Speculative as is much of the foregoing essay, it appears undesirable to
include in it anything still more speculative. For this reason I have
decided to set forth separately some views concerning the genesis of the
so-called elements during nebular condensation, and concerning the
accompanying physical effects. At the same time it has seemed best to
detach from the essay some of the more debatable conclusions originally
contained in it; so that its general argument may not be needlessly
implicated with them. These new portions, together with the old portions
which re-appear more or less modified, I here append in a series of
notes.
NOTE I. For the belief that the so-called elements are compound there
are both special reasons and general reasons. Among the special may be
named the parallelism between allotropy and isomerism; the numerous
lines in the spectrum of each element; and the cyclical law of Newlands
and Mendeljeff. Of the more general reasons, which, as distinguished
from these chemical or chemico-physical ones, may fitly be called
cosmical, the following are the chief.
The general law of evolution, if it does not actually involve the
conclusion that the so-called elements are compounds, yet affords _a
priori_ ground for suspecting that they are such. The implication is
that, while the matter composing the Solar System has progressed
physically from that relatively-homogeneous state which it had as a
nebula to that relatively-heterogeneous state presented by Sun, planets,
and satellites, it has also progressed chemically, from the
relatively-homogeneous state in which it was composed of one or a few
types of matter, to that relatively-heterogeneous state in which it is
composed of many types of matter very diverse in their properties. This
deduction from the law which holds throughout the cosmos as now known to
us, would have much weight even were it unsupported by induction; but a
survey of chemical phenomena at large discloses several groups of
inductive evidences supporting it.
The first is that since the cooling of the Earth reached an advanced
stage, the components of its crust have been ever increasing in
heterogeneity. When the so-called elements, originally existing in a
dissociated state, united into oxides, acids, and other binary
compounds, the total number of different substances was immensely
augmented, the new substances were more complex than the old, and their
properties were more varied. That is, the assemblage became more
heterogeneous in its kinds, in the composition of each kind, and in the
range of chemical characters. When, at a later period, there arose salts
and other compounds of similar degrees of complexity, there was again an
increase of heterogeneity, alike in the aggregate and in its members.
And when, still later, matters classed as organic became possible, the
multiformity was yet further augmented in kindred ways. If, then,
chemical evolution, so far as we can trace it, has been from the
homogeneous to the heterogeneous, may we not fairly suppose that it has
been so from the beginning? If, from late stages in the Earth's history,
we run back, and find the lines of chemical evolution continually
converging, until they bring us to bodies which we cannot decompose, may
we not suspect that, could we run back these lines still further, we
should come to still decreasing heterogeneity in the number and nature
of the substances, until we reached something like homogeneity?
A parallel argument may be derived from consideration of the affinities
and stabilities of chemical compounds. Beginning with the complex
nitrogenous bodies out of which living things are formed, and which, in
the history of the Earth, are the most modern, at the same time that
they are the most heterogeneous, we see that the affinities and
stabilities of these are extremely small. Their molecules do not enter
bodily into union with those of other substances so as to form more
complex compounds still, and their components often fail to hold
together under ordinary conditions. A stage lower in degree of
composition we come to the vast assemblage of oxy-hydro-carbons, numbers
of which show many and decided affinities, and are stable at common
temperatures. Passing to the inorganic group, we are shown by the salts
&c. strong affinities between their components and unions which are, in
many cases, not very easily broken. And then when we come to the oxides,
acids, and other binary compounds, we see that in many cases the
elements of which they are formed, when brought into the presence of one
another under favourable conditions, unite with violence; and that many
of their unions cannot be dissolved by heat alone. If, then, as we go
back from the most modern and most complex substances to the most
ancient and simplest substances, we see, on the average, a great
increase in affinity and stability, it results that if the same law
holds with the simplest substances known to us, the components of these,
if they are compound, may be assumed to have united with affinities far
more intense than any we have experience of, and to cling together with
tenacities far exceeding the tenacities with which chemistry acquaints
us. Hence the existence of a class of substances which are
undecomposable and therefore seem simple, appears to be an implication;
and the corollary is that these were formed during early stages of
terrestrial concentration, under conditions of heat and pressure which
we cannot now parallel.
Yet another support for the belief that the so-called elements are
compounds, is derived from a comparison of them, considered as an
aggregate ascending in their molecular weights, with the aggregate of
bodies known to be compound, similarly considered in their ascending
molecular weights. Contrast the binary compounds as a class with the
quaternary compounds as a class. The molecules constituting oxides
(whether alkaline or acid or neutral) chlorides, sulphurets, &c. are
relatively small; and, combining with great avidity, form stable
compounds. On the other hand, the molecules constituting nitrogenous
bodies are relatively vast and are chemically inert; and such
combinations as their simpler types enter into, cannot withstand
disturbing forces. Now a like difference is seen if we contrast with one
another the so-called elements. Those of relatively-low molecular
weights--oxygen, hydrogen, potassium, sodium, &c.,--show great readiness
to unite among themselves; and, indeed, many of them cannot be prevented
from uniting under ordinary conditions. Contrariwise, under ordinary
conditions the substances of high molecular weights--the "noble
metals"--are indifferent to other substances; and such compounds as they
do form under conditions specially adjusted, are easily destroyed. Thus
as, among the bodies we know to be compound, increasing molecular weight
is associated with the appearance of certain characters, and as, among
the bodies we class as simple, increasing molecular weight is
associated with the appearance of similar characters, the composite
nature of the elements is in another way pointed to.
There has to be added one further class of phenomena, congruous with
those above named, which here specially concerns us. Looking generally
at chemical unions, we see that the heat evolved usually decreases as
the degree of composition, and consequent massiveness, of the molecules,
increases. In the first place, we have the fact that during the
formation of simple compounds the heat evolved is much greater than that
which is evolved during the formation of complex compounds: the
elements, when uniting with one another, usually give out much heat;
while, when the compounds they form are recompounded, but little heat is
given out; and, as shown by the experiments of Prof. Andrews, the heat
given out during the union of acids and bases is habitually smaller
where the molecular weight of the base is greater. Then, in the second
place, we see that among the elements themselves, the unions of those
having low molecular weights result in far more heat than do the unions
of those having high molecular weights. If we proceed on the supposition
that the so-called elements are compounds, and if this law, if not
universal, holds of undecomposable substances as of decomposable, then
there are two implications. The one is that those compoundings and
recompoundings by which the elements were formed, must have been
accompanied by degrees of heat exceeding any degrees of heat known to
us. The other is that among these compoundings and recompoundings
themselves, those by which the small-moleculed elements were formed
produced more intense heat than those by which the large-moleculed
elements were formed: the elements formed by the final recompoundings
being necessarily later in origin, and at the same time less stable,
than the earlier-formed ones.
NOTE II. May we from these propositions, and especially from the last,
draw any conclusions respecting the evolution of heat during nebular
condensation? And do such conclusions affect in any way the conclusions
now current?
In the first place, it seems inferable from physico-chemical facts at
large, that only through the instrumentality of those combinations which
formed the elements, did the concentration of diffused nebulous matter
into concrete masses become possible. If we remember that hydrogen and
oxygen in their uncombined states oppose, the one an insuperable and the
other an almost insuperable, resistance to liquefaction, while when
combined the compound assumes the liquid state with facility, we may
suspect that in like manner the simpler types of matter out of which the
elements were formed, could not have been reduced even to such degrees
of density as the known gases show us, without what we may call
proto-chemical unions: the implication being that after the heat
resulting from each of such proto-chemical unions had escaped, mutual
gravitation of the parts was able to produce further condensation of the
nebulous mass.
If we thus distinguish between the two sources of heat accompanying
nebular condensation--the heat due to proto-chemical combinations and
that due to the contraction caused by gravitation (both of them,
however, being interpretable as consequent on loss of motion), it may be
inferred that they take different shares during the earlier and during
the later stages of aggregation. It seems probable that while the
diffusion is great and the force of mutual gravitation small, the chief
source of heat is combination of units of matter, simpler than any known
to us, into such units of matter as those we know; while, conversely,
when there has been reached close aggregation, the chief source of heat
is gravitation, with consequent pressure and gradual contraction.
Supposing this to be so, let us ask what may be inferred. If at the time
when the nebulous spheroid from which the Solar System resulted, filled
the orbit of Neptune, it had reached such a degree of density as
enabled those units of matter which compose the sodium molecules to
enter into combination; and if, in conformity with the analogies above
indicated, the heat evolved by this proto-chemical combination was great
compared with the heats evolved by the chemical combinations known to
us; the implication is that the nebulous spheroid, in the course of its
contraction, would have to get rid of a much larger quantity of heat
than it would, did it commence at any ordinary temperature and had only
to lose the heat consequent on contraction. That is to say, in
estimating the past period during which solar emission of heat has been
going on at a high rate, much must depend on the initial temperature
assumed; and this may have been rendered intense by the proto-chemical
changes which took place in early stages.[21]
Respecting the future duration of the solar heat, there must also be
differences between the estimates made according as we do or do not take
into account the proto-chemical changes which possibly have still to
take place. True as it may be that the quantity of heat to be emitted
is measured by the quantity of motion to be lost, and that this must be
the same whether the approximation of the molecules is effected by
chemical unions, or by mutual gravitation, or by both; yet, evidently,
everything must turn on the degree of condensation supposed to be
eventually reached; and this must in large measure depend on the natures
of the substances eventually formed. Though, by spectrum-analysis,
platinum has recently been detected in the solar atmosphere, it seems
clear that the metals of low molecular weights greatly predominate; and
supposing the foregoing arguments to be valid, it may be inferred, as
not improbable, that the compoundings and recompoundings by which the
heavy-moleculed elements are produced, not hitherto possible in large
measure, will hereafter take place; and that, as a result, the Sun's
density will finally become very great in comparison with what it is
now. I say "not hitherto possible in large measure", because it is a
feasible supposition that they may be formed, and can continue to exist,
only in certain outer parts of the Solar mass, where the pressure is
sufficiently great while the heat is not too great. And if this be so,
the implication is that the interior body of the Sun, higher in
temperature than its peripheral layers, may consist wholly of the metals
of low atomic weights, and that this may be a part cause of his low
specific gravity; and a further implication is that when, in course of
time, the internal temperature falls, the heavy-moleculed elements, as
they severally become capable of existing in it, may arise: the
formation of each having an evolution of heat as its concomitant.[22] If
so, it would seem to follow that the amount of heat to be emitted by
the Sun, and the length of the period during which the emission will go
on, must be taken as much greater than if the Sun is supposed to be
permanently constituted of the elements now predominating in him, and to
be capable of only that degree of condensation which such composition
permits.
NOTE III. Are the internal structures of celestial bodies all the same,
or do they differ? And if they differ, can we, from the process of
nebular condensation, infer the conditions under which they assume one
or other character? In the foregoing essay as originally published,
these questions were discussed; and though the conclusions reached
cannot be sustained in the form given to them, they foreshadow
conclusions which may, perhaps, be sustained. Referring to the
conceivable causes of unlike specific gravities in the members of the
solar system, it was said that these might be--
"1. Differences between the kinds of matter or matters composing
them. 2. Differences between the quantities of matter; for, other
things equal, the mutual gravitation of atoms will make a large
mass denser than a small one. 3. Differences between the
structures: the masses being either solid or liquid throughout, or
having central cavities filled with elastic aeriform substance. Of
these three conceivable causes, that commonly assigned is the
first, more or less modified by the second."
Written as this was before spectrum-analysis had made its disclosures,
no notice could of course be taken of the way in which these conflict
with the first of the foregoing suppositions; but after pointing out
other objections to it the argument continued thus:--
"However, spite of these difficulties, the current hypothesis is,
that the Sun and planets, inclusive of the Earth, are either solid
or liquid, or have solid crusts with liquid nuclei."[23]
After saying that the familiarity of this hypothesis must not delude us
into uncritical acceptance of it, but that if any other hypothesis is
physically possible it may reasonably be entertained, it was argued that
by tracing out the process of condensation in a nebulous spheroid, we
are led to infer the eventual formation of a molten shell with a nucleus
consisting of gaseous matter at high tension. The paragraph which then
follows runs thus:--
"But what," it may be asked, "will become of this gaseous nucleus
when exposed to the enormous gravitative pressure of a shell some
thousands of miles thick? How can aeriform matter withstand such a
pressure?" Very readily. It has been proved that, even when the
heat generated by compression is allowed to escape, some gases
remain uncondensible by any force we can produce. An unsuccessful
attempt lately made in Vienna to liquify oxygen, clearly shows this
enormous resistance. The steel piston employed was literally
shortened by the pressure used; and yet the gas remained
unliquified! If, then, the expansive force is thus immense when the
heat evolved is dissipated, what must it be when that heat is in
great measure detained, as in the case we are considering? Indeed
the experiences of M. Cagniard de Latour have shown that gases may,
under pressure, acquire the density of liquids while retaining the
aeriform state, provided the temperature continues extremely high.
In such a case, every addition to the heat is an addition to the
repulsive power of the atoms: the increased pressure itself
generates an increased ability to resist; and this remains true to
whatever extent the compression is carried. Indeed it is a
corollary from the persistence of force that if, under increasing
pressure, a gas retains all the heat evolved, its resisting force
is _absolutely unlimited_. Hence the internal planetary structure
we have described is as physically stable a one as that commonly
assumed."
Had this paragraph, and the subsequent paragraphs, been written five
years later, when Prof. Andrews had published an account of his
researches, the propositions they contain, while rendered more specific
and at the same time more defensible, would perhaps have been freed from
the erroneous implication that the internal structure indicated is an
universal one. Let us, while guided by Prof. Andrews' results, consider
what would probably be the successive changes in a condensing nebulous
spheroid.
Prof. Andrews has shown that for each kind of gaseous matter there is a
temperature above which no amount of pressure can cause liquefaction.
The remark, made _a priori_ in the above extract, "that if, under
increasing pressure, a gas retains all the heat evolved, its
resisting force is _absolutely unlimited_", harmonizes with the
inductively-reached result that if the temperature is not lowered to its
"critical point" a gas does not liquify, however great the force
applied. At the same time Prof. Andrews' experiments imply that,
supposing the temperature to be lowered to the point at which
liquefaction becomes possible, then liquefaction will take place where
there is first reached the required pressure. What are the corollaries
in relation to concentrating nebulous spheroids?
Assume a spheroid of such size as will form one of the inferior planets,
and consisting externally of a voluminous, cloudy atmosphere composed of
the less condensible elements, and internally of metallic gases: such
internal gases being kept by convection-currents at temperatures not
very widely differing. And assume that continuous radiation has brought
the internal mass of metallic gases down to the critical point of the
most condensible. May we not say that there is a size of the spheroid
such that the pressure will not be great enough to produce liquefaction
at any other place than the centre? or, in other words, that in the
process of decreasing temperature and increasing pressure, the centre
will be the place at which the combined conditions of pressure and
temperature will be first reached? If so, liquefaction, commencing at
the centre, will spread thence to the periphery; and, in virtue of the
law that solids have higher melting points under pressure than when
free, it may be that solidification will similarly, at a later stage,
begin at the centre and progress outwards: eventually producing, in that
case, a state such as Sir William Thomson alleges exists in the Earth.
But now suppose that instead of such a spheroid, we assume one of, say,
twenty or thirty times the mass; what will then happen? Notwithstanding
convection-currents, the temperature at the centre must always be
higher than elsewhere; and in the process of cooling the "critical
point" of temperature will sooner be reached in the outer parts. Though
the requisite pressure will not exist near the surface, there is
evidently, in a large spheroid, a depth below the surface at which the
pressure will be great enough, if the temperature is sufficiently low.
Hence it is inferable that somewhere between centre and surface in the
supposed larger spheroid, there will arise that state described by Prof.
Andrews, in which "flickering striae" of liquid float in gaseous matter
of equal density. And it may be inferred that gradually, as the process
goes on, these striae will become more abundant while the gaseous
interspaces diminish; until, eventually, the liquid becomes continuous.
Thus there will result a molten shell containing a gaseous nucleus
equally dense with itself at their surface of contact and more dense at
the centre--a molten shell which will slowly thicken by additions to
both exterior and interior.
That a solid crust will eventually form on this molten shell may be
reasonably concluded. To the demurrer that solidification cannot
commence at the surface, because the solids formed would sink, there are
two replies. The first is that various metals expand while solidifying,
and therefore would float. The second is that since the envelope of the
supposed spheroid would consist of the gases and non-metallic elements,
compounds of these with the metals and with one another would
continually accumulate on the molten shell; and the crust, consisting of
oxides, chlorides, sulphurets, and the rest, having much less specific
gravity than the molten shell, would be readily supported by it.
Clearly a planet thus constituted would be in an unstable state. Always
it would remain liable to a catastrophe resulting from change in its
gaseous nucleus. If, under some condition of pressure and temperature
eventually reached, the components of this suddenly entered into one of
those proto-chemical combinations forming a new element, there might
result an explosion capable of shattering the entire planet, and
propelling its fragments in all directions with high velocities. If the
hypothetical planet between Jupiter and Mars was intermediate in size as
in position, it would apparently fulfil the conditions under which such
a catastrophe might occur.
NOTE IV. The argument set forth in the foregoing note, is in part
designed to introduce a question which seems to require
re-consideration--the origin of the minor planets or planetoids. The
hypothesis of Olbers, as propounded by him, implied that the disruption
of the assumed planet between Mars and Jupiter had taken place at no
very remote period in the past; and this implication was shown to be
inadmissible by the discovery that there exists no such point of
intersection of the orbits of the planetoids as the hypothesis requires.
The inquiry whether, in the past, there was any nearer approach to a
point of intersection than at present, having resulted in a negative, it
is held that the hypothesis must be abandoned. It is, however, admitted
that the mutual perturbations of the planetoids themselves would
suffice, in the course of some millions of years, to destroy all traces
of a place of intersection of their orbits, if it once existed. But if
this be admitted why need the hypothesis be abandoned? Given such
duration of the Solar System as is currently assumed, there seems no
reason why lapse of a few millions of years should present any
difficulty. The explosion may as well have taken place ten million years
ago as at any more recent period. And whoever grants this must grant
that the probability of the hypothesis has to be estimated from other
data.
As a preliminary to closer consideration, let us ask what may be
inferred from the rate of discovery of the planetoids, and from the
sizes of those most recently discovered. In 1878, Prof. Newcomb, arguing
that "the preponderance of evidence is on the side of the number and
magnitude being limited", says that "the newly discovered ones" "do not
seem, on the average, to be materially smaller than those which were
discovered ten years ago"; and further that "the new ones will probably
be found to grow decidedly rare before another hundred are discovered".
Now, inspection of the tables contained in the just-published fourth
edition of Chambers' _Descriptive Astronomy_ (vol. I) shows that whereas
the planetoids discovered in 1868 (the year Prof. Newcomb singles out
for comparison) have an average magnitude of 11.56 those discovered last
year (1888) have an average magnitude of 12.43. Further, it is
observable that though more than ninety have been discovered since Prof.
Newcomb wrote, they have by no means become rare: the year 1888 having
added ten to the list, and having therefore maintained the average rate
of the preceding ten years. If, then, the indications Prof. Newcomb
names, had they arisen, would have implied a limitation of the number,
these opposite indications imply that the number is unlimited. The
reasonable conclusion appears to be that these minor planets are to be
counted not by hundreds but by thousands; that more powerful telescopes
will go on revealing still smaller ones; and that additions to the list
will cease only when the smallness ends in invisibility.
Commencing now to scrutinize the two hypotheses respecting the genesis
of these multitudinous bodies, I may first remark concerning that of
Laplace, that he might possibly not have propounded it had he known that
instead of four such bodies there are hundreds, if not thousands. The
supposition that they resulted from the breaking up of a nebulous ring
into numerous small portions, instead of its collapse into one mass,
might not, in such case, have seemed to him so probable. It would have
appeared still less probable had he been aware of all that has since
been discovered concerning the wide differences of the orbits in size,
their various and often great eccentricities, and their various and
often great inclinations. Let us look at these and other incongruous
traits of them.
(1.) Between the greatest and least mean distances of the planetoids
there is a space of 200 millions of miles; so that the whole of the
Earth's orbit might be placed between the limits of the zone occupied,
and leave 7 millions of miles on either side: add to which that the
widest excursions of the planetoids occupy a zone of 270 millions of
miles. Had the rings from which Mercury, Venus, and the Earth were
formed been one-sixth of the smaller width or one-ninth of the greater,
they would have united: there would have been no nebulous rings at all,
but a continuous disk. Nay more, since one of the planetoids trenches
upon the orbit of Mars, it follows that the nebulous ring out of which
the planetoids were formed must have overlapped that out of which Mars
was formed. How do these implications consist with the nebular
hypothesis? (2.) The tacit assumption usually made is that the different
parts of a nebulous ring have the same angular velocities. Though this
assumption may not be strictly true, yet it seems scarcely likely that
it is so widely untrue as it would be had the inner part of the ring an
angular velocity nearly thrice that of the outer. Yet this is implied.
While the period of Thule is 8.8 years, the period of Medusa is 3.1
years. (3.) The eccentricity of Jupiter's orbit is 0.04816, and the
eccentricity of Mars' orbit is 0.09311. Estimated by groups of the first
found and last found of the planetoids, the average eccentricity of the
assemblage is about three times that of Jupiter and more than one and a
half times that of Mars; and among the members of the assemblage
themselves, some have an eccentricity thirty-five times that of others.
How came this nebulous zone, out of which it is supposed the planetoids
arose, to have originated eccentricities so divergent from one another
as well as from those of the neighbouring planets? (4.) A like question
may be asked respecting the inclinations of the orbits. The average
inclination of the planetoid-orbits is four times the inclination of
Mars' orbit and six times the inclination of Jupiter's orbit; and among
the planetoid-orbits themselves the inclinations of some are fifty times
those of others. How are all these differences to be accounted for on
the hypothesis of genesis from a nebulous ring? (5.) Much greater
becomes the difficulty on inquiring how these extremely unlike
eccentricities and inclinations came to co-exist before the parts of the
nebulous ring separated, and how they survived after the separation.
Were all the great eccentricities displayed by the outermost members of
the group, and the small by the innermost members, and were the
inclinations so distributed that the orbits having much belonged to one
part of the group, and those having little to another part of the group;
the difficulty of explanation might not be insuperable. But the
arrangement is by no means this. The orbits are, to use an expressive
word, miscellaneously jumbled. Hence, if we go back to the nebulous
ring, there presents itself the question,--How came each
planetoid-forming portion of nebulous matter, when it gathered itself
together and separated, to have a motion round the Sun differing so much
from the motions of its neighbours in eccentricity and inclination? And
there presents itself the further question,--How, during the time when
it was concentrating into a planetoid, did it manage to jostle its way
through all the differently-moving like masses of nebulous matter, and
yet to preserve its individuality? Answers to these questions are, it
seems to me, not even imaginable.
* * * * *
Turn we now to the alternative hypothesis. During revision of the
foregoing essay, in preparation for that edition of the volume
containing it which was published in 1883, there occurred the thought
that some light on the origin of the planetoids ought to be obtained by
study of their distributions and movements. If, as Olbers supposed,
they resulted from the bursting of a planet once revolving in the region
they occupy, the implications are:--first, that the fragments must be
most abundant in the space immediately about the original orbit, and
less abundant far away from it; second, that the large fragments must be
relatively few, while of smaller fragments the numbers will increase as
the sizes decrease; third, that as some among the smaller fragments will
be propelled further than any of the larger, the widest deviations in
mean distance from the mean distance of the original planet, will be
presented by the smallest members of the assemblage; and fourth, that
the orbits differing most from the rest in eccentricity and in
inclination, will be among those of these smallest members. In the
fourth edition of Chambers's _Handbook of Descriptive and Practical
Astronomy_ (the first volume of which has just been issued) there is a
list of the elements (extracted and adapted from the _Berliner
Astronomisches Jahrbuch_ for 1890) of all the small planets (281 in
number) which had been discovered up to the end of 1888. The apparent
brightness, as expressed in equivalent star-magnitudes, is the only
index we have to the probable comparative sizes of by far the largest
number of the planetoids: the exceptions being among those first
discovered. Thus much premised, let us take the above points in order.
(1) There is a region lying between 2.50 and 2.80 (in terms of the
Earth's mean distance from the Sun) where the planetoids are found in
maximum abundance. The mean between these extremes, 2.65, is nearly the
same as the average of the distances of the four largest and
earliest-known of these bodies, which amounts to 2.64. May we not say
that the thick clustering about this distance (which is, however, rather
less than that assigned for the original planet by Bode's empirical
law), in contrast with the wide scattering of the comparatively few
whose distances are little more than 2 or exceed 3, is a fact in
accordance with the hypothesis in question?[24] (2) Any table which
gives the apparent magnitudes of the planetoids, shows at once how much
the number of the smaller members of the assemblage exceeds that of
those which are comparatively large; and every succeeding year has
emphasized this contrast more strongly. Only one of them (Vesta) exceeds
in brightness the seventh star-magnitude, while one other (Ceres) is
between the seventh and eighth, and a third (Pallas) is above the
eighth; but between the eighth and ninth there are six; between the
ninth and tenth, twenty; between the tenth and eleventh, fifty-five;
below the eleventh a much larger number is known, and the number
existing is probably far greater,--a conclusion we cannot doubt when the
difficulty of finding the very faint members of the family, visible only
in the largest telescopes, is considered. (3) Kindred evidence is
furnished if we broadly contrast their mean distances. Out of the 13
largest planetoids whose apparent brightnesses exceed that of a star of
the 9.5 magnitude, there is not one having a mean distance that exceeds
3. Of those having magnitudes at least 9.5 and smaller than 10, there
are 15; and of these one only has a mean distance greater than 3. Of
those between 10 and 10.5 there are 17; and of these also there is one
exceeding 3 in mean distance. In the next group there are 37, and of
these 5 have this great mean distance. The next group, 48, contains 12
such; the next, 47, contains 13 such. Of those of the twelfth magnitude
and fainter, 72 planetoids have been discovered, and of those of them
of which the orbits have been computed, no fewer than 23 have a mean
distance exceeding 3 in terms of the Earth's. It is evident from this
how comparatively erratic are the fainter members of the extensive
family with which we are dealing. (4) To illustrate the next point, it
may be noted that among the planetoids whose sizes have been
approximately measured, the orbits of the two largest, Vesta and Ceres,
have eccentricities falling between .05 and .10, whilst the orbits of
the two smallest, Menippe and Eva, have eccentricities falling between
.20 and .25, and between .30 and .35. And then among those more recently
discovered, having diameters so small that measurement of them has not
been practicable, come the extremely erratic ones,--Hilda and Thule,
which have mean distances of 3.97 and 4.25 respectively; AEthra, having
an orbit so eccentric that it cuts the orbit of Mars; and Medusa, which
has the smallest mean distance from the Sun of any. (5) If the average
eccentricities of the orbits of the planetoids grouped according to
their decreasing sizes are compared, no very definite results are
disclosed, excepting this, that the eight Polyhymnia, Atalanta,
Eurydice, AEthra, Eva, Andromache, Istria, and Eudora, which have the
greatest eccentricities (falling between .30 and .38), are all among
those of smallest star-magnitudes. Nor when we consider the inclinations
of the orbits do we meet with obvious verifications; since the
proportion of highly-inclined orbits among the smaller planetoids does
not appear to be greater than among the others. But consideration shows
that there are two ways in which these last comparisons are vitiated.
One is that the inclinations are measured from the plane of the
ecliptic, instead of being measured from the plane of the orbit of the
hypothetical planet. The other, and more important one, is that the
search for planetoids has naturally been carried on in that
comparatively narrow zone within which most of their orbits fall; and
that, consequently, those having the most highly-inclined orbits are the
least likely to have been detected, especially if they are at the same
time among the smallest. Moreover, considering the general relation
between the inclination of planetoid orbits and their eccentricities, it
is probable that among the orbits of these undetected planetoids are
many of the most eccentric. But while recognizing the incompleteness of
the evidence, it seems to me that it goes far to justify the hypothesis
of Olbers, and is quite incongruous with that of Laplace. And as having
the same meanings let me not omit the remarkable fact concerning the
planetoids discovered by D'Arrest, that "if their orbits are figured
under the form of material rings, these rings will be found so
entangled, that it would be possible, by means of one among them taken
at hazard, to lift up all the rest,"--a fact incongruous with Laplace's
hypothesis, which implies an approximate concentricity, but quite
congruous with the hypothesis of an exploded planet.
Next to be considered come phenomena, the bearings of which on the
question before us are scarcely considered--I mean those presented by
meteors and shooting stars. The natures and distributions of these
harmonize with the hypothesis of an exploded planet, and I think with no
other hypothesis. The theory of volcanic origin, joined with the remark
that the Sun emits jets which might propel them with adequate
velocities, seems quite untenable. Such meteoric bodies as have
descended to us, forbid absolutely the supposition of solar origin. Nor
can they rationally be ascribed to planetary volcanoes. Even were their
mineral characters appropriate, which many of them are not (for
volcanoes do not eject iron), no planetary volcanoes could propel them
with anything like the implied velocity--could no more withstand the
tremendous force to be assumed, than could a card-board gun the force
behind a rifle bullet. But that their mineral characters, various as
they are, harmonize with the supposition that they were derived from
the crust of a planet is manifest; and that the bursting of a planet
might give to them, and to shooting stars, the needful velocities, is a
reasonable conclusion. Along with those larger fragments of the crust
constituting the known planetoids, varying from some 200 miles in
diameter to little over a dozen, there would be sent out still more
multitudinous portions of the crust, decreasing in size as they
increased in number. And while there would thus result such masses as
occasionally fall through the Earth's atmosphere to its surface, there
would, in an accompanying process, be an adequate cause for the myriads
of far smaller masses which, as shooting stars, are dissipated in
passing through the Earth's atmosphere. Let us figure to ourselves, as
well as we may, the process of explosion.
Assume that the diameter of the missing planet was 20,000 miles; that
its solid crust was a thousand miles thick; that under this came a shell
of molten metallic matter which was another thousand miles thick; and
that the space, 16,000 miles in diameter, within this, was occupied by
the equally dense mass of gases above the "critical point", which,
entering into a proto-chemical combination, caused the destroying
explosion. The primary fissures in the crust must have been far
apart--probably averaging distances between them as great as the
thickness of the crust. Supposing them approximately equidistant, there
would, in the equatorial periphery, be between 60 and 70 fissures. By
the time the primary fragments thus separated had been heaved a mile
outwards, the fissures formed would severally have, at the surface, a
width of 170 odd yards. Of course these great masses, as soon as they
moved, would themselves begin to fall in pieces; especially at their
bounding surfaces. But passing over the resulting complications, we see
that when the masses had been propelled 10 miles outwards, the fissures
between them would be each a mile wide. Notwithstanding the enormous
forces at work, an appreciable interval would elapse before these vast
portions of the crust could be put in motion with any considerable
velocities. Perhaps the estimate will be under the mark if we assume
that it took 10 seconds to propel them through the first mile, and that,
by implication, at the end of 20 seconds they had travelled 4 miles, and
at the end of 30 seconds 9 miles. Supposing this granted, let us ask
what would be taking place in each intervening fissure a thousand miles
deep, which, in the space of half a minute, had opened out to nearly a
mile wide, and in the subsequent half minute to a chasm approaching 3
miles in width. There would first be propelled through it enormous jets
of the molten metals composing the internal liquid shell; and these
would part into relatively small masses as they were shot into space.
Presently, as the chasm opened to some miles in width, the molten metals
would begin to be followed by the equally dense gaseous matter behind,
and the two would rush out together. Soon the gases, predominating,
would carry with them the portions of the liquid shell continually
collapsing; until the blast became one filled with millions of small
masses, billions of smaller masses, and trillions of drops. These would
be driven into space in a stream, the emission of which would continue
for many seconds or even several minutes. Remembering the rate of motion
of the jets emitted from the solar surface, and supposing that the
blasts produced by this explosion reached only one-tenth of that rate,
these myriads of small masses and drops would be propelled with
planetary velocities, and in approximately the same direction. I say
approximately, because they would be made to deviate somewhat by the
friction and irregularities of the chasm passed through, and also by the
rotation of the planet. Observe, however, that though they would all
have immense velocities, their velocities would not be equal. During its
earlier stages the blast would be considerably retarded by the
resistance which the sides of its channel offered. When this became
relatively small the velocity of the blast would reach its maximum; from
which it would decline when the space for emission became very wide,
and the pressure behind consequently less. Hence these almost infinitely
numerous particles of planet-spray, as we might call it, as well as
those formed by the condensation of the metallic vapours accompanying
them, would forthwith begin to part company: some going rapidly in
advance, and others falling behind; until the stream of them,
perpetually elongating, formed an orbit round the Sun, or rather an
assemblage of innumerable orbits, separating widely at aphelion and
perihelion, but approximating midway, where they might fall within a
space of, say, some two millions of miles, as do the orbits of the
November meteors. At a later stage of the explosion, when the large
masses, having moved far outwards, had also fallen to pieces of every
size, from that of Vesta to that of an aerolite, and when the channels
just described had ceased to exist, the contents of the planet would
disperse themselves with lower velocities and without any unity of
direction. Hence we see causes alike for the streams of shooting stars,
for the solitary shooting stars visible to the naked eye, and for the
telescopic shooting stars a score times more numerous.
Further significant evidence is furnished by the comets of short
periods. Of the thirteen constituting this group, twelve have orbits
falling between those of Mars and Jupiter: one only having its aphelion
beyond the orbit of Jupiter. That is to say, nearly all of them frequent
the same region as the planetoids. By implication, they are similarly
associated in respect of their periods. The periods of the planetoids
range from 3.1 to 8.8 years; and all these twelve comets have periods
falling between these extremes: the least being 3.29 and the greatest
8.86. Once more this family of comets, like the planetoids in the zone
they occupy and like them in their periods, are like them also in the
respect that, as Mr. Lynn has pointed out, their motions are all direct.
How happens this close kinship--how happens there to be this family of
comets so much like the planetoids and so much like one another, but so
unlike comets at large? The obvious suggestion is that they are among
the products of the explosion which originated the planetoids, the
aerolites, and the streams of meteors; and consideration of the probable
circumstances shows us that such products might be expected. If the
hypothetical planet was like its neighbour Jupiter in having an
atmosphere, or like its neighbour Mars in having water on its surface,
or like both in these respects; then these superficial masses of liquid,
of vapour, and of gas, blown into space along with the solid matters,
would yield the materials for comets. There would result, too, comets
unlike one another in constitution. If a fissure opened beneath one of
the seas, the molten metals and metallic gases rushing through it as
above described, would decompose part of the water carried with them;
and the oxygen and hydrogen liberated would be mingled with undecomposed
vapour. In other cases, portions of the atmosphere might be propelled,
probably with portions of vapour; and in yet other cases masses of water
alone. Severally subject to great heat at perihelion, these would behave
more or less differently. Once more, it would ordinarily happen that
detached swarms of meteors projected as implied, would carry with them
masses of vapours and gases; whence would result the cometic
constitution now insisted on. And sometimes there would be like
accompaniments to meteoric streams.
See, then, the contrast between the two hypotheses. That of Laplace,
looking probable while there were only four planetoids, but decreasing
in apparent likelihood as the planetoids increase in number, until, as
they pass through the hundreds on their way to the thousands, it becomes
obviously improbable, is, at the same time, otherwise objectionable. It
pre-supposes a nebulous ring of a width so enormous that it would have
overlapped the ring of Mars. This ring would have had differences
between the angular velocities of its parts quite inconsistent with the
Nebular Hypothesis. The average eccentricities of the orbits of its
parts must have differed greatly from those of adjacent orbits; and the
average inclinations of the orbits of its parts must similarly have
differed greatly from those of adjacent orbits. Once more, the orbits of
its parts, confusedly interspersed, must have had varieties of
eccentricity and inclination unaccountable in portions of the same
nebulous ring; and, during concentration into planetoids, each must have
had to maintain its course while struggling through the assemblage of
other small nebulous masses, severally moving in ways unlike its own. On
the other hand, the hypothesis of an exploded planet is supported by
every increase in the number of planetoids discovered; by the greater
numbers of the smaller sizes; by the thicker clustering near the
inferred place of the missing planet; by the occurrence of the greatest
mean distances among the smallest members of the assemblage; by the
occurrence of the greatest eccentricities in the orbits of these
smallest members; and by the entanglement of all the orbits. Further
support for the hypothesis is yielded by aerolites, so various in their
kinds, but all suggestive of a planet's crust; by the streams of
shooting stars having their radiant points variously placed in the
heavens; and also by the solitary shooting stars visible to the naked
eye, and the more numerous ones visible through telescopes. Once more,
it harmonizes with the discovery of a family of comets, twelve out of
thirteen of which have mean distances falling within the zone of the
planetoids, have similarly associated periods, have all the same direct
motions, and are connected with swarms of meteors and with meteoric
streams. May we not, indeed, say, that if there once existed a planet
between Mars and Jupiter which burst, the explosion must have produced
just such clusters of bodies and classes of phenomena as we actually
find?
And what is the objection? Merely that if such an explosion occurred it
must have occurred many millions of years ago--an objection which is in
fact no objection; for the supposition that the explosion occurred many
millions of years ago is just as reasonable as the supposition that it
occurred recently.
It is, indeed, further objected that some of the resulting fragments
ought to have retrograde motions. It turns out on calculation, however,
that this is not the case. Assuming as true the velocity which Lagrange
estimated would have sufficed to give the four chief planetoids the
positions they occupy, it results that such a velocity, given to the
fragments which were propelled backwards by the explosion, would not
have given them retrograde motions, but would simply have reduced their
direct motions from something over 11 miles per second to about 6 miles
per second. It is, however, manifest that this reduction of velocity
would have necessitated the formation of highly-elliptic orbits--more
elliptic than any of those at present known. This seems to me the most
serious difficulty which has presented itself. Still, considering that
there remain probably an immense number of planetoids to be discovered,
it is quite possible that among these there may be some having orbits
answering to the requirement.
NOTE V. Shortly before I commenced the revision of the foregoing essay,
friends on two occasions named to me some remarkable photographs of
nebulae recently obtained by Mr. Isaac Roberts, and exhibited at the
Royal Astronomical Society: saying that they presented appearances such
as might have been sketched by Laplace in illustration of his
hypothesis. Mr. Roberts has been kind enough to send me copies of the
photographs in question and sundry others illustrative of stellar
evolution. Those representing the Great Nebulae in Andromeda and Canum
Venaticorum as well as 81 Messier are at once impressive and
instructive--illustrating as they do the genesis of nebulous rings round
a central mass.
I may remark, however, that they seem to suggest the need for some
modification of the current conception; since they make it tolerably
clear that the process is a much less uniform one than is supposed. The
usual idea is that a vast rotating nebulous spheroid arises before there
are produced any of the planet-forming rings. But both of these
photographs apparently imply that, in some cases at any rate, the
portions of nebulous matter composing the rings take shape before they
reach the central mass. It looks as though these partially-formed annuli
must be prevented by their acquired motions from approaching even very
near to the still-irregular body they surround.
Be this as it may, however, and be the dimensions of the incipient
systems what they may (and it would seem to be a necessary implication
that they are vastly larger than our Solar System), the process remains
essentially the same. Practically demonstrated as this process now is,
we may say that the doctrine of nebular genesis passes from the region
of hypothesis into the region of established truth.