matter exist in different regions of the universe, the
Solar System may, in its motion through space, come into their
immediate neighborhood at different times, and such nebulous
matter would be drawn, by the attractive influence of the sun
and planets, into the* system, and it would appear in the
form of comets — either retrograde or direct, according to circum-
stances — and meteors. All comets so formed would necessarily
have a comparatively long period of revolution, unless (which
might be the case in some instances) the perturbative influence
of the planets should change their cfrbits. We may hence con-
clude that all, or nearly all, comets having a short period, will
have a direct motion ; and of the comets of long periods, the
direct and retrograde should, considering all time, be nearly
equally divided, so far as we can determine.

2. The Planets and their Satellites.

48. After the rings from which the planets were formed were
broken up, and all the parts of any one ring reduced to a planet,
euch planet, as we have shown, would have a rotation on an
axis. This axis would, necessarily, be a natural or principal
cads. It would be a delicate adjustment to give a solid body,
differing from a sphere, a rotation around a principal axis ; but
a fluid body woula readily adapt itself to such an axis. We do
not doubt but that Infinite Wisdom and Power could cause any
solid body to rotate around a natural axis ; but we have not the
least evidence that Infinite Wisdom ever works in that special
manner. God always adapts means to ends, so that all things
are produced under the action of fixed natural laws. We, there-
fore, conclude that the planets, formed as required by the Nebu-
lar Hypothesis, should all be found to rotate on natural ax^s.

44. After the parts of the broken-up rings had united, and
the resulting bodies commenced their rotatory motion, the cooling
of the masses, in consequence of the radiation of heat, would
cause their rotatory velocities to be increased, and this process
would continue till, in most instances, a secondary ring would
be abandoned by such planetary bodies." The outer planets be-
ing larger and much less dense than the inner ones, would aban-
don several secondary rings. In reference to the number of these
secondary rings cast off by each of the planets, all that we can

*• We have attempted here to be guided by strictly reasonable concluaiods, with-
out any reference to the phenomena of the Solar System.

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D. Trowbridge on the Nebular Hypothesis. 31

at present conclude on, with any degree of certainty, is, that the
number should, npon the whole, increase from the sun outward,
"We cannot, at present, say that the outermost planet ought to
have abandoned the greatest number of rings. These secondary
rin^ would, in general, break up and form secondary planets, or
satellites. Under certain conditions — such as Prof. Peirce has
found to exist in the System of Saturn — a ring, or rings might
remain entire, or at least, not break up into a -single satellite.
According to this view, rings, if they exist, must be found in-
terior to several satellites. In every case — unless changed by
disturbing forces — the planet should rotate on its axis in less
time than is required for any ring or satellite to revolve around
the primary. The same must hold in the case of the sun and
the planets.

45. When the last ring has been abandoned by any one of
the planets, the remaining part** must cool down and thus form
a primary planet. The outer portions being exposed to the low
temperature of space — at least 50° below zero Fah. — they will
cool much more rapidly than the inner parts, and after the
whole is reduced to a liquid, a crust would, comparatively soon,
form around the liquid planet, and further radiation would take
place very slowly compared with its former rate. A certain
amount of heat would be received from the other bodies, partic-
ularly the sun, (whatever might be its condition), and finally a
balance would be reached beyond which the planet would not
cool, — or at most very slowly, — and thus the inner parts would
remain liquid. The outer planets being from the beginning less
dense than the others, a crust would, perhaps, be formed so com-
paratively early as to leave the mean density of the planet com-
paratively small. We should, therefore, look for an increase in
mean density from the outermost planet to the innermost. We
see no reason, however, to believe that any simple law regulates
this variation of mean density from one planet to another.

46. It would at first seem as if the satellites of the primaries
should follow the same law of rotation that the primaries them-
selves do ; but we must recollect that the numbers representing
the distances of the former, expressed in radii of the latter, may
differ very considerably from the numbers representing the dis-
tances of the latter expressed in radii of the sun. Again, the
rings from which the satellites were formed, were abandoned
when the primaries were much reduced in temperature, and con-
densed, when compared with the condition of the primary rings

• *• In the Nebular Hypothesis, after a fluid body has abandoDcd all the ringg pos-
Bible, there mutt remain a central body of comparatively large dimensions, and of a
mass far greater than the sum of the masses of all (he rings separated. Hov
would the Jiuthor of the meteoric theory as g^ven in the 204th number of the Korth
American Review, account for the fact that our Solar System is constructed npoo
this principle !

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32 jD* Trowbridge on the Nebular Hypothesis.

when they were separated from the primitive solar spheroid. All
the satellites will be much smaller than the primaries; and,
being comparatively small bodies, they will cool down and be-
come solid much sooner than the primaries will. In conse-
quence of the forces acting on the planets, both primaries and
secondaries, they will become spheroidal in shape as soon as the
rings from which they are made are broken up and the parts
united. The attraction of the primaries on the fluid satellites,
will raise the fluid particles into great tidal- waves ; and as the
waves on opposite sides are slightly unequal, the result will be
a retardation of the rotatory velocity of the secondaries. William
Ferrel, Esq., of the Nautical Almanac OflSce, Cambridge, Mass.,
has given** a mathematical discussion of the retarding eflFect of
the tides of the earth on its rotatory velocity. According to his
conclusions, the retarding effect of the earth upon the moon's ro-
tatory velocity, both acting under similar circumstances, would
be between 500 and 600 times as great as that of the moon on
the earth's. According to his results, it would amount to an entire
circumference of the moon, or one period of rotation of the
moon in a hundred years. Even if these numbers be wide of
the truth, the investigation shows us that, in general, the retard-
ing effect of the attraction of the primaries on their secondaries,
when in a fluid state, is sufficient, in the course of immense ages,
to reduce the periods of revolution and rotation of the latter to
isochronism. We have, therefore, great reason to suppose that
as a general rule the satellites turn on their axes but once during
a revolution around their primaries.

47. If there exists a cosmical ether, as is at present pretty gen-
erally admitted, in order that it may remain spread throughout
universal space, it is only necessary for it to possess an elasticity
80 great that the action of luminous bodies is sufficient to pro-
duce a mechanical action in it that will enable it to maintain its
temperature and fluid condition under all circumstances. This
cosmical ether being material in its nature, it would necessarily
partake of the motion of those bodies with which it remains in
contact for immense ages of time. In the Solar System, the mo-
tion of the ether around the sun would be in the general direc-
tion of all the planets. It would also be regulated in its motion

** GouliTs Ast Joarnal, iii, 188-141. Professor Ferrel informs me that some
nambers which be employed he now knows to be about ten times too large, and

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