If the heat were, at a given moment--tha_New Theories in Astronomy

stopped--brought into existence uniformly throughout the entire mass,

which, according to the law of conversion of motion into heat and _vice

versâ_, would most assuredly be the case, and each pound of the mass

possessed 100,000,000,000 foot-pounds of heat, it could not be heaped

up on the outer layers of the blocks--it matters not whether this means

the layers of the outside of the whole mass, or at the outsides of

the blocks--for the energy of lost motion, converted into heat, must

have existed at the centres of the blocks or masses just in as great

force as it did at the surfaces when motion was stopped. If each pound

of matter carried along with it 100,000,000,000 foot-pounds of heat,

that given out by one pound at the centre of a block would be as great

as that given out by one pound at its surface; and the pounds at the

surface could not acquire any greater heat from a neighbouring pound,

because its neighbour could have no greater quantity to give it. Pounds

of matter would be melted and vaporized, or converted into gas, just

as readily at the centre of the mass or block as at its surface; and

storing up of heat in the interstices of the blocks is rather a strange

notion, because we are not at liberty to stow away heat in a vacuum.

Besides, it is impossible to conceive how anything in the shape of

a block could exist in any part of the whole mass, long enough for

it to be blown out into space as a block. But supposing that a block

could exist, it would most notoriously be in a state of _unstable

equilibrium_; and were it then to receive from an explosion of gas, an

impulse sufficient to drive it off to the verge of the sun's power of

attraction--or rather to a distance equal to what that is--which would

imply a velocity of not less than 360 miles per second, the shock would

be quite sufficient to blow it into its constituent atoms. Moreover, as

already stated, the heat of the explosion of the gas required to give

the impulse would be immediately converted into motion, and disappear;

so that out of the heat produced by the stoppage of a motion of 476

miles per second, that required to produce a motion of 360 miles per

second, in each one of the blocks blown out to the distance above

mentioned, would be entirely lost to the stock of heat schemed for so

boldly. Of course, the less the distance from the centre the blocks

were blown the less would be the loss, but the fact remains that there

would be a loss instead of a gain of heat, in dispersing the matter

of two half suns into space by explosions of gas. In fine, a given

amount of heat will raise the temperature of a given amount of matter

to an easily calculable degree, and no more; and if part of that is

expended in expanding the volume of the matter, the whole stock of

heat will be diminished by exactly the quantity required to produce

the expansions. So that we come back to what we have said at page 54,

viz., that when the matter and the heat of the collision of the two

half suns were dispersed, under the most favourable circumstances, into

a sphere of 6,000,000,000 miles in diameter, the mean density of the

matter would be equal to about 1/270th part of an atmosphere, and its

temperature--what is called--273° C. of absolute temperature, always

considering the quantity of the heat to have been 300,000,000° C.

Dr. Croll says that if a velocity of 476 miles per second were not

sufficient to produce the quantity of heat required, any other

necessary velocity might be supposed, but when we consider that his

supply of 300,000,000° C. would have to be increased to 82,000,000,000°

C., in order to add 1° C. of heat to the matter dispersed through a

sphere of 6,000,000,000 miles in diameter, it seems unnecessary to

pursue the subject any farther.

We may now take a look at Dr. Braun's Impact Cosmogony, of which we

know nothing beyond what is set forth in the Review in "Nature" already

alluded to, but that is enough for our purpose. We understand that he

extends his operations to the whole universe, which he conceives to

have been formed out of almost unlimited, and almost imponderable,

nebulous matter, not homogeneous, but with local irregularities in it,

which "would lead to the breaking up of the nebula into a vast number

of separate fragments." Out of one of these fragments he supposes the

solar system to have been formed. This fragment would contain local

irregularities also, which through condensation would lead to the

formation of separate bodies, and these bodies are supposed to have

been driven into their present forms, and gyrating movements of all

kinds, by centric and eccentric collisions among themselves, caused by

their mutual attractions. Of course anything can be supposed, but in a

construction of this kind the idea is forced upon us of the necessity

of the active superintendence of the Creator, to create in the proper

places and bring in the matter at the exact moment required, and to

see that the collisions were directed with the proper degree of energy

and eccentricity, to construct the kind of machine that was proposed.

To this idea we have no objections whatever, but we would like to see

the necessity for it acknowledged. Perhaps Dr. Braun does acknowledge

it, but the cosmogony is given to us, it would seem, to show what most

probably was the original scheme of construction, and implying that no

continual supervision and direction were required during the process.

If Dr. Braun could show us some method of attraction, and suspension

and variation of attraction, by which some of the separate bodies could

be drawn towards each other so as to form a central mass, nebula, or

sun, and to give it, by their impacts of collision, a rotary motion;

and how others of the separate bodies could be formed and held in

appropriate places, so as to be set in motion at the right moment; and

how they were to be so set in motion without the direct action of the

constructor, to revolve as planets around the central mass, we might

be able to recognise that a mechanism such as that of the solar system

might be brought into existence; but when we are left to discover all

these requisites, and their _modus operandi_, we find that we might be

as well employed in designing a cosmogony of our own.

Dr. Braun indulges in somewhat startling numbers in temperature and

pressure. He considers that the temperature of the sun, at the surface,

may be from 40,000° to 100,000° C., and that it may reach to from ten

to thirty million degrees at the centre. In this he may be right for

anything we know to the contrary. When riding over a sandy desert,

under an unclouded vertical sun, we could easily have believed

anything of the central heat of such a fire, especially when we

considered that it was at a distance of ninety-three millions of miles

from us. But when he tells us that in the depths of the sun's interior

the pressure reaches a maximum of two thousand millions of atmospheres,

we "pull in resolution and begin to doubt." Air at that pressure would

have a density 2,585,984 times that of water, or 456,887 times the mean

density of the earth, and we should have a species of matter to ponder

over, of which no physicist has ever as yet dreamt.

We have been able to study M. Faye's cosmogony in his work on

"L'Origine du Monde," second edition of 1885, and can give a better

account of it than of Dr. Braun's.

(1) He repudiates almost all existence of heat in the cosmic matter he

is about to deal with, recognising that its temperature must have been

very near the point of absolute zero, and also that its tenuity must

have been almost inconceivable; so tenuous that a cubic miriamètre of

it would not contain more perhaps than 5·217 grammes in weight. And

very properly, we think, he looks upon the solar systems as having,

at one time, formed a part of the whole universe, all of which was

brought into existence, created, more or less, about the same time. In

this universe, he considers that the stars have been formed, as well

as the sun, by the progressive concentration of primitive materials

disseminated in space, which conception gives rise to a totally new

notion of the most positive character: viz. that each star owes to its

mode of formation a provision of heat essentially limited; that it is

not permissible, as Laplace thought he could do, to endow a sun with an

indefinite amount of heat; and that what it has expended and what it

still possesses, depend upon its volume and actual mass. And also that

the primitive materials of the solar system were, at the beginning,

part of a universal chaos from which they were afterwards separated, in

virtue of movements previously impressed on the whole of the matter;

and sums up his first ideas in the following manner or theorem:

_"At the beginning the universe consisted of a general chaos, of

extreme tenuity, formed of all the elements of Chemistry more or less

mixed and confounded together. These materials under the force of their

mutual attractions were, from the beginning, endowed with diverse

movements which brought about their separation into masses or clouds.

These still retained their movements of rapid translation, and very

gentle interior gyrations. These myriads of chaotic fragments have

given birth, by means of progressive condensations, to the diverse

worlds of the universe."_

(2) So much for the formation of the universe, including, of course,

the solar system, for which he acknowledges the necessity for the

intervention of a creating power, because it is impossible to account

for it simply by the laws of nature; and adds: It is unnecessary to

say that the universe is an indefinite series of transformations, that

what we see results logically from a previous condition, and thus

necessary in the past as in the future; we cannot see how a previous

condition could tend towards the immense diffusion of matter, to the

chaos out of which the actual condition has arisen; and that it is,

therefore, necessary to begin with a hypothesis, and postulate of God,

as Descartes did, the disseminated matter and the forces which govern

it.

(3) From dealing with the universe, M. Faye comes to the formation

of an isolated star, and begins with an entirely ideal case, that of

a spherical homogeneous mass, without interior movement of any kind,

and concludes that the molecules would fall in straight lines towards

the centre; that the mass would condense regularly without losing

its homogeneity, and would end in producing an incandescent sphere

perfectly immovable; and that that would be a star, but a star without

satellites, without rotation, without proper movement. This not being

what was wanted, he goes on to show how, previous to its separation and

complete isolation from the universal chaos, such a mass would possess,

and carry with it when separated, a considerable velocity of rotation,

and would still retain the internal movements it had acquired from the

attraction of the other masses with which it had been previously in

contact; and how the molecules, drawn towards the centre in obedience

to gravitation, would not fall in straight lines but in concentric

ellipses.

(4) From this state of affairs, two very different results might arise.

One, that the molecules might resolve themselves into a multitude of

small masses without the centre acquiring a preponderating increase.

The other, that the central condensation might greatly exceed the

others, and there would be formed a central star accompanied by a crowd

of small dark bodies. M. Faye accepts the second result, in which case

the ellipses described by the small bodies, now become satellites,

would, as the central mass increased in preponderance, have one of

their centres at the centre of the preponderating mass, and their times

of revolution would vary from one to another in conformity to the third

law of Kepler.

(5) For the formation of the solar system M. Faye finds that it is of

little importance whether the movements of bodies around the sun be

very eccentric or almost circular; the first cause is always the same.

They arise from the eddies, _tourbillonnements_, they have brought

with them from their rectilinear movements in the primitive chaos. But

the circle is such a particular case of the ellipse, that we ought not

to expect to see it realized in any system. It is therefore necessary

that, among the initial conditions of the chaotic mass, one should be

found which would prevent the gyrations, eddies, from degenerating into

elliptical movements, and which has at first made right, and afterwards

firmly preserved, the form, more or less circular, in all its changes.

(6) For the formation of circular rings he gives us the following

conceptions: In order that a star should have companions, great or

small, circulating round the centre of gravity of the system, it is

necessary that the partial chaos from whence it proceeded should have

possessed, from the beginning, a gentle eddying movement affecting a

part of its materials. Besides, if the partial chaos has been really

round and homogeneous, we shall see that these gyrations must have

taken up, and to some extent preserved, the circular form. He then

requests the reader not to lose sight of the feeble density of the

medium, in which a succession of mechanical changes are to be brought

about; and not to conclude that that density was such that a cubic

miriamètre of the space occupied by it might not contain 3250 grammes

of matter, as he stated in the preceding chapter (we think he said

5217 grammes), but that it might contain only 3 grammes or even less.

And adds that in such a medium, the small agglomerations of matter

which would be formed all through it, would move as if they were in an

absolute vacuum, and any changes in them would be produced extremely

slowly.

(7) Then he goes on to say that the gyrating movements belonging to

the chaotic mass, would have very little difficulty in transforming a

part of a motion of that kind into a veritable rotation, if this last

were compatible with the law of the internal gravitation; that it is

the nature of that kind of masses to only permit, to the bodies moving

in them, revolutions, elliptic or circular, concentric and of the

same duration; that therefore notable portions of the gyrating matter

could take the form and movements of a flat ring, turning around the

centre with the same angular velocity, exactly as if this nebulous

ring were a solid body; that all the particles which have the proper

velocity in the plane of the gyrations, will arrange themselves under

the influence of gravitation in a flat ring with a veritable rotation

around the centre; that any other parts having velocities too great or

too small, will move in the same plane, describing ellipses concentric

to the ring; that if the ellipses are very elongated the materials

composing them will approach the centre, where they will produce a

progressive condensation, communicating to the central globe formed

there a rotation in the same plane with the primitive gyrations; and

finishes off the whole scheme by specifying the first results to

be: (1) The formation of concentric rings turning in one piece, in

the manner of a solid body, around a centre almost empty (_d'abord

vide_); and (2) A rotation in the same direction, communicated to

the condensation which would be produced, little by little, by means

of matter coming in, partly, from regions affected by the internal

eddyings (_tourbillonnements_).

(8) It is unnecessary to go any farther, and take note of his method

of the formation of planets and satellites from rings, as it is much

the same as what we have seen described by others who have written on

the same subject; only interpreted by him in a way to suit his own

purposes, and in which interpretation he does not do full justice

to Laplace, through not having paid sufficient attention to his

explanation of how planets could be formed out of rings. Except in so

far as to note that all along he has considered that rings were formed,

and even those nearest to the centre condensed into globes, long before

the central condensation had attained any magnitude of importance, or

assumed any distinctive shape, and that afterwards all the disposable

matter of the rings and also all the exterior matter that had not

formed part of what was separated from the original universal chaos,

had fallen in towards the small central mass, and so completed the

formation of the sun last of all.

We shall now proceed to make a few remarks with respect to this

condensation of M. Faye's cosmogony, which we think we have made

without adding to or omitting anything of importance that we have met

with in his work, for which purpose we have numbered the paragraphs

containing it, in the last six pages, in order to do away with the

necessity of repeating the parts to which we refer.

No. 1. All those who believe that "the solar system did originate

somehow, by the condensation of a primitive nebula," agree with M.

Faye in considering that the density of the nebulous matter must have

been extremely low, and some of them seem almost to vie with each

other in showing how great must have been the degree of its tenuity;

but M. Faye is one of the few who, paying due respect to the law of

the interdependence of temperature and pressure in a gas or vapour,

maintain that it must have been almost devoid of temperature, and we

have to acknowledge that he is in the right. Then we believe that his

assumption, that the whole universe of stars, including the sun, was

created, humanly speaking, about the same time, is shared by the great

majority of those who have thought at all seriously on the subject.

Also, we agree with him firmly in his statement that each star--and we

add planet, satellite, etc.--was originally supplied with an extremely

limited quantity of heat, and that what it has expended and what it

still retains has been derived entirely from the condensation of the

original cosmic matter out of which it was made.

With regard to his theorem: we cannot follow him in his statement

that the diverse movements caused by the mutual attractions of parts

of the original universal mass of cosmic matter, have brought about

its separation into myriads of fragments; nor how these fragments

could carry with them a rapid movement of translation, unless the

whole universal mass was endowed with a rapid movement of translation

through space, in which case we think that such a motion would have

had no greater particular effect in producing new forms of motion in

the fragments, than if the whole had been created in a state of rest.

Stray movements of translation might give rise to collisions among

the multitude of fragments, and perhaps that was one of the modes of

formation into suns through which they had to pass; but we cannot

follow it out. Neither can we see clearly how translation could be

effected of one mass into the space occupied by another mass--unless

empty spaces were reserved for that purpose from the beginning. Without

that, translation could not exist: it would be collision.

No. 2. We have nothing to object to what is said in this paragraph;

except that a rotating sphere might have been postulated at once,

in imitation of Laplace, instead of trying like Descartes to join

fragments together, endowed with movements so adjusted that, among the

whole of them, they would produce in the whole mass, when united, the

kind of movement that was wanted.

No. 3. To the ideal case of the formation of an isolated sun from a

homogeneous mass without interior movement of any kind, we cannot

agree in any way. The molecules of matter would not, could not, fall

in towards the centre in straight lines. Their mutual collisions would

drive them generally in curved lines in all directions as they fell in,

which would create new internal movements; and these movements would

prevent the possibility of the formation of an immovable incandescent

sphere such as is described. There could be no immobility in the

interior of a sun, as long as its temperature was sufficient to keep

the surface incandescent. But we cannot give our reasons here for this

assertion--to most people they will, we think, occur at once--because

we have a long road to travel before we can do so.

When M. Faye abandons the isolated case, he leaves us without giving

us any help, to conceive for ourselves how the mass would possess and

carry with it a considerable velocity of rotation, and still retain the

internal movements it had acquired from the attraction of the other

masses--of the universal chaos--with which it had been in contact;

and also how the molecules drawn towards the centre would not fall in

straight lines but in concentric ellipses. And this last we have to

do without his giving us any reason why the molecules should fall in

towards the centre at all; or rather in spite of the fact that one of

his principal ideas would lead us to expect exactly the contrary, as we

shall see presently.

No. 4. Here he places before us again, two cases in one of which the

molecules might resolve themselves into a multitude of small masses,

without the centre acquiring any preponderating increase; and the other

where the central condensation might greatly exceed the others, and

there would be formed a central star accompanied by a crowd of small

dark bodies, now become satellites, describing ellipses around the

central preponderating mass. This second case he seems, for the time

being, to accept as the most probable; but it is strangely at variance

with what he sets forth afterwards. He does not give us the least

hint as to why or how the satellites acquired their various times of

revolution, but only assumes that they did so; and we are very sure

that it was not the third law of Kepler that was the agent in the case,

however much it might suit his purpose.

No. 5. Although this part of his exposition is dedicated to the

formation of the solar system, all that M. Faye says is that it is

of little importance whether the movements of bodies around the sun

be very eccentric or almost circular; and that among the initial

conditions of the chaotic mass, all that we require is that one should

be found which would prevent the gyrations from degenerating into

elliptic movements, and which had first put right and afterwards firmly

preserved the form, more or less circular, in all its changes. But

he does not make any attempt to show what that one condition is, and

allows us to find it out for ourselves.

No. 6. What M. Faye says about the formation of circular rings is more

or less a repetition of what he has adduced, to explain all the other

movements which he has derived from the universal chaos; and which he

seems to think sufficient to account for such movements being nearly

circular. For our part we do not think they are sufficient, and he does

not show us how they influence each other to bring about the final

movements he wants to present to us.

We duly take note of the tenuity of the cosmic matter on which he

operates, which at 3 grammes in weight to 1 cubic miriamètre would

correspond to one grain in weight to 771,947,719,300 cubic feet of

space, or 1 grain to a cube of 9173 feet--more than 3000 yards--to

the side. We do this in order to remind him of what he says at page

151 of his work, when dealing with the rotation of the Kant-Laplace

nebula--namely, that it is impossible to comprehend how an immense

chaos, of almost inconceivable tenuity, could possess such a rotation

from the beginning, and that for want of that inadmissible supposition

nothing remains to fall back upon but the _mouvements tourbillonnaires_

of Descartes. Thus he wants us to believe that his _tourbillons_ could

move in straight or curved lines, have motions of translation, could

attract, restrain, and drive each other into all sorts of movements

with the tenuity he has indicated; but that Laplace's nebula, with a

density of 1 grain to a cube of 90 feet--or at most 150 feet--to the

side, could not be conceived to have the single movement of rotation.

And lastly, we repeat that if the centre of the chaos was almost

empty, we do not see what induced the cosmic matter to fall into it in

elliptic orbits.

Nos. 7 and 8. In these paragraphs, the main features are repetitions of

the simple assertions made in all the others, that certain movements

possessed by matter in one state would produce other movements in

another state, without attempting to show how they all came to so

far coincide with each other and form one harmonious whole, with

movements in almost one single direction. It is clear that one side

of the separated chaos might have acquired motion in one direction

from the universal chaos with which it had been in contact, and that

the opposite side might have acquired motion in exactly the opposite

direction from the original chaos with which it had been in contact;

and we are left to find out how these came to agree with each other

in the end. And, going back to the beginning, we are left to find out

where the mass, out of which he constructs his solar system, was stowed

away, after it was separated from the original universal chaos. We

can conceive of its being separated by condensation, in obedience to

the law of attraction, from the surrounding chaos, in which case it

might fall towards a centre, or that some parts of it might come to

revolve round each other, and that finally the whole of these parts

might come to rotate about a common centre; but that is evidently very

different from the mode of formation of the solar system which M. Faye

has advocated. It comes to be by far too like the nebula which Laplace

supposed to be endowed with rotary motion from the beginning, probably

because he did not see, or did not take the trouble to see, how such

a motion could be produced. In any case, Laplace did not consider

that the primary motion of rotation was the most important part of

his hypothesis; neither was it, as it seems to have been in the case

we have been considering. And he did not go much further than M. Faye

in postulating primary motion, only he did it in a more effectual and

business-like manner. He drew on the bank at once for all the funds he

required, instead of having to draw afresh every time he found himself

in difficulties, as has been the lot of his critic and successor.

Finally, M. Faye tries to show that after all his rings, flat or

otherwise, converted or not converted into globes, had been formed

according to his ideas, the greater mass by far of the chaos had fallen

into the centre, and had formed the sun there last of all. Now, if the

preponderating mass of the chaos had been outside of the field of his

operations, up to the period when all his planets, satellites, etc.

were formed, or at least laid out, it is more natural to suppose that

the matter inside of his structure, if there was any, would be drawn

outwards by the attraction of the greatly preponderating mass outside,

than that any portion of it should have fallen in, in elongated

ellipses, towards the insignificant mass that he supposes to have

been inside his structure. This, of course, would be nearly exactly

the reverse of the mode of formation he was trying to demonstrate,

and clearly shows that he was working on unsound principles from the

beginning to the end of his cosmogony. It had never occurred to him

that matter could be attracted outwards as well as inwards, most

probably because it would seem to him ridiculous to imagine that

anything in the universe could _gravitate_ upwards.

There are other theories of the formation of the solar system from

meteorites and meteors, giving us the idea of its being made out of

manufactured articles instead of originally created raw material,

which does not in any way simplify the process. In some of them, the

inrush of meteor swarms is invoked as the cause of gyratory motion,

which places them in much the same category as impact theories. We know

that broadcloth is made out of woollen yarn, but we also know how the

yarn is made out of wool, and how it is woven into the cloth, whereas

we are not told by what process, or even out of what the meteors and

meteorites are made, although some of them are said to have thumb-marks

upon them.

All these theories and cosmogonies may be very appropriately classified

as variations of the nebula hypothesis, and like variations in another

science, may be very brilliant, scientific, imaginative, grand, but

after all the flights of fancy exhibited by them are set before us,

we feel in a measure relieved when a return is made to the original

air. They all assume original motion, varied, accidental, opportune,

more dependent upon the will of the cosmogonist than on the laws of

nature, which tend to confound rather than enlighten any one who

tries to understand and bring them, mentally, into actual operation.

Laplace assumed rotary motion for the whole of his nebula, and was

thus able to account at once for the relation which exists among the

planets in respect of distance from, and period of revolution around

the sun--arising from the original rotation of the whole mass in one

piece--a result which, in any impact theory, has to be accounted for

separately, and, in plain truth, empirically in each case, and at each

step.

Seeing, then, that we have not been able to find any cosmogony, or

speculation, that gives us a more plausible idea of how the solar

system has been formed, we shall try whether from the original nebula

as imagined by Laplace, it is possible to separate the various

members, and form the system in the manner described in his celebrated

hypothesis. In other words, we shall endeavour to analyse the

hypothesis.

CHAPTER IV.

PAGE

72 Preliminaries to analysis of the Nebular hypothesis.

73 Definition of the hypothesis.

75 Elements of solar system. Tables of dimensions and masses.

78 Explanation of tables and density of Saturn.

79 Volume, density and mass of Saturn's rings, general remarks about

them, and satellites to be made from them.

79 Future of Saturn's rings.

80 Notions about Saturn's satellites and their masses.

81 Nature of rings seemingly not well understood.

81 Masses given to the satellites of Uranus and Neptune,

Explanations of.

82 Volumes of the members of the solar system at density of water.

PRELIMINARIES TO ANALYSIS OF THE NEBULAR HYPOTHESIS.

It may be thought that there is little benefit to be derived from

analysing an hypothesis which has been declared, by very eminent

authorities in the matter treated of, to be erroneous in some points of

very serious importance; but hypotheses are somewhat of the nature of

inventions, and we know that it has often happened that many parties,

aiming at the same invention, have altogether failed, while some other

person using almost exactly the same means as his predecessors, has

been entirely successful in his pursuit. How many times has it been

pointed out to us, that if such a person had only gone one step further

in the process he was following, or had only studied more deeply the

matter he had in hand, he would have anticipated by many years one of

the greatest discoveries of the age! In some cases the failure to take

that one step was occasioned through want of knowledge acquired long

years afterwards; whereas we think that in the case we have in hand, it

can be shown that the want of knowledge acquired many years after he

had formulated his hypothesis, or if otherwise, the want of faith in

what he knew, enabled Laplace to construct an edifice which otherwise

he could hardly have convinced himself could be built up in a practical

form. We think also that if he had made the proper use of the knowledge

he must have had of the law of attraction, he would have seen that no

nebula could ever have existed such as the one he assumed, extending

far beyond the orbit of the remotest planet. Furthermore, we think it

can be shown that if he had thoroughly considered what must have been

the interior construction of his nebula, he would have found one that

would have suited his hypothesis in the main point, viz. condensation

at the surface, at least equally as well as endowing it with excessive

heat. But to be able to show these things our first step must be to

analyse the hypothesis, to examine into it as minutely and deeply as

lies in our power.

For this purpose it will be necessary to define what the hypothesis is.

Many definitions have been given, more or less clear, and it would be

only a waste of time to try to set forth Laplace's own exposition of

it, with all its details, which he had no doubt studied very carefully.

But in those definitions that have come under our observation,

several of the conditions he has specified are wanting, or not made

sufficiently prominent; so instead of adopting any one of them we

will make a sort of condensation of the whole, adding the conditions

that have been left out; because the want of them, has been the cause

of mistaken conceptions of the evolution of the system having been

formed by very eminent astronomers. Our definition will therefore be as

follows:--

I. It is supposed that before the solar system was formed the portion

of space in which its planets and other bodies now perform their

revolutions and other movements, was occupied by an immense nebula

of cosmic matter in its most simple condition--of molecules or

atoms--somewhat of a spherical form, extending far beyond its present

utmost limits, and that it was endowed with excessive heat and a slow

rotary motion round its centre; which means that while it made one

revolution at the circumference it also made one at the centre. The

excessive heat, by counteracting in a certain measure the force of

gravitation, kept the molecules of matter apart from each other; but

as the heat was gradually radiated into space, gravitation became more

effective, and then began to condense and contract more rapidly, by

which process its rotary motion was, in accordance with the areolar

law, gradually increased at the surface, _in the atmosphere of the

sun_, where the cooling took place, and condensation was most active;

and the increase of rotation was propagated from there towards the

centre.

(2) As the contraction and rotation increased a time or times arrived,

when the centrifugal force produced by the rotation came to balance the

force of gravitation, and a series of zones or rings were separated

from the nebula, each one of them continuing to rotate--revolve

now--around the central mass, with the same velocities they had at

the times of their separation; until at last the nebula became so

contracted that it could not abandon any more rings, and what of it

remained condensed and contracted into a central mass which ultimately

assumed the form of the actual sun.

(3) In the meantime, or following afterwards, each one of the rings

which were abandoned by the nebula, acquired, through the friction

of its molecules with each other, an equal movement of revolution

throughout its entire mass, so that the real velocities of the

molecules furthest removed from the centre of the nebula were greater

than those of the molecules nearest to its centre, and the ring

revolved as if it were in one solid piece. Arrived at this stage the

rings broke up and formed themselves into smaller nebulæ, each of which

condensed into a globe or planet, and continued to revolve around the

central mass in the same time as its mass had done when in the form of

a ring. And some of these sub-nebulæ, imitating the example of their

common parent more perfectly than others, abandoned in space in their

turn smaller rings which in the same manner condensed, broke up, and

formed themselves into smaller globes or satellites; all, as far as we

know, except the rings of Saturn, which have not as yet been converted

into satellites.

TABLE I.

ELEMENTS AND OTHER DATA OF THE SOLAR SYSTEM EMPLOYED

IN THIS ANALYSIS.

PART I.--SUN AND PLANETS.

--------+-------------+----------+-----------------------+-----------+

--------+-------------+----------+-----------------------+-----------+

Sun | -- | 867,000 |341,237,637,800,000,000| 1·413 |

Mercury | 35,987,000| 2,957 | 13,537,968,847| 6·850 |

Venus | 67,245,000| 7,660 | 235,334,728,260| 4·810 |

Earth | 92,965,000| 7,918 | 259,923,832,335| 5·660 |

Mars | 141,650,000| 4,185 | 38,378,333,333| 4·188 |

planet| 260,300,000| -- | -- | -- |

Jupiter | 483,678,000| 87,680 | 352,940,162,601,626| 1·358 |

Saturn | 886,779,000| 73,713 | 209,716,183,575,000| 0·736 |

Uranus |1,783,383,000| 33,563 | 19,796,209,090,910| 1·302 |

Neptune |2,794,000,000| 36,620 | 25,713,106,508,876| 1·132 |

--------+-------------+----------+-----------------------+-----------+

| Volume at Density of | Time of Revolution |

Name. | Water in Cubic Miles. | round Sun in Days. |

| | |

--------+------------------------+-----------------------+

Sun | 482,169,000,000,000,000| -- |

Mercury | 92,735,000,000| 87·9692 |

Venus | 1,131,960,000,000| 224·7007 |

Earth | 1,471,169,000,000| 365·2563 |

Mars | 160,728,460,000| 686·9796 |

Supposed| | |

planet| 367,792,000,000| 1,714·1876 |

Jupiter | 479,292,741,000,000| 4,332·2548 |

Saturn | 154,351,000,000,000| 10,759·2198 |

Uranus | 25,874,664,000,000| 30,688·5076 |

Neptune | 29,107,237,000,000| 60,186·6385 |

--------+------------------------+-----------------------+

PART II.--SATELLITES OF PLANETS.

----------+--------------+-------------+-----------------+

| Mean Distance| Equatorial | Volume |

Names. | from Primary | Diameter | in Cubic Miles. |

| in Miles. | in Miles. | |

----------+--------------+-------------+-----------------+

| _Of the Earth._ |

Moon | 238,833 2160 5,276,682,926 |

| |

| _Of Jupiter._ |

Jo | 267,380 2252 5,980,050,000 |

Europa | 425,160 2099 4,842,133,708 |

Ganymede | 678,390 3436 21,240,229,268 |

Callisto | 1,192,820 2929 13,157,027,273 |

| |

| _Of Saturn._ |

Mimas | 120,800 1000 523,600,000 |

Enceladus | 155,000 ? 65,450,000 |

Tethys | 191,000 500 65,450,000 |

Dione | 246,000 500 65,450,000 |

Rhea | 343,000 1200 904,780,417 |

Titan | 796,000 3300 18,816,606,060 |

Hyperon | 1,007,000 ? 3,053,634,965 |

| |

Japetus | 2,314,000 1800 3,053,634,965 |

| |

| _Of Uranus._ |

Ariel | 123,000 } Total mass taken at |

Umbriel | 171,000 } 1/15,000th of primary |

Titania | 281,000 } 1,724,977,600 |

Oberon | 376,000 } |

| |

| _Of Neptune._ |

----- | 220,000 } Mass taken at |

| } 1/40,000th of primary |

| 727,680,925 |

----------+----------+-----------------+-----------------+

| Density. |Volume at Density| Total Volume at |

Names. |(Water=1.)| of Water in |Density of Water |

| | Cubic Miles. | in Cubic Miles.|

----------+----------+-----------------+-----------------+

| |

| _Of the Earth._ |

Moon | 3·438 .. 18,141,236,000 |

| |

| _Of Jupiter._ |

Jo | 1·132 6,769,416,600 |

Europa | 2·141 10,367,008,269 |

Ganymede | 1·868 39,676,748,273 |

Callisto | 1·472 19,367,144,146 |

| ----------------- |

| 76,180,317,288 |

| |

| _Of Saturn._ |

Mimas | ... |

Enceladus | ... |

Tethys | ... |

Dione | ... |

Rhea | ... |

Titan | ... Total Volume |

Hyperon | ... in Cubic Miles. |

| |

Japetus | 0·7 36 26,548,606,407 19,539,774,315 |

-----------+----------------------------------------------+

PART III.--RINGS OF SATURN.

---------+-----------------------------+--------------------------+

| | |

Rings. | Diameters of Rings | Areas of Rings |

| in Miles. | in Square Miles. |

---------+-----------------------------+--------------------------+

Outer { | Outer | 172,240 | } 5,252,035,427 |

{ | Inner | 151,590 | } |

| | | |

Middle { | Outer | 148,100 | } 6,919,075,757 |

{ | Inner | 114,560 | } |

| | | |

Dark { | Outer | 110,060 | } 3,040,689,488 |

{ | Inner | 90,993 | } |

| | | |

| | Total | 15,211,800,672 |

---------+----------+------------------+---------+----------------+

---------+----------+------------------+---------+----------------+

Outer { | | | | |

{ | | | | |

| | | | |

Middle { | | | | |

{ | | | | |

| | | | |

Dark { | | | | |

{ | | | | |

| | | | |

| 90 | 1,369,062,060,480| ·0001425| 195,000,000 |

---------+----------+------------------+---------+----------------+

(4) All of these bodies, planets, satellites, and rings were supposed

to revolve around their primaries, and to rotate on their axes, in the

same direction viz., from right to left, in the opposite direction to

the hands of a watch.

In addition to the above definition it is necessary to give some sort

of description of the various parts of the machine or system which has

to be made out of the nebula, with their positions, dimensions, and

details. This we believe will be made plain enough, in the simplest

manner, by Table No. I., taken and calculated from the elements of the

solar system given in almost all astronomical works, from which we have

selected what we believe to be the most modern data.

The construction of this table requires some explanation on account of

its being made to show complete results from incomplete data. There has

been no difficulty with the sun, the major planets, and the satellites

of the earth and Jupiter, but for the minor planets, the satellites of

the three outer planets, and the rings of Saturn, we have been obliged

to exercise our judgment as best we could.

There being almost no data whatever of the dimensions and densities of

the minor planets, to be found, we have been driven in order to assign

some mass to them, to imagine the existence of one planet to represent

the whole of them (in fact Olbers's planet before it exploded), which

we have supposed to be placed at the mean distance of 260,300,000 miles

from the centre of the sun; and we have given to it a mass equal to

one-fourth of the mass of the earth, that being, in the opinion of some

astronomers, the greatest mass which the whole of them put together

could have. This assumption we shall explain more fully at a more

suitable time.

In the case of Saturn the diameters of two of the satellites are

wanting which we have assumed to be the same as those of the smallest

of those nearest to them, and thus have been able to compute the

volumes of the whole of them; but we have not been able to find any

statement anywhere of their densities, and to get over this difficulty

we have reasoned in the following manner.

The density of the moon is very little over two-thirds of that of the

earth, while that of the satellites of Jupiter varies from a little

more than the same to a little more than twice as much as the density

of their primary. Why this difference? To account for it we appeal to

the very general opinion of astronomers, that the four inner planets

are in a more advanced stage of their development, or existence, than

the four outer ones. In this way it is easy to conceive that the earth

has arrived at the stage of being more dense than its satellite; while

in the case of Jupiter, his satellites being of so very much less

volume than their primary, have already arrived at a higher degree of

development. Carrying this motion forward to Saturn, we have supposed

that from his being considerably less dense than any other of the

outer planets--quite possibly from having been formed out of material

comparatively (perhaps not actually) less dense than the others--his

satellites may not have condensed to a greater degree than his own

mass, and we have, therefore assumed their density, that is the density

of the volume of the whole of them, to be the same as that of their

primary.

To determine some mass for the rings of Saturn, is a much more

intricate matter than for his satellites, and presents to us some

ideas--facts rather--which had never before crossed our imagination.

The most natural way to look upon these rings is to suppose that they

are destined to become satellites at some future time. All the modern

cosmogonies that have come under our notice are founded upon the idea

that rings are the seed, as it were, of planets and satellites, and if

those of Saturn have been left, as it has been said, to show how the

solar system has been evolved, it cannot be said that the supposition

is not well founded. In this way we are led to speculate upon how many

satellites are to be made out of the rings before us. Considering,

then, that the nearest satellite is 120,800 miles from the centre of

Saturn, leaving only 83,500 miles between his surface and that of

Mimas, and also that the distances between satellites diminish rapidly

as they come to be nearer to their primaries, there is not room to stow

away a great number of satellites. On the other hand, seeing that there

are at least three distinct rings, we cannot reasonably do less than

conclude that three satellites are intended to be made out of them. But

let the number be what it may, all that we have to do with them for our

present purpose is to assign some mass to them. With this view, we have

given, arbitrarily, to each one of the three we have supposed, a volume

equal to that of one of the satellites of 500 miles in diameter, that

is, about 65,000,000 cubic miles, and we have supposed their density to

be the same as that of water, instead of that of the planet. Thus, in

the table, we have assigned to the three a mass of 195,000,000 cubic

miles at density of water, which would be more than sufficient to make

four other satellites for the system of 500 miles in diameter each, and

of the same density as the planet.

For the table referred to we have calculated the areas of the three

rings to be 152,110,800,172 square miles, and we have assumed the

thickness as 90 miles, that is about two-thirds of that estimated by

Chambers in his handbook of Astronomy, but almost the same as that

given by Edmund Dubois; nevertheless their total volume comes up to

1,369,062,060,480 cubic miles, which reduces their average density

to 0·0001425 that of water, to make up the mass of 195,000,000 cubic

miles at the density of water, which we have adopted for the three.

This density corresponds to very nearly one-tenth of that of air,

which, however strange it may appear to us, may be considered to be

a very full allowance, seeing that we shall find, later on, that the

planet itself was formed out of matter whose density could not have

been more than one twenty-six millionth part of that of air. All the

same, it is hardly matter that we could liken to brickbats. After being

driven to this low estimate of density, which startled us, we referred

to an article in "Nature" of Nov. 26, 1886, on Ten Years' Progress

in Astronomy, where we find what follows:--"He (Newcomb) finds the

mass of Titan to be about 1/12,000 that of Saturn. It may be noted,

too, that Hall's observations of the motions of Mimas and Enceladus

indicate for the rings a mass less than 1/10 that deduced by Bessel;

instead of being 1/100 as large as the planet, they cannot be more than

1/1000, and are probably less than 1/10,000." (We make them 1/791514).

Thinking over the numbers herein given we cannot help being surprised

by them. If Titan be 1/12500 of the mass of Saturn, we cannot conceive

how the mass of his rings can be so much greater than that of Titan. We

cannot pretend to fit even one satellite of that size, mechanically,

into a space of 83,500 miles wide, while Titan revels in an ample

domain with a width of 332,000 miles. But we shall not pursue this part

of our speculations any further. Astronomers may be able to demonstrate

that the rings are of a totally different nature to those out of which

the planets and their satellites are supposed to have been made, or

that the nebular hypothesis or anything resembling it is no better than

a foolish dream. All that we have pretended to do has been to give them

their due place in the hypothesis we are attempting to analyze, and to

look upon them in a practical and mechanical light, as an unfinished

part of the solar system.

To determine masses for the satellites of the two outer planets, we

have to be more empirical even than we have yet been. A little trouble

will show that the whole mass of all the satellites and rings of Saturn

put together is about 1/7820th of the mass of the planet, and we shall

avail ourselves of this proportion to assign masses for the satellites

of the remaining planets, the numbers and names of which are the only

data we have been able to find. Considering then, that Uranus has only

four satellites and no rings, we think if we give them 1/15,000th of

the mass of their primary, it will be a very fair allowance; and with

the same empiricism we have adopted for the solitary satellite of

Neptune 1/40,000th of the mass of its primary.

However rude and crude these approximations may be, we have the

satisfaction of thinking that the masses obtained by their means, can

have no appreciable effect upon the operations into which they are to

be introduced, whilst they enable us to deal with a complete system

or machine. But for these we have another Table No. II. to present, a

_résumé_ of the foregoing one, for greater facility of reference.

TABLE II.--VOLUMES OF THE VARIOUS MEMBERS OF THE

SOLAR SYSTEM AT THE DENSITY OF WATER.

---------+------------+-------------------+-----------------------+

| | Volume in | Total Volume in |

Name. |Designation.| Cubic Miles at | Cubic Miles at |

| | Density of Water. | Density of Water. |

---------+------------+-------------------+-----------------------+

Sun | | |482,169,000,000,000,000|

| | |-----------------------|

Mercury | Planet | | 92,735,000,000|

Venus | " | | 1,131,960,000,000|

Earth | " | 1,471,169,000,000| |

Moon | Satellite | 18,141,236,000| 1,489,310,236,000|

| |-------------------| |

Mars | Planet | | 160,728,460,000|

---- | Asteroids |One fourth of Earth| 367,792,000,000|

Jupiter | Planet |479,292,741,000,000| |

" |4 Satellites| 76,180,317,000| 479,368,921,317,000|

| |-------------------| |

Saturn | Planet |154,351,000,000,000| |

" |8 Satellites| 19,539,774,315| |

" | 3 Rings | 195,000,000| 154,370,734,774,315|

| |-------------------| |

Uranus | Planet | 25,874,664,000,000| |

" |4 Satellites| 1,724,977,600| 25,876,388,977,600|

| |-------------------| |

Neptune | Planet | 29,107,237,000,000| |

" |1 Satellite | 727,680,925| 29,107,964,680,925|

---------+------------+-------------------+-----------------------+

Total of Planets, Satellites and Rings | 691,966,535,445,840|

------------------------------------------+-----------------------+

Dividing 482,169,000,000,000,000 by 691,966,535,445,840

makes the mass ofthe whole of the members to be 1/696·86th

part of the mass of the sun, instead of 1/700th as

generally stated by astronomers.

CHAPTER V.

PAGE

83 Analysis of the Nebular Hypothesis. Separation from the nebula

of the rings for the separate planets, etc.

84 Excessive heat attributed to the nebula erroneous and impossible.

85 Centigrade thermometer to be used for temperatures.

86 Temperature of the nebula not far from absolute zero.

86 Erroneous ideas about glowing gases produced by collisions of

their atoms, or particles of cosmic matter in the form

of vapours.

87 Separation of ring for Neptune. It could not have been thrown

off in one mass, but in a sheet of cosmic matter.

88 Thickness and dimensions of the ring.

89 Uranian ring abandoned, and its dimensions.

90 Saturnian ring do. do.

91 Jovian ring do. do.

93 Asteroidal ring do. do.

94 Martian ring do. do.

95 Earth ring do. do.

96 Venus ring do. do.

97 Mercurian ring do. do.

98 Residual mass. Condensation of Solar Nebula to various diameters,

and relative temperatures and densities.

100 Unaccountable confusion in the mode of counting absolute

temperature examined and explained. Negative 274 degrees

of heat only equal 2 degrees of absolute temperature.

103 The Centigrade thermometric scale no better than any other,

and cannot be made decimal.

104 The sun's account current with the Nebula drawn up and represented

by Table III.

ANALYSIS OF THE NEBULAR HYPOTHESIS.

We may now proceed to take the original nebula to pieces, by separating

from it all the members of the solar system, in performing which

operation we shall suppose the divisions between the nebula and each

successive ring to have taken place at a little more or less than the

half distances between the orbits of two neighbouring planets, because

we have no other data to guide us in determining the proper places.

These divisions have manifestly been brought about in obedience to

some law, as is proved in great measure by what is called Bode's Law;

although no one has as yet been able to explain the action of that

law. It is no doubt certain that a division must have taken place much

nearer to the outer than the inner planet in each case, if we think of

what would be the limit to the sphere of attraction between the nebula

and a ring just detached from it--for the attraction of the abandoned

ring, and even of all those that were outside of it, would have

very little influence in determining the line where gravitation and

centrifugal force came to balance each other--but the data necessary

for calculating what these would be are wanting. Even if they existed

the calculations would become too complicated for our powers as the

number of rings increased; and for our purpose it is really of very

little importance where the divisions took place. The breadths of

the rings would be practically the same, whether they were divided

at the half distances between, or much nearer to, the outermost of

two neighbouring planets; and although the extreme diameters of the

consecutive residuary nebulæ would be somewhat greater, their densities

and temperatures would not materially differ from those we shall

find for them as we proceed in our operations. Their masses would be

the same in all cases, which is the principal thing in which we are

interested.

This premised, we shall first examine into the excessive heat

attributed to the nebula, that being the first condition mentioned in

our definition of the hypothesis.

The diameter of the sun being 867,000 miles, his volume is

341,238,000,000,000,000 cubic miles, and his density being 1·413 times

that of water, his volume reduced to the density of water would be

482,169,000,000,000,000 cubic miles. Now, astronomers tell us that the

whole of the planets, with their satellites and rings, do not form a

mass of more than 1/700th part of the mass of the sun. If, then, we add

1/700th part to the above volume, we get a total volume, for the whole

of the system, of 482,857,590,478,000,000 cubic miles at the density

of water, which corresponds to a sphere of about 973,360 miles in

diameter. On the other hand, the diameter of the orbit of Neptune being

5,588,000,000 miles, if we increase that diameter to 6,600,000,000

miles, so that the extreme boundary of the supposed nebula may be as

far beyond his orbit, as half the distance between him and Uranus is

within it, we shall still be far within the limit at which the process

of separation from the nebula, of the matter out of which Neptune was

made, must have begun. From these data we can form a very correct

calculation of what the density--tenuity rather--of the nebula must

have been. For, as the volumes of spheres are to each other as the

cubes of their diameters, the cube 973,630 is easily found to be to the

cube of 6,600,000,000, as 1 is to 311,754,100,720, or in other words,

the density of the nebula turns out to have been 1/311,754,100,720th

part of density of the whole solar system reduced to that of water.

Carrying the comparison a little further, we find that as water is

773·395 times more dense than air, and 11,173·184 times more dense

than hydrogen, the density of the nebula could not have been more than

1/403,000,000th part that of air, and 1/27,894,734th that of hydrogen.

But, confining the comparison to air, as it suits our purpose better,

we see that it would take 403,000,000 cubic feet of the nebula to be

equal in mass to 1 cubic foot of air at atmospheric pressure; and that

were we to expand this cubic foot of air to this number of times its

volume, the space occupied by it would be as nearly in the state of

absolute vacuum as could be imagined, far beyond what could be produced

by any human means. Now, were heat a material, imponderable substance,

as it was at one time supposed to be, we could conceive of its being

piled up in any place in space in any desired quantity; but it has been

demonstrated not only not to be a substance at all, but that its very

existence cannot be detected or made manifest, unless it is introduced

by some known means--friction, hammering, combustion--into a real

material substance. Therefore, we must conclude that if it existed at

all in the nebula, it must have been in a degree corresponding to the

tenuity of the medium, and the air thermometer will tell us what the

temperature must have been if we only choose to apply it.

Applying, then, this theory of the air thermometer, if we divide[B]

274° by 403,000,000--the number of times the density of the nebula

was less than that of air--we get 0·00000068°, as the absolute

temperature of the nebula, something very different to excessive heat,

incandescence, firemist, or any other name that has been given to its

supposed state. Furthermore, as a cubic foot of air weighs 565·04

grains, 403,000,000 divided by 565·04, which is equal to 713,223,

would be the number of cubic feet of the space occupied by the nebula,

corresponding to each grain of matter in the whole solar system, which

would be equal to a cube of very nearly 90 feet to the side. And as the

only means by which the nebula could acquire heat would be by collision

with each other of the particles of matter of which it was composed; to

conceive that two particles weighing 1 grain each, butting each other

from an average distance of 90 feet, could not only bring themselves,

but all the space corresponding to both of them--which would be

1,426,446 cubic feet, _of what_?--up to the heat of incandescence, or

excessive heat of any kind, is a thing which passes the wit of man.

Consequently, neither by primitive piling up, nor by collisions among

the particles, could there be any heat in the nebula at the dimensions

we have specified, beyond what we have measured above.

[B] Here we beg to state that in all our coming operations, we will use

the Centigrade Scale for temperatures without adding C to each number

specified, unless a different scale has to be referred to, in which

case the distinctive of the scale shall be given in the usual way. This

we do because it is the fashion, not because we think it possesses any

advantage over any other scale, but rather the contrary. Perhaps we

may have something more to say about scales after we have handled the

Centigrade a little more than it has been our lot to do hitherto.

Some people believe, at least they seem to say so, that meteors or

meteorites colliding would knock gas out of each other, sufficient

to fill up the empty space around them, and become incandescent, and

so pile up heat in nebulæ sufficient to supply suns for any number

of millions of years of expenditure. But they forget that gas is not

a _nothing_. It possesses substance, matter, of some kind, however

tenuous. Therefore, if the meteors knock matter out of each other in

the form of gas, they must end by becoming gas themselves, and we come

back to what we have said above; we have two grains, in weight, of gas

abutting each other at an average distance of 30 yards, instead of two

grains of granite or anything else, and things are not much improved

thereby. And if we compare 30 yards with M. Faye's 3000, where are we?

The next thing to deal with is the formation of the planets.

SEPARATION OF RING FOR NEPTUNE.

When the nebula was 6,600,000,000 miles in diameter its volume would

be 150,532,847,222^{18}[C] cubic miles, and we have just seen that

its density must have been 311,754,100,720 times less than that of

water, or 403,000,000 less than air, and its temperature 0·00000068°

above absolute zero. On the other hand, we find from Table II. that

the volume of Neptune and his satellite is 29,107,964,680,925 cubic

miles at the density of water. Multiplying, therefore, this volume by

311,754,100,720 we get 9,074,530^{18} cubic miles as the volume of the

ring for the formation of Neptune's system at the same density as the

nebula. Then, subtracting this volume from 150,532,847,222^{18}, there

remain 150,523,772,692^{18} cubic miles as the volume to which the

nebula was reduced by the abandonment of the ring out of which Neptune

and his satellite were formed.

[C] The exponent 18 in 150,523,772,692^{18} means that 18 cyphers have

to be added to complete the number. The same is the case with any other

number and exponent of large quantities.

Then the mean diameter of the orbit of Neptune being 5,588,000,000

miles, its circumference or length will be 17,555,261,000 miles, and if

we divide the volume of his system as stated above, by this length, we

get 516,912,620,000,000 square miles as the area of the cross section

of the ring, which is equal to the area of a square of 22,735,123

miles to the side. Again, if we divide the circumference of the orbit

by this length of side, we find that it is 1/772·165th part of it,

and therefore about 28 minutes of arc. Also if we divide the diameter

of the orbit by an arc of 22,735,123 miles in length, we find that it

bears the proportion of 1 to 246 to the diameter of the orbit. Thus the

cross section of the ring would bear the same ratio to its diameter

that a ring of 1 foot square would bear to a globe of 246 feet in

diameter. Here we find it difficult to believe that by rotating a ball

of 246 feet in diameter of cosmic matter, meteorites, or brickbats,

we could detach from it, mechanically, by centrifugal force a ring

of 1 foot square, and the same difficulty presents itself to us with

respect to the nebula. We cannot conceive how a ring of that form could

be separated by centrifugal force from a rotating nebula, and have

therefore to suppose it to have had some different form, and to apply

for that to the example of Saturn's rings--just the same as Laplace no

doubt did. We cannot tell how the idea originated that the ring should

be of the form we were looking for--perhaps it was naturally--but it

seems to have been very general, and in some cases to have led to

misconceptions. It is not difficult to show how a Saturnian or flat

ring could be formed, but we shall have a better opportunity hereafter

of doing so. We must try, nevertheless, to form some notion, however

crude it may be, of what might be the thickness of a flat ring of the

cross section and volume we have found for Neptune.

Let us suppose that the final separation of the ring took place

somewhere near the half-distance between his orbit and that of

Uranus, say, 2,290,000,000 miles from the centre of the nebula, the

breadth of the ring would be the difference between the radius of

the original nebula, i.e. 33,000,000,000 miles and the above sum,

which is 1,010,000,000 miles. Then if we divide the area of the cross

section of the ring by this breadth, that is, 516,912,620,000,000 by

1,010,000,000, we find that the thickness would be 511,794 miles;

provided the ring did not contract from its outer edge inwards during

the process of separation. This could not, of course, be the case,

but, as we have no means of finding how much it would contract in that

direction, we cannot assign any other breadth for it; and we shall

proceed in the same manner in calculating the thicknesses of the rings

for all the other planets as we go along. We can, however, make one

small approach to greater accuracy. We shall see presently that the

density of the ring would be increased threefold at its inner edge as

compared with the outer during the process of separation, which would

reduce its average thickness to somewhere about 341,196 miles at

density of water, of course. The nebula remaining after Neptune's ring

we may now call

THE URANIAN NEBULA.

The volume of the nebula after abandoning the ring for the system

of Neptune was found to be 150,523,772,692^{18} cubic miles at its

original density, but during the separation it has been condensed

into a sphere of 4,580,000,000 miles in diameter, whose volume would

be 50,303,255,814^{18} cubic miles; so that if we divide the larger

of these two volumes by the smaller, we find that the density of the

Uranian nebula would be increased 2·9923 times, and therefore it would

then be 311,754,100,720 divided by 2·9923, equal to 104,184,535,721

times less dense than water. Furthermore, if we compare it to the

density of air, which we can do by dividing this last quantity by

773·395, we find it to have been 134,710,620 times less than that

density; and if we apply the air thermometer to it, we shall find that

its absolute temperature must have been 274 divided by 134,710,620 =

0·000002034° or -273·9999796.°

We can now separate the ring for the system of Uranus from the

Uranian nebula, reduced as we have seen to 4,580,000,000 miles in

diameter, volume of 50,303,255,814^{18} cubic miles, and density

of 104,184,535,721 times less than water. Referring to Table II.,

we find the volume of the whole system of Uranus to have been

25,876,388,977,690 cubic miles at the density of water, but we have to

multiply this volume by the new density of 104,184,535,721 times less

than water in order to bring it to the same density as the nebula,

which will make the volume of his system to be 2,695,918,851^{15}

cubic miles at that density. Then, subtracting this volume from

50,303,255,814^{18}, we find that the nebula has been reduced to

50,300,559,895,149^{15} cubic miles in volume.

Then the diameter of the orbit of Uranus being 3,566,766,000 miles, its

circumference will be 11,205,352,065 miles, so that dividing the volume

2,695,918,851^{15} of his system by this length of circumference, the

area of the cross section of the ring would be 240,592,061,166,666

square miles. If we now suppose the diameter of the nebula, after

abandoning the ring for the whole system of Uranus, to have been

2,672,000,000 miles--dimension derived from nearly the half-distance

between the orbits of Uranus and Saturn--we find that the breadth of

the ring would be 954,000,000 miles, which would be the difference

between the radii of the Uranian and Saturnian nebulæ, respectively

2,290,000,000 miles, and 1,336,000,000 miles; so that if we divide the

area of cross section of Uranus' ring or 240,592,070,232,288 square

miles by this breadth we find the thickness of the ring to have been

252,193 miles. But the density of the inner edge of the ring would be

5·036 times more dense than the outer edge, for the same reason as in

the case of the Neptunian ring, which would make the average thickness

to have been about 100,553 miles.

SATURNIAN NEBULA.

We have seen that the volume of the nebula after the separation of

the ring for Uranus' system would be 50,300,559,859,149^{15} cubic

miles, but as we have reduced the diameter of the Saturnian nebula to

2,672,000,000 miles, its volume would also be reduced, or condensed to

9,988,700^{21} cubic miles, so that dividing the larger volume by the

smaller we find that its density must have been increased 5·036 fold.

Then dividing 104,184,535,721 by 5·036, we see that the density would

be reduced, or increased rather, to 20,689,000,000 times less than that

of water. This can be easily found to be 26,750,876 times less than the

density of air, and the air-thermometer would show that the absolute

temperature of the Saturnian nebula must have been 0·000010242° or

-273·99998976°.

We have just seen that the Saturnian nebula has been condensed to

2,672,000,000 miles in diameter, to volume of 9,988,700^{21} cubic

miles, and density of 20,689,000,000 times less than that of water.

Then from Table II. we get the volume of the whole of the system of

Saturn as 154,370,734,774,315 cubic miles at the density of water, and

multiplying this by 20,689,000,000 will give 3,193,775,478^{15} as its

volume at the same density as the nebula; and subtracting this from

9,988,700^{21} we find that the volume of the nebula had been reduced

to 9,985,506,224,522^{15} cubic miles.

Then the diameter of the orbit of Saturn being 1,773,558,000 miles its

circumference would be 5,571,809,813 miles in length, and if we divide

the volume of his system, viz. 3,193,775,478^{15} cubic miles, by this

length, we find the area of the cross section of the ring to have been

573,202,529,391,503 square miles. Now, supposing the diameter of the

nebula, after abandoning the ring, to have contracted to 1,370,800,000

miles and radius consequently of 685,400,000 miles, the breadth of the

ring would be 1,336,000,000 less 685,400,000 or 650,600,000 miles;

and if we divide the area of the cross section of the ring, that is,

573,202,529,391,503 square miles, by this breadth, we get 881,037 miles

for its thickness. But in the same way as before, the inner edge of the

ring would be 7·4037 times more dense than the outer edge, which would

reduce its average thickness to 238,000 miles.

JOVIAN NEBULA.

The volume of the nebula after separation of the ring for Saturn's

system having been 9,985,506,224,522^{15} cubic miles, this volume has

to be condensed into the volume of the Jovian nebula of 1,370,800,000

miles in diameter, which would be 1,348,720,186,335^{15} cubic miles.

Then if we divide the first of these two volumes by the second, we find

the density of the Jovian nebula to have been increased 7·4037 fold

over the previous one. But the density of the Saturnian nebula was

20,689,000,000 times less than water, dividing which by 7·4037 makes

the Jovian nebula to have been 2,794,417,420 times less dense than

water. Dividing this by 773·395 we get a density for it of 3,613,182

times less than that of air, which corresponds to the absolute

temperature of 0·00007583° or -273·99992417°.

From the Jovian nebula of 1,370,800,000 miles in diameter, volume of

1,348,720,186,335^{15} cubic miles, and density of 2,794,417,420

times less than water, we have now to deduct the whole of the system

of Jupiter, which, by Table No. II., is 479,368,921,317,000 cubic

miles at density of water. Multiplying this by 2,794,417,420 we get

the volume of 1,339,557,155^{15} cubic miles for his system at the

same density as the nebula; therefore, substracting this amount from

1,348,720,186,335^{15} we get 1,347,380,629,180^{15} cubic miles as the

volume to be condensed into the succeeding nebula which we shall call

Asteroidal, the dimensions of which we can determine in the following

manner, although only very approximately.

According to the nebula hypothesis, there must have been a ring

detached from the nebula for the formation of the Asteroids, as well as

the formation of the other planets. So, in order to be able to assign

elements for that ring, corresponding to those we have found for the

others, we shall suppose the whole of them to have been collected

into one representative planet, at the mean distance from the centre

of the nebula of 260,300,000 miles, more or less in the position

denoted by the number 28 in Bode's Law; also its mass to have been

one-fourth of that of the earth, or 367,792,000,000 cubic miles at

density of water, which, in the opinion of probably most astronomers,

is a considerably greater mass than would be made up by the whole of

them put together--discovered and not yet discovered. With the above

distance from the centre of the nebula, the divisionary line between

the Jovian and the Asteroidal nebulæ would be 372,000,000 miles from

the said centre, and the diameter of the latter 744,000,000 miles in

consequence.

We know that some of the Asteroids move in their orbits beyond this

supposed divisionary line, and it may be that when we come to determine

the divisionary line between the supposed Asteroidal and the Martian

nebulæ, some of them may revolve in their orbits nearer to Mars than

that line, but that will not interfere in any way with our operations,

because we are only dealing with the whole of them collected into one

representative.

For finding the dimensions of the ring for Jupiter's system, we have

the mean diameter of his orbit as 967,356,000 miles, which makes

its circumference to be 3,039,045,610 miles in length. Therefore,

dividing the volume of the ring as found above, viz. 1,339,557,155^{15}

cubic miles by this length, the area of its cross-section comes to be

440,782,188,524,000 square miles, which divided in turn by the breadth

of 313,400,000--the difference between the radii of the Jovian and

Asteroidal nebulæ, or 685,400,000 less 372,000,000--makes the thickness

of the ring to have been 1,406,771 miles. But, as before, the inner

edge of the ring had become 6·2484 times more dense than the outer

edge, so that the average thickness would be only 450,282 miles.

ASTEROIDAL NEBULA.

The volume of the nebula after the separation of the ring for the

system of Jupiter having been 1,347,380,629,180^{15} cubic miles,

this volume has to be condensed into the volume of the Asteroidal

nebula of 744,000,000 miles in diameter and consequently of volume of

215,634,925,373,133,820^{9} cubic miles. Then if we divide the first of

these volumes by the second, we find the density to have been increased

6·2484 fold, as used above for the average thickness of Jupiter's ring.

But the density of the Jovian nebula was 2,794,417,420 times less than

water, dividing which by 6·2484 makes the Asteroidal nebula to have

been 447,218,905 times less dense than water. This again divided by

773·395 makes it 578,254 times less dense than air, which will give us

0·00047384° as its absolute temperature--or the same as -273·99952616°.

Next, from the Asteroidal nebula 774,000,000 miles in diameter, volume

of 215,634,925,373,133,820^{9} cubic miles, and density 447,218,905

times less than water, we have to deduct the volume of the whole

of the system which in Table No. II. we have supposed to have been

367,792,000,000 cubic miles at density of water. Multiplying this

by 447,218,905 we get the volume to have been 164,482,717,200^{9}

cubic miles for the ring at the same density as the nebula; so,

deducting this quantity from 215,634,925,133,820^{9}, we get

215,634,760,890,416,620^{9} cubic miles as the volume to which the

nebula had been reduced by the separation of the ring.

For the dimensions of the ring we have the mean diameter of the orbit

of the representative Asteroid as 520,600,000 miles, that is twice its

distance from the centre of the nebula, which makes its circumference

to be 1,635,516,960 miles in length. Dividing then the volume of the

ring, which we found to have been 164,482,717,200^9 cubic miles by this

length, the area of its cross-section must have been 100,569,251,938

square miles, which divided by the breadth of 171,000,000 miles--the

difference between the radii of the Asteroidal and Martian nebula,

namely 372,000,000 less 201,000,000--makes the thickness of the ring to

have been 588 miles. But the inner having been 6·339 times more than

the outer edge, as we shall see presently, the average thickness would

be 185 miles.

MARTIAN NEBULA.

The volume of the last nebula after the separation of the ring for

the Asteroids was found to have been 215,634,760,890,416,620^{9}

cubic miles, which had to be condensed into the volume of the Martian

nebula of 402,000,000 miles in diameter, which would give a volume of

34,015,582,677,165,354^{9} cubic miles. Dividing then, the larger of

these volumes by the smaller, we find that the density of the Martian

nebula had been increased 6·339 times by the condensation. But we found

the density of the Asteroidal nebula to have been 447,218,905 times

less dense than water, dividing which by 6·339 makes the Martian nebula

to have been 70,547,110 times less dense than water. This divided again

by 773·395 makes it 91,259 times less dense than air, and consequently

its absolute temperature to have been 0·00300243° or -273·99699757°.

From the Martian nebula of 402,000,000 miles in diameter, volume

34,015,582,677,165,354^{9} cubic miles, and density 70,547,110 times

less than water, we have to deduct the volume of his ring, which by

Table II., was estimated at 160,728,460,000 cubic miles at density

of water. Multiplying this by 70,547,110 we find its volume to be

11,338,927,154^{9} cubic miles at the same density as the nebula,

deducting which from its whole volume we get 34,015,571,338,237,20^{9}

cubic miles as the volume after the separation of the ring.

For finding the dimensions of the ring we have 283,300,000 miles as

the mean diameter of the orbit of Mars, which makes its circumference

890,015,280 miles in length. Then dividing the volume of the ring

11,338,927,154^{9} cubic miles by this length, the area of its

cross-section comes to be 12,740,148,859 square miles, which, divided

by the breadth of 83,690,000 miles--that is one-half of the difference

between the diameters of the Martian and Earth nebula, respectively

402,000,000 and 234,620,000 miles--makes the thickness of the ring to

have been 152 miles. But as before, the inner having become through

condensation, 5·0302 times more dense than the outer edge, the average

thickness would be 61 miles.

EARTH NEBULA.

As the volume of the nebula was 34,015,571,338,237,200^{9} cubic miles

after the separation of the ring for Mars, we have to condense it into

the volume of the earth nebula, which at 234,620,000 miles in diameter

would be 6,762,303,076,923,031^{9} cubic miles. Dividing the larger of

these volumes by the smaller we find that the density of the nebula

has been increased 5·0302 times, as employed above. But we found the

density of the Martian nebula to have been 70,547,110 times less than

that of water, dividing which by 5·0302 makes the earth nebula to have

been 14,024,781 times less dense than water. Dividing this again by

773·395 we find it to have been 18,134 times less dense than air, and

274° divided by this density of air--the same as in all the respective

cases--gives 0·0151097° as the absolute temperature of the nebula and

corresponds to -273·9848903°.

From the earth nebula 234,620,000 miles in diameter,

6,762,303,076,923,031^{9} cubic miles in volume, and 14,024,781 times

less dense than water, we have to subtract the volume of the ring of

the earth's system, which, in Table II., appears as 1,489,310,236,000

cubic miles at density of water. Multiplying this by 14,024,781 we find

it to have been 20,887,249,553^{9} cubic miles at the same density as

the nebula. And subtracting this quantity from 6,762,303,076,923,031^9,

we get 6,762,282,189,673,478^9 cubic miles for the volume of the

previous nebula after the separation of the ring for the system of the

earth.

For finding the dimensions of the ring we have 185,930,000 miles for

the mean diameter of the Earth's orbit, which makes the circumference

584,117,688 miles in length, and dividing the volume of the ring for

the system, which was found to be 20,887,249,553^9 cubic miles, by

this length, the area of its cross section comes to be 35,760,344,109

square miles, which divided by the breadth of 37,205,000 miles--that

is one-half of the difference between the diameters of the Earth and

Venus nebulæ, respectively 234,620,000 and 160,210,000 miles--makes

the thickness of the ring to have been 961 miles. But the inner will

presently be seen to have been 3·141 times more dense than the outer

edge when its separation was completed, so that the average thickness

would be 612 miles.

VENUS NEBULA.

As the volume of the nebula was 6,762,282,189,673,478^9 cubic miles

after the separation of the ring for the system of the Earth, we

have to condense it into the volume of the Venus nebula, which at

160,210,000 miles in diameter would be 2,153,120,792,079,208^9 cubic

miles. Then dividing the larger of these two volumes by the smaller, we

find that the density of the Venus nebula had been increased to 3·141

times what that of the Earth nebula was. But we found the density of

that nebula to have been 14,024,781 times less than that of water,

dividing which by 3·141 makes the Venus nebula to have been 4,465,512

times less dense than water. Dividing this again by 773·395 we find

it to have been 5,774 times less dense than air, which would make its

absolute temperature to have been 0·04745486°, which corresponds to

-273·9525459°.

From the Venus nebula of 160,210,000 miles in diameter, volume

2,153,120,792,079,207,921^{6} cubic miles, and density 4,465,512

times less than that of water, we have now to deduct the volume of

her ring, which by Table II. is 1,131,960,000,000 cubic miles at the

density of water. Multiplying this volume by 4,465,512 we find the

volume of the ring to have been 5,054,780,604,651^{6} cubic miles

at the same density as the nebula, and subtracting this amount from

2,153,120,792,079,207,921^{6} we get 2,153,115,737,298,603^{6} cubic

miles for the volume to be condensed into the nebula following.

To find the dimensions of the ring we have 134,490,000 miles for

the diameter of the orbit of Venus, which makes its circumference

422,513,784 miles in length. Then dividing the volume of the ring,

i.e. 5,054,780,604,651^{6} cubic miles by this length, the area of its

cross-section comes to be 11,963,821,788 square miles, which, divided

by the breadth of 28,489,000 miles--that is one-half of the difference

between the diameters of the Venus and Mercurian nebulæ, respectively

160,210,000 and 103,232,000 miles--makes the thickness of the ring to

have been 420 miles. But the inner edge having become, in the process

of separation, 3·738 times more dense than the outer one (see below)

the average thickness would be reduced to 225 miles.

MERCURIAN NEBULA.

As the volume of the nebula was 2,153,115,737,298,603,270^{6} cubic

miles after the separation of the ring for Venus, we have to condense

it into the volume of the Mercurian nebula, which at 103,232,000 miles

in diameter would be 576,026,613,333,333,333^{6} cubic miles. Then,

dividing the larger of these two volumes by the smaller, we find that

the density of the Mercurian nebula must have been increased 3·738 fold

over that of its predecessor. But we find the density of the Venus

nebula to have been 4,465,512 times less than water, dividing which

by 3·738 makes the Mercurian nebula to have been 1,194,666 times less

dense than water. Dividing again this density by 773·395 we find it

to have been 1545 times less than air, and 274° divided by this air

density gives 0·1773463° as its absolute temperature, which corresponds

to -273·8226537°.

From the Mercurian nebula 103,232,000 miles in diameter, volume of

576,026,613,333,333,333^{6} cubic miles, and density of 1,194,666

times less than water, we have to deduct the volume of his ring,

which by Table II. is 92,735,000,000 cubic miles at density of water.

Multiplying this volume by 1,194,666 makes the ring to have been

110,787,355,300^{6} cubic miles in volume at the density of the nebula,

and subtracting this amount from 576,026,613,333,333,333^{6}, we get

576,026,502,545,978,033^{6} cubic miles for the volume to be condensed

into the nebula following.

To find the dimensions of the ring we have 71,974,000 miles for the

mean diameter of the orbit of Mercury, which makes its circumference

226,113,518 miles in length. Then dividing the volume of his ring,

i.e. 110,787,355,300^{6} cubic miles, as above, by this length, the

area of its cross-section comes to be 489,963,459 square miles. Here

we have to determine the breadth of the ring in a new way, that is

empirically. Seeing that the breadth of the ring for the earth's system

was 37,205,000 and of that for Venus 28,489,000 miles, we shall assume

20,000,000 miles for the breadth of the ring for Mercury. This will

make the residuary, now the Solar nebula, to have been 31,616,000 miles

in radius and 63,232,000 miles in diameter. Returning now to the area

of the cross-section of the ring, that is, 489,963,459 square miles,

and dividing it by the assumed breadth 20,000,000 miles, makes the

thickness of the ring to have been 25 miles. But, as before, its inner

edge having become 4·354 times more dense than the outer one during the

process of separation (see below) the average thickness must have been

only 11 miles.

SOLAR NEBULA.

Lastly, as the volume of the nebula was

576,026,502,545,978,033^{6}

cubic miles after the separation of the ring for Mercury, we have to

condense it into the volume of the Solar nebula, which at 63,232,000

miles in diameter would be

132,376,310,975,609,756^6

cubic miles. Then dividing the first of these two volumes by the

second, we find that its density must have been increased 4·3514 fold.

But we found that the density of the Mercurian nebula was 1,194,666

times less than that of water, dividing which by 4·3514 makes the Solar

nebula to have been 274,546 times less dense than water. Dividing this

in turn by 773·395 shows it to have been 355 times less dense than

air, and, still further, dividing 274° by this air density makes its

absolute temperature to have been 0·7718585° equal to -273·2281415°.

We might conclude our analysis here, but it will be more convenient

to carry our calculations a few steps further, to save the additional

trouble that might be occasioned by having to return to them later on.

First we shall condense the Solar nebula to 211,911 times less dense

than water, and therefore 274 times less dense than air, which we may

note will increase its density 1·2956 times. This supposed to be done,

its diameter would be 58,002,920 miles, its volume 102,176,129,412^{12}

cubic miles, and its density 1/274th of an atmosphere--about

_one-ninth_ inch of mercury--which would, in consequence, make its

absolute mean heat equal to _one degree_ of the ordinary Centigrade

scale, or, in another way of expressing it, equal to -273°.

Second. Let us condense this same nebula to 773·395 times less dense

than water, and consequently to the density of air at atmospheric

pressure, then its diameter will be 8,930,309 miles, volume

372,905,560,345^9 cubic miles, and the mean heat 0°, or the heat of

freezing water--which by some unexplained process of thought has

hitherto been considered to be 274° of absolute _temperature_.

Third. By again condensing the Solar nebula to the density of water,

corresponding to a pressure of more than 773 atmospheres, its diameter

becomes 972,285 miles, its volume 482,167^{12} cubic miles, and mean

heat 775°, including the 2° acquired in condensing it to the pressure

of 1 atmosphere, as is plainly shown in Table III.

Before going any further we must enter into a digression to examine

into the process of thought by which the absolute zero of heat has

come to be called the absolute zero of temperature, and absolute

temperature to be so many degrees of negative--less than 0° or

nothing--heat counted from the lower or wrong end, to be called

positive absolute temperature; thus making heat and temperature appear

to be two very different things, without giving any explanation of what

is the difference between them.

Science has, as it were, gone down a stair of 274 steps carrying along

with it the laws of gases, and has found, most legitimately, with their

assistance the total absence of even negative heat at the bottom of it;

and, leaving these laws there, has jumped up to the top of the stair,

thinking that it carried along with it 274° of absolute heat, which it

now calls temperature; instead of bringing the said laws up with it

and verifying, if not at every step at least at intervals, how much it

brought up with it of what it had taken down. Had it done so it would

have found that at the top of the stair it had got what was equal to

only 2° of positive heat as measured by the Centigrade scale, as has

been shown above, which might be called temperature, but that would

not mend matters. Science seems to have forgotten, for the time being

at least, all about the laws of gases; it had got something which it

thought would enable it to mount much higher, and was satisfied. It

will not be difficult to do away with the confusion of thought that is

thus shown to have occurred.

The laws of gases are founded upon the fact that in gases there is a

necessary interdependence between heat and pressure, and the starting

points adopted by science for calculating this interdependence in them

are 0° of heat and 1 atmosphere of pressure at 0° of heat. Obeying

these laws, we have argued, from the beginning of our operations, that

heat requires something to hold it in, and that the nebula from which

the Solar system was formed--if it was so formed--could only contain

heat in proportion to its density; that is being a gas, or vapour in

the form of a gas, it could not contain, i.e. hold in it, more than 2°

of positive heat when its density was equal to the pressure belonging

to 1 atmosphere of a gas; all as shown in the most irrefragable manner

in this chapter and in the accompanying Table III.

A gas can be easily compressed in a close vessel to a pressure of 100

atmospheres, which would enable it to hold 100° of heat due to that

compression; in fact, were it compressed to that degree by a piston in

a cylinder, without any loss of heat, it would be raised to that heat

by that act alone, but that would raise it to only 102° instead of 374°

of what is called absolute temperature according to present usage;

because as a gas it could not hold any more heat at that pressure. It

is, therefore, evident that this _usage_ has not been derived from the

laws of gases. Neither has it been derived from the other two states

of liquid and solid to which all gases can be reduced, as can be very

easily demonstrated.

To cool steam at atmospheric pressure from its gaseous to its liquid

state 519° of heat of one kind and another--as measured by the

Centigrade thermometer--have to be abstracted from it, which leaves

the liquid at its boiling point of 100°--a quantity that has been

arbitrarily adopted to mark the difference between the freezing and

boiling points of this liquid. In order, after this, to reduce the

liquid, now water, to the freezing, or what is called 0° of heat,

these 100 degrees of heat have to be extracted from it, which is not

very difficult to do because the heat put into it arbitrarily can be

extracted from it; but if it is now wanted to change the steam from

its liquid to its solid state, the work, or operation assumes a very

different character, because heat cannot be extracted from a substance

which contains none at all. It is well known that 80° of heat are

required to change one pound of ice at 0° into a pound of water also

at 0° of heat; but it is equally well known that 80° of heat cannot be

taken out of the pound of water which has none in it; how then, is the

water to be changed into ice?

Even in cooling water to 0° it has to be put into a bath of some kind,

either of cold water or some cold mixture of other substances at least

as cold; because, otherwise, extraneous heat from any source might find

its way into it, and prevent it from cooling down to zero of heat.

In the same manner, to change the water into its solid state of ice

it has to be put into a similar bath, not to extract heat from it,

because it has not any to extract, but to prevent extraneous heat from

getting into it. This being the case, it is evident that if water is

put into a bath at what is called -1° of heat, or even a fraction of

that amount, it will be converted into ice though very gradually, by

keeping extraneous heat from getting to it to sustain the collisions,

or vibrations, of its constituent atoms necessary to maintain it in

its liquid state. All for the very same reason why a stone, a piece

of metal, or of anything assumes the same degree of heat, or absence

of heat, as the medium by which it is surrounded; be it derived from

sun-heat, earth-heat, or heat produced chemically or mechanically, and

is not cooled down to a lower degree than the surrounding bath, be it

what it may.

The heat required to change a solid into a liquid is called _latent

heat_, which in the case of ice and water may be a fraction of

-1° or -80°, or _minus_ almost anything according to the time it

is necessary for it to act; so that no quantity of what is called

absolute temperature can be ascribed to ice without the element time

being involved in it. The absolute temperature of water and ice, just

changing from freezing to frozen, might be counted as the same, seeing

that a fraction of a degree of heat may make all the difference between

them; but no fixed absolute temperature can be applied to ice, as it,

in conjunction with all solid bodies, may have any degree of absolute

temperature between its melting point and the absolute zero of heat, as

far as is at present known. The same, of course, must be the case with

any gas or vapour, or nebulous matter changed into its liquid and then

solid state; and this fact enables us to go a little further.

We have seen that what, according to present usage, is called the

absolute temperature of solid hydrogen may be anything between -257°

and -274° of heat, that is, between the absolute temperature of 0° and

17°, which, of course, is no measure at all; and, therefore, absolute

temperature can only be looked upon as a conventional term, which,

when added to positive Centigrade, or other, heat, conveys no clear

idea to the mind, as it must always be mixed up with the concomitant

idea of latent heat and its time of action. This leads us to think of

what remains in the vessel, in which pure hydrogen has been changed

into its liquid and then solid state, after these operations have been

performed; and our first conclusion comes to be that there can be

nothing in it but a small piece of solid hydrogen; but from the limited

accounts we have seen of these operations, there does appear to be

something remaining, because it seems that by it the degree of negative

heat in the vessel can be measured. What that remaining something may

be can hardly be anything but a matter of conjecture. The first and

most probable idea that occurs is that it may be some lighter gas mixed

with the pure (?) hydrogen that was put into the vessel; the next is

that it may be the vapour of solid hydrogen; and the last refuge for

speculation is that it may be radiant matter, whatever that may turn

out to be. At one time it was supposed to be impurities mixed with the

gases operated upon, which in the case of common air, were found to be

removed to a certain extent by means of absorbents; but the numerous

components of common air discovered since that time, have gone far to

throw light upon that supposition, and we are thus led to think of what

a true gas really is. But we are not yet prepared to follow up this

thought.

This is not an inappropriate place to say that when we adopted the

Centigrade scale for our work, we thought that a special thermometer,

decimal throughout and consequently more handy, might be arranged for

science alone, leaving every man the free use of whatever scale he

liked best; but our experience acquired in this chapter put an end to

that thought, and has left us totally unable to see how any decimal

scale can be contrived, which will start from absolute zero of heat

and will admit of any combination with any existing scale, or will

assist humanity in any of its operations in connection with heat and

temperature, whichever science may choose to call it. We therefore see

that no known thermometer scale is superior to another, and end where

we began by saying that the Centigrade is the fashionable one at the

present time. It is decimal as far as boiling water and resulting steam

are concerned, but all the world is not boiling water; even steam has

to be complicated with latent heat.

TABLE III.--ABSTRACT OF MEASUREMENTS, ETC., RESULTING

FROM THE CALCULATIONS MADE IN CHAPTER V.

-------------+--------------+-------------------+---------------+-----

| | | |

| | Volume of the | |Incr.

Nebulæ | | Mass of each | Times less | of

---- |Explanations. | Separate System at| Dense than |Dens-

Diameter | | Density of Water | Water. | ity

in miles. | | in cubic miles. | | in

| | | |times

-------------+--------------+-------------------+---------------+-----

Original or | | | |

Neptunian | | | |

6,600,000,000| Volume of | |311,754,100,720|

| Neptune's | | |

| Ring | 29,107,964,680,925|311,754,100,720|

| | | |

| Volume of | | |

| Nebula | | |

| less ring | | |

-------------+--------------+-------------------+---------------+-----

Uranian |Condensed from| | |

4,580,000,000| Neptunian | | |2.9923

| Nebula | | |

| | | |

| Volume of | | |

| Uranus' Ring | 25,876,388,977,000|104,184,535,721|

| | | |

| Volume of | | |

| Nebula | | |

| less ring | | |

-------------+--------------+-------------------+---------------+------

Saturnian |Condensed from| | |

2,672,000,000| Uranian | | |5.0357

| Nebula | | |

| | | |

| Volume of | | |

|Saturn's Ring |154,370,734,774,315| 20,689,000,000|

| | | |

| Volume of | | |

| Nebula | | |

| less ring | | |

-------------+--------------+-------------------+---------------+------

Jovian |Condensed from| | |

1,370,800,000| Saturnian | | |7.4037

| Nebula | | |

| | | |

| Volume of | | |

|Jupiter's Ring|479,368,921,317,000| 2,794,417,420|

| | | |

| Volume of | | |

| Nebula | | |

| less ring | | |

-------------+--------------+-------------------+---------------+------

Asteroidal |Condensed from| | |

744,000,000| Jovian Nebula| | |6.2484

| | | |

| Volume of | | |

| Asteroidal | | |

| Ring | 367,792,000,000| 447,218,905|

| | | |

| Volume of | | |

| Nebula | | |

| less ring | | |

-------------+--------------+-------------------+---------------+------

Martian |Condensed from| | |

402,000,000| Asteroid | | |6.3392

| Nebula | | |

| | | |

| Volume of | | |

| Martian Ring | 160,728,460,000| 70,547,110|

| | | |

| Volume of | | |

| Nebula | | |

| less ring | | |

-------------+--------------+-------------------+---------------+------

Earth |Condensed from| | |

234,620,000|Martian Nebula| | |5.0302

| | | |

| Volume of | | |

| Earth Ring | 1,489,310,236,000| 14,024,781|

| | | |

| Volume of | | |

| Nebula | | |

| less ring | | |

-------------+--------------+-------------------+---------------+------

Venus |Condensed from| | |

160,210,000| Earth Nebula | | |3.1410

| | | |

| Volume of | | |

| Venus Ring | 1,131,960,000,000| 4,465,512|

| | | |

| Volume of | | |

| Nebula | | |

| less ring | | |

-------------+--------------+-------------------+---------------+------

Mercurian |Condensed from| | |

103,232,000| Venus Nebula | | |3.7379

| | | |

| Volume of | | |

|Mercurian Ring| 92,735,000,000| 1,194,666|

| | | |

| Volume of | | |

| Nebula | | |

| less ring | | |

-------------+--------------+-------------------+---------------+------

Solar |Condensed from| | |

63,232,000| Mercurian | | |

| Nebula | | 274,546|4.3514

| | | |

|Volume @ 1/274| | |

58,002,920| of 1 atm. | | 211,911|1.2956

| | | |

|Vol. @ density| | |

8,930,309| of 1 atm. | | |274.000

| | | |

|Vol. @ density| | |

972,895| of water | | |773.395

-------------+--------------+-------------------+---------------+------

-------+---------------------------------------+-----------+-----------

| | |

| Volumes at Densities | Times | Absolute

| of Respective Nebulæ in | less Dense| Tempera-

| cubic miles. | than Air. | ture.

| | |

| | | (Degrees.)

| | |

-------+---------------------------------------+-----------+-----------

| | |

Neptun-|150,532,847,222,000,000,000,000,000,000|403,000,000| 0·00000068

ian | | |

| 9,074,530,000,000,000,000,000,000| .. | ..

-------+---------------------------------------| |

|150,523,772,692,000,000,000,000,000,000| |

Uranian| | |

| 50,303,255,814,000,000,000,000,000,000| |

| | |

| 2,695,918,851,000,000,000,000,000|134,710,620|0·000002034

-------+---------------------------------------| |

| 50,300,559,895,149,000,000,000,000,000| |

Saturn-| | |

ian | 9,988,700,000,000,000,000,000,000,000| |

| | |

| 3,193,775,478,000,000,000,000,000| 26,750,876| 0·00001024

-------+---------------------------------------| |

| 9,985,506,224,522,000,000,000,000,000| |

Jovian| | |

| 1,348,720,186,335,000,000,000,000,000| |

| | |

| 1,339,557,155,000,000,000,000,000| 3,613,182| 0·00007583

-------+---------------------------------------| |

| 1,347,380,629,180,000,000,000,000,000| |

Aster- | | |

oidal | 215,634,925,373,133,820,000,000,000| |

| | |

| 164,482,717,200,000,000,000| 578,254| 0·00047384

-------+---------------------------------------| |

| 215,634,760,890,416,620,000,000,000| |

Martian| | |

| 34,015,582,677,165,354,000,000,000| |

| | |

| 11,338,927,154,000,000,000| 91,259| 0·00300244

-------+---------------------------------------| |

| 34,015,571,338,237,200,000,000,000| |

Earth | | |

| 6,762,303,076,923,031,000,000,000| |

| | |

| 20,887,249,553,000,000,000| 18,134| 0·0151097

-------+---------------------------------------| |

| 6,762,282,189,673,478,000,000,000| |

Venus | | |

| 2,153,120,792,079,207,921,000,000| |

| | |

| 5,054,780,604,651,000,000| 5,774| 0·047454

-------+---------------------------------------| |

| 2,153,115,737,298,603,270,000,000| |

Mercur-| | |

ian | 576,026,613,333,333,333,000,000| |

| | |

| 110,787,355,300,000,000| 1,545| 0·1773463

-------+---------------------------------------| |

| 576,026,502,545,978,033,000,000| |

Solar | | |

| 132,376,310,975,609,756,000,000| 355| 0·771831

| | |

| 102,176,129,412,000,000,000,000| 274| 0·99635

| | |

| 372,905,560,345,000,000,000| 0| 2·0000

-------+-+---------------------------------+---+-----------+------+---

| At Density of Water. | At Air Density. |

+---------------------------------+---------------+------+

| Dimensions of Rings. |Space to Grain | |

| | of Matter. | |

+--------------+------------------+-------+-------+ I |

| | Thick- | age | | of | c |

---------+--------------+---------+--------+-------+-------+------|

| | | | | | |

Neptunian| ... | ... | ... |713,223| 89·327| |

| | | | | | |

| 1,010,000,000| 511,794| 341,196| | | |

---------+--------------+---------+--------+-------+-------+------+

| | | | | | |

| | | | | | |

| 954,000,000| 252,193| 100,553|238,357| 61·994| |

---------+--------------+---------+--------+-------+-------+------+

| | | | | | |

| | | | | | |

| 650,600,000| 881,037| 238,000| 47,313| 36·168| |

---------+--------------+---------+--------+-------+-------+------+

| | | | | | |

| | | | | | |

| 313,400,000|1,406,771| 450,282| 6,303| 18·472| |

---------+--------------+---------+--------+-------+-------+------+

| | | | | | |

| | | | | | |

| 171,000,000| 588| 185| 1,023| 10·075| |

---------+--------------+---------+--------+-------+-------+------+

| | | | | | |

| | | | | | |

| 83,690,000| 152| 61| 161| 5·445| |

---------+--------------+---------+--------+-------+-------+------+

| | | | | | |

| | | | | | |

| 37,205,000| 961| 612| 32| 3·178| |

---------+--------------+---------+--------+-------+-------+------+

| | | | | | |

| | | | | | |

| 28,489,000| 420| 225| 10·2 | 2·170| |

---------+--------------+---------+--------+-------+-------+------+

| | | | | | |

| | | | | | |

| 20,000,000| 25| 11| 2·734| 1·398| |

---------+--------------+---------+--------+-------+-------+------+

| | | | | | |

| ... | ... | ... |0·6283 | 0·8565| 10·28|

| | | | | | |

| ... | ... | ... |0·4848 | 0·7856| 9·43|

| | | | | | |

| ... | ... | ... |0·00177| 0·121| 1·452|

---------+--------------+---------+--------+-------+-------+------+

Returning now to page 84, we see that the volume of the sun alone was

considered to be 482,169^{12} cubic miles, which corresponds to a

diameter of 972,869 miles. Comparing this with the volume 482,167^{12}

cubic miles, see page 99, left after all the members of the Solar

system have been separated from the original nebula, we find that

there is a remainder of 2,000,000,000,000 cubic miles _less_ than we

ought to have. But it will be remembered that we added only 1/700th

part to the mass of the sun for the mass of the whole Solar system,

whereas it will be seen, by referring to Table II., that we ought to

have added 1/696·86th part. Had we done so the sphere containing the

whole Solar system at the density of water would have been 973,361·31

miles in diameter with volume of 482,860,744^{9} cubic miles, which

would have added 3,153,681,000,000 cubic miles to the volume we started

with, and would have left us with 1,375,903,430,000 cubic miles _more_

than we ought to have had. Besides, for the sake of round numbers, we

made the diameter of the nebula containing the whole Solar system, at

the density of water, to be 973,360 instead of 973,359·208 miles, and

thereby really added more to the original volume than we should have;

so that the defects in accuracy at the beginning of our work partially

counterbalanced each other, which accounts so far for the difference

noted at the end not being much more than half of what it should have

been. Taking all this into consideration, and the really insignificant

magnitudes of the differences that would result from the corrections

that could be made, we have not thought it necessary to reform the

whole of our calculations. Besides, the data we have been working upon

are not so absolutely exact as to insure us that we should get nearer

to the truth by making the revision. The whole error would be much more

than obliterated were we to apply 5·67 instead of 5·66 for the mean

density of the earth to the debit side of the sun's account.

To simply describe arithmetical operations conveys no really

satisfactory meaning to the mind; of working them out in full there is

no end; and to partially represent them as we have done in these pages,

although showing how the results are arrived at, still leaves them so

mixed up together that it is difficult to compare them with each other,

and to note the sequences from the beginning to the end of the whole

operation. For these reasons we have compiled Table III., where the

whole of the principal and most important data, and results from them,

may be followed out and examined.

We may now say that we have taken our nebula to pieces, with the

exception of the parts belonging to the satellites of those planets

which have them; which would only be a tiresome repetition of what we

have done for each principal member of the system, provided we had the

necessary data, which we have not; and have thus acquired a certain

amount of knowledge of the primitive conditions of each one of them.

But we have still to examine into and draw conclusions from what we

have seen and learned during the operation; which in some points,

differ very much from our notions, formed from what we had previously

read on the subject.

CHAPTER VI.

PAGE

108 Analysis continued. Excessive heat of nebula involved condensation

only at the surface. Proof that this was Laplace's idea.

109 Noteworthy that some astronomers still believe in excessive heat.

110 Interdependence of temperature and pressure in gases and vapours.

Collisions of atoms the source of heat.

110 Conditions on which a nebula can be incandescent. Sir Robert Ball.

112 No proper explanation yet given of incandescent or glowing gas.

115 How matter was thrown off, or abandoned by the Jovian nebula.

116 Division into rings of matter thrown off determined

during contraction.

117 How direct rotary motion was determined by friction and collisions

of particles.

118 Saturn's rings going through the same process. Left to show

process.

120 Form gradually assumed by nebulæ. Cause of Saturn's

square-shouldered appearance.

120 A lens-shaped nebula could not be formed by surface condensation.

121 Retrograde rotary motion of Neptune and Uranus, and revolution

of their satellites recognised by Laplace as possible.

123 Satellites of Mars. Rapid revolution of inner one may be

accounted for.

124 Laplace's proportion of 4000 millions not reduced but enormously

increased by discoveries of this century.

ANALYSIS OF THE NEBULAR HYPOTHESIS--_continued_.

When Laplace elaborated his hypothesis, heat was considered to be an

imponderable material substance, and continued to be thought of as

such--though perhaps not altogether believed to be so--for somewhere

about half a century afterwards; so that it cannot be wondered at that

he thought the nebula could have been endowed with excessive heat, more

especially as it was looked upon as imponderable, and could in no way

have any effect on the mass of the nebula. He only accepted the idea

that was common to almost all astronomers of his time, that nebulæ were

masses of cosmic matter of extreme tenuity but self-luminous, and

consequently possessed of intense heat; they saw the sun gave light

and felt its heat, and very naturally thought the nebula must be hot

also. Without this idea he could not have formed the hypothesis at

all, because he could not have conceived that the condensation of the

nebula could only take place at its surface, or, as he terms it, "in

the atmosphere of the sun," as most assuredly would be the case with

an excessively hot body. And in order that there may be no doubt about

this being his idea, we quote his own words as guaranteed by M. Faye in

"L'Origine du Monde": "La considération des mouvements planétaires nous

conduit donc à penser qu'en vertu d'une chaleur excessive l'atmosphère

du soleil s'est primitivement étendu au delà des orbes de toutes les

planètes, et qu'elle s'est reserrée successivement jusqu'à ses limites

actuelles." And again: "Mais comment l'atmosphère solaire a-t-elle

déterminé les mouvements de rotation et de révolution des planètes et

des satellites? Si ces corps avaient pénétré profondément dans cette

atmosphère, sa résistance les aurait fait tomber sur le soleil. On

peut donc conjecturer que les planètes ont été formées à ses limites

successives par la condensation des zones de vapeurs qu'elle à dû, en

se refroidissant, abandonner dans le plan de son équateur." Proceeding

on these ideas Laplace was quite in order and logical in conceiving

that successive rings could be abandoned by the hot nebula, through the

centrifugal force of rotation, for the formation of planets, more or

less just in the way we have separated them. Having obtained his end

quite legitimately, as he thought, in this way, he had no occasion to

look any deeper into the affair, and consequently was not under the

necessity of taking any thought of what the interior construction of

the nebula might be, any more than so many others have not done since

his day.

If the heat were, at a given moment--that is, when motion was