Now, if the collisions and encounters am_New Theories in Astronomy

small, always exactly balanced each other, the whole mass of the nebula

would gradually contract towards the region of greatest density,

and the whole would ever remain without any other kind of motion in

it than what can be seen in a mity cheese--a kind of congeries of

particles heaving in every, and at the same time in no, direction.

But as an absolute balance of collisions could not be maintained for

ever, especially where they would be constantly varying in force and

direction, a time would come when movements of translation, as well as

of collision, would be instituted on a large scale, in many directions,

which, if they also did not manage to balance each other--an affair

equally as impossible as in the other case--would ultimately resolve

themselves into motion in one predominating direction through the whole

nebula.

We do not forget that we are dealing with the shell of a hollow sphere,

not with a ring, or section of a cylinder, and we can conceive that

there would be, from the first, partial motions of translation in

multitudes of directions, radial, angular, transverse, etc. etc.,

constantly changing, even being sometimes reversed, but also constantly

combining with each other, and gradually leading on to decided, though

partial, uniformity in one direction. As a matter of course this

motion of translation would be controlled by its own constituent parts

attracting each other to some extent, and thus a rotary motion would

be established in the interior of the nebula in the region of greatest

density. We can also conceive that when the motions of translation

had become nearly uniform, the plane of that uniform motion might be

in any direction through the whole mass of the nebula, and might be

continually varying until final uniformity was attained, when the

greater part of the mass was moving in combination, and the rotation

was thereby firmly established in one direction, though still not

embracing the whole.

We have to take into account also that when the rotary movement had

settled down into one plane, it would be most active at the distance

of the region of greatest density of the nebula from its centre; in

fact it would be instituted at that region and be, therefore, most

active there; and then the most active part of the matter would be in

the form of a rotating ring, still surrounded by an immense mass of

nebulous matter, both inwards and outwards, to which it would gradually

communicate its own motion, until the whole mass would rotate, in one

direction, on an axis. But it is evident that in the whole rotating

mass there would be different degrees of velocity of rotation at

different places, decreasing from the supposed ring inwards towards

the centre, and outwards to the surface at what would thus become the

equatorial region; and also decreasing from the equatorial plane to

the poles. Following up this idea, we have a more reasonable manner of

accounting for the different velocities of rotation observed on the

surface of the sun, between the equator and the poles, than we have

seen suggested in any speculations on the cause that have come under

our observation. Until rotation was fully instituted, the areolar law

could have no power over the multitudinous movements going on in the

nebula, but from that time it would begin to act, and condensation

would increase it at the region where it began; and as all increase had

to be propagated from there, inwards, outwards, and in all directions,

the differences in velocity of rotation throughout the sun must endure

as long as he continues to contract. In this we find an immense field

for producing heat in the sun, from the eternal churning which must be

going on in the interior.

A rotary motion produced in this way might have two different results:

in one case the rotation might be continued until the matter at the

polar regions had all fallen in towards the centre, and had been thrown

out afterwards by centrifugal force and the whole mass converted into a

nebular ring, in the form of the annular nebula in Lyra. In the other

case we could conceive that, in a smaller nebula, the centrifugal force

of rotation caused zones to be abandoned at the equatorial surface, in

the manner set forth by Laplace in his hypothesis, and that the matter

from the polar regions fell in more or less rapidly for the formation

of the different members of a system like the sun's; and that the

dimensions of the planets would be determined by the rapidity with

which the matter fell in as the process went on. Such a conception

would help to account for the outer planets of the solar system being

so much larger than the inner ones, because there would be more matter

falling in; and make us think that the nebula in Lyra is destined to

form a system of multiple stars.

Some years after this mode of instituting rotary motion in a

nebula was thought and written out, and also an extension of it to

which we may refer later on, we came upon a kind of confirmation

of the correctness of our views in an article in "Science Gossip"

of January 1890, on the nebular hypothesis, where it is said: "We

have established, then, the existence of irregular nebulæ which are

variable--that is, the various parts of which are in motion.... Now,

with the parts of the nebula in motion, whether the motion is in the

form of currents determined hither and thither according to local

circumstances, or in any other conceivable way, such motions bearing

some reference to a common centre, unless the currents exactly balanced

each other--a supposition against which the chances are as infinity

to one--one set must eventually prevail over the other, and the mass

must at last inevitably assume the form peculiar to rotating bodies in

which the particles move freely upon each other. It must have become

an oblate spheroid flattened at the poles and bulging at the equator,

rotating faster and faster as it contracted. In some such manner has

our solar system acquired its definite rotation from west to east."

The writer in "Science Gossip" has taken the irregular motions in the

nebula as made to his hand, and has come to the same conclusion as we

have, namely, that they would all resolve themselves into motion in one

direction only, always subject to the general attraction towards the

centre of gravity of the nebula, which means motion round a centre,

perhaps not necessarily rotary motion. However, the only difference

between his ideas and ours is that we deal with a hollow nebular shell,

in which, it will be acknowledged, it would be much more easy for the

law of attraction to produce marked and distinct motions of any kind,

and which would lead to one motion in one direction throughout, than

in a nebula homogeneous, or nearly so, from the surface to the centre.

Whether it would lead to the formation of an oblate spheroid is another

question, as that might depend on a variety of circumstances, one or

more of which we shall have to touch later on; in fact, we have already

shown how the very reverse might be the case.

CHAPTER XVI.

PAGE

282 The sun's neighbours still exercise their attraction over him.

283 Regions of greatest density in the 9 nebulæ dealt with; compared

with the orbits of the planets made from them.

287 Results of comparison favourable to the theory.

289 Differences of size in the planets have arisen from variations

in the quantity of matter accumulating on the nebulæ.

290 Causes of the retrograde motions in Neptune, Uranus, and

their satellites.

292 Probable causes of the anomalous position of Neptune.

293 Rises and falls in the densities and dimensions of the

planets explained.

295 The form of the nebulæ must have resembled a dumb-bell.

296 More about rises and falls in densities.

297 Reason why the Asteroid nebula was the least dense of the system.

298 Not necessary to revise the dimensions given to the 9 nebulæ.

299 Causes of the anomalies in the dimensions, densities, etc.,

of the Earth and Venus.

299 The strictly spherical form of the sun accounted for.

But it may yet be varied.

300 Repetition that a spherical body could not be made from a

lens-shaped nebula by attraction and condensation.

TESTING THE PRACTICABILITY OF THE HOLLOW SPHERE THEORY. RETROGRADE

MOTIONS, POSITIONS, DENSITIES, MASSES, ETC. ETC., CONSIDERED.

Before going any farther it will be convenient to try to find out

whether the solar system could have been constructed from a hollow

nebula such as we have been describing gradually contracting as the

matter for the formation of one planet after another was abandoned

until--as we have put it--the nebula could abandon no more matter, and

finally resolved itself into the sun. For this purpose we may suppose

it to have been condensed and contracted until its extreme diameter was

6,600,000,000 miles; the same as we supposed it to have been, when we

began the analysis of the nebular hypothesis. We will not now, however,

suppose it then to have contained the whole of the cosmic matter out

of which the system was formed, as we did before; because we have seen

as we have come along that a very considerable part of that matter

must have been left behind, almost from the moment that contraction

commenced. We have already given the reasons for this in describing the

domains of the sun; and, leaving the peaks out of account altogether

for the present, we will only deal with the regions of what we have

called the main body.

Although we have fixed a limit beyond which the neighbouring stars

could not draw off any cosmic matter from the domains of the sun,

that does not mean to say that their attractive powers would cease at

that limit; because we have had to acknowledge that each one of them

continues, even now, to exert its attractive power up to the very

centre of the sun. They would still have power to counteract, in some

measure, the sun's attraction of the matter of the nebula towards his

centre, and the result would follow that there would be one or more,

even many, fragments of the main body which would be left more or less

behind, and in varied forms, when the more central part had contracted

to the dimensions to which we have now reduced the nebula--all much the

same as we have already said a few pages back.

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

be 150,533^{24} cubic miles--as we have seen at page 87--the half

of which is 75,266^{24} cubic miles, corresponding to a diameter of

5,238,332,000 miles, or radius of 2,619,166,000 miles. Now, according

to our theory, it would be at this distance from the centre that the

greatest density and activity of the nebulous matter would be, where we

have just been showing how a movement of rotation could be generated,

and where, in consequence, its motive power, so to speak, originated

and existed. Here we find by dividing 5,238,332,000 by 6,600,000,000

that the region of greatest density in such a nebula would be at 0·7937

of its diameter. In our calculations about the earth, as it is, the

proportion was found to be 0·7939, but the densities of the outer

layers were empirically arranged by us; and, besides, almost the whole

of the mass was supposed to be solid matter, so that no accurate result

could be expected from that operation. There also we found that the

inner surface of the hollow shell was at 0·5479 of the whole diameter,

which we may adopt for the nebula we are about to deal with, as that

dimension may be varied considerably--so may the other also--without in

any way vitiating our theory.

Having found these proportions, which can only be considered as

distantly approximate, let us go back to the 9 nebulæ--excluding the

final solar one--into which we supposed the original nebula to have

been divided--in the analysis just alluded to--and see how the regions

of greatest density in them would correspond to the orbits of the

planets formed out of them. This examination requires a good deal of

calculation and accompanying description, which it might be found

tiresome to follow, and would really answer no good end were it written

out; so we shall suppose it to be made and the results obtained from

the calculations to be represented in the form of Table IX., where they

can be seen at a glance almost, and compared without much trouble. This

arrangement will also furnish a readier means of reference for the

remarks we shall have to make on, and the information obtained from,

the examination. And we have still to add that the extreme diameters of

the 9 nebulæ are the same as those we used for the analysis; as also,

that we make use of only the first of the proportions just cited, viz.,

0·7937, it being the only one required for determining the positions of

the regions of greatest density in the nebulæ.

TABLE IX.--DIMENSIONS OF THE NINE NEBULÆ, WITH THEIR

DIAMETERS AND REGIONS OF GREATEST DENSITY

COMPARED WITH THE DIAMETERS OF THE ORBITS

OF THE PLANETS FORMED FROM THEM.

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

| Nebula. |Region of greatest Density.|

| | |

Name of |--------------+-------------+-------------+

Planet. |Outer Diameter| Diameter | Radius |

| in Miles. | in Miles. | in Miles. |

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

| | | |

Neptune | 6,600,000,000|5,238,332,000|2,619,166,000|

| | | |

Uranus | 4,580,000,000|3,635,146,000|1,817,573,000|

| | | |

Saturn | 2,672,000,000|2,120,766,400|1,060,383,200|

| | | |

Jupiter | 1,370,800,000|1,088,003,960| 544,001,480|

| | | |

Asteroids | 744,000,000| 590,512,800| 295,256,400|

| | | |

Mars | 402,000,000| 319,067,400| 159,533,700|

| | | |

Earth | 234,620,000| 186,217,894| 93,103,947|

| | | |

Venus | 160,210,000| 127,158,677| 63,579,339|

| | | |

Mercury | 103,230,000| 81,933,651| 40,966,825|

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

| Had the position of Neptune been normal, |

| the above data for him and Uranus would |

| have been as under. More or less. |

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

Neptune | 8,299,786,830|6,587,540,800|3,293,270,000|

| | | |

Uranus | 5,144,439,613|4,083,042,000|2,041,521,000|

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

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

| Orbit of Planet. | Region of greatest Density |

| | compared with Orbit. |

Name of |-------------+-------------+-----------+-----------+------+

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

| | | | | |

Neptune |5,588,000,000|2,794,000,000|174,734,000| | 6·26|

| | | | | |

Uranus |3,566,766,000|1,783,383,000| | 34,190,000| 1·92|

| | | | | |

Saturn |1,773,558,000| 886,779,000| |173,604,200| 19·58|

| | | | | |

Jupiter | 967,356,000| 483,678,000| | 60,323,480| 12·47|

| | | | | |

Asteroids| 520,600,000| 260,000,000| | 35,256,400| 13·56|

| | | | | |

Mars | 283,300,000| 141,650,000| | 17,883,700| 12·63|

| | | | | |

Earth | 185,930,000| 92,965,000| | 138,947| 0·15|

| | | | | |

Venus | 134,490,000| 67,245,000| 3,665,660| | 5·45|

| | | | | |

Mercury | 71,974,000| 35,987,000| | 4,979,825| 13·84|

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

|Had the position of Neptune been normal, the above data |

|for him and Uranus would have been as under. More or less.|

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

Neptune |5,588,000,000|2,794,000,000| |499,270,000| 17·86|

| | | | | |

Uranus |3,566,766,000|1,783,383,000| |258,138,800| 14·48|

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

From the table we see that the region of greatest density of our

original nebula was at 6·26 per cent. _within_ the distance of

Neptune's orbit from the sun, a state of matters which precludes the

idea of condensation during, at least, a great part of the act of

abandoning the ring for the formation of that planet. But it will be

remembered that we gave it the diameter of 6,600,000,000 miles without

assigning any adequate reason for doing so, and, we can say with

truth, with the idea, more than anything else, of not increasing the

almost unimaginable tenuity of the matter composing the nebula; and

the position of Neptune in the system is so peculiar compared with the

other planets, that it cannot be properly used as a standard for any

kind of inquiry. The result obtained above can therefore be of no use

for the investigation we have undertaken. Not only so, but the almost

similar result in the case of Uranus is also rendered useless from the

same cause, in which we find that the region of greatest density of the

nebula is only 1·92 per cent. beyond the orbit of the planet. If the

mean distance from the sun of Neptune's orbit had been what was used

by Leverrier in the calculations which led to his discovery, namely,

36·152 radii of the earth's orbit, the region of greatest density of

the Uranian nebula would have been 14·48 per cent. beyond his orbit, as

may be seen from the addition to Table IX., in finding which we have

used the same system as in all our work.

In the next four nebulæ of the table--including the one we introduced

to represent the Asteroids--we see that their regions of greatest

density are respectively 19·58, 12·47, 13·56 and 12·63 per cent.

farther out from the centre of the sun than the orbits of the planets

formed from them. Here, then, we see a very apparent approach of

uniformity, and can say with much reason that planets could certainly

be formed out of the matter abandoned, through centrifugal force, by

hollow nebulæ similar in construction to what we have demonstrated

that of the original nebula to have been; each of them occupying the

position corresponding to its orbit.

Following these come the Earth and Venus nebulæ. In the former, the

region of greatest density almost coincides with the orbit of the

planet, being only 0·15 per cent. beyond it, instead of something like

12 per cent. as it ought to be to conform with the four preceding

cases; and in the latter it is 5·25 per cent. within the orbit of the

planet to be made from it. But in this case we have to note that the

orbit of Venus is 3·33 per cent. beyond the position pointed out for

it by Bode's law, and that it is the only one of the whole number of

planets whose orbit is farther removed from the sun than the distance

assigned to it by that law. Also we see from our reversal of Bode's

law, that the rates of acceleration of rotation for these two planets

are 1·880 for the earth and 1·626 for Venus, instead of the average of

2·5896 of the four preceding planets; that the density of Venus is less

than that of the Earth, instead of being greater as it is successively

in all the other planets from Saturn inwards; and we may add that

the diameters are nearly equal. All showing that influences had been

at work in the formation of these two planets, different to those in

the preceding four; and that until we know what these influences have

been, we cannot account for any anomalies produced by them. Neither

are we called upon to consider that our theory is destroyed by these

anomalies, any more than it can be by the anomaly in the case of

Neptune's position.

Lastly, we have in Mercury the region of greatest density of his nebula

at 13·55 per cent. beyond his orbit, and the rate of acceleration of

revolution over Venus 2·5543 times, both of which conform fairly well

with the same noted facts; in relation to Mars, the Asteroids, Jupiter,

Saturn, and, we may add, Uranus. But, in justice, we must not omit to

add that there may be some error in the excess of 13·55 per cent. in

the distance from the sun beyond his (Mercury's) orbit, arising from

the fact that there may have been some difference from what we made it

to be, in the line of separation between his nebula and that of Venus;

and also that we had to guess at the line of separation between his

and the residuary nebula. Moreover, it has to be taken into account

that his orbit is 3·22 per cent. within the position assigned to it by

Bode's law.

From the Table IX., and an examination of it, we learn that out of the

9 nebulæ into which we divided the original one, in the analysis of the

nebular hypothesis, we have five--four of which are consecutive--which

may have been almost of the same construction, and not far from

the same proportions; that the original nebula cannot, for reasons

assigned, be looked upon as either similar, or the reverse, to the five

just classed; that one, the Uranian, is practically similar to the

five, and might be exactly similar could the anomaly in the position

of Neptune be explained; and that the remaining two, the Earth and

Venus nebulæ, seem to show that they have been abandoned in a manner

different from the others. Perhaps we may be able, later on, and in a

different way, to give a reasonable explanation of the anomalies in the

positions occupied by Neptune, the Earth, and Venus, and also of the

peculiarities of their dimensions. So far, we believe we are justified

in concluding that out of the 9 nebulæ, 6 may really be considered as

supporting our theory, and the remaining 3 as, in all probability,

capable of being shown to be, at least, not opposed to it. To this we

may add that on several occasions we have stated our opinion, that

the divisions between the nebulæ we have established, could not have

taken place at the half-distance between the orbits of any two planets,

but much nearer to the outer one. It is evident, then, that if we had

made the divisions at any distance farther out, say at three-fourths

of that distance from the inner orbit, the extreme diameter of each

one of the nebulæ would have been just so much greater, the region of

greatest density farther out from the centre of the sun, and even that

of Neptune would have been beyond his orbit. All this could be done,

yet but it would serve no good purpose, as will be seen presently; and

we might be accused of cooking our data in order to produce a result

favourable to our theory.

We have made the foregoing examination because, when we began our work,

the general idea was that, according to the nebular hypothesis, the

material for the formation of each planet was abandoned by the ideal

nebula in a distinct and separate mass from any other--we are not at

all sure, however, that this was Laplace's idea. This, we found out,

could not be the case when we attempted to give some sort of separate

or distinct form to the matter out of which Neptune was supposed to

have been formed; and when we became convinced that all the matter

abandoned by the nebula, from first to last, must have been thrown off

in one continuous and, most probably, uninterrupted sheet. This, of

course, makes us think of how the division of the sheet into separate

rings was brought about, for there must have been absolute separation

between them, otherwise separate planets could not have been made out

of the sheet; and the only explanation that can be given is, that

it must have depended on the quantity of matter that was abandoned,

in nearly equal times, at different periods of the operation; for

the areolar law precludes the idea of there having been very rapid

changes in the rate of rotation of the nebula, and certainly of its

decrease at any period as long as condensation and contraction went

on. Whereas, although the sheet thrown off may have been continuous,

we have no reason to suppose that it was of constant volume or density

from beginning to end of the operation; in fact, we have already

seen that its density was constantly increasing, and have suggested,

in the reversal of Bode's law, that the differences in dimensions

and densities of the planets have arisen, from irregularity in the

quantities of matter abandoned from time to time. This irregularity

could only arise from the mode of construction of the nebula, and from

the forms it assumed during condensation, as we shall attempt to show

in due time. Meanwhile we can conclude that the region of greatest

density in any of our nebulæ had no influence whatever on the position

of the orbit of the planet that was formed out of it.

We have shown, very clearly we believe, at page 109, from

quotations--at second hand--from his own exposition of his hypothesis,

that Laplace considered that condensation could only take place at

the surface, or in the atmosphere as he called it, of his nebula,

on account of its being possible only after radiation into space of

part of its excessive heat; and that consequently there could be

no acceleration of rotation in the nebula, due to the areolar law,

except where there was condensation. On the other hand, in our cold

hollow-sphere nebula, condensation could only take place at the region

of greatest density, or greatest mass, which must be always very much

nearer to the surface than to the centre; so that in both cases,

equally, the abandoning of matter under the influence of centrifugal

force would be virtually the same, and no further remarks are called

for, on our part, on that head.

Neither is it necessary for us to show how planets could be formed out

of the rings abandoned by their respective nebulæ, for everybody seems

to agree that when they broke up, the fragments could not do otherwise

than form themselves into small nebulæ, which in the course of time

condensed into planets. M. Faye's explanations are good for that.

With respect to their motions of rotation being direct or retrograde,

we have seen, at page 116, and following, that Laplace's description of

how the former motion could be brought about is mechanically correct;

and, at page 121, that he did not consider that the direction of

revolution of a ring necessarily demands that the rotation of a planet

formed from it should be in the same direction. As already said, he has

shown how direct rotation could be produced, and we have no doubt that

he could have shown how retrograde rotation could also be produced, had

he found it to be at all necessary. Be that as it may, however, it is

a very simple matter to show how, following our method of construction

of the primitive nebula, the retrograde rotation of Uranus and Neptune

could, or rather must, have been determined.

It will be remembered that when we were "getting up" the original

nebula in the domains of the sun, whose form we described as well as

our limited means would admit of, we said that when the cosmic matter

contained in them began to contract, not only the parts contained in

the peaks and promontories would soon be left behind, and come in at

a slower rate, but also large masses of the outer part of the main

body, especially of what was on the sides opposite to the deep hollows

made in the domains by the most powerful of the sun's neighbours, in

the form of fragments, crescents, and parts of hollow segments. Let

us now, then, suppose the operation of planet-making to have advanced

so far that the whole nebula was rotating on its axis, and abandoning

matter through centrifugal force, from its equatorial regions in a

continuous sheet, as we have said several times that it must have

done, and that the matter destined for Neptune and Uranus has not only

been abandoned, but divided into two distinct rings--a supposition

made in this case only for facility of description. Then some of the

matter which had been left behind, but still being gradually drawn in,

would be almost totally intercepted in the equatorial regions of the

nebula by these two rings, and would fall in greater quantity upon

their outer edges than anywhere else, more especially in the case of

the outer one. These adventitious additions would come in without

any angular, or tangential, movement whatever, because rotary motion

was not yet established in them, and would retard the revolutionary

movement of the rings--in decreasing degree from their outer to their

inner edges--while acquiring angular motion themselves; and would also

intensify the original difference in revolutionary motion already

existing at these edges. At the same time these additions of extraneous

matter would seriously impede the contraction of the rings in the

radial direction on account of their volume, but would have little

or no effect on contraction in the circumferential direction; the

consequence of which would be that they would break up before friction,

and the mutual collisions of their particles, had time to produce a

uniform revolving motion throughout their whole breadth; that is, while

their inner edges would be still revolving with more rapid velocities

than the outer ones; and the rotary motions of the planets derived from

them would be retrograde, according to M. Faye's demonstration--or

that of any other who has taken the trouble to think over the matter.

And we may add that this mode of reasoning, applied with a little more

detail, will very fully account for the rotation of Neptune being

more decidedly retrograde than that of Uranus, because the quantity

of matter so deposited on the outer flat ring in this process would

unquestionably be greater than on the inner one, and consequently the

difference of velocity between the outer and inner edges of the two

rings also greatest on the outer one.

We take it to be unnecessary even to say that, the revolution of the

satellites of these two planets being retrograde and anomalous, the

rotation of their principals must be retrograde and anomalous also.

Before going any farther we have something to say about the anomalous

position of the orbit of Neptune, which is certainly not the position

sought for by M. Leverrier; in fact, the elements employed by him in

his calculations to discover a perturbing planet--whose existence

may be said to have been known--are so different from the elements

of the one actually discovered, that there would be nothing out of

reason in saying that Neptune is not the perturber that was sought

for, but only an instalment of the perturbing force. It may raise a

storm in some quarters to say so, but the fact remains the same, or

it must be confessed that mathematics is a more elastic science than

it professes to be. He has not the power of attraction required to

produce the perturbations in the movements of Uranus which gave rise

to the search for an outer planet. M. Leverrier made his calculations

under the belief that a planet of 1/9300th part of the mass of the sun

was required to produce the perturbations that had been observed in

the orbital motion of Uranus; whereas the planet discovered has only

1/20,000th of that mass--not one-half of what was required. On the

other hand, the semi-axis major of the orbit of the planet discovered

is found to be 30·037 instead of 36·154 (Bode's law measures) used for

the search; which greater proximity to the sun, it is true, increases

its power of attraction 1·449 times, but as its mass is only 0·465 per

cent. of what was expected, the attractive force would amount to less

than 0·68 per cent. of what was required. Then the question comes to

be, Where did the wanting 0·32 per cent. of attractive force come from?

And the answer is that some astronomers have been searching for another

planet to make up the weight, with more or less diligence, ever since

the deficiency came to be recognised. But all that we want to have to

do with the question is to suggest a very plausible reason for the

anomalous position of the orbit of Neptune.

If there is another planet beyond Neptune, the ring (perhaps the

rings) out of which he and the others were made, must have been much

greater in breadth than what we have assigned to it at page 88, viz.

1,010,000,000 miles; perhaps even one-half more, as may be deduced from

the addition made to Table IX., and what we have said in connection

with the semi-axis major adopted for the sought-for planet, by M.

Leverrier in his calculations. Now, that a ring of such enormous

breadth should have held together in one piece, until it finally broke

up through condensation and contraction, requires an extraordinary

effort of imagination, after seeing what has taken place with the

rings of Saturn; even the breadth of 954,000,000 miles appropriated

to the Uranian ring (see page 90) demands an elastic imagination to

conceive its holding together; so that the outer ring of the system

may very well have been divided into two, as we have said at page 134,

and two not very unequal planets made out of it--one into Neptune, and

the other into one as far beyond M. Leverrier's adopted distance of

36·154, and of such mass as would make up the missing 0·32 per cent. of

deficient attractive power. No doubt the outer ring may have broken up

into several planets, or even into a swarm of asteroids, but we prefer

to think of only two planets; because it seems to us that to draw

Uranus into the position he occupied when Neptune was discovered, the

two planets must have been operating in conjunction; an idea that is

not so easily entertained when there are several planets, or a host of

asteroids, to be taken into account.

We have already discussed, at page 115, the mode of formation of the

sheet of matter abandoned by the nebula, its posterior division into

separate rings, and how the part of these rings from Saturn inwards

could revolve themselves into planets having direct motion, so it is

not necessary to go over the same ground again, merely because we are

dealing with a hollow nebula instead of one full of cosmic matter to

the centre.

We have also shown, at page 119, that the nebula must have been

somewhat in the form of a cylinder terminated at each end by what

may be looked upon as a segment of a sphere, although it would more

probably be an almost shapeless mass of cosmic matter, because the

greater part of it would be very slowly brought under the influence

of centrifugal force as it fell in from the polar directions; and

again, a few pages back, that almost all the matter coming in from

its equatorial regions--even what might be called its tropical

regions--would be intercepted before it could reach the Saturnian

nebula. Likewise, at page 137, when examining Bode's law reversed, we

have seen a limit set to the acceleration of the movement of revolution

in the planets of the system as they approached the centre, because

any acceleration beyond a certain limit, clearly marked out, would of

necessity be within the nebula itself, and the rate of revolution would

be less than that of the sun on its axis at the present day. This may

be used as an argument against the nebular hypothesis, but we think

we have shown in the same Chapter VII. that this is not the case. But

we have still to try to account for the repeated rises and falls in

density in the planets from Neptune to Mercury, or even farther; which

operation causes us to bring forward, first of all, a new idea as to

what the form of the nebula would come to be.

[Illustration: FIG. 2.]

The accompanying rough sketch (Fig. 2), drawn to a scale of one-quarter

inch to 1,000,000,000 miles shows that, supposing the Saturnian nebula

to have been a perfect sphere, and to have abandoned matter till the

velocity of rotation came to be equal in a region corresponding to

the tropical region of the earth, the cylindrical part of it would

present a straight side of more than 1,000,000,000 miles in length;

provided always that the general diameter of the nebula did not

decrease through condensation and contraction during the operation;

but as this could not be the case the length of the cylindrical part

would be considerably less than that. How much less we have no means

of calculating. On the other hand we have seen, when discussing,

in the case of Jupiter, how matter must have been abandoned by any

nebula, that from the time the original nebula began to abandon matter

through centrifugal force, it must have gone on acquiring a constantly

increasing length of straight side as it contracted. Thus the Saturnian

nebula would begin work with the accumulated cylindrical length it had

inherited from Neptune and Uranus, so that the straight side may have

been very much longer than that shown by the sketch; a simple look at

it is enough to make one believe that this would be the case. But this

idea naturally leads us to another digression.

Looking again at Fig. 2, we see that acceleration of rotation in the

nebula would originate where condensation was greatest, that is at

the region of greatest density, and have to be propagated from there

to its periphery so that it would reach the middle of the cylindrical

part sooner than the ends; and as the nebulous matter at the ends of

the cylindrical part could not be abandoned until it had acquired the

centrifugal force necessary to overcome gravitation, it would lag

behind and overhang, as it were, the middle of the cylindrical part;

which means that instead of continuing to be straight, the line of

separation between the nebula and the abandoned matter would come to be

concave; and in this manner the nebula would soon assume the form of a

dumb-bell, gradually becoming more and more pronounced as condensation

proceeded. One can hardly help concluding that this must have been the

way in which the dumb-bell nebula near star 14 Vulpeculæ was formed.

The representations of it given by Chambers, Vol. III., page 92, Figs.

76 and 77, as seen by Smyth and Sir John Herschel are most confirming

of this idea; notwithstanding the changes of appearance shown by Lord

Rosse's reflectors of 3 feet and 6 feet diameter, Figs. 78 and 79,

which are not difficult to account for. It is easy to imagine how

Fig. 78 could be converted into Fig. 79 when observed with a much

more powerful telescope. We can conceive the roundest end of it being

reduced into the sort of compact segmental form on the left hand side

of the figure, and the spread-out part of it into the more diffused

segment on the other side; but the form of the whole figure forces

us into another conception. Mr. Chambers says the general outline

resembles a chemical retort, but to our eyes it is infinitely more like

one half of a dumb-bell broken off from the other. So like it that we

feel inclined to ask what has become of the other half. This again

makes us think of an enormous dumb-bell nebula dividing itself into two

parts, one of which has disappeared or broken up in some manner without

leaving any distinguishable traces of its existence, and the other,

either forming itself into a double star, assuming in the process the

form of a dumb-bell, or actually of one rotating in a direction almost

at right angles to that of the original one; more probably the former

of the two. Perhaps we have allowed our ideas, or fancy, to run on

too far; nevertheless, looking over the forms of nebulæ represented

in Chambers's classical work, and duly considering how inconceivably

strange some of them are, there is nothing impossible in all we have

said.

Returning to the repeated changes of density in the solar planets,

we know that the matter first abandoned by the original nebula,

through centrifugal force, would be at the lowest stage of density,

and that what followed would go on gradually increasing in density

as it contracted to the Saturnian nebula. But, as we have shown that

immense quantities of matter belonging, so to speak, to the sun, though

actually separated from the original nebula, must have fallen in upon

the sheet after being abandoned, it is not difficult to see that the

part of the sheet out of which Neptune and Uranus were made, might be

more dense than the Saturnian nebula, on account of this matter being

added to it; and that, as the greater portion of it must, at the more

advanced stage of the process of condensation, have fallen upon the

Uranian part of the ring, because the space from which it fell would

be higher, the density of that would be greater than the Neptunian

part of the sheet; both of them exceeding the density of the Saturnian

nebula. Again, we have supposed, very naturally we think, that all

extraneous matter coming in from the equatorial direction would be

intercepted by the rings destined for Neptune and Uranus, so that the

density of the ring for Saturn would be only what had been acquired

through condensation, and the planet formed out of it would be less

dense than those made out of matter accumulated in a different way. It

may be argued against this deduction, that density would depend on the

degree of contraction, but it is natural to think that lighter would

take longer time than heavier matter to condense to the same degree;

besides Saturn is of necessity the youngest of the three planets, and

may in due time come to be as dense as either of the other two, but his

diameter will decrease proportionately.

Coming now to the Jovian nebula, whose diameter we have made to be

1,370,000,000 miles, we have seen, at page 115, that--had it been a

perfect sphere--by the time it had contracted one thousand miles in

diameter, it must have had a flat side of more than 1,400,000 miles in

length? then if we add to that length all that the nebula had inherited

from Neptune, Uranus, and Saturn, the cylindrical part of it must

have been many millions of miles in length, and the polar very much

greater than the equatorial diameter of the nebula. In other words

we have to deal with a body having the form of a very long cylinder

terminating in spherical caps. To this we have to add that the density

of the Jovian was more than 111 times greater than that of the original

nebula. Still farther we have to take into account that the whole of

the matter abandoned by that nebula must have been thrown off in less

than one-half of the space in which the ring for even Saturn had been

abandoned, the breadth of the two rings, as shown by us, see Table

III., having been 650,600,000, and 313,400,000 miles respectively. All

these things considered, it is clear that the thickness of the ring for

Jupiter's system must have been very much greater than what we have

given it in the table; which, coupled with its matter being over six

times more dense than that of the preceding ring, is sufficient to

account for the rise in density, the immense size, and mass of Jupiter.

Next, we have the means of accounting for the fact that, the space

occupied by the Asteroids is, and has always been, the least dense

of any portion of space occupied by the solar system. It is easy to

understand that the enormous mass of matter abandoned by the nebula for

the formation of the Jovian ring--more especially towards the end of

the process--would have a very appreciable effect, by its attractive

power, in helping centrifugal force in freeing matter from the power of

gravitation; the consequence of which would be, that the matter thrown

off for the formation of the Asteroidal ring would be considerably less

dense than it would otherwise have been. In this way, then, we have the

decrease of density, as well as the quantity of matter, in that space

very plausibly accounted for.

Then, as the nebula continued to contract, the attractive power of

Jupiter's ring would decrease proportionally to the square of the

distance of the receding mass, ceasing in doing so to lend so great

assistance to centrifugal force in the nebula, and so letting it

subside into its normal state; so that the matter abandoned would

increase in density in comparison to the space over which it was

distributed, thus accounting for the rise in density towards Mars and

the Earth.

With regard to the fall towards Venus and final rise towards Mercury,

we have to take into consideration the anomalies--already taken notice

of--in the dimensions, densities, etc. etc., of the two planets Earth

and Venus; it being, we may confidently say, certain that the whole

of them have arisen from the same causes. Following up the idea of a

dumb-bell nebula--as we might have done in the case of Jupiter also--as

the breadth of space for receiving matter abandoned by the nebula went

on rapidly decreasing, the thickness of the ring left behind would go

on increasing, and the overhanging matter of the dumb-bell would be

deposited always in greater quantity on the outer than the inner part

of the ring as it broadened; we can conceive that the whole extent of

the sheet of matter allotted to the Earth and Venus would be thicker

at the outer than the inner part. Hence, when this part of the sheet

came to be divided into two parts for the formation of two planets,

the outer would naturally be the greater and denser of the two, and

thus occasion the rise in density from Mars to the Earth, and the

fall to Venus. Finally the rise in density to Mercury would be only

the beginning of the gradual, and final, rise to the sun as it is at

present.

If the idea of a nebula in the form of a cylinder with hemispherical

ends is admitted as possible, or somewhat like a dumb-bell, the

extreme diameters of the 9 successive nebulæ we have dealt with would

be considerably different in their equatorial directions to what we

have given them, although their polar diameters might continue to be

not far from the same; but that would have very little effect on the

operations we have gone through, seeing we have shown that there could

be no actual divisions between them such as we have adopted; and that

the division of the sheet of matter abandoned into separate rings

must have been brought about by some means which we cannot explain; a

process, nevertheless, which has been subject to some law, or laws,

operating evidently in a regular and steady manner throughout the whole

time, during which the matter was being abandoned, as is proved by the

general uniformity, or harmony, in the distances of the planets from

the sun. Should anyone come to be able to account for the division of

this sheet of matter into distinct and separate rings, he will also be

able to account for the acceleration of rate of revolution from one

planet to another, and for the anomalous rates in the cases of the

Earth and Venus.

In a former part of our work we have followed up, at different

stages, the condensation of the original nebula until it attained the

dimensions, appearance, and some of the features of the sun as it is,

but we have still something to add as to how the condensation could

produce a body so strictly spherical as the sun is represented to be.

All the other bodies of the solar system, as far as astronomers have

been able to measure them, are spheroids more or less oblate, and it

seems strange that the principal should be the only one that does

not conform to the general figure. It is rather hard on the notion

that the original nebula gradually assumed the form of a lens, for

it would require a special mode of manipulation of a very mechanical

kind, rather than the steady, imperceptible self-action of the law

of attraction, to transform a lens into even an oblate spheroid; to

transform it into a perfect sphere would be absolutely impossible.

For, if at the end of the process it was found that there was too

much material to form a sphere, it would be hard to get rid of the

superabundance, unless it was converted into meteorites--evidently

another hand process. On the other hand, should a hole remain to be

filled up, the material would have to be lugged in somehow from some of

the errant masses, or lambeaux, which impact-theorists find it so easy

to have at hand when required. Let us then think of why and how it came

to pass that the sun is an almost perfect sphere.

If we suppose that, when cosmic matter ceased to be thrown off by

it, the form of the nebula was that of a cylinder terminating in

semi-spherical caps at the ends, it requires no great stretch of

imagination to conceive that, between attraction and centrifugal force,

the whole mass should be converted through time, first into a prolate

spheroid, and then into a perfect sphere. And very possibly time only

is required for the sun to become an oblate spheroid, the same as his

dependent planets.

Should this form of nebula not be admissible--and we can see no

mechanical reason why it should not--and we are thrown back on a

lens-shaped nebula, the only resource left us is to suppose that

through continued action of attraction, and of centrifugal force,

or rather revolution constantly increasing, the latter gaining the

victory over attraction, finally converted the lens into an actual

ring, something of the nature of the ring in Lyra; and that that ring,

no longer increasing in revolution, would have to yield to the law of

attraction, and would condense and contract and close up into an oblate

spheroid, and then into a sphere. It is a roundabout, rather fanciful,

process, but any other way of converting a lens-shaped nebula into a

sphere, under the law of attraction, is absolutely impossible.

CHAPTER XVII.

PAGE

301 Former compromises taken up and begun to be fulfilled.

302 Estimates of the heat-power of the sun made only from

gravitation hitherto.

303 Contraction and condensation of a nebula solid to the centre.

Heat produced from attraction as well as by gravitation.

304 What quantity of heat is produced by a stone falling upon

the earth.

305 Showing again that there is a difference between attraction

and gravitation.

305 Contraction and condensation of a hollow-sphere nebula, in the

same manner as the solid one.

306 Differences of rotation would be greater in a hollow nebula;

because a great deal of the matter would be almost motionless

in a solid sphere.

307 In neither case could matter be brought to rest, but only

retarded in motion. Different periods of rotation

accounted for.

309 Table of different rates explained.

310 Heat produced by gravitation, attraction, and churning,

not all constituents of the heat-power of the sun.

311 There can be no matter in the sun so dense as water.

312 The hollow part of the sun acting as a reservoir of gases,

heat and pressure.

313 The behaviour of heat produced in the nebula, and its power.

314 How sun-spots are produced.

315 Cyclonic motions observed in sun-spots. Why not all in certain

directions, and why only observed in a very few.

316 Cyclonic motions in prominences treated of.

317 Many other things might be explained, on some of which we

do not dare to venture. Concluding observations.

At the end of Chapter VII., when making some remarks on the heat of

the sun produced by gravitation, we said that according to the areolar

law the condensation produced thereby would originate difference of

rates of rotation in the nebula--provided it did rotate as Laplace

assumed--depending on its degree of contraction and consequent density

increasing as the centre was approached; and that these differences

of velocity of rotation would give rise to a churning action in its

interior which, owing to the friction caused thereby amongst the

particles of its matter, would produce heat over and above what was

produced by gravitation alone. Again, at the end of Chapter XII., we

said it would not be difficult to show what tremendous commotions

throughout the whole nebula would be produced by these differences

of rotation; but that this could not be properly done until we had

reconstructed the original nebula, and had shown how from it the solar

system might be constructed. Now, therefore, that we have set forth, as

fully as we can, our ideas of the formation of a hollow nebula and the

construction from it of the solar system, we shall proceed to show how

heat was, and must still be, produced by the churning action, over and

above the definite quantity that could possibly be produced by simple

gravitation. And also to show how our notions of the interior of the

nebula first, and afterwards of the sun, are simplified and made more

natural by looking upon it as a hollow sphere.

We will begin by considering, first, what would take place during

the contraction and condensation of a rotating nebula solid to the

centre--i.e. filled with cosmic matter to the centre--as that is the

condition under which such a body has been studied hitherto--as far as

we know at least....

Not to weary humanity--our own included--by repeating, what almost

every one knows, who the parties were and how they came to the

conclusion, that by far the greatest part--almost the whole--of the

heat expended by the sun, ever since it had any to expend, has been

produced by condensation caused by gravitation; we shall for the

time being accept this as the general, almost universal, opinion at

the present day. If any proof of this being the case is considered

necessary, we have only to appeal to Sir William Thomson's lecture,

delivered at the Royal Institution on January 21, 1877, in which he

showed how a cone of matter, similar to that of which the sun is

made, with base at the surface and apex near the centre, falling into

a similar hollow cone excavated in his body, would, in descending

a certain distance, generate as much heat as would maintain a

proportional part of his expenditure for a year; and in which, beyond

stating that a very small part might be produced by the fall of

meteoric matter on his surface, he makes no mention whatever of any

heat-producing power except gravitation pure and simple. The weight

of the cone falling into the conical pit alone, produced almost the

whole of the desired supply. That this manner of calculation is one

of those modes which, as we have said from the very beginning of our

work, could never have been adopted had a little more thought been

expended on them, can be easily demonstrated even in the case we are

now considering. This we say with all due deference to so great an

authority; more especially as we know how difficult it is, how seeming

unnecessarily laborious, to examine everything to the very bottom;

and how pleasant and satisfying it is to feel contented, when we have

obtained what suits our purpose.

When we began to consider, in Chapter XV., what would be the interior

construction of the nebula, we supposed, at page 269, that it had

assumed a somewhat globular form when its diameter came to be three

times that of the orbit of Neptune, which would be 16,764,000,000

miles; and we will return to that supposition to set forth our

conception of how heat would be produced in a nebula of that diameter

solid to the centre--that is full to the centre of cosmic matter. In

that case a particle of matter starting from the surface, under the

power of gravitation, would have to travel 8,382,000,000 miles before

it reached the centre, and would carry with it a constantly increasing

power of producing heat, derived solely from the action of gravitation.

Next, we have to consider what would stop it when it reached the

centre and enable it to give out its heat--for until it was stopped it

could give out no heat at all--and the most easily conceived means of

stoppage would be to suppose that an equal and similar particle coming

in from exactly the opposite side of the nebula met it there. If it

was not that it would be something equivalent and much more difficult

to describe, while the result would be the same. The result would be

that, as each particle came in with equal power of producing heat,

the the amount produced when the two met and stopped each other would

be just double what each of them brought with it; that is our way of

looking at it at least, considering that the velocity with which they

met would be just double what each brought with it, and the force of

the shock would be double what it would have been had only one of them

been stopped in some other way; that other way would have had to give

or furnish its half of the shock, and would therefore be able to give

out as much heat as the stopped particle. Whether two of Sir William

Thomson's cones meeting at the bottom of his pit, from exactly opposite

sides of the sun, would have the same effect as we have found for the

two particles, may perhaps give rise to the discussion; but we do not

see why the result should be in any way different. When a stone falls

from a height upon the earth it gives out, in the form of heat, all

the heat-producing power it had accumulated in its fall, but we are

apt to forget, perhaps have never thought at all of, the why and the

how it gives it out, especially of the latter. The why is because it

is stopped, and the how is by the earth coming to meet it, and these

two ways have an inseparable relation to each other. And if the earth

comes to meet it, which it most undoubtedly does, though we cannot

measure how far it travels, it must bring along with it an amount of

heat-producing power equal to that possessed by the stone, when it

in its turn is stopped by the stone; thus the amount of heat arising

from the fall of a stone to the earth is, apparently, just double what

it is usually estimated to be. This fact comes under the category of

splitting hairs or, more truly speaking, of negligible quantities; but

the whole mass of the sun falling to the centre cannot enter into that

category, and whether we will or no we have to take it all into account.

We have conducted two particles of matter from exactly opposite points

of the surface of the nebula to its centre, and shown that by simple

gravitation a certain amount of heat would be produced by them when

they met there and stopped each other; now, we propose to conduct two

particles, not far from each other, from one side only of the nebula to

the centre, and point out what would happen to them on their voyage

thither. The road is long, as we have seen, and during their voyage

there would be time enough for a good many things to happen, but we

shall only take notice of two for the present, namely, gravitation--of

which we have already almost disposed--and attraction; for as far

as their journey is concerned there is a very marked difference in

the meaning of the two words. Gravitation--that is, the action of a

ponderable body falling--acts only in a straight line from any point

to a centre of attraction, while attraction acts in every possible or

imaginable direction. We have already seen what happened to the first

particle despatched to the centre under the power of gravitation alone,

and have only to say, that the same would happen, under that power, to

the two we have now in hand; but attraction--actually the father or

mother of gravitation--would have a good deal to do with their journey.

From the moment they started--very likely they were practising before

they left--they would rush at and continue to bombard each other during

the whole voyage. At each encounter or collision, however caused, a

certain amount of heat would be produced in each of them which they

would carry along with them, and would augment the gravitational

quantity they would have to give out when stopped in their fall, in the

way we have pointed out would be the only one that could bring them

to rest. It may be said that that heat would be left behind in space

on the way but space cannot absorb heat unless it contains something

to hold it in, and that something could only be similar particles

of matter on the same voyage, also creating heat and having as much

to dispose of, no doubt, as the two we are conducting. This lateral

attraction, so to speak, is really what instituted rotary motion in

the nebula, and produced the differences of rotation and the churning

action in it with which we shall have to deal presently.

Having passed under examination the quantity of heat produced by the

contraction and condensation of the solar nebula into a globe solid

to the centre, we have now to do the same for the case of its being a

hollow sphere, and we may say that our work has already almost come

to an end; for we have only to vary to a small extent what we have

just set forth. Beginning then as before, with one particle of matter

falling, or rather being attracted, from the surface of a hollow-sphere

nebula, we find that it would not reach the centre at all, but would

be stopped by another drawn out from the centre by its own attraction,

which would meet it--say for brevity--half-way between the starting

points of the two, each bringing along with it its own heat-producing

power and giving it out to its opponent, there being nothing else to

give it to; so that if each brought with it _x_ heat-power they would

have 2_x_ heat-power between them, just as we have said would happen

in the first case, and the heat of each one of them would consequently

be doubled. In this case we have to observe, though it is really

unnecessary, that as yet we have spoken of attraction as acting in one

direction only, that is, in doing only the work of gravitation; so we

have still to consider the voyage of two particles of matter proceeding

from the surface and meeting two coming from the centre, and have only

to say that their mutual collisions caused by lateral attraction on the

way, would enable them to bring along with them certain quantities of

heat produced by these collisions, which would be over and above what

they acquired in their straight-line imaginary voyage.

If any one doubts that additional heat would be produced by this

lateral attraction and bombarding, let him take two hammers and

strike the one against the other as rapidly as he can for some time,

and he will be able, by touch, to convince himself that heat can be

produced by this lateral attraction as well as by the _attraction of

gravitation_; and, if he could measure it afterwards, he would find

that if he dropped the hammers on the ground, they would not give out

any of that heat but only what they had derived from gravitation in

falling from his hands to the ground, unless the ground was colder

than they, and if the ground was not colder, the heat it had would be

augmented from this source also.

If the heat produced in both of the cases we have been examining

caused differences of rotation in the nebula--as we have said on a

former occasion--increasing in velocity as the region was approached

where the stopping process came into action, it is clear that these

differences would be greater near that region in a hollow-sphere

nebula than near the centre of a solid sphere; for the reason that

the particles of matter would there have more freedom, that is, more

room to act in. We have shown that in the solid sphere the particles

would come to be more or less inert, in proportion as they approached

the centre; and also that in a hollow-sphere nebula no particle could

ever come to be near to a state of rest, but that each could be freely

driven by the collisions produced by lateral, angular, universal

attraction over every part of the hollow shell--an effect that could by

no means be produced in a nebula solid to the centre. We, therefore,

think that there would be more life-power in a hollow-sphere sun than

in the kind of sun from which all calculations of length of life have

hitherto been made--at least, as far as we know.

It will be understood that we have spoken of particles of matter being

stopped, or stopping each other, before they could give out their heat,

only for facility of explanation; for no particle of matter can ever

be brought to absolute rest, until all its heat and heat-producing

power, _i.e._ motion, could be taken out of it, and that can only be

when it is reduced to absolute zero of temperature. Cosmic matter could

be reduced to the state of rock or steel, but its particles would not

be at rest then, or else our ideas of the nature and construction of

rock and steel are very erroneous; but it must be acknowledged that

it would be much more easily reduced to the state of rock in a body

solid to the centre than in the shell of a hollow sphere. In fact it

is difficult to conceive how matter could exist at the centre of the

sun at the present day without being as solid as rock, considering

the enormous pressure it must be subjected to there, if its whole

mass is condensing to the centre. But although the particles of the

nebula could not be absolutely stopped, they might be so far retarded

in their velocities derived from attraction that they would give out

heat to each other, and wherever a collision took place there heat

would be made evident, and condensation might take place. Particles

of matter would not have to fall to a centre, but only to a a meeting

place, in order to condense and create heat, and might form layers of

condensation anywhere between the centre and the surface, either in

a solid or hollow sphere, which would ultimately, even in the former

case, form a hollow shell, as we have supposed, at page 274, might be

the case. For even a small sphere formed around the centre in that way

would be hollow, and would be undone when the different concentric

layers approached each other, under proportionate forces of attraction,

and formed into one hollow sphere. Thus we again come to the conclusion

that the formation out of cosmic matter acted upon by the law of

attraction, of a sphere full of that matter to the centre would be a

mechanical impossibility. In either case the total quantity of heat

produced by the contraction and condensation of the nebula would

include, not only what has hitherto been looked upon as belonging to

gravitation alone, but that other part derived from attraction in all

other directions. So the age and duration of the sun still remain to be

estimated.

We have not said, but we have not forgotten that it may be said that,

if in Lord Kelvin's estimate of the sun's heat, a cone of matter

falling in from one side of it was stopped by a similar cone falling in

from the exactly opposite side, one half of the sun's mass stopping the

other could only produce the amount of heat calculated by him. Neither

do we deny that the same may be said of the two half-volumes of the sun

meeting at the region of greatest density in a hollow sphere, and that

the amount of heat produced by gravitation alone would be the same in

both cases. All that we have wanted to show is that, in addition to the

quantity so produced, the quantity produced by lateral attraction, so

to speak, has to be taken into account, in order to estimate the total

quantity ever possessed by the sun.

Referring now to what we have said towards the end of Chapter XV., of

rotary motion being instituted at the region of greatest density of the

nebula, and being propagated from there to all parts both outwards and

inwards, we can at once account for the different periods of rotation

observed on different parts of the surface of the sun; and not only

that, we can assert that these differences of rotation must exist

throughout the whole volume and mass of its body up to the present day.

We have no need to appeal for producing them to showers of meteors

falling on its equatorial regions; neither do we pretend to say that

such showers have no part in producing them; but we do say that the

part they play in the affair, and the depth to which they can penetrate

into the sun's body, must be altogether insignificant compared to what

we have pointed out as the true and indisputable cause.

We may now proceed to consider what would result from the commotions

produced by these differences of rotation in the interior of the sun,

and we shall begin by observing that an enormous amount of heat would

be produced thereby. The churning action, as we have called it, must

be of a very formidable character, for, supposing the whole of the

interior to be in a gaseous or gasiform state, it must be effected

under a pressure of not less than 28 atmospheres at the surface, and at

what pressures as the centre is approached no one can tell; and if the

matter in the interior is in a viscous condition, the friction caused

by the churning will only be the greater. But let us try to form an

idea of what the force, or rather violence, of that churning action

must be in the sun if constructed in the manner we are advocating;

for which purpose we have to form some definite notion of what is

the difference of velocity of rotation at different parts of its

circumference, which can hardly be better shown than by Table X., in as

far as these rotations have been approximately measured.

The first thing to be observed in the table is that the rate of

rotation at the equator is 75·10 miles per minute, and that at Lat. 45°

it is only 48·23 miles, giving a difference of 26·87 miles per minute

in one-fourth part of the sun's circumference, which is a velocity 27

times greater than our fastest express trains. And the next is to note,

in the last column, how these 26·87 miles of difference, when divided

over spaces of 5° each, show decreases in velocity of from 0·39 at Lat.

5° to 5·06 miles between degrees 40 and 45.

A little thought bestowed on these two points will show what

commotions must be produced at the surface by this enormous variation

of rotation and make us speculate on how much greater it must be near

the poles than at the half distance from the equator. Then, if we look

upon the sun as a hollow sphere we have to consider that, according to

the theory that the condensation of a nebula increases its rotation in

proportion to its approach to the region of greatest density, of the

velocities of all the rotations expressed in the table, the greatest

must be at that region, the others diminishing from there outwards to

those of the surface, and inwards to almost nothing at the centre; for

we have seen that there must be gases enclosed in the hollow, and that

motion must be communicated to them, through friction, down to the very

centre. Taking all these things into consideration, it is certain that

the churning must be very much greater than anything we have thought of

up to the present moment, the commotions created more tumultuous, and

the heat produced by friction incalculable.

TABLE X.--SHOWING THE DIFFERENCES IN VELOCITY OF ROTATION

OF THE SURFACE OF THE SUN, AT DISTANCES OF 5° FROM

EACH OTHER, FROM THE EQUATOR TO 45° OF LATITUDE.

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

|0° to 45°.| | | | | 5 degrees. |

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

| | | | | | |

0 | 2,723,767| 25·187 | 108,142| 4506 | 75·10 | ... |

| | | | | | |

5 | 2,713,367| 25·222 | 107,581| 4483 | 74·71 | 0·39 |

| | | | | | |

10 | 2,682,387| 25·327 | 105,910| 4413 | 73·55 | 1·16 |

| | | | | | |

15 | 2,631,058| 25·500 | 103,170| 4299 | 71·65 | 1·90 |

| | | | | | |

20 | 2,559,504| 25·737 | 99,441| 4143 | 69·06 | 2·59 |

| | | | | | |

25 | 2,468,572| 26·040 | 94,799| 3950 | 65·83 | 3·23 |

| | | | | | |

30 | 2,358,852| 26·398 | 89,357| 3723 | 62·05 | 3·78 |

| | | | | | |

35 | 2,231,179| 26·804 | 83,242| 3468 | 57·81 | 4·24 |

| | | | | | |

40 | 2,086,526| 27·252 | 76,564| 3190 | 53·17 | 4·64 |

| | | | | | |

45 | 1,925,994| 27·730 | 69,455| 2894 | 48·23 | 5·06 |

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

NOTE.--The times of rotation are taken from

Messrs. Newcomb and Holden's "Astronomy," p. 290.

Lest we should have been misunderstood in what we have said a few pages

back, and it be thought we consider that all the heat produced by this

churning action ought to be added to that produced by gravitation

alone, when attempts have been made to compute the total quantity

ever possibly possessed by the sun, we have to insist that the idea

of gravitation in itself--that is, of matter falling to a centre--is

altogether erroneous in connection with the construction of the sun

from a nebula, and that it is in truth utterly misleading. We know

perfectly well that in the construction of the sun, heat could only be

produced, in the main, by bodies colliding with, or rubbing against,

each other, and that a large part of that produced by universal

attraction must have been expended in producing rotary motion; but we

also know that in its construction no particle of matter can ever,

as yet, have been brought to the state of rest of solid matter even,

that it has still the power of colliding with its neighbours and of

producing heat, and that it will continue to preserve that power

until it is bound up into a solid state along with its neighbours.

Even then it will not be absolutely at rest, but will have lost its

heat-producing power, and will begin to lose the quantity it then

possesses when it gets permission from its neighbours. It is a fallacy,

therefore, to suppose that the matter of which the sun is composed

has no other heat-producing power than what is derived from its fall,

through gravitation alone, from the potential position it held to the

centre of the incipient nebula. The only end to heat-producing power is

fixed position.

If science chooses to fix that position at the centre of the sun, or

as near to it as successive particles can reach, there must be any

quantity of it in a solid state even now in that neighbourhood, if

due consideration is given to the pressure it must be subjected to

there. If it chooses to entertain the idea of the sun's being a hollow

sphere, somewhat in the form we have described, there can be nothing

in its whole body so dense as even water up to the present time. In

the first case it has to remember what we have done our best to prove:

That _gravitation_ ceases to act when a body falls to a fixed centre

or position and can fall no farther. From there it cannot rise except

through upper or exterior attraction, and in that case it would leave

a hollow space in the place it had occupied. It is altogether illusory

to dream of convection currents where no means or force of any other

kind than attraction could give rise to them, in which case we should

have attraction and gravitation working against each other, two things

that have been confounded into one turning out to be antagonistic, as

no doubt they sometimes actually are--as we have shown when treating

of the discovery of Neptune--but when they are so, they never can

produce convection currents. In the second case in which, as we have

seen, there can be no matter at all near to the solid state or fixed

position up to the present day, we can conclude that the life of the

sun, measured by heat-producing power, must be very much longer than in

the first case, in which a very large part of the matter of which it is

composed must have lost that power ages ago.

We have still to bring to mind what we have said in Chapter XV. of

the region of greatest density of the nebula being the region of

greatest activity and greatest heat; and to add now, that the whole

space between that region and the centre must have been acting as

a reservoir--partly material, partly gasiform--of heat, ever since

the nebula began to contract and condense, quite independently of

its carrying before it the minus or plus sign. From that time that

region would be the regulator of the radiation of heat into space, or

to wherever it was radiated; because no heat produced on the inner

side could escape into space without passing through and acquiring

the temperature of that region, or first giving out to the outer side

any greater heat that it might have produced and accumulated; facts

which involve the necessity of the whole of the interior space, or

volume being heated up or lowered down to the same degree before any

of it could be transmitted outwards. Thus, in addition to all we have

said of the means of lengthening the sun's life, we have to take

into consideration that all heat radiated from the surface must be

conducted, or carried somehow, through a distance somewhere between

about 2,000,000 and 90,000 miles, before it could escape into space

or elsewhere, according to when it began to be radiated at all. And

we have also to take into consideration the probability that the heat

produced and accumulated in the inner half of the volume would, by

its repulsive force, retard the condensation of the nebula, and thus

prolong its heat-giving life.

Looking back on our description of the construction of the sun, how

rotary motion was established in it, and how that motion has produced

the different velocities of rotation, not only on the surface where

they have been observed and measured, but which must penetrate to the

very centre; we may now proceed at the expense of some repetition--in

which we have already somewhat indulged--to show how our mode of

construction and development enables us to understand a great many

things that have been observed in it, much better than we have been

able to do from any explanations that have hitherto been available. It

gives the most satisfactory reason possible for the sun-spots occupying

principally two zones at marked distances from the equator. There is

one belt round the equator of 16° to 20° wide on which we know, from

Table X., that the differences of velocity of its edges and of those

of the contiguous zones, one on either side, hardly exceed 1 mile per

minute. Towards the poles there are two segments measuring from 80° to

90° broad, at the borders of which the rotary velocity is slower by

26·37 miles per minute than it is at the equator, and 5·06 miles per

minute slower than at 5° less latitude, as also shown by the table.

And between the central belt and these segments there are two belts or

zones, each 30° to 35° wide, in which sun-spots are almost only to be

found. In these two zones the churning of the interior would be in all

its vigour, most probably more active at their centres than where they

meet the central belt and the polar segments; where our knowledge of

the diminished velocity ceases, but where we have no reason to suppose

that it actually stops.

Were the period of rotation the same throughout the whole body of the

sun--with the exception of what has hitherto been considered to be a

mere surface difference produced by external causes--we could conceive

that the heat produced solely by condensation would find its way to

the surface equally in all directions, even bubble up all round like

steam rising from the surface of the water in a boiler, in this way

forming what is called the sierra; and that there would be neither

sun-spots nor eruptive prominences, hardly any of the violent movements

recorded in works on astronomy. But the churning action we have been

exhibiting, extending to the deepest recesses of the sun, must produce

commotions quite adequate to give birth to the most violent phenomena

that have been recorded. Viscous gases and vapours, gasiform vapours,

ground against each other at depths of hundreds of thousands of miles,

under pressures of hundreds, much more likely of many thousands, of

atmospheres, and confined by superincumbent strata, so to speak, would

acquire a dynamitical explosive force that could be conceived to be

powerful enough to rend the sun into fragments, were it composed of

anything comparable to solid matter. On the other hand, the friction

of the solar matter operated under the pressure of 28 atmospheres at

the surface, and up to the unknowable number at the greatest depth,

converted into heat, would have explosive energy enough to give rise

to all the phenomena that have been observed; from the veiled spot to

Professor Young's prominence, which was thrown up to the height of

350,000 miles above the photosphere.

A veiled spot seems to be one that has broken through the photosphere,

perhaps not even entirely, but not through the light or white clouds

which float immediately over it; which, in consequence, goes a long

way to prove that sun-spots have their origin in up-rushes of heated

vapours from beneath; for a downfall of cooled metallic or other

vapours would break through the light clouds first of all; and which

is confirmed, as far as anything in solar physics can be confirmed,

by what we are exposing. That there is a down-rush also, goes without

saying, because there is no other way of giving account of what becomes

of the vapours of metals and other elementary substances brought up by

the outpours of heat, after they are cooled in the solar atmosphere.

That they should fall down into the same opening they had made in

rising up, is the most natural supposition that can be made; for,

otherwise, they would have to be carried beyond, or outside of, the

spot before falling. Moreover, a sun-spot is said to be generally

surrounded by prominences which bring up vapours of elementary

substances, that we must believe to be much heavier than those from

eruptions of sun-spots, because they issue much more violently,

showing that they must have been expelled by much greater force,

which must form a sort of wall all round the spot through which the

matter, thrown out by it, would have to be carried before it could be

deposited; and outside these walls there are no visible signs of where

it falls, so that we are forced to believe that all the substances,

those from prominences as well as those from sun-spots, fall into the

same general receptacle. Surely it could not be argued that there can

be no eruptions from a sun-spot, seeing that the force required to

drive matter through it must be less than when it is expelled from

depths very much greater than the depths of the spots. Thus we have

both up-rush and down-rush in sun-spots accounted for very plainly; and

they are always large enough for both operations being carried on at

the same time. Besides, they have been credited by eminent astronomers

with the faculty of sucking in the cooled vapours from the surrounding

prominences into the common pit.

In some sun-spots, said to be about 3 per cent. of those observed,

cyclonic motions have been observed in the umbræ and penumbræ, which

under the churning process might be expected to be universal in all of

them, but it is not necessarily so; even leaving out the consideration

of the difficulty of detecting them. We see in a deep smooth-flowing

river eddies revolving in all directions, caused by currents of

different velocities approaching each other, quite independent of the

form of the banks of the river or obstructions in the places where we

see them, but without doubt derived from sources of that kind higher up

in the river; and so it may be with cyclonic motions in the sun-spots.

The velocity and direction might be given to the vaporous matter by

the churning action before issuing into the spot, which would cause

eddies in it in all directions, the same as those in the water of the

river. It would be absurd to think that in a space so immense as the

bottom of a sun-spot, there should be only one orifice of emission of

vaporous matter: there might be any number; consequently, there may

be times when the out-flowing currents annul each other and none at

all are seen, or when there are partial currents in any direction;

others when they may be all so uniform as to produce a cyclonic motion

all round a spot, or nearly all round it, or two or more in opposite

directions, all as has been recorded on more than one occasion. Neither

could it be supposed that any cyclonic motion, caused by the churning,

could depend on which side of the equator the spot was formed in. There

must be little churning going on under the surface at the equatorial

belt, hence the paucity of spots there; but between the surface and

the centre there must be some point of meeting of the motions that are

produced on each side of the equator which, even were there no special

reason for it, would destroy all chance of uniformity, or distinctive

direction, in the upheaved matter when it arrived at the surface, let

it reach that place on whichever side of the equator it might. The

original salient motion at the bottom of a sun-spot might be to right

or left, or according as the material from which it proceeded had been

tumbled about, and the issuing motion might also be controlled greatly

by the form and position of the orifice, or rather tunnel, through

which it escaped. Common churning, we know, could not drive all the

milk in one direction, even were the paddles of the churn solid; and

in our case, the paddles have to be looked upon as even more divided,

magnitude for magnitude, than they are in an ordinary churn, for the

matter itself forms the paddles.

The cyclonic motions observed in prominences must come from the same

causes, and ought to be more general in them, seeing that they must

proceed from apertures much fewer in number than in the sun-spots, and

very probably from one orifice in the case of jet prominences. One

would expect also that these cyclonic motions would be more regular

in the prominences, from being generated deeper down in the interior

than those of the sun-spots, and less affected by the motions they

encountered on their way out, owing to the great original energy

required to force them through the superincumbent mass of matter,

and might even have--in jet prominences especially--the motion to be

expected according to the hemisphere from which they proceeded. But we

have already said that, deep in the interior, the churning motion may

be in any direction whatever. It is natural to suppose that the highest

prominences are ejected from the greatest depths, because they require

the greatest ejective force to throw them to such immense heights,

and because the greatest ejective force must be where the heat and

pressure are greatest, that is, at the densest and most active depths.

And probably the reason why prominences generally surround sun-spots

is that they have had their exits facilitated by the relief from

pressure, brought about by the discharge of churned matter into them

(the sun-spots), and thus, as it were, attracting the eruptions of the

prominences towards them.

We had almost omitted to say that the churning theory would very well

account for almost every sun-spot having more or less proper motion of

its own independent of all others, and for all of them drifting towards

the central belt, or towards the polar segments when they begin to

dissolve and disappear.

There are many other things in connection with the sun that could

be explained through our mode of construction, some of which are so

evident that they will occur to anyone, and others that lead into

depths too profound for us to enter.

To conclude. The construction of the sun we have set forth would be of

great service towards the completion of either of what Professor A.

C. Young calls the competing theories of M. Faye and Fr. Secchi, in

which the former would find the origin of the solar storms, to which

he appeals for producing sun-spots in particular zones, and a better

way of accounting for the differences in velocity of rotation between

the equator and the poles than in the depths of the strata between

these regions; and the latter the means of forming the dense clouds of

eruption which he assumes to form sun-spots by settling down into the

photosphere. But theorists seem to be partially right by a divination,

and to have only failed through their not having found out the sources

of the powers they called into existence, in order to have some

foundation to build their theories upon.

CHAPTER XVIII.

PAGE

319 Return to the peaks abandoned by the original nebula.

An idea of their number.

320 Example of their dimensions. What was made out of them.

321 What could be made from one of them.

322 How it could be divided into comets and meteor swarms.

323 An example given. How a comet may rotate on its axis.

And what might be explained thereby.

Orbits and periods of revolution.

324 Not ejected from planets. Their true origin.

326 Study of the velocities in orbit of comets, and results thereof.

327 How far comets may wander from the sun and return again.

328 No reason why comets should wander from one sun to another.

Confirmatory of the description, in Chapter XV. of

the sun's domains.

329 Of the eternal evolution and involution of matter.

The atmosphere and corona of the sun.

331 Partial analogy between it and the earth's atmosphere.

332 The density of it near the sun's surface cannot be normally

less than 28 atmospheres, but might be so partially

and accidentally.

332 Probable causes of the enormous height of its atmosphere.

334 The mass taken into account, but cannot be valued.

335 Most probably no matter in the sun exceeds half the density

of water. The unknown line in the spectrum of the corona

belongs to the ether.

When we were attempting to describe in some measure the region of space

from which the sun obtained the nebulous matter out of which it was

formed, we found that it would produce a nebula somewhat resembling a

most gigantic starfish, with arms or legs stretching out from it in

every direction, which might be likened to mountain-peaks rising from

a tableland or range of mountains; and when we began to condense the

nebula we concluded that these peaks would very soon, comparatively,

be left behind the main condensation, owing to their being more under

the influence of the attraction of surrounding suns. And we might then

have added less under the attraction of the main body, on account of

its gradually increasing distance arising from its greater rapidity

of contraction. Now, we propose to return to these portions of the

sun's property so long left out in the cold, to think of what in all

probability became of them, seeing that they must all have had somehow

a part of some kind to take in the formation of the solar system.

First of all, we have to form some idea, however vague, of their

number, which may be divined to a very limited extent from the

following considerations: We see, from Table VIII., that the sun's

sphere of attraction extends to more than 4000 Neptune distances in

the direction of [Greek: a] Centauri, the star nearest to the earth,

which corresponds to 11 billions of miles. Then, although we have said,

in Chapter XV., that instead of there being a peak on the nebula in

that direction there would be a deep hollow in it, we shall proceed

to find out what might be the diameter of the base of a peak at that

distance supposing it to be somewhat in the form of a cone. We know

that the moon does more than eclipse the sun, which is 867,000 miles

in diameter; so, for facility of calculation, we may suppose that it

eclipses a portion of space at its distance of 1,000,000 miles in

diameter. Consequently, the base of a peak such as we are measuring

would be eclipsed were it 129,000 millions of miles in diameter, and

then only. Moreover, we have deduced the diameter of the base of such a

peak from _one_ diameter of the moon; so that wherever we see two stars

only one breadth of the moon from each other, there we have room for

at least one peak with a base of the above diameter. Last of all, when

we come to think that there are as many as six to seven thousand stars

visible to the naked eye, and of the intervening spaces between them,

we have to conclude that the number of peaks surrounding the original

nebula before they began to be left behind, or cut off, must have been

almost beyond our conception; more especially if we look at Table VII.,

where we see that the star Canopus is 25 times farther from the sun

than [Greek: a] Centauri. We are accustomed to look with wonder on the

volcanic peaks of the moon, but they can do nothing more than give us

an exceedingly faint representation of the original nebula seen from

an appropriate distance outside, when it had begun to contract more

rapidly than the peaks could follow it; seeing that we are comparing a

diameter of 2,160 miles with one really almost infinitely greater.

Finding ourselves, then, with an innumerable host of peaks, or cones,

of cosmic matter on our hands, we have to think of what can be done

with them, and we begin by saying that the use to be made of them was

suggested to us when we discovered the jagged nature of the domains

of the sun. Some of them have been most probably swallowed up in the

formation of the sun, and could we believe in the plenum of meteorites

in all space, that has been fancied to exist by some physicists, we

might derive its origin from a part of these peaks; but if there can be

such a plenum in space, its origin might be much more naturally derived

from a suggestion made in a former chapter, at page 258, to which we

shall refer presently. In the meantime, looking upon the multitude

of comets, meteor-swarms, etc., which revolve around the sun, or are

supposed to exist somehow in its neighbourhood, it is very natural to

entertain the belief that they have been made out of some of the most

important peaks--or the refuse from them--that must have formed part

of the original nebula. To deal with all of them when we cannot number

them, or even with the six of Table VIII., about which we actually know

something, is out of the question, so we shall only try to show what

could be made out of one of them.

Confining ourselves, then, to the peak of [Greek: a] Geminorum, whose

collecting ground had originally reached to 24,000 Neptune distances,

or 67 billions of miles--this being the point of space where the

attractions of the sun and that star balance each other--if we suppose

it to have been contracted till its base was of the same diameter, and

its distance the same from the sun, as that of the base of the peak we

measured not many minutes ago, 129,000 million miles, and 11 billions

of miles, respectively, we can easily conceive that its height may have

been 10 times as great as the diameter of the base, or more than 1-1/4

billions of miles. Here then we have in the direction of only one

star a mass of cosmic matter out of which something more than a comet,

even of the grandest known to modern astronomy, could be made. Of its

tenuity, all that we have any necessity to think is, that it would be

much less--i.e. more dense--than that of the original nebula.

Beginning then with the dimensions we have just stated, we know that

the attraction of the nebula would draw the matter of the base-end

of the peak more rapidly towards itself than that of the apex-end;

we know also that there would be different rates of contraction

going on in different parts of the length of the peak--for the same

reason we have given for the peaks being cut off from the nebula; so

that the condensation throughout its whole height, or length, would

be proceeding at different rates at different places, which would

certainly divide the peak into several parts, perhaps into many. If now

we suppose that the leading part of it--the one nearest to the nebula

or sun--or even the whole of it, formed itself into a comet, it is not

difficult to see that it might have a tail infinitely longer than any

comet the length of whose tail has been measured.

There can be no doubt that in the whole length of the peak the action

of attraction would be exactly the same as we have found it to be in

the nebula itself; that is to say there is no reason why it should not

come to be a hollow cone--comets are reported to be hollow in most

cases--condensed into layers, and to revolve on their axes throughout

a great part at least of where their diameters are greatest. This mode

of formation seems to throw light on some of the phenomena that have

been observed in comets. We have just said that our peak would be

divided into several parts, so if we suppose the leading part of it to

have been made into a comet, we can see why its tail should have the

appearance of a hollow cylinder; and there might be no reason why the

second division, or even the third, should not become a comet also.

Then for further divisions, where the diameter came to be too small to

make a comet, its matter might have formed itself into a meteor-swarm,

and account for the fact of some comets and meteor-swarms revolving

round the sun in the same orbits; perhaps even for some of the observed

meteor-swarms being denser at one part than another, owing to two or

more of the sections of the peak following each other at some distance.

We have to notice, after what we have just said, that it is quite

possible that if the different sections of our peak did come to revolve

round the sun, their perihelion distances might be so different that it

would be impossible to trace any connection between them and the peak

from which they were derived. But if we were to attempt to set forth

all the explanations of the phenomena of comets and meteor-swarms that

have occurred to us, there would be no end to our labour.

Passing now from one to the whole host of peaks, we have seen that at

one time they projected from all sides of the nebula; it is clear,

therefore, that the bodies formed from them must have fallen in

towards the sun from all directions, which is exactly what they have

been found to do. Then, if we think of the multitude of them there

would be, we have also to think that there would most certainly be

collisions among them, which would smash them to atoms, and thus

help to make the plenum, or host of independent meteorites that are

supposed to exist, or would be swallowed up by the sun in mouthfuls.

Others might coalesce, which they could only do through coming in from

slightly different directions and with nearly similar velocities; and

they would thus account to us for comets with a plurality of tails.

Again, looking back to what we have just said of the form that might

be assumed by the leading end of the peak [Greek: a] Geminorum, which

was suggested by Donati's comet, we could imagine another, the same in

almost all respects, coalescing with it, and between the two showing

us how Coggia's comet was formed. Furthermore, with respect to one of

the gigantic comets with endless tails: If we suppose it to rotate on

its axis, and to be not so smooth on its outside as a cone formed in a

turning lathe, we could account for the light from the sun reflected

from it having an appearance of flickering; and, were the outside very

rough, for the reflected light flashing from millions of miles of its

length in a few seconds.

All this about nebular peaks, comets, etc. formed from them, will, far

more than likely, be looked upon as imagination or speculation run

mad; but if it is looked into properly, it will be found that no part

of it is based on assumption; farther than that, the universe has been

formed out of cosmic matter of some kind. There is no step in the whole

process, from cosmic matter to the sun--even myriads of suns--that does

not conform to what are generally called the laws of nature; whereas

it is not difficult to show that some other speculations on the same

subject have never been carried beyond the stage of conception.

When thinking of how comets might be formed, we could not help

thinking of their orbits and periods of revolution. It was easy to

see that their orbits depended on where, and how far, they came from;

that the where might be from any and every direction, and that the

how far would be the principal element in their greater or lesser

ellipticity, which could only be determined by measurement; but their

periods of revolution, as far as we can see, could only be determined

by observation, which would involve the study of several revolutions.

On these points the data we have been able to collect are not very

satisfying, neither are they given to us as very reliable, except

as to those whose orbits have been often observed and measured; and

even among these the orbits are said to vary, and some of the comets

to disappear altogether. Again, some of them are said to have a

disposition to become associated with particular planets; and yet

again, some people have gone the length of supposing that they have

been ejected from some of the planets. To us it seems much more

rational to suppose that the known periodical comets have been made out

of part of the multitude of peaks which must have surrounded the nebula

at one time, if the sun was formed out of nebulous matter, subject to

the attraction of similar matter surrounding it on all sides. It seems

to be only a way of getting out of a difficulty to suppose that matter

ejected from, say the earth, with a velocity of 7 miles per second

would be freed from its attraction, that it would be involved somehow

in the sun's attraction, and that it would revolve thenceforth round

the sun like any other wanderer; because we cannot see what would stop

its progress upwards, so to speak, from the earth after getting beyond

its control, or communicate to it at the right height and time, the

exact velocity required to make it revolve for ever afterwards round

the sun; nor, supposing the sun would have nothing to do with it, where

it would go. When it left the earth, it might have a direct motion

of near one-third of a mile per second derived from its rotation,

and also one of 18 miles per second due to the revolution of the

earth round the sun. It might also be ejected in a direction exactly

away from, or directly towards the sun; so we should have two very

different cases to reconcile in order to set up the theory of ejection

of comets from planets, and of their being involved somehow in the

sun's attraction. It presents us with a very strong case for calling

for either the immediate intervention of some power other than what we

conceive attraction to be, and of which we know nothing physically, or

we have to trust in _man_ipulation of which we have no very exalted

idea. We prefer to look upon the formation of all comets as derived

from the peaks we have been treating of, or, if that is inadmissible,

from shreds and patches of the original nebula; where no immediate

intervention, or instant application, of supernatural power is

required, but only the even and tranquil operation of original design.

For comets larger, and which travel to greater distances, than those

alluded to above, it is very difficult to get data on which we can

form satisfactory calculations of the lengths of their orbits and mean

velocities of revolution, for there is almost always awanting some

one or more of their elements, or totally different statements given

of their value; but we think we have found a few from which we can

collect data sufficiently accurate to enable us to show that there is

no necessity for going beyond the domains of the sun, as described by

us in a former chapter, to account for any one of the comets which have

been taken notice of in astronomical history; and still less necessity

to suppose that any of them have wandered, or been shot forth, from

some neighbouring star into the solar system.

From the data we have been able to collect it would appear that when

a comet comes to have a period of over 70 years, it is either too

far removed from the sun at its aphelion passage, or its mass is too

great for it to be perturbed by the attraction of any of the planets.

For instance, we have Halley's comet, which has been observed for

not far from 2000 years, whose period has averaged very close upon

77 years during the whole of that time, showing that it has not

been perturbed to any appreciable extent when near its perihelion

passage. No doubt 2000 years is a very small period of time to judge

from, and its aphelion distance being only 3,258,000,000 miles, it

might be influenced to some extent by some planet, so we can hardly

count upon its being permanently exempt from perturbation. Indeed,

Halley himself supposed that its velocity of revolution had been

considerably increased when it was in the neighbourhood of Jupiter in

the interval between 1607 and 1682; but if it was so, there must be

some counter-perturbation which restores the balance so as to make

the average period of 77 years. Looking over the register of its

appearances, we find that in its re-appearances of the years 66 and

1758, the period was about 75 years, and that in those of 451 and 1066

it was 79 years; so that if there are perturbations, we must claim

that there are also compensations. Seeing, then, that we can find no

evidence to the contrary, we may suppose that when the periods of

comets, and, perhaps more especially, when their aphelion distances

reach to beyond--and the farther the more so--the orbit of the most

distant planet, they may be looked upon as not being liable to be

seriously perturbed by any of the members of the solar system, until

something to the contrary had been proved. Following this idea, then,

it occurs to us that something may be learnt from their mean velocities

in their orbits, as will be seen from the following very small list

of those we have been able to submit to calculation, which form the

accompanying

TABLE XI.--SHOWING THE MEAN VELOCITIES IN ORBIT OF SEVERAL COMETS.

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

| | Period of| Mean Velocity |

Designation of Comet. |Aphelion Distance|Revolution| in Orbit. |

| (Miles) | (Years) | (Miles/Sec) |

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

Halley's comet | 3,258,000,000 | 77 | 4·18 |

| | | |

Comet of 1532 & 1661 | 4,464,000,000 | 129 | 3·45 |

| | | |

Donati's comet | 13,873,280,000 | 2,000 | 0·69 |

| | | |

Comet of 1811 | 40,000,000,000 | 3,065 | 1·3 |

| | | |

Comet of 1680 | 78,468,852,000 | 15,864 | 0·49 |

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

These orbital mean velocities per second have been calculated from

aphelion distances as diameters and from circular orbits, which

probably give results rather lower than would be derived from

elliptical orbits--were they known--but on the other hand, the

perihelion distances have not been taken into account in fixing the

diameters--because they were unknown--so the error will be so far

compensated, if not altogether.

We know that the mean velocities in orbit of the planets decrease as

their distances from the sun increase, and our table, as far as it

goes, leads us to believe that the same holds good with comets whose

aphelion distances are comparable to those of the planets, in being

measured by hundreds of years or less of revolution; but with those

whose periods are measured by thousands of years, the same rule seems

to fail. One thing, however, that we seem entitled to believe is that,

generally speaking, the greater the period of revolution of a comet

is, the less will be its mean velocity per second in its orbit. It

will be observed that the average mean velocity of the three remote

comets in the table is only 0·83 mile per second, and it is by no means

unreasonable to suppose that the average mean velocity per second of

any number of comets whose aphelion distances are greater than the

highest of those in the table, is not likely to be so great as the

average of the three; on this understanding, then, let us take, or

suppose, one whose mean velocity in orbit per second is only one mile,

and look into what may be learnt from it.

Going back to the peak of [Greek: a] Geminorum which we supposed, at

page 321, to be condensed to 129,000 million miles in diameter of base,

its height 1-1/4 billion miles, and distance from the sun 11 billion

miles, we may take a comet formed from it as an example. If, then, we

suppose the leading part of it to have been formed into a comet with

that aphelion distance--11 billion miles--and other dimensions suitable

to its new condition; taking its mean velocity in orbit at 1 mile per

second, we find that its period of revolution might be 1,200,000 years,

or three times greater than that of the comet of 1882, namely 400,000

years, mentioned by Mr. Chambers as being not very reliable, probably

because its angles in orbit could not be measured with sufficient

accuracy. Then, when we think that the sphere of the sun's attraction

in that direction--of [Greek: a] Geminorum--extends to 67 billions of

miles, and that there are stars more than 6 times farther off, e.g.

Canopus, see Table VII., we see that a supposed comet might have an

aphelion distance equal to that; and were we further to consider that

were its major axis 67 billion miles long, including aphelion and

perihelion distances, and that it went straight from the one end of

it to the other and back again, its period of revolution, if it could

be so called, would be 8,500,000 years; that is 20 times greater than

Mr. Chambers's doubtful 400,000 years for the comet of 1882. There

seems, therefore, to be no necessity for the solar system sending its

cometary produce to a foreign market; and our mechanical imagination is

not sufficiently vivid to allow us to conceive what kind of potential

energy even Jupiter can have to give an impetus to a comet, great

enough to send it flying to so great a distance. What velocity would

it have when it left the sun? And what would remain in it to carry it

over the debatable land between the sun and a distant neighbour? Or

are we to believe that all the solar system's produce of that kind

is only sent over the channel, as it were, to our nearest neighbour,

[Greek: a] Centauri? Conceptions of that kind are too elevated for

us, and we must leave them alone. Mr. Chambers expresses doubts as to

the determination of whether the orbit of a comet is elliptical or

parabolic when its period of revolution is measured by hundreds of

thousands of years, and we think we are safe in following him until

actual proofs are presented. If the comet of 1882 never comes back, we

may then believe it has gone elsewhere.

Having used up all the nebulous matter in the sun's domains, as

described at the beginning of Chapter XV., or at least shown how it

may have been, or may yet be, used up, we have now only to make a few

remarks to prove that our description of the said domains is not by any

means fanciful. It matters very little whether the solar system was

begun to be brought into existence at the same time as the surrounding

systems or before or after them. What is certain is that the sun's

sphere of attraction among its neighbours is bounded, at the present

time, just in the way we have taken to describe its domains. How they

were filled with cosmic matter may be disputed, but filled they must

have been somehow, if the solar system was formed out of a nebula; and

the way adopted by us was the only one that occurred to us when we

began to reconstruct the original nebula. Since then we have had time

to reflect on our work, and to see how it points out the simplest way

that can be conceived, which may be expressed in the few following

words. We may suppose that the ether was the primitive matter, as we

have done at page 258, and that the whole material universe has been

formed from it and through it. This idea will assist physicists in

forming their theory of a plenum of meteorites or meteoric matter, if

such they choose to call it. It will also enable us to complete the

circle of our notions with respect to matter. We believe that we can

neither destroy nor produce the smallest portion of it, although we can

change its form. Thus, looking upon the ether as primitive matter, we

can understand how the solar system could be elaborated from it; and

how, after having accomplished the purposes for which it was brought

into existence, it may again be resolved into the primitive element out

of which it was made, ready to take its part in the evolution of some

other system with, perhaps, a new earth "without form and void."

We have now to direct our thoughts, as far as we can, to the mass,

which furnishes the really effective power of the sun as the ruler of

the system; and, first of all, we have to think of what are the real

active elements which form that mass. Hitherto we have looked upon

them as all included within a diameter of 867,000 miles, but now we

have to take notice of the clouds of meteoric matter which have been

supposed by some astronomers and physicists to be revolving round the

sun and continually raining into it; and of the enormous atmosphere

which surrounds it. With regard to the former of these two elements,

we shall compound our ignorance by looking upon it as a merchant does

on his account of Bills Receivable, as not being available in the

case of a sudden demand for cash, and therefore as not forming a part

of the mass, any more than as the attraction of the earth aids the

sun in its management of the planet Neptune; the same as the bills

receivable strengthen the credit of the merchant. But with regard to

the second element of the two, we must recognise that it forms part of

the mass and power over the whole of the system, and from all that is

known about it we are not authorised to look upon it as a negligible

quantity. It so happens that the only thing we have to which we can

compare it is the atmosphere of the earth, and we immediately find

that there is absolutely nothing to be learnt from such a comparison.

We know that one-half of the weight or mass of the earth's atmosphere

is contained in a belt of 3-1/2 miles high above its surface, so that

double the volume of that belt estimated at atmospheric pressure gives

us the true measure of its mass. This mass, when reduced to the density

of water, and compared to that of the earth as we have dealt with it

all along, turns out to be about 1/824,000th part of it; and were

we now to add that to the earth's mass we have been using, its mean

density would be 5·66065 instead 5·66 times that of water.

Now, let us suppose the sun to have an atmosphere of the same kind

as the earth's: Seeing that the force of gravity at its surface is

about 28 times greater than it is at the surface of the earth, a belt

around it which would contain one-half of its mass would be 28 × 3-1/2

= 98 miles, or say 100 miles thick. Dealing then with this dimension

in the same manner as we have done in the case of the earth, we find

that its supposed atmosphere would be 1/836,000th part of its mass,

which, if added to the mass we have used for it, would make its mean

density 1·413016 instead of 1·413 times that of water. Then again, if

we suppose the earth's atmosphere to extend to 100 or 200 miles above

its surface, the supposed atmosphere of the sun would extend to 2800 or

5600 miles above its surface, according to which of the above heights

on the earth is adopted; whereas the highest of our authorities say

that the corona, or apparent atmosphere, extends to at least 350,000

miles from its surface.

It would appear then that there is no analogy whatever between the

atmospheres of the sun and the earth; but there must be some analogy,

because the law of attraction cannot be suppressed at the surface of

the sun; neither can any vaporous matter near it cease to be attracted

in the same proportion as it is at the surface. Our atmosphere causes

a pressure of 29-1/2 inches of mercury at the earth's surface, and

the attraction of the sun at its surface must cause a pressure equal

to nearly 28 times that without fail, i.e. 420 lb. per square inch

instead of the 15 lb. of the earth. We know that some spectroscopists

believe that the pressure at the surface of the sun is sometimes as

low as it is at the surface of the earth, even lower; but we require

an explanation of why it is so. At the surface of the sun one second

of arc corresponds to a height of 450 miles above its surface, and

Mr. Proctor states in his "Sun," page 295, that if even "two or three

hundred miles separated the lower limit of chromatosphere from the

photosphere, no telescopes we possess could suffice (when supplied with

suitable spectroscopic appliances) to reveal any trace of this space.

A width of two hundred miles at the sun's distance subtends an arc of

less than half a second; and telescopists, who know the difficulty of

separating a double star whose components lie so close as this, will

readily understand that a corresponding arc upon the sun would be

altogether unrecognisable." We can understand this, and perhaps find an

explanation for ourselves.

According to our supposition that the sun may have an atmosphere

similar to the earth's, at one hundred miles in height it would be

reduced in pressure to 14 atmospheres, and, extending the analogy, at

2800 miles high the pressure would still be equal to one-eighth of 28

atmospheres, or equal to something less than 2 lb. per square inch at

the surface of the earth; so that if spectroscopists have measured the

sun's atmosphere at the disk, and found it to be lower than the earth's

at its surface, their results must have been caused by some fortuitous

circumstance which they did not notice at the time; because the force

of attraction at the surface of the sun can never be overcome except by

some counteracting force, which, if in the form of a vapour, or what

we call a gas, issuing from its interior, would increase rather than

diminish the pressure. We know that in the heart of a cyclone on the

earth there is sometimes a vacuum sufficient to explode (pull out the

walls of) houses near which it passes; and, at the same time, we know,

more or less, what heat the sun sheds upon the outer atmosphere of the

earth, and also the rate of rotation of the earth in the regions where

the fiercest of these cyclones occur, the only two causes which can

produce them. Now, if we compare these causes in the two bodies, that

is, the earth's rotation of about 16 miles per minute and the sun's of,

say, 60 to 75 miles per minute, and the temperatures of the sun and the

earth at their respective surfaces, we can imagine that in the heart of

a cyclone on the sun there may be a vacuum much nearer absolute zero

than there can be in any one on the surface of the earth. If then the

spectroscopists, without knowing it, have caught the spectra of the

hearts of cyclones, we can conceive them to be right, otherwise no.

Again, we know that when big guns are fired off partial vacuums are

formed near them, sufficient to cause disaster to windows, doors, and

even walls of houses too near them, but whatever we may have said of

force sufficient to produce explosions in the sun, we have never

believed that matter is ejected from the sun by explosions. We have

supposed the sierra, or chromosphere, to have oozed out through its

pores, sometimes to less, sometimes to greater heights, like steam

from an open boiler, and the prominences to be eruptive, neither of

which modes could produce anything approaching to vacua in their

neighbourhoods. There can be no resemblance between the ejection of

matter or gas from the sun and from a cannon, but there is between

the ejection of vapours and the escape of steam from the safety-valve

of a closed steam boiler; both of them continue to pour out their

vapours till the pressure within falls down till it is equal to the

resistance to their escape; there is no explosion, therefore no vacuum,

appreciable at least, in the neighbourhood. There may be surrounding

matter drawn up by the velocity of the outward current, but that is all.

Notwithstanding all this, we see no reason why the sun should not have

an atmosphere of exactly the same kind as the earth's, composed of

exactly the same kinds of gases, including vapour of water in some part

of it, though, perhaps, far removed from the photosphere. Every other

element found on the earth can be found in the sun, and so it is not

unreasonable to suppose that the same kind of atmosphere may exist upon

it; we have only to acknowledge that its conditions must be somewhat

varied, all the difference being that the atmosphere of the sun must

be heated up to the temperature of the photosphere where it comes in

contact with it, while that of the earth is only of the temperature of

the earth at its surface. In the case of the earth, if this were at

a white heat, one-half of the weight of its atmosphere would not be

comprehended in a belt around it of 3-1/2 miles thick. That balance of

mass might take place at a height of even hundreds of miles--we have no

means of calculating how high--and still its pressure at the surface

would be the same as now, as long as the earth's attraction remained

the same; so must it be with the sun. Instead of limiting its height

to 5600 miles at the utmost as we have done above, it would be no

stretch of imagination to suppose that it might extend to ten, twenty,

or more times that height. In addition to this we have to take into

consideration that the sun's atmosphere must be swept up to something

far beyond 5800 miles high by the whirlwinds created by the velocity

of rotation at its surface, the same as we saw the earth's might be

when we were explaining how an aurora could be made to glow at heights

far beyond what we were accustomed to believe its atmosphere could

reach. Adding, then, together these two motive forces for elevating

the atmosphere of the sun, it would be a bold assertion to say that

it cannot have one exactly similar to the earth's, reaching up to the

height of 350,000 miles mentioned a few pages back. And now, having got

this length, we may venture to assert that the corona of the sun is

made up of this atmosphere, and of the vapours of the elements thrown

out from its interior, somewhat in the manner we have described in last

chapter; to which we have only to add that the bubbling up of vapours

all around the sun, which produces the sierra or chromosphere, would

not be interfered with in any way by the tremendous commotions which we

have shown must be produced between the surfaces of the sun-spot zones

and the centre; and that the projection of the high prominences would

assist in elevating the aeriform atmosphere.

If then the sun has a compound atmosphere of this kind, it must be

considerably more dense, proportionately, than that of the earth, and

will consequently form a greater addition to its mass than we have

found would be made by its airlike atmosphere. But, whatever density

has to be added to it on that account has to be subtracted from the

interior having been ejected from thence; because, in whatever manner

its mass has been calculated in respect of the other members of the

system, the total amount must turn out to be always the same. We have

always estimated its mass from a diameter of 867,000 miles, which gave

us a volume of 341,237,638^{9} cubic miles, so that if we now include

in the diameter the 350,000 miles height of the atmosphere, we get a

volume of 2,053,500^{12} cubic miles, which is as near as possible six

times the volume in which we had to distribute the volume of the sun.

How to do this, we know not. We cannot fix the region of greatest

density in the same manner we have done at page 221, but we know that

it must be considerably nearer to the surface of the photosphere than

we have there placed it; and of one thing we are sure, and that is,

that the densities we have named for that region and the outer and

inner surfaces of the shell, at page 223, must be less than those there

expressed; how much we cannot calculate, but we have certainly found

that the limits must be lower, and that most probably there is no

matter in the sun exceeding the half of the density of water.

Whatever the composition of the sun's atmosphere, or corona if

that name be preferred, may be, spectroscopists have found in it a

_spectral_ line derived from some substance totally unknown to science.

Now, looking back on our work from almost the very beginning, it seems

to have been gradually borne in upon us that this unknown substance

is the ether. That it is a material substance we were hardly ever in

doubt, and our studies of it have substantiated and confirmed our

belief. In our analysis of the Nebular Hypothesis in Chapter VI.,

after combating the notion that the light of nebulæ is occasioned by

incandescent gas, we showed, by the example of an air furnace, that an

incandescent gas is composed of two elements, one consisting of solid

matter which takes up and gives out heat and has all the properties of

a heated solid or liquid substance, and the other of gaseous matter

which, being the element that fills up the empty spaces between the

solid atoms of a gas or vapour, only performs the office of carrying

the solid part into the furnace. This forced upon us the idea of the

gaseous part being a carrying agent, and very naturally to think of its

being really the ether, that being the only acknowledged agent for the

carriage of light, heat, and electricity, two of which are easily seen

and felt, and the third cannot be awanting, in an air furnace. Again,

when treating in Chapter VII. of what effect the ether might have on

the density of the original nebula, we concluded that its density must

be much lower than what we then knew it had been estimated to be, and

also that its temperature in space must be lower than -225°; which two

circumstances combined showed us that if it is a gaseous substance it

must be very different to any gas that had been liquefied up to that

time. This we repeated in great part in Chapter XII., calling attention

to the peculiarity of its being able to carry a higher temperature than

its own--to all appearance--into a "hot box." Then we have dedicated

two Chapters, XIII. and XIV., almost exclusively to the study of the

ether, and have been led from one stage to another to look upon it as

the only substance that agrees with the definition of a gas as given

by science; true gas there is; as the primitive and sole element in

the formation of all matter and in the evolution of the universe; and

what is something more than an unfounded guess, as the mysterious and

incomprehensible agent attraction, unfortunately almost universally

spoken of as gravitation. And now to conclude: From what we have been

able to learn, very slight differences have been found in various

spectra of the position of the line representing the unknown substance,

but this can cause very little doubt of its always being the same, as

spectra often contain several lines of hydrogen, owing most probably to

combinations with other substances; and if the ether is the primitive

chemical element, there may be slight differences in the position of

its line, as shown in all the phases in which we seem to have found it,

but they must be slight as compared with the hydrogen lines, because

even these must be in some measure, perhaps even great, influenced by

the unfailing and inevitable mixture of the ether in their composition.

LONDON: PRINTED BY WILLIAM CLOWES AND SONS, LIMITED,

GREAT WINDMILL STREET, W., AND DUKE STREET, STAMFORD STREET, S.E.

Transcriber Note

Several tables were reformatted to fit a maximum 75-column width.

End of Project Gutenberg's New Theories in Astronomy, by Willam Stirling

Now, if the collisions and encounters amongst the masses, great and