intense heat was, as we have already said, a natural consequence of the
mistaken notions of the nature of heat at that period; but that so many
astronomers should, up to the present day, think that the nebula must
have been intensely hot, even to the degree required to dissociate the
meteorites of which they conceive it to have consisted, seems to us to
be almost inconceivable. We believe we have shown abundantly plainly,
that there could have been almost no heat in the primitive nebula,
because there was hardly any cosmic matter to hold it in. We have given
as proof of this the laws of gases recognised and accepted by every
scientist, according to which a gas cannot contain a stated amount of
heat except it be at a pressure corresponding to that temperature,
that is, unless it is subjected to conditions foreign to its natural
state. Therefore we must either persist in maintaining that there was
almost no heat in the original nebula, or we must throw the laws of
gases to the winds, for they all depend one upon another. There may be
nebulæ possessed of very high temperature, that of incandescence for
example, but certainly the nebula out of which the solar system was
made, could not have contained more heat than what we have shown it had
at the various stages through which we have carried it. If there be
nebulæ at the temperature of incandescence, they must be possessed of
densities, or pressures, corresponding to that temperature. A few pages
back we have spoken of the impossibility of two grains of matter 90
feet apart, raising, by mutual collisions, their temperature and that
of the space occupied by each to the temperature of incandescence, and
if we now substitute for them meteorites of a pound weight each, the
space occupied by each of them will be a cube of 1670 feet to the side,
which does not help us in any way to believe that the spaces occupied
by them could be heated up by their collisions, so as to shine with the
temperature of incandescence. So we get no help from meteorites.
Some people evidently seem to think that nebulæ can be incandescent
and give the spectrum of incandescent gas, without their density or
pressure being increased to the corresponding degree. Sir Robert Ball
seems to be one of them, though at the same time he appears to be not
altogether sure of it. When discussing the self-luminosity of the
nebula in Orion, in his "Story of the Heavens," Ed. 1890, p. 465, he
says: "We have, fortunately, one or two very interesting observations
on this point. On a particularly fine night, when the speculum of the
great six-foot telescope of Parsonstown was in its finest order, the
skilled eye of the late Earl of Rosse and of his assistant, Mr. Stoney,
detected in the densest part of the nebula myriads of minute stars,
which had never before been recognised by human eye. Unquestionably
the commingled rays of these stars contribute not a little to the
brilliancy of the nebula, but there still remains the question as to
whether the entire luminosity of the great nebula can be explained, or
whether the light thereof may not partly arise from some other source.
The question is one which must necessarily be forced on the attention
of any observer who has ever enjoyed the privilege of viewing the great
nebula through a telescope of power really adequate to render justice
to its beauty. It seems impossible to believe that the bluish light of
such delicately graduated shades has really arisen merely from stellar
points. The object is so soft and so continuous--might we not almost
say ghost-like?--that it is impossible not to believe that we are
really looking at some gaseous matter."
Here we see that his own belief about the matter is not very firm. He
admits that the stars contribute not a little to the brilliancy of
the nebula, and the most he can say in favour of its shining with its
own light is, that it seems impossible to believe that the light has
arisen merely from stellar points. He then goes on to show how the
self-luminosity may be explained, as follows:--
"But here a difficulty may be suggested. The nebula is a luminous body,
but ordinary gas is invisible. We do not see the gases which surround
us and form the atmosphere in which we live. How, then, if the nebula
consisted merely of gaseous matter, would we see it shining on the far
distant heavens? A well-known experiment will at once explain this
difficulty. We take a tube containing a very small quantity of some
gas: for example hydrogen; this gas is usually invisible; no one could
tell that there is any gas in the tube, or still less could the kind of
gas be known; but pour a stream of electricity through the tube, and
instantly the gas begins to glow with a violet light. What has the
electricity done for us in this experiment? Its sole effect has been
to heat the gas. It is, indeed, merely a convenient means of heating
the gas and making it glow. It is not the electricity which we see, it
is rather the gas heated by the electricity. We infer, then, that if
the gas be heated it becomes luminous. The gas does not burn in the
ordinary sense of the word; no chemical change has taken place. The
tube contains exactly the same amount of hydrogen after the experiment
that it did before. It glows with the heat just as red-hot iron glows.
If, then, we could believe that in the great nebula of Orion there were
vast volumes of rarefied gas in the same physical condition as the gas
in the tube while the electricity was passing, then we should expect to
find that this gas would actually glow."
There is a great deal to be said about this explanation. We presume
that a very small quantity of hydrogen gas means that it was
considerably below atmospheric pressure. Even so we admit that by
introducing sufficient heat into the tube by means of electricity or
otherwise, the gas could be raised to the temperature of incandescence,
but its pressure would, at the same time, be increased to the
corresponding force measured in atmospheres; and we also admit that
when the gas was allowed to cool down to its original temperature, the
same quantity of hydrogen would be found in the tube; but how about
the tube? When the gas came to be at the temperature of incandescence
the tube would be the same, or very soon raised to it, and being
made of glass would be sufficiently plastic to be distorted, or even
burst by the pressure within, probably even before the gas reached
the temperature of incandescence. We must not forget that the first
appearance of incandescence begins with red heat whose temperature
is not far from 500° in daylight, and that white heat rises to above
1000°. If the experiment was made in an almost capillary tube,
sufficiently thick to prevent accidents, then it might appear to prove
a foregone conclusion, but nothing else; it might keep the idea of
pressure out of sight, but it could not prove that the gas inside was
in a rarefied state when incandescent. That the gas glowed the same as
a red-hot bar of iron has not been shown. The gas had to be shut up
in a tube to make it glow, but the bar of iron could glow outside of
the tube. Could a streak of hydrogen be put into a furnace along with
a bar of iron and heated to incandescence by its side, there might be
some fair comparison between them, as long as they were in the furnace
together, but the moment they were taken out the glow would disappear
from the gas, whereas the iron would glow for some time. On the other
hand we might _say_ that a stream of incandescent gas might be made to
heat a bar of iron in an oven to its own temperature, but the moment
the stream of gas and the iron bar were removed from the oven, the
former would disappear at once and the latter would continue to glow,
simply because it was dense enough to contain a very considerable
supply of heat compared to what the gas could, or rather, because the
pressure of the gas, even did it correspond to the temperature, would
disappear at once and the heat with it. So it is not always safe to
_say_ things. But it is quite safe to say that no gas--or substance
such as we are accustomed to look upon as gas--can abide in a state
of incandescence, and merely glow, unless its pressure, or density,
corresponds to the temperature of incandescence; which for red heat (in
the dark) would be 370° = 2·35 atmospheres, and for white heat at 1000°
= 4·65 atmospheres, above absolute zero of pressure in both cases. And
also, that if the self-luminosity of a nebula arises from incandescent
gas, the pressure in the gas of that nebula must be somewhere between 2
and 5 atmospheres above absolute zero of pressure. Now we have shown,
at page 85, that the density and pressure in the solar nebula, at the
stage there specified, could not have been more than the 403 millionth
part of those of our atmosphere, and consequently were justified in
asserting that in it there could be almost no heat whatever.
We have just been speaking of a streak of gas and a bar of iron being
heated in an oven to a red or white heat side by side, but everybody
knows that this could not be done; but everybody has not thought of
why it could not be done, otherwise Sir Robert Ball would not have
favoured us with his laboratory experiment of a streak, or remnant, of
hydrogen in a glass tube. We know that a plate, or bar, of iron can be
heated up to the temperature of incandescence in an oven, but it has
never occurred to anyone, who has seen the thing done, that the gas,
air, or vapour which heats them must be at a pressure corresponding
to that temperature. Multitudes of people may have thought of how the
thing is done, but apparently very few have thought that it is not the
gaseous part of the current of heated matter introduced into the oven,
that heats it and the metal in it, but the solid part which is the
distinctive and most important part of the constituents of the current.
The solid part of the matter--let it be gas or any other element--is
heated to incandescence in some furnace and carried along by the
gaseous part--that is the _stuff_ that fills the empty spaces between
the solid molecules--to give it out to the oven and iron. We are not
sure that the gaseous part even glows. We see plainly enough that
the walls of the oven glow, but with respect to the gas, or carrying
agent, we are inclined to think that it rather dims the glow of the
oven and iron than otherwise. In passing, we say it is not unreasonable
to suppose that the solid matter which contained the heat till it was
given out, consisted of the elements which were put into the furnace
to raise the heat, and of those which were drawn in by the draught--in
a word, the elements of combustion--but about the carrying constituent
there is a great deal to be said after we know more about it. It seems
to us from all this that the hydrogen gas in Sir Robert Ball's tube was
not made to glow by heating up to the temperature of incandescence,
but somehow by the electricity passing through it, if it did pass.
We, therefore, come to the conclusion that the light of nebulæ does
not come from gas--or what we call gas--heated up to be incandescent
merely to make it glow, and that it might be as cold as the light that
comes from the aurora, or as that of a glow-worm. Sir Robert Ball
refers to stellar points seen through the nebula, and acknowledges that
part of the glow may be due to them, which shows that the nebula must
have been excessively tenuous; for we know how thin a cloud will hide
Sirius from us, and we think that nobody will assert that two grains
of matter dispersed in 1,426,445 cubic feet of space, as we have seen
at page 86, would hide Sirius from us. Therefore, we must acknowledge
that the glow of nebula in Orion, observed by Sir Robert Ball, was
caused either by the stellar points, or by some other thing that most
assuredly could not be gas heated to the temperature of incandescence,
or in part from both. For we believe that the glowing of nebulæ,
fluorescence, phosphorescence, Will-o'-the-wisp, auroras, fire-flies,
fire-on-the-wave, etc., etc., all, all proceed from the same cause.
We may now proceed to say a few words about the separation of the rings
for the planets, brought about by the rotation of the nebula on its
axis, and the centrifugal force produced throughout it thereby. We have
shown, at page 88, that a ring could not be detached from the nebula
at once in one large annular mass, as it seems to have been the common
notion was the mode of separation; and we shall now try to show with
some detail what the process must have been, notwithstanding that it
has been in a general way described by others; because, like everything
else, there is something to be learnt from it. For this purpose we
shall select what we have called the Jovian nebula, because we can
suppose, for the present, it must have been more nearly in the form
of a sphere than either the original or any of the exterior nebulæ,
which may not have been properly licked into shape, as it were; and
also because we have found that the thickness and mass of the ring
for his, Jupiter's, system were vastly greater than those for any
other one of the planets. We have made the Jovian nebula to have been
1,370,800,000 miles in diameter, and the greatest thickness of the ring
detatched from it to have been 1,406,771 miles. Now in a circle of
that diameter, a chord of the length of that thickness would subtend
an arc of very little more than 7 minutes, one half of which we shall
suppose to be measured on each side of the equatorial diameter of the
nebula at right angles to the diameter; then, the middle ordinate of
a chord of 1,406,771 miles long, would be 359 miles long. This length
would be a very small fraction of the radius of the circle which
would be 685,400,000 miles long, but in a rotating sphere of the same
dimension, we must acknowledge that the centrifugal force at the middle
of the arc would be greater--however small the difference--than at
its ends, and would sooner come to balance the force of gravitation;
therefore we must admit that the process of separation would begin
there by abandoning a thin layer of matter, convex on the outer side
and in a measure concave on the inner side, for the reason just
given, much the same as a layer that could be peeled off from the
equator of an orange--the poles and equator of an orange are easily
distinguished. As the velocity of rotation increased another layer
would be abandoned following the first, so far curved on both sides,
i.e. convex and concave, and the same process would continue on and
on, according as the centrifugal force continued to balance that of
gravitation, till the whole of the matter for all the attendants of
the sun was abandoned; so that in the process itself no such division
of rings as we have been following could have taken place, but one
continuous sheet, as it were, would be formed from first to last.
Whether the thickness of the ring for Jupiter's system, or any other
system or planet, was limited to the length of the chord we have been
dealing with, or came to be many times greater or even less, makes no
difference on our explanation. After being abandoned in a sheet, as we
have shown it would be, the centrifugal force they had acquired would,
for a time at least, keep the particles of the sheet near the radial
positions they then occupied, and their mutual attraction would go on
diminishing its thickness, till finally the radial attractions among
the particles divided the sheet into entirely separate rings after the
manner of those of Saturn; which would in due course break up and form
themselves into the smaller nebulæ from which the planets were supposed
to have been made.
M. Faye has made it a great point against the nebula hypothesis that
when these rings broke up, the rotary motions of the planets resulting
from them would be retrograde, because the outer parts of them would
be travelling at a slower rate than the inner ones, and has taken the
trouble to construct a diagram to show how this would be the case;
but he himself has told us, in "L'Origine du Monde," that Laplace had
duly considered this point, and had shown how the friction of the
particles of the flat rings among themselves would, through course of
time, retard and accelerate each other, so that a ring would come to
revolve as if it were one solid piece, and consequently that the outer
edge of the ring would come to be travelling faster than the inner
one, which according to his (M. Faye's) own showing would produce,
on breaking up, a planet with direct motion of rotation. Laplace's
words, as cited by him, are:--"Le frottement mutuel des molécules de
chaque anneau a dû accélérer les unes et retarder les autres jusqu'à ce
qu'elles aient acquis une même mouvement angulaire. Ainsi les vitesses
réelles des molécules éloignées du centre de l'astre out été plus
grandes. La cause suivante a dû contribuer encore à cette différence
de vitesse: les molécules les plus distantes du soleil et qui, par les
effets du refroidissement et de la condensation, s'en sont rapprochées
pour former la partie supérieure de l'anneau out toujours décrit les
aires proportionnelles aux temps, puisque la force centrale dont elles
étaient animées a été constamment dirigée vers cet astre; or cette
constance des airs exige un accroissement de vitesse à mesure qu'elles
s'en sont rapprochées. On voit que la même cause a dû diminuer la
vitesse des molécules qui se sont élevées vers l'anneau pour former sa
partie inférieure."
In his method of bringing all the molecules of matter in a ring, to
revolve round the centre as if they formed one sole piece, Laplace does
not appeal to any accommodating force among them except friction, while
he might have called in that of the collisions of the molecules amongst
themselves. It is not to be supposed that each molecule would remain
fixed in the position it occupied when separated from the nebulæ,
and only went on rubbing against--and creating friction with--its
neighbours, and only creeping closer to the centre or farther from it,
as it was acted upon by the attraction of the other parts of the ring.
The molecules would be rushing against each other in all directions,
in spite of, although in the main obedient to, the law of attraction;
and we could conceive the possibility of molecules gradually working
their way from the extreme outer edge to the extreme inner edge of a
ring, or _vice versâ_, which would be a much more effectual means of
bringing about one period of revolution throughout the whole ring, than
the simple force of rubbing against each other. When physicists get a
gas shut up in a close vessel, they grant to its molecules the power of
committing exactly the same kind of freaks; and a planetary ring is,
to all intents and purposes, a closed vessel to our molecules; because
they have been placed in it by the laws of attraction and centrifugal
force, and there is no other force acting upon them sufficiently
powerful to liberate them from it. Therefore there is no reason why a
molecule in a ring should be always wedged up in one place, especially
after we have shown that each molecule of matter, in any of the rings
we have been dealing with, must have had a much greater free path to
move about in, than a molecule of gas shut up in any of the vessels
used by physicists.
We have no reason to look upon the rings of Saturn otherwise than
as in process of being converted into one or more satellites, most
probably more than one; because if the matter they are composed of has
been separated from the planet in the form of a sheet, the same as we
have seen must have been the case with the matter separated from the
original nebula for the planets, the sheet has been already divided
into at least three distinct parts, and surely that cannot have been
done without some object. If these rings have been left, as has been
said, in order to show us how the solar system has been formed, that
does not authorise us to conclude that they will always remain in the
form they have. There is no reason why the lesson should not be carried
out to the very end, through the breaking up of the rings, formation of
spherical nebiculæ, and finally satellites. It would be rash to assert
that the matter of which any one of them is composed--be it atoms,
molecules, meteorites, or brickbats--cannot, through friction and
collisions of its particles among themselves, come to revolve around
Saturn as if it were one solid piece. But should anyone do so, and
adopt M. Faye's condemnation of Laplace's mode of forming rings, he
must confess that when Saturn's rings are converted into satellites,
their rotations must be retrograde; and it might be, for him, an
interesting inquiry to find out whether the rotations of the existing
satellites are direct or retrograde.
Astronomers have learnt the lesson as far as it has gone, have
noted and registered the state of affairs as it is at present, and
their successors will no doubt do the same as changes succeed each
other. The day may be inconceivably remote, but it will inevitably
come for the rings to be changed into satellites, unless they are
disposed of in some other way. It has been said that were the rings
to break up, in consequence of their being in a state of unstable
equilibrium, they would fall back upon the planet, but that would
depend on circumstances. If the motion of their revolution were stopped
altogether, they would certainly fall back upon the planet; but if it
were not stopped then each molecule would retain its centrifugal force,
and would revolve around the primary on its own account, just as,
according to very general opinion, it does at present. We do not see
why, or for what purpose, these rings could have been separated from
Saturn merely to fall back upon him again. It would be rather a strange
way of giving a lesson if it were stopped, by a cataclysm of some
kind, just when the most interesting part of it was in a fair way of
being exhibited. Such a proceeding would assuredly not suit the ideas
of those who believe that the solar system has been self-formed by a
simple process of evolution.
During the whole process of separation of rings from the original
nebula, the nebulous matter would be abandoned in what we may call the
form of thin hoop-shaped rings, so that the equatorial region of the
nebula would be flat--as we have shown at p. 115--and when the nebula
came to be so much reduced that it could abandon no more matter through
centrifugal force, its form would be, in some measure, like that of a
rotating cylinder terminating at each end in a cap in the form of a
segment of a sphere. When explaining the formation of planetary rings,
we have seen that in the Jovian nebula the length of the flat part
would have come very soon to be nearly 1,500,000 miles, and that it
would increase rapidly. But, remembering that the flattening of the
equatorial part must have begun on the original nebula, we see that
the flat part must have increased vastly in length before it reached
Jupiter, and that by the time the residuary, or solar, nebula was
reached--which we made to be only a little over 63,000,000 miles in
diameter--the cylindrical part of it would bear no small proportion
to that diameter. Taking this form of the nebula into consideration,
and also the fact that the separation of matter from it by centrifugal
force could not always be absolutely equal all around it, the swaying
in its rotary motion produced by the all but inevitable inequality
of mass, at the two ends of the cylindrical part, and at the sides
of the segmental caps, may have been the cause of the differences in
the inclinations of the orbits of the planets to the ecliptic; and
especially of why the difference came to be so much greater in the case
of Mercury than in any of the others.
In connection with this very reasonable conclusion as to the form of
the nebula almost from the beginning, we may add that, when it ceased
to throw off rings, it would be very much in the same condition as
Saturn is at the present day. Therefore we may conclude with very great
safety, that the present form of Saturn is that of a cylinder with
segments of spheres forming the ends; and in this manner can account
for his square-shouldered appearance, which has puzzled more than one
astronomer.
The idea has been very general that in condensing and contracting, the
nebula would gradually come to assume the form of a lens of a very
pronounced character, from the circumference of which the rings would
be abandoned one after the other; but when thoroughly looked into, it
is difficult to see how this could be the case. In a sphere of cosmic
matter contracting equally all round towards the centre through the
force of attraction, it is more natural to suppose that the separation
of matter from its equator through centrifugal force, would have
a tendency to diminish the equatorial more rapidly than the polar
diameter, as we have been trying to show above, more especially as
the attraction of the matter in the rings as they were abandoned one
after the other would, in a constantly increasing degree, assist the
centrifugal force in facilitating the separation by drawing the matter
outwards. Matter falling in from the polar regions would afterwards
require to have its motion turned off at right angles before it could
be sent off by centrifugal force to the equator, an operation which
would be more easily effected in the equatorial regions, where the
gravitating motion had only to be retarded; and as very unequal amounts
of density could not be created in the interior parts of such a sphere
by gravitation, so as to cause pressure outwards, it is difficult to
show how the polar diameter could be more rapidly reduced than the
equatorial diameter, which was being continually shorn of its length.
It may be said that all that we have been writing in the last few pages
is absurd, because we have been proceeding on the supposition that
the condensation of the nebula was effected at or near its surface.
Laplace procured this condition by piling up imponderable heat in his
nebula, but he might have got it otherwise. Given a nebula such as
the one we are dealing with of 6,600,000,000 miles in diameter, where
would condensation be most active? Most undoubtedly where there was the
greatest mass of matter. Compare, then, the mass of 1,000,000 miles
in diameter at the surface with the mass of the same diameter at the
centre, and we cannot hesitate for a moment in concluding that the most
active condensation would not be very far from the surface. Not only
so, but the same would continue to be the case, at least until the last
ring was abandoned. Thus by working upon what may have appeared to
be an absurd foundation, i.e. condensation at the surface due to the
intense heat of the nebula, we have been able to acquire more correct
ideas than we had before, of how the solar system was elaborated. But
we shall have much more to say on the same subject hereafter.
There has been a great outcry raised about the rotation of the planets
Neptune and Uranus being retrograde, as is correctly concluded to be
the case from the revolution of their satellites being retrograde, but
we do not see that there has been any good reason for it. Laplace,
no doubt, concluded, wrongly, that the motions of all the bodies of
the solar system--as known to him--were direct, and therefore used
that conclusion in showing that there were 4000 milliards against 1 in
favour of his hypothesis being right; but at the same time it cannot be
concluded that he thought that it would be destroyed by the motion of
rotation of one or even several of the forty-three bodies turning out
to be retrograde; because, when discussing the hypothesis of Buffon,
he states, most distinctly, that it is not necessary that the rotation
of a planet should be in the same sense as that of its revolution, and
that the earth might revolve from east to west, and at the same time
the absolute movement of each of its molecules might be directed from
west to east. His words as cited by M. Faye in "L'Origine du Monde,"
at page 158, are: "A la verité, le mouvement absolu des molécules
d'une planète doit être alors dirigé dans le sens du mouvement de
son centre de gravité, mais il ne s'ensuit point que le mouvement de
rotation de la planète soit dirigé dans le même sens; ainsi la Terre
pouvait tourner d'orient en occident, et cependant le mouvement absolu
de chacune de ses molécules serait dirigé d'occident en orient, ce qui
doit s'appliquer au mouvement de révolution des satellites, dont la
direction, dans l'hypothèse dont il s'agit, n'est pas nécessairement la
même que celle de la projection des planètes." He seems to say, "This
would suit Buffon's hypothesis, but I do not require it for mine." Even
were this not so, it would not be very difficult to account for the
retrograde rotation of these two planets, but we are not yet prepared
to show, in a convincing manner, how these motions were produced. We
have to show first how the nebula itself was brought to the dimensions
at which we took it up, and there is a great deal to be done before we
can show that.
Should our belief in being able to explain how the retrograde rotations
of Uranus and Neptune were brought about turn out to be unacceptable,
we would not condemn the nebular hypothesis, because, as M. Faye
himself says, if we add the asteroids to Laplace's 43 we should have
somewhere about 500 bodies, all with direct motion, agreeing with the
hypothesis, against 4 that do not, that is about 125 to 1 instead of
43 to 1, which was all Laplace could claim. Moreover, we have not been
able to see that M. Faye's objections to it are well founded, rather
the contrary; nor can we agree with him when he says that when one
point in a hypothesis is found to be erroneous it ought to be abandoned
altogether, and something better sought for. Is his something any
better? All acquired knowledge has been built up from ideas collected
from all sides, and from errors reformed. What would a grammarian say
were we to return to him his grammar as useless, because we had found
one exception to one of his rules against 125 cases in which we had
found it to be right? Perhaps it would put him in mind of the name
of a tree. And grammar is not the only case in which we say that the
exception confirms the rule.
In taking the nebula to pieces, we have taken no notice of the
satellites of Mars, not only because they are so small that they would
have had no sensible effect on our calculations, but because we cannot
conceive that they could have been abandoned by the planet, when in a
nebulous state, in the same manner as the planetary rings are supposed
to have been by the parent nebula; and we might simply refer to the
dimensions, especially the thinness, we have found for the ring out
of which Mercury was formed, for proof of our assertion; but for
more satisfactory corroboration, we will go a little deeper into the
affair. Let us take the diameters of Mars and of the orbits of his
satellites, as they are stated in text-books of astronomy; that is
2957, 11,640 and 29,200 miles respectively, and suppose the diameters
of what--in the method we have applied to the planets--we would call
the Deimos and Phobos nebulæ to have been 40,000 and 20,420 miles also,
respectively; then these two diameters would make the breadth of the
ring for the formation of Deimos to have been 9790 miles. With these
data, if we go through a series of calculations with respect to this
outer satellite, in all respects similar to those we have made for each
of the rings of the planets, we shall find that the ring for Deimos
would have been only 5·64 _inches_ thick, without taking into account
its condensation during the process of separation. This, of course,
points out at once the impossibility of any such operation going on in
Nature. We can imagine the possibility of a ring of even millions of
miles broad, and of very great tenuity, holding together provided it
be hundreds of thousands of _miles_ thick, but to think of one 10,000
miles broad and less than 6 _inches_ thick holding together is another
affair altogether. With respect to Phobos, it is only necessary to say
that he revolves round Mars in considerably less than one-third of the
time that he ought to, and is therefore not a legitimate production
of the nebular hypothesis any more than Deimos can be. Here, then, we
have come upon two bodies, one of which has not been formed in the way,
and the other has not the proper motion, prescribed in the hypothesis;
but we do not think ourselves justified in declaring it to be worthy
of condemnation on that account, seeing that we have found no other
difficulty in working out the solar system from it.
Moreover, it is not impossible, nor do we think it at all improbable,
that through the course of time astronomers may discover that Phobos
is a captured asteroid--perhaps Deimos also--gradually working its
way into final annexation. And who can tell how many of these erratic
bodies Jupiter and Mars may have captured already? In the dark as it
were, for they may have been too small to be noticed when they were
being run in. Neither of these two worthies has ever been very much
celebrated in song or history for respect for his neighbour's property.
Jupiter is credited with sorting out the asteroids and arranging them
in bands, and perhaps he has been human enough to exact a commission
for his labour; and it might be more in his line, and certainly much
more easy for Mars, to take forcible possession of as many of them as
came within his reach.
CHAPTER VII.
PAGE
126 Analysis continued. No contingent of heat could be imparted to
any planet by the parent nebula.
127 Only one degree of heat added to the nebula from the beginning
till it had contracted to the density of 1/274th
of an atmosphere.
127 Increase in temperature from 0° to possible average of 274°
when condensed to 4,150,000 miles in diameter.
128 Time when the sun could begin to act as sustainer of life and
light anywhere. Temperature of space.
129 The ether devised as carrier of light, heat, etc. etc. What
effect it might have on the nebula.
130 First measure of its density, as far as we know.
133 The estimate _too_ high. May be many times less.
134 Return to the solar nebula at 63,232,000 miles in diameter.
134 Plausible reason for the position of Neptune not conforming
to Bode's Law. The ring being very wide had separated
into two rings.
135 Bode's law reversed. Ideas suggested by it.
137 Rates of acceleration of revolution from one planet to another.
138 Little possibility of there being a planet in the position
assigned to Vulcan.
138 Densities of planets compared. Seem to point to differences
in the mass of matter abandoned by the nebula at
different periods.
139 Giving rise to the continuous sheet of matter separating into
different masses. Probably the rings had to arrive at a
certain stage of density before contracting circumferentially.
140 Possible average temperature of the sun at the present day.
Central heat probably very much greater.
140 Churning of matter going on in the interior of the sun, caused by
unequal rotation between the equator and the poles.
Coming back to the period when we reduced the residuary nebula to the
density of our atmosphere with temperature of 0°, or freezing water, we
can with confidence affirm that none of the rings abandoned by it for
the formation of planets, could have carried with them any contingent
of heat to help them in their formation--any beyond the temperature
of space--for even if they did it would very soon be reduced to
that. Each one of them in condensing, breaking up, rejoining the
broken fragments, converting itself into a minor nebula, and finally
constituting itself as a planet, must have accumulated in the process
its own heat requisite to convert it into a molten liquid globe--a
stage of existence through which they are all, that is, the major
planets, acknowledged to have passed, or have to pass. During that
process its primitive annular form, and the multitude of fragments into
which each one of them broke up, would present sufficient radiating
surface, not only to dispose of all the heat it could have brought with
it from the nebula, but a considerable part of the little it could
create for itself while contracting and condensing. We may even go
farther and assert that no one of them would have any necessity for
being supplied with extraneous heat until it had, in a great measure,
exhausted the stock it had produced for itself, or so far as to cool
down from the molten liquid to the solid state, and to the stage when
vegetable and animal life could exist upon its surface. We have no
reason for supposing that an enormous supply of extraneous heat was
crammed into each nebula, merely to be radiated into space before
condensation could take place, and thus retard the execution of the
work in hand. If there are astronomers or physicists who believe that
the sun could not acquire by gravitation, all the heat he must have
expended during geological time, they must look for it in some other
source than that of useless and impossible cramming.
Hitherto we have said nothing of heat being radiated into space by the
nebula during our operations, because there could be almost absolutely
none to radiate from it at 0° of temperature. No doubt there is a
large range between this and the absolute zero of temperature which is
-274°; but we have seen, at page 99, that when the nebula was condensed
from 403,000,000 to 274 times less dense than air, only _one degree_
was added to its temperature--that is, it was raised from -274° to
-273°--and that these -273° of absolute temperature were added to it
in its condensation from being only 274 times less dense than air to
atmospheric pressure, when its temperature became 0° of the ordinary
Centigrade scale. Therefore the only period when there could be any
measurable radiation of heat into space would be between the times
when the diameter of the nebula was (see Table III.) between 58,000,000
miles and 9,000,000 miles. Even when the end of this period came, the
temperature, after a contraction of 49,000,000 miles in diameter, would
be only -1° raised to 0°--in other words -273° raised to 0°--and that
would not furnish much positive heat--heat such as we are accustomed
to deal with--to be radiated into space, whose temperature is without
doubt somewhat warmer, so to speak, than -273°. And let us repeat, and
fix it in our memory, that this -273° was equal to only 1° of positive
heat.
If we now suppose the nebula to be condensed to one-tenth of its
volume, with consequent density of 10 atmospheres, and corresponding
diameter of about 4,150,000 miles, its temperature would be 2740° of
the ordinary Centigrade scale--according to our mode of calculating
hitherto--provided no heat had been radiated from it into space in the
meantime. Of course this could not be the case, but we have no means of
calculating what the amount of radiation would be, and it will not make
much difference on our operations to take no notice of it. However,
it is here necessary to take into consideration that 2740° would be
the average temperature of the nebula; consequently, if condensation
was most active where the greatest mass was, which certainly could not
be at the centre or even near it, there also heat would be produced
most rapidly, from whence it would spread towards the centre and
surface. From the centre it would have no outlet, and would accumulate
there as condensation advanced; whereas from the surface it would be
radiated into space, and would tend to decrease in amount, so that we
may conclude that the surface must have been considerably colder than
the centre. If to this we add the fact that, in order to get to the
surface, heat would have to be conducted, or conveyed by currents; over
from one to two millions of miles, it becomes all the more certain
that the central heat would be very much greater than that of the
surface. How much less it would be at the surface we cannot pretend
to calculate, but we may suppose it to have been from one-fifth to
one-third of the average, or rather, somewhere between 370° and 1000°,
which we have taken, at page 110, to be the temperatures of red-heat
and white-heat. And thus we come to find that the nebula, which was
supposed to be endowed with excessive heat when it extended far beyond
the orbit of Neptune, could not have radiated either heat or light into
space to much purpose, until it had been condensed into not much more
than 4,000,000 miles in diameter. This then we must acknowledge to be
the earliest period at which the sun began to act as the life sustainer
of his system; because, even were it to be found that there are other
planets revolving within the orbit of Mercury, which we do not think
very probable, we have seen that he could have no light or heat with
sufficient vivifying power to radiate to them, till his diameter was
reduced to not far from what we have shown above. Even then the sun
would most likely be very much less brilliant than he is now, but the
light may have been sufficient to promote vegetation on Mars--or the
earth, if it was sufficiently cooled down from its molten state--and
not much heat would be required by him, as there would probably be
a remnant of his own interior heat, still sensible at the surface,
sufficient for vegetation at least.
We have had occasion to refer several times to the temperature of
space, and, though we cannot pretend to determine what it is, our
operations enable us to show that it must be very much less than
any estimate of it that has ever come under our notice. The nearest
approach made to absolute zero by M. Olzewski, in his experiments on
the liquefaction of gases, as reported in the "Scientific American" of
June 2, 1887, was -225°, or so-called 49° of absolute temperature,[D]
which would correspond to a density of 0·1788 of an atmosphere. This
could not be the density of space, because it can be easily shown that
our nebula, when at the same density, must have had a diameter of about
29,000,000 miles, and we must admit that were a globe of this diameter
rotating in a medium of its own density, the friction between the two
would have been so great as to put a stop to the rotation before very
long. We may even say that distinct rotation could never have been
imparted to it. Following the same reasoning, we must acknowledge that
the density of space must be much lower than that of our original
nebula, if that could be, and therefore we can assert with confidence
that the temperature of space must be far below -225°.
[D] From the same source, date June 6, 1896, we learn that the greatest
cold probably ever reached was -243·5° or 31·5° of so-called absolute
temperature, but that will have very little effect on our calculations,
and so it is not worth while altering them all to suit.
Here our operations put us in mind that we have said nothing yet about
the ether, or what effect it might have on our nebula and the bodies
formed out of it. We have not done so for the simple reason that, with
one exception, it has never been taken into account in any scientific
work that has come into our hands, except so far as its being called
upon to perform the offices of a dog that has been taught to carry
and fetch, and we have not known how to deal with it. But as we have
come along, we have seen that it must have had something to do with
the density, and consequent temperature, of all the bodies we have
been dealing with, and that, if properly studied, it may enable us to
account for some things that we have never seen, to our mind, properly
explained. We know that it was devised, or conceived of--somewhere
between thousands of years ago and the birth of modern astronomy--as a
medium for carrying light, heat, and anything that was hard to move,
through space, or to where it was wanted to be moved, by its vibrations
or undulations, in the same way that sound is conveyed by wave motion,
or vibration, through air, water, and a multitude of bodies; and we
understand that some time during that long period it began to be looked
upon as a material substance. We are told that it is supposed to
pervade all bodies of all classes, but we think this idea must be taken
in a limited sense, because, whether it is combined with electricity,
as some suppose, or is only a carrier of electricity, a good conductor
must have a larger supply of it than a bad one, and an absolute
non-conductor, if there be such a substance, must contain none at all,
always provided the ether is the conducting or carrying power. We are
told also, that it is neither of the nature of a gas nor a liquid, but
may be of the nature of a jelly, and of its nature we shall have more
to say hereafter. It was natural that it should be conceived to be a
material substance, because if light and heat were to be carried from
one place to another by wave motion, as sound is by water and air,
then the medium for carrying it must be of the same nature as air and
water--or any other carrier of sound--that is, it must be a material
substance and, in consequence, possessed of some density or specific
gravity. The only place where we have seen any density assigned to it
has been, in a series of articles on the "Origin of Motion," published
in "Engineering" of 1876, where it is estimated to be 1/5,264,800th[E]
of the density of air. How this estimate was formed is explained in the
number for December 1, 1876, page 461, from which we make the following
very long quotation, because we look upon it as of great importance.
[E] Years after this was written we have seen it stated that the
density of the ether has been calculated from the energy with which
light from the sun strikes the earth, and that to represent it there
are twenty-seven cyphers after the decimal point before the figures
begin. But as this gives something like one thousand quadrillionth part
of the density of water, we refuse to accept or even think of it.
"Steel of the best quality in the form of fine wire has been known to
bear a tensile strain represented by not less than 150 tons per square
inch before breaking, and even this cannot be said to be the limit to
the tensile strength of steel, since the tenacity increases as the
diameter of the wire is reduced. Rejecting 'action at a distance,'
therefore, these molecules of the wire must be controlled by some
external agent, and therefore, the pressure of the external agent must
_at least_ equal the static value of the strain. The pressure of the
ether therefore cannot be less than 150 tons per square inch. Now,
since it is a known fact that the strain required to separate molecules
in 'chemical union' would be very much greater than in a mere case of
'cohesion,' it follows that the ether pressure must be greater than
the above figure. If we suppose the strain required to separate the
molecules of oxygen and hydrogen combined in the state of water (one
of the most powerful cases of chemical union) to be only three times
greater than in the case of the molecules of steel, then this would
give 450 tons per square inch as the effective ether pressure. It may
be taken as certain that the strain required would be greater than
this, as it has not been found possible by any ordinary mechanical
means to separate molecules in chemical union. However, as it is only
our object to fix a limiting value for the ether pressure, or a value
that is less than the actual fact, we will therefore take in round
numbers 500 tons per square inch as the total ether pressure, having
thus valid grounds for inferring that this estimate is within the facts
as they actually exist. The existence of such a pressure as this might
well be sufficient to strike one with astonishment and legitimately
excite incredulity, if it were not kept in mind that this pressure
is exercised against _molecules_ of matter, a perfect equilibrium of
pressure existing, so that it may be deduced with certainty beforehand,
that, however great this pressure might be, it could not make itself
apparent to the senses. The air exercises a pressure of some tons
on the human body without such pressure being detected, how much
more cause, therefore, is there for the perfect concealment of the
ether pressure, which is exercised against the molecules of matter
themselves. This great pressure is the absolutely essential mechanical
condition to enable the ether to control forcibly the molecules of
matter in stable equilibrium, and to produce forcible molecular
movements when the equilibrium of pressure is disturbed (as exemplified
in the molecular movements of 'chemical action,' etc.).
"It is generally admitted that the ether must have a very low density,
one reason being the almost imperceptible resistance opposed by it
to the passage of cosmical bodies (the planets, etc.) at high speed
through its substance. The pressure of an aëriform body constituted
according to the theory of Joule and Clausius, being less as its
density is less, it will therefore be necessary to show that the ether
can exert so great a pressure as the above, consistent with a very low
density. From the known principles belonging to gases, the pressure
exerted by an aëriform medium is as the _square_ of the velocity of
its component particles, and as the density. We will, in the first
place, consider what the density of the ether would be, if it only gave
a pressure equal to that of the atmosphere (15 lb. per square inch).
From the above principles, therefore, it follows that for the ether to
give a pressure equal to that of the atmosphere, the ether density will
require to be as much less than that of the atmosphere, as the _square_
of the velocity of the other particles is greater than the square of
the velocity of the air molecules. The velocity of the air molecules
giving a measure of 15 lb. per square inch is known to amount to 1600
feet per second. Taking, therefore, the square of the velocity of the
ether particles in feet per second, and the square of the velocity of
the air molecules and dividing the one by the other, we have the number
of times the ether density must be less than that of the atmosphere, in
order for the ether to give a pressure of 15 lb. per square inch, or we
have
(190,000 × 5280)^{2}/1600 = 393,120,000,000.
This result shows therefore that the density of ether, if it only
gave a pressure equal to that of the atmosphere, would be upwards of
390,000,000,000 times less than the density of the atmosphere. This
result expresses such an infinitesimal amount of almost vanishing
quantity, that the ether density might be well much greater than this.
We will now, therefore, consider what the ether density would be to
give a pressure of 500 tons per square inch. Pressure and density being
proportional to each other, it follows that for the ether to give a
pressure of 500 tons per square inch, the ether density would require
to be as much greater than the above value, as 500 tons is greater than
15 lb. Multiplying, therefore, the above value for the density by this
ratio, we have
1/393,120,000,000 × (500 × 2240)/15 = 1/5,264,800;
or this shows that the density of the ether to give a pressure of 500
tons per square inch would be only 1/5,000,000th of the density of the
atmosphere. This value representing a density less than that of the
best gaseous _vacua_ is therefore quite consistent with the known fact
of the extremely low density of the ether. It follows, therefore, as a
mathematical certainty dependent on the recognised principles belonging
to gaseous bodies, that the ether could exert a pressure of not less
than 500 tons per square inch consistent with such an extremely low
density as to harmonize with observation."
If the ether is possessed of a density equal to that shown above, then
the density of our original nebula must have been greater than what we
have shown it to be. The density we found for it was 1/403,000,000th
that of air, or 0·000000002481 of an atmosphere, and 1/5,264,800th is
equal to 0·00000019 of an atmosphere; if then we add these two together
we get 0·0000001925 of an atmosphere as the density of our nebula.
This comes to be very slightly greater than the density of the ether,
and shows that the estimate in the foregoing quotation is too high;
unless it is asserted that the ether can exert no frictional action
at all, which, we believe, no one has ever done; while the absolute
temperature of the nebula at the new density would be 0·000053°,
which would be a very small addition indeed to the 0·00000068°, we
found for it at first. On the other hand, when the nebula was reduced
to 29,000,000 miles in diameter the density of the ether would have
increased its density from 0·1788, which we showed it then to have,
only to 0·17880019 of an atmosphere, which would make no appreciable
difference on its temperature, and would be so immensely greater than
the 0·00000019 of an atmosphere of the ether that it could hardly
be supposed to have any effect in retarding the rotation of so much
heavier a body. And should it be found that the density of the ether
is 1/4, 1/3, or 1/2 less, or even a great deal more, than that shown
in the above quotation, it would only have proportionately less effect
on our nebula, in every sense, than what we have just shown. We may,
therefore, conclude that the introduction of the element ether has not
vitiated our operations in any way up till now, and we shall leave it
until we have acquired more knowledge of its nature and effects.
Although we have already condensed our nebula to somewhere about
4,000,000 miles in diameter, where we have shown it might begin to
radiate light--radiation of heat may have begun when the diameter
was ten times as great, or even before that--we propose to return to
the period when it had just abandoned the ring for the formation of
Mercury and was 63,232,000 miles in diameter, and became what we have
called the Solar nebula; because there is a good deal to be learned
from a careful study of our operations up to that period, and of what
must have taken place during further condensation up till the final
establishment of the sun such as it is at the present time.
When the planet Neptune was discovered, Bode's Law fell into disrepute
for a time, because the new planet was found to be much nearer to the
sun than, according to it, it should have been. All the other planets
occupied the places assigned to them within 5 per cent. of the exact
appointed distance from the sun, but Neptune turned out to be 22·54
per cent. out of his exact place, and hence the discredit thrown
upon the law. It was hard treatment for a servant that had helped so
unmistakably--as we know to have been the case--to the discovery of
the first four asteroids, which has afterwards been followed by the
discovery of a whole host of them, and that had been pressed into the
service for the discovery of the very planet which was the cause of
its discredit--but such is the world. However, first offences against
the law are generally looked upon with merciful eyes, and the Series
of Titius seems to have been so far received into favour again that,
some astronomers are said to have been looking out for another planet
farther off than Neptune, being convinced that there must be some
reason why a law that has shown itself to be right in eight cases
should be altogether wrong in the ninth. Here, we think that the most
likely explanation that can be given is, that the ring out of which
Neptune was formed divided itself, after breaking up, into two planets
instead of one, and that this is the reason why, Bode's Law could not
point out the true position of either of them. It is hard enough to
believe that the ring out of which Uranus was made--which we have seen
may have been 954,000,000 miles broad, and over 3,400,000,000 miles
in extreme diameter--could have united its fragments, after breaking
up, into one planet, and the difficulty of belief becomes greater the
greater the diameter comes to be. We have, in our work, considered the
breadth of Neptune's ring to have been 1,010,000,000 miles, but then
we limited the diameter of the nebula to 6,600,000,000 miles--we had to
draw the line somewhere--whereas it may have been a thousand million
miles greater, which would very greatly increase the probability of
two planets, perhaps even more, having been formed out of the ring.
If it has been so, the law could not apply to the case. A new Act was
required. Besides, it is not a law, never has been, but only a register
of facts; and we know that truths are often discovered from similar
registers. It registers, and at the same time shows, that there is a
nearly fixed inter-relation, even proportion, in the distances of the
planets from the centre of the sun as far out as Uranus; and were we
to make a similar register, beginning at the (present) outside of the
planetary system, and registering the number of revolutions, beginning
with 1 for Neptune, rates of acceleration of revolution in number of
days, and densities of the planets, we may draw from it some useful
knowledge. But we shall first extend Bode's Law to embrace Neptune, and
show the discrepancies between the actual positions of the planets and
those pointed out by the law.
Here we see that, with the exception of the first step from Neptune
to Uranus which is only 1·9577, we have an average gradation of
acceleration of 2·5898 times, from one planet to another, from the
outermost as far in as Mars; and that had Neptune had the period
of revolution sought for by Leverrier in his discovery of that
planet, viz. 217·387 years, or 79,399·602 days, the average rate of
acceleration would have been 2·5896 times, from planet to planet,
as far in as Mars. This, we think, is pretty strong evidence that
one law of acceleration was in force from the beginning of the
separation of rings from the nebula up to the time when the ring for
Mars was separated--the departure from it in the case of Neptune,
notwithstanding--and goes far to prove that part of the nebular
hypothesis which implies that each of the planets is now revolving
round the sun in the orbit, and with the velocity, belonging to the
centre of gyration of the ring out of which it was formed. From
Mars to Venus the law--the areolar law, of course--had changed to a
variable decreasing law, as seen from the foregoing register, which
then again changed into an increasing one, till at Mercury the rate of
acceleration rose again to 2·5543 times from Venus, or very nearly the
same rate of increase that existed from Uranus to Mars. The causes of
these changes may or may not be able to be accounted for--we shall have
to return to them hereafter, in the cases of Neptune, the earth and
Venus--but there is one thing of some importance that is deducible from
the register, which we shall endeavour to make clear.
BODE'S LAW EXTENDED.
--------------+----------+----------+----------+-----------+-----------
---- | Mercury. | Venus. | Earth. | Mars. | Asteroids.
--------------+----------+----------+----------+-----------+-----------
Numbers in }| | | | |
progression }| 0 | 3 | 6 | 12 | 24
| | | | |
Add 4 to each}| | | | |
for distance }| | | | |
from sun, }| 4 | 7 | 10 | 16 | 28
Earth's = 10 }| | | | |
| | | | |
Distance from}| | | | |
sun according}|37,186,000|65,075,500|92,965,000|148,744,000|260,300,000
to the law, }| | | | |
(Miles) }| | | | |
| | | | |
Actual |35,987,000|67,245,000|92,965,000|141,650,000| ..
distance | | | | |
| | | | |
Percentage }| | | | |
of distance }| .. | 3.34 | .. | .. | ..
beyond law }| | | | |
| | | | |
Percentage }| | | | |
of distance }| 3.22 | .. | .. | 4.77 | ..
within law }| | | | |
--------------+-------------------------------------------------------
---- | Jupiter. | Saturn. | Uranus. | Neptune.
--------------+-----------+-----------+-------------+-----------------
Numbers in }| | | |
progression }| 48 | 96 | 192 | 384
| | | |
Add 4 to each}| | | |
for distance }| | | |
from sun, }| 52 | 100 | 196 | 388
Earth's = 10 }| | | |
| | | |
Distance from}| | | |
sun according}|483,418,000|929,650,000|1,782,114,000|3,607,042,000
to the law, }| | | |
(Miles) }| | | |
| | | |
Actual |483,678,000|886,779,000|1,783,383,000|2,794,000,000
distance | | | |
| | | |
Percentage of}| | | |
distance }| 0.05 | .. | 0.07 | ..
beyond law }| | | |
| | | |
Percentage of}| | | |
distance }| .. | 4.50 | .. | 22.54
within law }| | | |
--------------+-----------+-----------+-------------+-----------------
Our register as specified above will be the following:--
-----------+--------+-------+---------------------+-----------------+
Planet. | Rev. of Planet,|Accel. of revolution,|Density of Planet|
|(in solar days) |(Neptune taken as 1) | |
-----------+----------------+---------------------+-----------------+
Neptune. | 60,180.8600 | 1.0000 | 1.132 |
Uranus. | 30,688.3000 | 1.9577 | 1.302 |
Saturn. | 10,759.2198 | 2.8523 | 0.736 |
Jupiter. | 4,332.5848 | 2.4833 | 1.358 |
Asteroids.| 1,714.1876 | 2.5606 | ... |
Mars. | 686.9796 | 2.4629 | 4.188 |
Earth. | 365.2563 | 1.8808 | 5.660 |
Venus. | 224.7007 | 1.6255 | 4.810 |
Mercury. | 87.9692 | 2.5543 | 6.850 |
-----------+----------------+---------------------+-----------------+
A good deal has been written about planets or other bodies existing
between Mercury and the sun, especially about Vulcan whose existence
seemed to be so certain, that his distance from the sun and period
of revolution were calculated to be about 13,000,000 miles and 20
days respectively. Now, with what we have seen about the rate of
acceleration of planets as their orbits approach the sun, we may
endeavour to form some notion of where any within the orbit of Mercury
may be found. If we take the same rate of acceleration we have found
between Venus and Mercury--that is 2·5543, which may be looked upon
as almost the general rate for all the planets--we find that there
might be a planet revolving round the sun in 34·4436 days; but here we
must stop, because, though we could make no objection to the existence
of a planet with the period of revolution just shown, were we to
take another equal step towards the centre of the nebula, the same
acceleration of rotation would give us a planet, or ring for a planet,
revolving round the sun in 13·4454 days; not much more than one-half
the average of his rotation round his axis at the present day, which
would knock on the head most completely the theory that each planet
was detached from the nebula at the time that it was rotating with the
velocity of the planet's orbit, or we should have to conclude that the
nebula had passed, by a long way, its power to abandon matter through
centrifugal force. No one could suppose that a ring for a planet could
be formed within the body of the nebula and abandoned, or thrown out,
afterwards, because centrifugal force could not throw out the ring and
at the same time retain the surrounding matter.
Turning our thoughts now to the supposed planet Vulcan, which was
calculated to revolve round the sun in about 20 days, we have either
to conclude that it was formed in the body of the nebula and come to
the same breakdown of the nebular hypothesis, or we have to acknowledge
that the sun is now rotating much more slowly on its axis than the
nebula did at the time the ring for Vulcan was abandoned.
If we now direct our attention to the densities of the several planets,
we shall find some suggestive matter in their study. A general look
shows us at once that there are four periods of rise and fall in their
densities. There is one rise and fall (referring to our register)
from Neptune to Uranus and on to Saturn; then another rise to Jupiter
and fall to, we suppose, the asteroids, because we are told that the
quantity of matter in the region where the asteroids travel is less
than in any other zone of the solar system, and the general density
must in consequence have been less there than anywhere else; still
another rise from the Asteroids to the Earth, and fall to Venus; and
then a final rise to Mercury accompanied, without doubt, by a fall
after the planet was abandoned, because the centrifugal force of the
rotating nebula must have been decreasing, at the least, preparatory
to its ceasing to have the power to throw off more matter. The first
rise and fall would seem to indicate that there had been a much closer
mutual relation in the births of Neptune, Uranus and Saturn than is
indicated in any way in the nebular hypothesis. We could imagine that
at one time they formed one flat ring, which afterwards divided itself
into three, following the same law as we see dividing the rings of
Saturn at the present day. With respect to Jupiter, his enormous size
is sufficient to entitle us to believe that his ring was separated from
the nebula independently of any of the others, and to account for there
having been the rise and fall in the density that we have noted between
Saturn and the Asteroids. Then the rise and fall from Mars to Venus,
or further on towards Mercury as it would be, may indicate one ring
divided into three in the same manner as we have supposed for the three
outer planets. And the final rise to Mercury and subsequent fall to the
sun or to the solar nebula might be either due to one operation or to
complication with other unknown bodies that may be travelling between
Mercury and the sun.
In support of the foregoing ideas, we may also refer to our having said
on a previous occasion, that the whole of the matter separated from the
nebula in the form of thin hoop-shaped rings, would condense into one
continuous sheet, perhaps even up to the time when centrifugal force
could not throw off any more matter against the force of gravitation.
In that case we can conceive that the radial attraction, outwards
and inwards, of the particles of the matter forming the sheet would
gradually establish lines of separation, dividing off the matter into
distinctly separate rings, preparatory to their transformation into
planets; but we cannot explain how these separate rings came to be
more dense in one place than another. We must leave that for future
discovery. Meanwhile the idea of one continuous sheet of matter
extending from the sun out to Neptune, suggests the possibility of all
the rings having been in existence as rings, more or less advanced in
their evolution, at the same time; and if not so much as that, makes
it more easy for us to see how the four inner planets, being made out
of more condensed cosmic matter, and being of so much smaller volume,
have arrived at a much more advanced stage of their being than the
four outer ones. Going a little further, we can see how the cosmic
matter of the rings condensing from both sides in the direction of
their thickness, and falling in impeded, so to speak, the tendency to
contract in length, or circularly, until they arrived at a certain
stage of density, when they began to contract in their orbital
direction, to break up into pieces, each one of which would form itself
into a small, probably shapeless, nebula with a tendency to direct
rotation, as explained and shown by M. Faye in "L'Origine du Monde,"
chapter xiii., page 267, entitled "Formation de l'Universe et du Monde
Solaire"--an explanation which must have occurred to everyone who has
taken the trouble to think seriously, of how nebulous spheres could be
formed out of a flat nebulous ring endowed with a motion of revolution.
We have seen at page 127 that when the nebula was condensed to a little
over 4,000,000 miles in diameter, its average temperature might have
been 2740°, provided no heat had been radiated into space. In like
manner, we can see that the sun being now condensed to 1·413 times the
density of water, or 1093 times the density of air, in other words,
that number of atmospheres, its present average temperature might
be about 300,000°--as each atmosphere corresponds to 274°--provided
no radiation of heat into space had been going on. But this way of
estimating could not in any way apply to the nebula after it had
ceased to throw off planetary matter; because from that time, or at
all events from the time when it came to be of a density equal to one
atmosphere and temperature of 0°, or freezing point of water, that
would be accumulated within it, owing to the difficulty of carrying
to the surface, to be radiated into space, what was produced by
condensation in the interior, as we have shown before. Both heat and
pressure would increase from the surface towards the centre, the former
rising, in spite of surface radiation, to something far beyond what we
have stated above that it might be, aided by the increase of pressure
which near the centre must be enormously greater than the average of
1093 atmospheres, seeing that the pressure at the surface of the sun
is estimated to be not far from 28 atmospheres. The first cause of the
increase of pressure would be the condensation produced by gravitation,
which according to the areolar law would increase the rotary velocity
of the nebula in proportion as the centre was approached; and as this
would begin long before it had given up abandoning rings, or rather
from the very beginning of its rotation; from that time, there would be
different rates of rotation at different distances between the surface
and the centre, which would cause friction among the particles of its
matter, in other words a churning of the matter shut up in the interior
of the nebula, and thus produce heat over and above that produced by
the condensation of gravitation alone. If two particles of matter would
produce a given quantity of heat, in falling from the surface of the
nebula to any point nearer to the centre, they would surely produce
more if they were rubbed against each other by churning action during
their fall.
Reflecting on what we have written up till now, we see that the
analysis of the nebular hypothesis we have made, which at first may
have appeared to be unnecessary or even useless, has shown us and
made us think over many details, of which we had only a vague notion
previously. It has shown us that without condensation at or near the
surface of the nebula--which we have pointed out must have been caused
by its greatest mass being near that region, and which Laplace procured
by endowing it with excessive heat--the various members of the solar
system could not have been evolved from it in terms of the hypothesis.
From it we have been able to learn, by means of the register of the
acceleration of revolution from one planet to another, when, and for
what reason, the nebula ceased to be able to throw off any planet
nearer to the sun than the supposed Vulcan, or almost even so near.
Finally, and not to go into greater detail, it has so far given us some
ideas, that we had not before, of the internal structure of the sun,
and has made us believe that a great deal may be learnt by attempting
to find out what that structure really is. For this purpose, it appears
to us that a careful examination into, and study of, the interior of
the earth might be a great help, and to this we shall appeal, as we
cannot think of any other process by which our object can be attained.
This, therefore, we shall endeavour to do in the following chapters.
CHAPTER VIII.
PAGE
142 Inquiry into the Interior Construction of the Earth. What is
really known of the exterior or surface.
143 What is known of the interior.
144 Little to be learned from Geology, which reaches very few
miles down.
145 Various notions of the interior.
146 What is learnt from earthquake and volcanoes.
Igno-aqueous fusion, liquid magma.
147 Generally believed that the earth consists of solid matter
to the centre. Mean density. Surface density.
148 More detailed estimate of densities near the surface.
148 Causes of increased surface density after the crust was formed.
150 Calculations of densities for 9 miles deep, and from there to
the centre forming Table IV.
151 Reflections on the results of the calculations.
151 Notion that the centre is composed of the heaviest metals.
"Sorting-out" theory absurd.
152 Considerations as to how solid matter got to the centre.
153 Gravitation might carry it there, but attraction could not.
154 How the earth could be made out of cosmic matter,
meteorites or meteors.
THE INTERIOR OF THE EARTH AND ITS DENSITY.
Before attempting to inquire into the nature and structure of the
interior of the earth, it will be convenient to specify the bases on
which the inquiry is to be made, in other words, the data we have to
proceed with; which data should be denuded of everything whatever
having the semblance of a hypothesis or theory, and should consist of
simple facts. Anything founded upon theory must come to an end should
the theory be afterwards found to be erroneous, and all the labour
would be lost.
What we really know of the earth in this way may be stated as follows:--
Of the exterior or surface we know that it is of a spherical form,
surrounded by an atmosphere of probably 200 miles or even more, in
height, consisting of common air mixed with vapour of water in more or
less degree; that, of its surface, nearly three-fourths are covered
by water, and the remaining fourth consists of dry land, intersected
in all directions by rivers; that on the dry land there are elevated
tablelands and ranges of mountains from two to three miles high, with
occasional ridges and peaks rising up to altitudes of from five to
near six miles, and that in the part covered by water or sea, there
are depressions or furrows with depths in them probably exceeding
the heights of the highest mountains; that the sea does not remain
constantly at the same level but rises and falls twice in every
twenty-four hours, or thereby, in obedience to the attraction of the
moon and sun, forming what are called tides; and that its polar regions
are enveloped in dense masses of snow and ice, which the persevering
energy of man has not been able to penetrate in centuries of continued
and determined effort.
What we know of the interior of the earth is found in great measure
from the exterior, that is, from the construction of the rocks as seen
in deep ravines, in precipices, and on the sides of hills or mountains;
and also from what we have been able to learn from the exploration of
mines and from deep wells, the deepest of which have penetrated it
very little beyond one mile in depth; all of which knowledge may be
summarised as follows: That the substances which compose the earth
are manifold and of manifold nature--or, more appropriately speaking,
simply the elements of chemistry--varying in density, or specific
gravity, from the same as that of water, or in some cases much less,
to three or four times as much in some kinds of rock and earths
(disintegrated rock), to more than twenty times in the heaviest metals;
that from a depth great enough not to be affected by the changes of
seasons, the heat of the earth increases in descending towards the
centre, by one degree of Fahrenheit's thermometer for every fifty to
sixty feet in depth--that is about thirty metres for each degree of the
Centigrade scale--as far down as we have been able to penetrate; that
at the greatest of these depths abundant supplies of water are found,
which shows that it must exist at much greater depths than any that
have yet been reached; and that at unknown depths, as shown by the
eruptions of volcanoes, there are masses of matter in a molten liquid
state, or that, owing to their great heat, can be suddenly liquefied by
diminution of pressure.
Over and above what has been stated, little can be learnt from geology,
because the earth must have been formed and fashioned almost to its
present condition before geology could begin to exist, and all its
teachings are confined to a very few miles from its surface. Its first
lesson could only begin when the earth was so far cooled down that a
crust could be formed on its surface, and that crust could be deluged
by copious falls of rain on it. Some help or guidance may be obtained
however, from the ideas which astronomers and physicists have formed
on its interior, and it may be useful to have the principal of these
ideas specified, as they may help to strengthen arguments that may be
advanced, or conclusions that may be drawn.
When it was discovered that the temperature of the earth increases,
as we go downwards, at what may be considered a rapid rate, it was
calculated that at a depth of from twenty-five to thirty miles, the
heat would be great enough to melt any substances that have been found
near the surface; and it was immediately concluded that from that depth
to the centre the whole of the interior was a molten liquid mass, whose
temperature far exceeded any heat that could be produced upon the
surface. Even up to the present day, the belief in a liquid interior
has not disappeared.
Many years afterwards, the supposed liquid state of the interior of
the earth was taken advantage of, to frame a theory that earthquakes
and eruptions of volcanoes are caused by the attraction of the moon
on the liquid interior producing tides, in the same manner as it
produces tides in the sea, which in their turn act upon the crust,
cracking and rending it to produce the one, and forcing the liquid
matter out through the rents, or up through the vents of volcanoes to
produce the other, in some way that it is more easy to imagine than
to explain mechanically. Also when the effect of the attraction of
the moon on the liquid internal matter came to be duly considered, it
was concluded that the crust, with only 25 to 30 miles in thickness,
could not be rigid enough to resist the pressure brought upon it by
the movements of the interior tides; and it began to be thought that,
owing to the pressure of the superincumbent strata, the density of
the matter at that depth might be so great that it would become solid
at a much higher temperature than it does at the surface; and some
physicists went the length of supposing that the earth has a solid
crust and solid nucleus with liquid matter between them. On the other
hand Sir William Thomson, Lord Kelvin, looking more as it would appear
to the effects of the moon's attraction on the crust than on the liquid
interior, concluded that the earth must be a solid globe, contracting
through gravitation in the interior, and cooling at the surface,
because a crust so thin as 25 to 30 miles, or even 100 miles, would be
continually rent and broken up by the tidal action of the moon; but
Professor Clerk Maxwell and others have thought that the elasticity of
the crust would be great enough to admit of its accommodating itself
to all the changes of form that would be caused by the action of those
tides. Notwithstanding that they agree with Lord Kelvin in the main, in
his objections to the existence of a liquid interior, many scientific
men suppose that, through the effects of pressure, the liquid interior
of the earth may have been changed into a viscous state, as it went on
contracting through gravitation, which would, according to the degree
of viscosity, either annul, or almost annul, the tidal action on it of
the moon. To which it may be added that that action would not raise
such high waves in even perfectly liquid molten matter as it would upon
water; because it would be easier for the moon to lift a cubic mile of
water three or four feet high, than to lift a cubic mile of melted rock
or metal to the same height.
Other parties look upon the earth as mainly solid to the centre, but
with large reservoirs of liquid matter in various parts of it near the
surface, which furnish all the material for volcanic eruptions and
are the causes of earthquakes. There are others also who, believing
the earth to be altogether solid, consider that when any part of the
intensely heated and dense interior is relieved suddenly from pressure,
as, for example, by the convulsive action of an earthquake, it will
immediately assume the liquid state and become material for volcanic
eruptions; a theory which they consider to be substantiated by the
fact of these two phenomena generally accompanying each other. And Mr.
Mallet seems to have demonstrated that earthquake-shocks proceed from
centres not far from the surface, which would seem to point out that
if a liquid interior did exist at 25 to 30 miles from the surface,
it could have no part in causing earthquakes. There are others still
who consider earthquakes and volcanic eruptions to be caused by water
penetrating deeply into the interior, but it is difficult to understand
how water could penetrate into the interior to a greater depth than
where it would be converted into steam, that is to a greater depth than
from three to four miles.
Many other notions about the interior state and conditions of the earth
have been formed, more or less entertainable, more or less fanciful, to
provide liquid matter for volcanic eruptions. One of these, referred
to in "Nature" of December 12, 1889, takes for granted "that granite
has consolidated from a state of igneo-aqueous fusion, and that the
liquid magma from which all granitic intrusions have proceeded contains
water-substance," and proceeds, "It is, therefore, only a further step
to assume that this water-substance is an essential constituent of
the liquid substratum (assumed by the author), and to suppose that it
has been there since the consolidation of the earth." This mixture of
water, fire, and molten granite is one that does not agree with what
we have been taught of the nature of any of the three components, and
we cannot accept it. Why we refer to it more particularly than to the
other ideas we have cited, is because it so far comprehends some of
them, and that we shall have to return to it hereafter, when we think
it will be seen that it has not been properly thought out.
Bearing in mind all these ideas we have cited, and working with the
data we have considered as actual facts, we may now proceed with our
inquiry.
The belief that the earth is a mass of matter increasing, whether
liquid or solid, or part of both, in density from the surface to the
centre is so general that we shall look at it in that light first, and
endeavour to find out what must be its density at any place between its
surface and its centre.
Astronomers and geologists concur in telling us that the mean density
of the earth is very near to 5·66 times that of water: knowledge that
has been acquired by measuring the attraction of high and precipitous
mountains for plummets; by the attraction of masses of metals for each
other, measured by the torsion balance; and by the acceleration or
retardation of the vibrations of pendulums, as observed in the depths
of mines and on the tops of mountains, compared with each other. They
also tell us that the average density of the matter and rocks of which
the crust is composed is about 2-1/2 times that of water; and then,
in a general way, that the average density of the crust, taking into
consideration that so much of its surface is covered by the sea, is not
much more than 1-1/2 times that of water. This estimate is manifestly
incorrect, for it implies that the whole of the crust of twenty-five to
thirty miles is affected by the presence of water, when we know that
the depth of the sea at any place does not exceed one-fourth of that
thickness. Therefore, we shall endeavour to obtain some more accurate
computation, as it is the only datum we have to go upon, and has a
greater effect upon the result, and upon all things relating to the
interior, than might at first sight be supposed.
We find in "Nature," of January 19, 1888, that Mr. John Murray has
calculated that if the whole solid land of the earth were reduced to
one level under the sea, its surface would be covered by an ocean with
a uniform depth of about 2 miles. Here we have a very good beginning
for our calculations.
Without taking into consideration the increase of density in water
at 2 miles deep, at that depth we may suppose we have come to solid
matter, the specific gravity of which could not be less than twice that
of water, on account of the pressure of that depth of water upon it.
If we now go down 2-1/2 miles further we shall have the solid matter
subjected to a pressure proportioned to that depth; and if we take
its weight per cubic foot at an average between granite (at 163 lb.)
and earth (at 77 lb.), or 120 lb., the pressure at 2-1/2 miles deep
of solid matter alone will be about 700 tons per square foot, or just
about the crushing strain of our strongest granites, and therefore, the
density of the matter under it must be equal to that of granite, or
2·5 times that of water. We do not add the pressure of the water, at
present, because that may be looked upon by some people as of the same
nature as of the atmosphere upon a human body, which neither increases
the pressure upon it nor adds to its weight; but we see that at that
depth the solid matter must have a density equal to the average between
water on its surface and 2·5--that of granite; and if we choose to take
the average between 2 miles of water and 2-1/2 miles of solid matter,
we shall have 1·82 as the average density of the outer 4-1/2 miles in
thickness of the crust of the earth. For our purposes, however, and for
obvious reasons, we shall consider the average density of the 2-1/2
miles alone of solid matter to be 2·25 times that of water.
We shall now go down to 9 miles deep, because the diameter of 7918
miles we have adopted for the earth will there be reduced to 7900
miles, which will be convenient for our further operations. At that
depth we shall have a superincumbent pressure at the very least as
follows:--
Tons.
At 2 miles deep, 2 miles of sea at 150 tons per mile 300
2-1/2 " 2-1/2 " solid matter at spec. grav. 2·25
equal to 331·25 tons per mile 828
9 " 4-1/2 " of rock at 163 lb. per cubic foot 1730
----
Total pressure per square foot 2858
or just about 4 times the crushing strain of our best granites. Then,
as when crushing takes place compression begins, it will, we believe,
be far below the mark to estimate the general specific gravity of the
earth at 9 miles deep to be 3 times that of water.
We have now added the pressure of the 2 miles of water, because
there could be no water at the depth of 9 miles; for the critical
temperature of water is known to be 412°, beyond which temperature
water cannot be maintained in its liquid state by any amount of
pressure, however great; and 9 miles would give 483° temperature at 1°
for each 30 metres. At that depth there might be steam, although it is
difficult to see how it could penetrate so far, because the only force
to help it to penetrate would be gravitation, and that would have to
act against the increasing repulsion of heat.
There is another circumstance to be considered which would tend to
increase the density of the outer portion of the crust, if there be a
crust, and if not, of the outer portion of the earth itself.
When the earth was in the molten liquid state, it is generally supposed
to have been surrounded by vapours of a great proportion of the metals
and of some of the metalloids, in addition to the vapour of water, air,
and other gases, which floated above them higher up in the atmosphere.
In that case when the crust began to be formed through cooling, these
vapours would be precipitated on the surface and mixed with the
half-liquid half-solid matter there, but the proportion of condensed
vapours would be very small compared with what they fell upon, and the
specific gravity of the mixture would not be great enough to cause it
to sink much below the surface, because it would soon meet with matter
as dense as itself; consequently we must consider that all these metals
would remain near the surface--most likely much nearer to it than the
9 miles which we have as yet descended to--and whatever may have been
the proportion of their density it ought to be added to the weights and
pressures that have been taken into account above. We believe that it
will be shown later on that this estimate of a density of three times
that of water at 9 miles deep in the earth is very much lower than it
should be; because, when the pressure upon the matter there came to be
greater than its crushing strain, compression would go on more rapidly
than shortly afterwards, and it might so be that with a strain of
very much less than four times that of crushing, compression would be
reduced to its utmost limit. But more of this hereafter.
Having determined densities for the matter composing the earth at
2, 4-1/2, and 9 miles below the surface, that is, to where the mean
diameter comes to be 7900 miles, if we divide that diameter into
layers of 25 miles each in thickness, compute the volume of each layer
or shell, increase the density of each layer as we descend in direct
proportion from 3--the density we have fixed for 9 miles deep--to
13·734 times the density of water, at the centre, and multiply the
volume of each layer from the surface downwards by its respective
average density, we shall find a mass nearly equal to the mass of the
earth at the density of water--always taking its mean diameter at
7918 miles, and mean density at 5·66 times that of water, as already
premised. These calculations have been carefully carried out, and are
represented in detail in Table IV. for future reference. They terminate
in a deficiency of over 70,000,000 of cubic miles, a deficiency which
would be more than made up by making the central density 13·736 instead
of 13·734. Thus we see that if the density of the earth increases
regularly from the surface to the centre, and if the densities we have
given to the layers between the surface and 9 miles in depth are not
greater than those adopted, the central density must be exceedingly
near 13-3/4 times that of water. Of course, if the three surface
densities are in reality _less_ than those we have adopted, the central
density must be greater than 13-3/4 times that of water. The whole
being a result to our calculations which leads us to speculate on what
kind of matter there is at the centre of the earth.
We are acquainted with various kinds of rocks, stones and other solid
matter that have densities (specific gravities) of 2-1/2 to 3 times
that of water, and we have to conceive that a cubic foot of one of
these would have to be compressed into a height of 2-3/4 or 2-1/4
inches in order to have the density of 13-3/4 required at the centre,
a result which presents us with a substance which it is difficult
to imagine or to believe to exist. It may be that the centre of the
earth is occupied by the heaviest metals we know, arranged in layers
proportioned in thickness to the masses required of them, and that
they are laid one over the other according to their densities, or
mixed together until a distance from the centre is attained, at which
ordinary rocks compressed as highly as their nature would admit of, may
exist; but we do not derive much knowledge or satisfaction from such
a supposition. An examination of our table of calculations will show
that 500 miles in diameter of the central part might be filled up with
platinum, the few other rarer and heavier metals, and gold amalgamated
with mercury in due proportions. Then there might be a mixture of
mercury and lead to 1800 miles in diameter, followed by a mixture of
lead and silver to 2400 miles. After that might come a compound of
silver, copper, tin, and zinc to 4900 miles, and some compounds of
iron might finish the filling process up to 6000 miles in diameter,
or thereby; where the known rocks, compressed to half their volume at
first, but gradually allowed to expand, might complete the whole mass
of the earth. It will be seen, also, that by the time compressed rocks
could be used for this filling process, more than 43 per cent. of the
whole volume of the earth would be occupied exclusively by pure metals
mixed by rule and measure.
It would appear then that the "sorting-out theory"--about which a
good deal has been written--whereby, in suns and planets, the metals
on account of being heavier fall more rapidly to the centre, and the
lighter metalloids remain near the surface--a theory probably got up
to get over the difficulty we are in--is not a very happy one, as too
much metal would be required for the process, at least for the earth.
No doubt it might be applied differently to what we have done by mixing
metals with rocks, stones, earth, etc., forming metallic ores--very
rich they would doubtless have to be--from the centre outwards; but
however disposed it would seem that very much the same quantity would
be required to furnish the desired densities up to 6000 miles in
diameter, where we have supposed compressed granites, etc., might come
into play. Besides, such an arrangement would do away with the whole
beauty of the theory; there would be no law to invoke; it would be all
pick-and-shovel work.
The sorting-out theory is one of these notions that occur to
humanity and are accepted at once, without consideration of what the
consequences may be. If it is made to account for the four inferior
planets being so much more dense, and of coming so much sooner to
maturity--so to speak--than the four superior ones, it is hard to
understand why the sun up to the present day almost ranks in low
density with the large planets. If that theory holds good, it would be
most natural to suppose that the mean density of the sun should be very
much greater than that of Mercury. But it appears to be only carried
as far as it suits the theorist, and to be there dropped, or rather
ignored.
Having been defeated in our attempt to build up or construct an earth
solid to the centre by appealing to the metals to make up the weight or
density required for the foundation layers, and that even to somewhere
about three-fourths of the diameter of the whole structure, we are
forced to fall back upon our known rocks, earths, etc., in order to
compound out of them the dense material we require, and of course we
feel that we have in hand a more hopeless task than we had with the
metals. How are we to compress the everlasting hills into one-fourth or
one-fifth of their volume? Some solution of the difficulty, or mystery,
must be found somewhere; but at the same time the mountains of gold,
silver, and less precious metals required have shown us how absurd,
even laughable, it is to appeal to them.
Let us suppose that we have a cubic foot of matter of any kind of
13-3/4 times the density of water, and that we place it in one of
the scales of a balance at the centre of the earth; we shall find
that it does not depress the scale one hair-breadth, for the very
good reason that it has nowhere to depress it to; it would be already
at what may be called the end of gravitation or tendency to fall
lower. As it could not get any lower it would have a tendency to fly
off anywhere--provided it was free to do so--and drag the scale and
balance along with it, in obedience to its own attractive power and
the attraction of all the matter of the earth surrounding it, except
that the attraction might be so equally distributed all around it that
it would not move in any direction. It would, however, be in a state
of very unstable equilibrium, and if by some means the attraction
were increased a little on one side more than the others, and it were
at liberty to do so, it would abandon the centre and fly off in that
direction never to return. Now, this being the case, we are forced to
consider how a cubic foot of matter, such as the one we are dealing
with, could ever have found its way to the centre of the earth; and
the law of gravitation, or rather of attraction, does not in any way
help us out of the difficulty. We know that we put our cubic foot of
extremely dense matter there for an experiment, but we do not know of
any process of nature that could place there any equal mass of matter
of that density.
Gravitation and attraction are generally used as synonymous terms,
more especially gravitation--somewhat after the manner of the likeness
between the two negroes, Cæsar and Pompey, the latter being most
especial in the likeness--but there is a very appreciable distinction
between them, if we want to use each of them in its proper and strict
sense. Gravitation implies the conception of a weight of some kind
falling to a fixed centre, while attraction gives the idea of two
weights, or masses, drawing each other to a common centre, which when
properly looked at is a different thing; because the centre may be
anywhere between the two, depending entirely on the difference, if
any, in the weights of the masses. The confounding of the two, or
rather the almost universal adoption of the less correct term, name,
expression--whichever it may be called--has been the cause of wrong
conceptions being formed of the construction of almost all--probably
all--celestial bodies, and of that most absurd expression, _attraction
of gravitation_, used by all our most eminent physicists. The
_gravitation_ of _attraction_ might be excused, but putting cause for
effect is hardly scientific. A name is nothing as long as what is meant
by it is understood and taken into consideration, but that is not
always the case, as we shall proceed to show.
The term gravitation may be applied with almost, but not absolutely,
perfect strictness to the attraction between the sun and the planets,
because the common centres of their attractions and the centre of the
sun are so near each other that they may be looked upon as one and
the same thing, or point; but it is not so with the attractions of the
planets for each other where there is no common fixed centre, or if
there is something approaching to it in a far off way, it is constantly
varying, so that the term gravitation cannot be strictly applied to
them, nor even to the sun, to speak truly. Planets sometimes _gravitate
away_ from each other and from the sun, otherwise Adams and Leverrier
could not have discovered Neptune from the perturbations of Uranus.
Neither can it be properly applied to the different masses of matter
in the sun or in the earth--although it was no doubt notions connected
with the earth that gave rise to the term, from all ponderable matter
falling upon it--because _per se_ they could have no tendency to fall
to the centre, for _at the centre_ there is no sufficient attractive
force to draw them towards it. Gravitation was a known term long
before the days of Newton, who had the glory of enlightening the
world by showing that attraction was the cause of it; and, perhaps
unfortunately, the name was continued to represent what it in reality
does not.
Let us suppose that we have an empty earth to fill up; if we place one
mass of matter at London and another at Calcutta, they could have no
tendency of themselves to fall to the centre, but if left alone would
go for each other in a straight line and meet half-way between the two,
provided they were equal in mass, and attraction, not gravitation,
would be the proper term to apply to them. But supposing that two
equal masses were placed at their antipodes and the four were left to
themselves, they would gravitate towards and meet at the centre in the
usual meaning of the word, but the force that drew them there would
be really that of attraction. We could, however, place four similar
and equal masses at the centre, and give the outer ones just and good
reason for gravitating or falling down to it, because those at the
centre being equally attracted in the four directions might remain
stationary there, but would be in a state of unstable equilibrium. We
may now suppose that when the masses had just left London and Calcutta
to meet the others, a goodly number of other equal masses were added to
those at these two places and began to attract the two bound towards
the centre, they would prevent the two from proceeding, or at least
retard them on their journey inwards. Moreover, the larger numbers at
these two places would attract the four masses at the centre with more
force than would the two at the antipodes, and would draw the whole of
the four away from the centre and outwards towards themselves; but we
might also suppose that at the same moment an equal number of equal
masses were added to those at the antipodes, which would again equalize
the attractions at the four outer posts, and things would continue as
they were at the first; with this difference, that the four at the
centre would not be able to balance the attractions at the four outer
posts, and the consequence would be--seeing that the forces at the four
outer stations were equal to each other, and far superior to the four
at the centre--that each one of the four at the centre would be drawn
away from it towards one of the outer stations--provided the law of
attraction acted impartially--and so the centre would be left without
any of the masses at it, that is empty. No doubt when the four outgoing
masses met the larger ones coming in, they would all then move towards
the centre; but the four places where they met would be immensely
nearer the places occupied at first by the outer masses than half-way
between them and the centre--proportioned, in exact conformance with
the law of attraction, to the excess of the numbers of the masses at
the outer stations over those at the centre--and they would be moving,
all of them together, to a remote and void space. We may now increase
the four outer stations to thousands or millions, with the security
that the mode of proceeding would be the same with the whole of them;
that is, that the first tendency of the masses at each one of the
millions of stations would be to draw away the filling we were pouring
into the hollow earth--provided we did it equally and impartially all
over the hollow--from the centre, and to leave a void there.
We are accustomed to look upon the earth as a solid body in which
there are no acting and counteracting forces, no movements of matter
from one place to another, similar to those we have been calling into
play, and as if there was only one force acting upon its whole mass
and driving it to the centre; we have, in our ideas, got the whole
mass so compressed and wedged in that it cannot move, and never has
been able to move in any direction except towards the centre, and
this is no doubt the case at the present day. We never stop to think
with sufficient care how this compression and wedging-in were brought
about, and we only accept what we have been accustomed to believe to
be facts, and trouble ourselves no more about it; but there must have
been a time, according to any cosmogony we may choose to adopt--even to
the vague one that the solar system was somehow made out of a nebula
of some kind--when the matter of the earth was neither compressed nor
wedged in, nor prevented from moving in any direction towards which it
was most powerfully attracted--before superincumbent matter came, so to
speak, to have any wedging-in force--and we must go back to that period
and study it deeply, if we want to acquire an accurate knowledge of the
construction of the earth.