CHAPTER IV

_Carving out the Universe_

We have commented on the surprising emptiness of space: six specks of

dust in Waterloo Station about represent the extent to which it is

occupied by stars in its most crowded parts. The comment might well

have taken another form. Six specks of dust contain, let us say, a

thousand million million molecules. Our model of space is empty because

this great number of molecules happens all to be aggregated into as few

as six lumps. In real space the unit of aggregation is the star, and

an average star contains about 10⁵⁶ molecules—a number so large that

it is quite useless to try to imagine it. The emptiness of space does

not originate from any paucity of molecules; it originates from the

circumstance that, apart from those which form the tenuous clouds of

gas stretching from star to star, the molecules are aggregated together

in the huge colonies we call stars, with about 10⁵⁶ members to each.

Why should the molecules in space herd together in this way, when the

molecules in the rooms in which I am writing and you are reading do not?

Following a well-tried scientific method, we may attempt to discover

why these aggregates have formed, by first examining what keeps them

together now that they have formed. The earth’s atmosphere consists of

about 10⁴¹ molecules. Why do they stay pressed down into an atmosphere

instead of spreading out through space? The answer is of course

provided by the earth’s gravitation. A bullet fired from the earth’s

surface with a speed of 6·93 miles a second or more will fly off into

space, because the earth’s gravitational pull is inadequate to hold

it back when it moves with so high a speed. But a bullet fired with a

speed of less than 6·93 miles a second does not leave the earth; its

speed is inadequate to take it clear of the earth’s pull. Thus the

molecule-bullets which form the earth’s atmosphere, flying with speeds

less than a third of a mile a second, have no chance at all of getting

away. The earth’s gravitation continually pulls them back to earth, so

that the earth retains its covering of air.

At rare intervals a molecule may experience a succession of

exceptionally lucky collisions with other molecules, and so attain a

speed of more than 6·93 miles a second. A molecule which arrives at

the outside of the earth’s atmosphere with such a speed will leave the

earth altogether, and join the interstellar crowd of stray molecules.

The earth is continually shedding its atmosphere in this way, but

calculation shews that the loss, even in millions of millions of years,

is quite insignificant, so that we may regard the earth’s atmosphere as

permanent.

It is the same with the sun. The sun’s heat has broken up the molecules

of its atmosphere into their constituent atoms, and these move with an

average speed of about 2 miles a second. But an atom-bullet would have

to move at about 380 miles a second to escape altogether from the sun,

so that the solar atoms remain to form an atmosphere.

If all the molecules of air in an ordinary room were collected into

a bunch at the centre of the room, the ball of air so formed would

of course exert a gravitational pull on its outermost molecules, of

the same kind as the earth and sun exert on the molecules of their

atmospheres. But, because the weight of this ball of air is so small,

the intensity of its gravitational pull would also be small; indeed

it would be so feeble that a speed of about a yard a century would be

enough to take the outermost molecules clear of it. As the molecules

of ordinary air move at about 500 yards a second, such a ball of air

would immediately scatter through the whole room. On the other hand, if

the room were big enough to contain the sun, all its molecules could

stay in a ball at the centre, just as they do in the sun. The outermost

molecules would need a speed of at least 380 miles a second to escape,

so that their actual speeds of 500 yards a second or so would be of no

service to them.

PLANETARY ATMOSPHERES. In general the question of escape or no escape

depends on the outcome of a battle between the molecular speeds of the

outermost molecules, and the intensity of the gravitational hold which

the remainder of the mass exerts on them. The solar system provides

many examples of this. The moon has only a sixth as much gravitational

hold over the molecules of an atmosphere as the earth has, with the

result that any atmosphere the moon may ever have had, has escaped by

now. Mercury has two-fifths of the earth’s gravitational hold, but,

owing to its nearness to the sun, its sunward surface is very hot, with

the consequence that its atmosphere also has escaped. The gravitational

hold of Mars on its molecules is only a fifth of the earth’s, but its

surface is cooler. Calculation shews that water-vapour and heavier

molecules ought to remain, while the lighter molecules of helium and

hydrogen ought to have escaped. This probably represents what has

actually happened. The largest satellite of Saturn and the two largest

satellites of Jupiter would exercise about the same gravitational

hold as the moon, but as their surfaces must be enormously colder

than that of the moon, they ought to be able to retain atmospheres.

Some observers claim to have seen indications of atmospheres on

all three satellites. All the four major planets exert stronger

gravitational holds over their molecules than the earth, and so retain

their atmospheres with ease, while Venus, with approximately the same

gravitational hold as the earth, also retains an atmosphere.

These considerations amply explain why the molecules of the stars must

necessarily remain aggregated now that the aggregates have once been

formed, but the question of how and why these aggregates formed in the

first instance is far more complex. What, for instance, determined that

there should be about 10⁵⁶ molecules in each star rather than 10⁵⁴ or

10⁵⁸?

GRAVITATIONAL INSTABILITY

It is natural to enquire whether the forces which now keep a star

together may not also have been responsible for its falling together

in the first instance. This leads us to study the aggregating power of

gravitation in some detail.

Five years after Newton had published his law of gravitation, Bentley,

the Master of Trinity College, wrote him, raising the question of

whether the newly discovered force of gravitation would not account for

the aggregation of matter into stars, and we find Newton replying, in a

letter of date December 10, 1692:

It seems to me, that if the matter of our sun and planets,

and all the matter of the universe, were evenly scattered

throughout all the heavens, and every particle had an innate

gravity towards oil the rest, and the whole space throughout

which this matter was scattered, was finite, the matter on

the outside of this space would by its gravity tend towards

all the matter on the inside, and by consequence fall down

into the middle of the whole space, and there compose one

great spherical mass. But if the matter were evenly disposed

throughout an infinite space, it could never convene into

one mass; but some of it would convene into one mass and

some into another, so as to make an infinite number of

great masses, scattered great distances from one to another

throughout all that infinite space. And thus might the sun

and fixed stars be formed, supposing the matter were of a

lucid nature.

An exact mathematical investigation on which I embarked in 1901, not

only confirms Newton’s conjecture in general terms, but also provides

a method for calculating what size of aggregates would be formed under

the action of gravitation.

THE FORMATION OF CONDENSATIONS. You stand in the middle of a room

and clap your hands. In common language you are making a noise; the

physicist, in his professional capacity, would say you are creating

waves of sound. As they approach one another, your hands expel the

intervening molecules of air. These stampede out, colliding with the

molecules of outer layers of air, which are in turn driven away to

collide with still more remote layers; the disturbance originally

created by the motion of your hands is carried on in the form of a

wave. Although the individual molecules have an average speed of 500

yards a second, the zig-zag quality of their motions reduces the speed

of the disturbance, as we have already seen, to about 370 yards a

second—the ordinary velocity of sound. As the disturbance reaches any

point the number of molecules there becomes abnormally high, for the

stampeding molecules add to the normal quota of molecules at the point.

This of course produces an excess of pressure. It is this excess

pressure acting on my ear-drum that transmits a sensation to my brain,

so that I hear the noise of your clapping your hands.

This excess of pressure cannot of course persist for long, so that the

excess of molecules which produces it must rapidly dissipate. It is

thus that the wave passes on. Yet there is one factor which militates

against its dissipation. Each molecule exerts a gravitational pull on

all its neighbours, so that where there is an excess of molecules,

there is also an excess of gravitational force. In an ordinary sound

wave this is of absolutely inappreciable amount, yet such as it is,

it provides a tiny force holding the molecules back, and preventing

them scattering as freely as they otherwise would do. When the same

phenomenon occurs on the astronomical scale, the corresponding forces

may become of overwhelming importance.

Let us speak of the gas in any region of space where the number

of molecules is above the average of the surrounding space, as a

“condensation.” Then it can be proved that, if a condensation is of

sufficient extent, the excess of gravitational force may be sufficient

to inhibit scattering altogether. In such a case, the condensation may

continually grow through attracting molecules into it from outside,

whose molecular speeds are then inadequate to carry them away again.

Whether this happens or not will depend of course on the speed

of molecular motion in the gas, as well as on the size of the

condensation. But it will not depend at all on the extent to which

the process of condensation has proceeded. By doubling the excess

number of molecules in any condensation, we double the extent to which

condensation has proceeded. In so doing, we double the gravitational

pull tending to increase the condensation, but we also double the

excess pressure which tends to dissipate it; we double the weights

on each side of the balance, but the balance still swings in the

same direction. If once conditions are favourable to its growth, a

condensation goes on growing automatically until there are no further

molecules left for it to absorb.

The greater the extent in space of a condensation, the more favourable

conditions are to its continued growth. Other things being equal,

a condensation two million miles in diameter will exert twice the

gravitational force of a condensation one million miles in diameter,

but the excess pressures are the same in the two cases. Thus, the

larger a condensation is the more likely it is to go on growing, and

by passing in imagination to larger and larger condensations we must

in time come to condensations of such a size that they are bound to

keep on growing. Nature’s law here is one of unrestricted competition.

Nothing succeeds like success, and so we find that condensations which

are big to start with have the capacity of increasing still further,

while those which are small merely dissipate away.

Suppose now that an enormous mass of uniform gas extends through

space for millions of millions of miles in every direction. Any

disturbance which destroys its uniformity may be regarded as setting up

condensations of every conceivable size.

This may not seem obvious at first; it may be thought that a

disturbance which only affected a small area of gas would only produce

a condensation of small extent. Such an argument overlooks the way

in which the gravitational pull of a small body acts throughout

the universe. The moon raises tides on the distant earth, and also

tides, although incomparably less in amount, on the most distant of

stars. Each time the child throws its toy out of its baby-carriage,

it disturbs the motion of every star in the universe. So long as

gravitation acts, no disturbance can be confined to any area less than

the whole of space. The more violent the disturbance which creates

them, the more intense the condensations will be to begin with, but

even the smallest disturbance must set up condensations, although

these may be of extremely feeble intensity. And we have seen that the

fate of a condensation is not determined by its intensity but by its

size. No matter how feeble their original intensity may have been, the

big condensations go on growing, the small ones disappear. In time

nothing is left but a collection of big condensations. The mathematical

analysis already referred to shews that there is a definite minimum

weight such that all condensations below this weight merely dissipate

away into space. To a good enough approximation for our present

purpose, this minimum weight is such that if a tenth of this weight of

gas were isolated in space, and all the rest of the gas annihilated,

the molecules would just and only just fail to escape from its

surface[20].

[20] This is near enough, but not absolutely accurate. Exact

mathematical analysis shews that the weight of the minimum condensation

_M_ is given by

____ _C_³

_M_ = ³√⅓πκ ———————,

³√γ √ρ

where _C_, γ, ρ, κ are the molecular velocity, gravitation constant,

initial density, and ratio of specific heats, whereas the weight from

which molecules moving with velocity _C_ just fail to escape is given by

3 _C_³

_M_ = —— —————————.

4π ³√γ √ρ

With κ = 1⅔ the minimum weight of condensation is 9·7 times the weight

which is just adequate to retain the molecules.

We may say that the original uniformly distributed mass of gas was

“unstable” because any disturbance, however slight, causes it to change

its configuration entirely; it had the dynamical attributes of a stick

balanced on its point, or of a soap-bubble which is just ready to burst.

PRIMAEVAL CHAOS. These general theoretical results may now be applied

to any mass of gas we please. Let us begin by applying them to Newton’s

hypothetical “matter evenly disposed throughout an infinite space.” We

return in imagination to a time when all the substance of the present

stars and nebulae was spread uniformly throughout space; in brief, we

start from the primaeval chaos from which most scientific theories

of cosmogony have started. Hubble has estimated that if the whole of

the matter in those parts of the universe we know were redistributed

evenly throughout space, the gas so formed would have only about 1·5 ×

10⁻³¹ times the density of water. This estimate is almost certainly on

the low side, even as representing present conditions, and in trying

to reconstruct the primaeval gas we must add something to allow for

the molecules and atoms which have melted away into radiation in the

intervening period. On the whole, perhaps 10⁻³⁰ is not an unreasonable

density to assign to the hypothetical primaeval nebula. It is almost

inconceivably low. In ordinary air, at a density of one eight-hundredth

that of water, the average distance between adjoining molecules is

about an eight-millionth part of an inch; in the primaeval gas we are

now considering, the corresponding distance is two or three yards. The

contrast again leads back to the theme of the extreme emptiness of

space.

What is the minimum weight of condensation that would persist in this

primaeval gas?

Calculation shews that if ordinary air were attenuated to this

extraordinary degree, no condensation could persist and continue to

grow unless it had at least 62½ million times the weight of the sun;

any smaller weight of gas would exert so slight a gravitational pull

on its outermost molecules, that their normal molecular speeds of

500 yards a second would lead to the prompt dissipation of the whole

condensation.

We can carry out similar calculations with reference to other assumed

densities of gas, and other molecular velocities. The following table

shews the weights of condensations which would be formed in primaeval

masses of chaotic gas having the densities shewn in the first column,

and the various molecular velocities mentioned at the heads of the

remaining columns. In each case the weights of the condensations are

given in terms of the weight of the sun:

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

| Density | Mol. vel. | Mol. vel. of| Mol. vel. of | Mol. vel. of|

| in terms | 500 yards | 1000 yards | 2000 yards | 3000 yards |

| of water | a sec. | a sec. | a sec. | a sec. |

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

|10⁻²⁹ | 25,000,000| 200,000,000| 1,500,000,000| 5,000,000,000|

|10⁻³⁰ | 62,500,000| 500,000,000| 4,000,000,000|13,000,000,000|

|1·5 × 10⁻³¹|160,000,000|1,300,000,000|10,000,000,000|30,000,000,000|

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

All known stars have weights comparable with that of the sun. Thus if,

as Newton conjectured, the stars first came into being as condensations

of this kind, then the entries in this table ought to be comparable

with unity. Newton’s conjecture, in the form in which we have just

considered it, is clearly untenable, since all the calculated weights

are many millions of times that of the sun. If there ever existed

a primaeval chaos of the kind we are now considering, it would not

condense into stars, but into enormously more massive condensations,

each having the weight of millions of stars.

THE BIRTH OF THE GREAT NEBULAE

Now it is significant that bodies are known in space having weights

equal to those just calculated, namely the great extra-galactic

nebulae. There are two nebulae whose weights can be determined with

fair accuracy, namely the Great Nebula in Andromeda (Plate IV, p. 30)

and the nebula N.G.C. 4594 in Virgo (Plate XV). Hubble estimates these

to be as follows:

Nebula _M_ 31: weight = 3500 million times that of sun

” N.G.C. 4594: ” = 2000 ” ”

These estimates are again probably both on the low side, but their

general order of magnitude is such as to suggest that the condensations

which would first be formed out of the primaeval nebula must have

been the great extra-galactic nebulae, and not mere stars. It is of

course at best only a conjecture that the great nebulae were formed in

this manner—if for no other reason because we can never know whether

the hypothetical primaeval nebula even existed—but it seems the most

reasonable hypothesis we can frame to explain the fact that the present

nebulae exist. These nebulae are so generally similar to one another

that it seems likely that they must all have been produced by the

action of the same agency, and that which we have just considered

provides a reasonable explanation which, apart from the postulated

existence of the continuous primaeval nebula, is based on _verae

causae_.

The great nebulae are of course not exactly similar, and our next

inquiry must be as to the origin of their differences.

[Illustration: PLATE XV The Nebula N.G.C. 4594 in Virgo]

[Illustration: _Mt Wilson Observatory_

The Nebula N.G.C. 7217]

If the condensations in the primaeval gaseous nebula had formed and

contracted in an absolutely regular fashion, the final product would

be an array of perfectly equal and similar masses of gas spaced

with perfect regularity. But nature is seldom as regular as this;

and we need not be surprised that the observed nebular array is not

evenly spaced, or that its members are neither equal in weight, nor

symmetrically arranged. As the original condensations in the primaeval

gas contracted, they must have produced currents, and these would

hardly be likely to occur absolutely symmetrically. If the motion in

each mass of condensing gas had been directly towards the centre of

the condensation at every point, the final result would have been a

spherical nebula devoid of all motion, but any less symmetrical system

of currents would result in a spin being given to each contracting

mass. This spin would no doubt be very slow at first, but the

well-known principle of “conservation of angular momentum” requires

that, as a spinning body contracts, its rate of spin must increase.

Thus when the process of condensation was complete, the final product

would be a series of nebulae rotating at different rates.

NEBULAR ROTATION. And this is exactly what is observed; so far as our

evidence goes the nebulae are in rotation, and at different rates. The

various parts of the surface of any rotating mass necessarily have

different speeds in space. The sun for instance rotates about its axis

in such a direction that the surface we see is moving always from east

to west; as a result the eastern limb is always advancing towards the

earth, while the western limb is receding from us. A spectroscope

turned on to different parts of the sun’s surface in succession at once

reveals these differences of speed; they not only assure us of the

sun’s rotation, but enable us to measure its amount. The nebulae may be

examined in the same way, and the examination shews that a large number

of them are rotating with the perfectly regular motion of a solid

body—a spinning-top, for instance. Measured by terrestrial standards

their rates of rotation seem extraordinarily slow; for instance the

Great Nebula _M_ 31 in Andromeda requires about 19,000,000 years to

make a complete rotation, but this apparent slowness is an inevitable

result of the huge size of the nebula. Even to get round once in

19,000,000 years, the outer parts of the nebula have to move with

speeds of hundreds of miles a second.

A few of the nebulae are quite irregular in shape, but the majority

have regular shapes, and it is highly significant that these are

precisely the shapes which, it can be calculated mathematically,

would be exhibited by rotating masses of gas. Actually there is a far

stronger case than this for supposing the nebulae to be rotating masses

of gas. From the purely observational evidence of surface-brightness

and other characteristics, Hubble found that nearly all of these

nebulae could be arranged in a single linear sequence—they could be

arranged in order like beads on a string. And this order proved to

be practically identical with the sequence which had previously been

calculated, by purely theoretical methods, for the configurations of

masses of gas rotating at gradually increasing rates of speed.

Let us examine this sequence of theoretical configurations in their

natural order.

A mass of gas which was not rotating at all would of course assume

a spherical shape under its own gravitation. A number of perfectly

spherical nebulae are known; a typical example is shewn in fig. 1 on

Plate XVI.

[Illustration: PLATE XVI Fig. 1 N.G.C. 3379]

[Illustration: Fig. 2 N.G.C. 4621]

[Illustration: Fig. 3 N.G.C. 3115]

[Illustration: Fig. 4 N.G.C. 4594 in Virgo]

[Illustration: Fig. 5 N.G.C. 4565 in Berenice’s hair

_Mt Wilson Observatory_

A sequence of Nebular Configurations]

With slight rotation the mass assumes the shape of a slightly flattened

orange, like the earth or Jupiter. Nebulae of this shape are also known

in abundance; an example is shewn in fig. 2 on the same plate.

With a higher degree of rotation the degree of flattening increases,

but theoretical calculation shews that the orange shape is soon

departed from. The equator first begins to shew a pronounced bulge,

until finally, with sufficient rotation, this develops into a sharp

edge, the rotating mass now being shaped like a double-convex lens.

This prediction of theory is abundantly confirmed by observation, a

large number of these lens-shaped nebulae being observed in the sky. An

example is shewn in fig. 3 on Plate XVI.

The next step is somewhat sensational. Further rotation does not, as

might be expected, result in still further flattening. Up to now, each

increase in rotation has made the bulge on the equator sharper, but

this is now as sharp as it can be. Theory shews that the flattening

has also proceeded to the utmost possible limit, and that the next

stage must consist in matter being ejected through the sharp edge of

the equator and spread throughout the equatorial plane. Here again

observation confirms theory; figs. 4 and 5 (Plate XVI) shew types of

nebulae actually observed, the former being the nebula in Virgo which

we have already had under discussion.

The comparatively thin layer of gas which now lies in the equatorial

plane is similar in one respect at least to Newton’s matter “evenly

disposed throughout an infinite space.” Disturbances can be set up in

it in a variety of ways, and any disturbance, no matter how slight,

must result in the creation of a series of condensations. As before,

those below a certain limit of size disappear of themselves, while

those above this limit continually increase in intensity until they

have absorbed all the gas in the equatorial plane. Again, as with the

hypothetical primaeval chaos, we can calculate the minimum size of

condensation which can be expected to have a permanent existence, and

once again the result proves to be highly significant.

Hubble’s estimates of the total weights of two conspicuous nebulae have

already been given. As the distances, and therefore also the sizes, of

both these nebulae are known, it is an easy matter to calculate the

average density of the gas throughout the whole nebula. The average

density in _M_ 31 is found to be about 5 × 10⁻²² of that of water;

the corresponding number for N.G.C. 4594 is 2 × 10⁻²¹. These figures

give us some idea of the density of matter in the outer regions of the

nebulae. Although these densities are about a thousand million times

as great as the estimated density of the original primaeval nebula of

space, they are still almost inconceivably low. There is still only

about one molecule to the cubic inch, and a single breath from the

lungs of a fly could fill a large cathedral with air of this density.

On proceeding to calculate the weights of the smallest condensations

which could form and persist in a gas of this low density, we obtain

the results shewn in the following table. The molecular velocities are

taken rather low, so as to allow for the cooling which must occur when

the gas is spread out in the equatorial plane of the nebula.

Again the weights of the condensations are given in terms of the

weight of the sun. And the significant fact emerges that most of the

entries in the table represent weights comparable with that of the sun.

We are dealing with stellar weights at last; the condensations which

must form in the outer regions of the great nebulae will have weights

comparable with those of the stars.

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

| Density in | Mol. vel. of | Mol. vel. of | Mol. vel. of |

|terms of water|100 yards a sec.|300 yards a sec.|500 yards a sec.|

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

| 10⁻²¹ | 1·7 | 36 | 220 |

| 10⁻²² | 5 | 130 | 625 |

| 10⁻²³ | 17 | 360 | 2200 |

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

THE BIRTH OF STARS

And indeed there can be but little doubt that the process we have just

been considering is that of the birth of stars. Even a casual glance at

photographs of nebulae suffices to shew that the matter which has been

ejected into the equatorial plane of a nebula does not lie uniformly

spread out in that plane; it is seen to have fallen into bunches, knots

or condensations. These are apparent enough in many of the nebular

photographs already shewn, but they can be seen still more clearly in

nebulae which are viewed nearly full-on, such as for instance the two

striking nebulae shewn in Plates XVII and XVIII.

These bunches are invariably too large to be interpreted as single

stars; they are more probably groups of stars. In the largest

telescopes they break up into great numbers of points of light in the

way already exhibited in Plate XI (p. 70). We have already mentioned

the reasons which compel us to regard these points of light as actual

stars, the principal being that some of them shew the characteristic

light-fluctuations of the Cepheid variables. It is not altogether

clear whether the stars are formed directly as condensations in the

equatorial plane of the nebula, or whether larger condensations form

first, namely the bunches observable in nebular photographs, which

subsequently form smaller condensations, the stars. On the whole it

seems likely that there are two processes involved—first the break-up

of the nebular matter into big condensations, and then the break-up

of these big condensations into stars. Such a succession of processes

might well accompany a gradual cooling of the matter, and it is of

course possible that there are even more than two processes involved.

There is no need to form a final opinion on this at present, as it is

in no way essential to the progress of the main argument.

A collection of nebular photographs enables us to follow nebular

evolution from the earliest stages shewn in Plate XVI (p. 207), through

the first appearance of granular bunches, such as are shewn in Plate

XVII, and the first distinct appearance of stars shewn in Plate XVIII,

down to the later stages, such as are shewn in Plates XIX and XX, in

which the nebula appears to be but little more than a cloud of stars.

Hubble has found it possible to follow the sequence still further, and

can trace a continuous transition from the nebulae of this last type to

pure star-clouds such as the Greater and Lesser Magellanic Clouds shewn

in Plate XXI.

[Illustration: PLATE XVII _Mt Wilson Observatory_

The “Whirlpool” Nebula _M_ 51 in Canes Venatici]

[Illustration: PLATE XVIII _Mt Wilson Observatory_

The Nebula _M_ 81 in Ursa Major]

Thus the stars appear to have been born in much the same way as we

have conjectured that their parents, the great nebulae, had been born

before them, namely, through the agency of what is generally known

as “Gravitational Instability.” This causes any mass of chaotic gas

to break up into detached condensations, and, the more tenuous the

original gas, the greater the weights of the condensations formed out

of it. The original primaeval nebula was of such low density that

the condensations which formed in it weighed thousands of millions

of times as much as the sun. These increased their density so much

in contracting that when their rotation caused them to eject gaseous

matter, this condensed into masses of stellar weight which we believe

actually to be stars.

We have less certain knowledge of the former process than of the

latter. Our only reason for thinking that the former process ever

occurred is that the extra-galactic nebulae now exist. There is no

evidence that the primaeval chaotic nebula ever existed, beyond the

fact that the hypothesis of its previous existence leads to a very

satisfactory explanation of the present nebulae existing as they now

do. On the other hand, we not only know that the stars exist: we also

know that the masses of gas exist out of which theory shews that stars

must necessarily be born. They are the tenuous equatorial fringes of

the great nebulae. Our telescopes shew us both the nebular fringes and

the stars, and we can almost study the actual process of birth.

THE GALACTIC SYSTEM OF STARS. If this is the true account of the birth

of the stars, then our sun and its companions in space must have been

born out of a rotating nebula. Observation gives strong support to

this conclusion. Since the time of the Herschels, it has been a matter

of frequent comment that the galactic system has the general shape of

the extra-galactic nebulae, the galactic plane of course representing

the equatorial plane of the original nebula. On purely observational

grounds, present-day astronomical thought is moving rapidly towards

regarding the whole galactic system either as a rotating nebula or

the remains of one. It is even possible that this may still retain a

central region which is as yet uncondensed into stars. In the direction

of the constellations Scorpio and Ophiuchus are dark clouds which may

either veil the centre of the system or may conceivably be the centre

itself.

In 1904, Kapteyn found that the directions of motion of the stars in

the vicinity of the sun were not distributed at random. The stars

appeared to prefer to move to and fro along a certain direction in the

galactic plane rather than in other directions—“star-streaming,” he

called it. This peculiarity in the motion of the stars may be expected

to throw some light on their origin.

Each star moves in a complicated orbit under the gravitational

attraction of all the other stars of the galactic system. It is not

possible to calculate this orbit in detail. The orbit of a planet round

the sun is easily calculated because only two bodies are involved, the

planet and the sun. But even when there are only three bodies involved,

it is impossible to calculate the orbits that each describes under the

attractions of the other two jointly: this is the famous problem of

three bodies, which has never been solved. When, as in the galactic

system, thousands of millions of stars are involved, it is naturally

useless to try to calculate the orbit of each star—it would be as

futile as trying to calculate the path of each molecule in a gas.

Yet the same statistical methods which give us useful information as to

the properties of a gas may be applied to studying the motions of the

stars. There are so many stars that we do not trouble about individuals

at all, we just treat them all together as a crowd. To treat them as

individuals would be as though the railway company tried to forecast

the Bank Holiday traffic from London to Brighton by considering the

finances, habits and psychology of each individual Londoner.

[Illustration: PLATE XIX _Mt Wilson Observatory_

The Nebula _M_ 101 in Ursa Major]

[Illustration: PLATE XX _Mt Wilson Observatory_

The Nebula _M_ 33 in Triangulum]

Without going into individual details, we can see that each star must

describe an orbit which, after touring round a large part of the

galaxy, comes back to somewhere near its starting point. Calculation

shews that each such circuit must take hundreds of millions of years

to complete. Even so, the stars will mostly have performed several

complete circuits while the earth has been in existence, and if we are

right in supposing the ages of the stars to be millions of millions of

years, each star must have toured round the galaxy several thousands

of times. We should accordingly expect the galaxy to have assumed a

definite permanent shape by now; the distribution of stars in its

different parts ought to have become something like steady, and the

stars ought to have settled down to a state approximating to one of

steady motion.

Statistical methods of investigation shew that there is not a great

number of possible arrangements for a system of stars which has lived

long enough to attain a steady state. If the system as a whole has

no rotation at all, there is only one arrangement; the stars form a

globular mass with perfect symmetry in all directions. The observed

globular clusters (Plate IX, p. 63) provide good approximations to this

type of formation, although Shapley has found that the majority are

not absolutely spherical in shape. If the system as a whole is endowed

with rotation, the possible configurations are all of a flattened

symmetrical shape, like a coin, a watch or a round biscuit—in other

words a system of stars in rotation must be shaped pretty much as we

believe the galaxy to be shaped. Furthermore the motions of these stars

must shew “star-streaming” of precisely the kind discovered by Kapteyn.

Thus both the shape of the galaxy and the peculiarities of motion of

its stars indicate that the galactic system as a whole must be in a

state of rotation. And, as we have seen (p. 67), recent observational

researches by Oort, Plaskett and others make it fairly certain that the

rotation required by theory is an actual fact. The motions of the stars

indicate that the whole galactic system is rotating at a rate which

varies from one region to another, being about one revolution every 230

million years in the vicinity of the sun. And the hub of this gigantic

wheel is found to coincide very closely with the spot which Shapley had

previously fixed as the geometrical centre of the galactic system from

his researches on the distribution of the globular clusters.

Thus, since rotation cannot be generated out of nothing, all the

phenomena agree in shewing that the galactic system must have been

born out of a rotating body. We are acquainted with only one type of

astronomical body which is of sufficient size to turn into a galactic

system, namely the great nebulae, and as the majority of these are

believed, and some are known with certainty, to be in rotation, it

seems reasonable to conclude that the galactic system must have been

born out of a nebula, unless indeed its structure is still such that

we should even now describe it as a nebula if we saw it from the great

distance from which we view the other great nebulae. The observed

period of rotation of the galactic system, of the order of 230 million

years, is substantially longer than the period, either known or

suspected, of any of the nebulae, but the dimensions of the galactic

system are also greater than those of any known nebula, and the two

facts hang together. Again, the number of stars in the galactic system

is probably substantially higher than in any nebula, as also is the

total weight of these stars[21]. All this makes it clear that if the

galaxy is, or ever has been, one of the great nebulae, it must have

been one of unusual size and weight.

[21] The following estimates have already been mentioned:

Weight of Galaxy in terms of sun 240,000,000,000

” nebula _M_ 31 in terms of sun 3,500,000,000

” ” N.G.C. 4594 in terms of sun 2,000,000,000

[Illustration: PLATE XXI _Harvard (Arequipa) Observatory_

The Lesser Magellanic Cloud]

[Illustration: _Franklin-Adams Chart_

The Greater Magellanic Cloud]

We have seen how the sun and all the stars are continually losing

weight as the result of their emission of radiation. It follows that

the total weight of the galactic system is for ever decreasing, and

as a consequence its gravitational hold on its constituent stars is

continually weakening. If this gravitational hold were suddenly to

vanish altogether, each star would replace its present curved path by

a perfectly straight line, along which it would travel at its present

speed, undeflected by any gravitational forces from other stars, so

that the stars which now constitute the galactic system would soon be

scattered through the whole of space. In brief, if the gravitational

pull of the stars were suddenly abolished, the galaxy would begin to

expand at a great rate.

Although this is not likely to happen, the gradual abolition of the

gravitational pull of the stars, as they turn their weight into

radiation, must cause the galaxy to expand all the time at a slow rate:

calculation suggests that its present rate of expansion would double

its size in about 30 million million years. The expansion must have

been far more rapid in the past, when the stars were full of youthful

vigour and squandered their substance more lavishly than now, so that

it seems probable that the galactic system was substantially smaller

and more compact in the past than now, and the original nebula probably

smaller still.

We have seen how the stars in the great nebulae appear to be

congregated in bunches or clusters. The globular clusters in the

galactic system may possibly be bunches of stars of the same general

type, which have remained undisturbed by other groups of stars and so

have assumed the globular form under their own attraction—just as a

mass of gas would do. Shapley finds that these clusters lie somewhat

outside the galactic plane; it looks as though they were broken up

or disorganised in travelling through this plane, where they would

encounter other stars.

By contrast groups of stars of the type generally described as moving

clusters—the Pleiades, the Hyades, the stars of the Great Bear and

a crowd of others voyaging in company with them through space—are

generally found to move in the galactic plane. These may quite possibly

represent the final vestiges of globular clusters which have been

broken up by interaction with other stars, all except the most massive

members having been knocked out of formation. Mathematical analysis

shews that the interaction between the stars of such moving clusters

and other stars in the galactic plane would cause each cluster to

assume the shape of a flat biscuit or watch, of diameter equal to 2½

times its thickness. It is significant that the majority of the moving

clusters shew a flattening of this kind, its amount agreeing tolerably

well with the calculated value. It is even conceivable that the “local

cluster” surrounding the sun (p. 65) may be the remains of such a bunch

of stars.

The motions of these clusters may also induce a further flattening,

in a direction perpendicular to their motion. Some clusters shew this

further flattening, the Ursa Major cluster being a striking example.

THE BIRTH OF BINARY SYSTEMS

In discussing the way in which nebulae might be born out of chaos,

we noticed that the existence of currents in the primordial medium

would endow the resulting nebulae with varying amounts of rotation.

For the same reason the children of the nebulae, the stars, must also

be endowed with rotation at their birth. There is a further reason

for such rotation. The general principle of the “conservation of

angular momentum” requires that rotation, like energy, cannot entirely

disappear. Its total amount is conserved, so that when a nebula breaks

up into stars, the original rotation of the nebula must be conserved in

the rotations of the stars. Thus the stars, as soon as they come into

being, are endowed with rotations transmitted to them by their parent

nebula, in addition to the rotations resulting from the currents set up

in the process of condensation.

Their continual loss of weight causes the physical conditions of the

stars to change, and we shall find in the next chapter that this

change generally involves a shrinkage of the star’s diameter. The same

principle of “conservation of angular momentum” now requires that, as a

star shrinks, its speed of rotation shall increase. In brief, as a star

ages, it spins faster and faster.

Now rotation was the essential factor in the birth of the stars out of

the parent nebula. A nebula perfectly devoid of rotation would not,

so far as we can see, break up into stars at all, and this prediction

of theory appears to be confirmed by observation, since nebulae of

the perfectly spherical type shewn in fig. 1 of Plate XVI can never

be resolved into stars in the telescope. On the other hand we saw how

nebulae which were initially endowed with rotation would continually

increase their speed of rotation under shrinkage, until finally their

rotation broke them up and produced a family of stars out of each.

The question now obviously arises whether, as the speed of rotation

of the stars increases, these are likely to break up in their turn,

and produce yet a third generation of astronomical bodies. Again we

might expect that mathematical analysis would apply to large and small

bodies equally, irrespective of scale. And a detailed examination of

the problem shews that in actual fact the process we have had under

consideration would repeat itself, and again bring a further generation

of smaller bodies into being, provided the physical conditions were

suitable.

The physical conditions, however, prove not to be suitable; they

certainly fail in one respect at least. Although a rotating star

may eject gaseous matter in its equatorial plane, the whole process

will be on a much smaller scale than in the nebulae. We might expect

the ejected matter to form condensations as before, but calculation

shews that, unless the molecular velocity is extraordinarily low, no

condensation can survive unless it has a weight greater than the whole

weight of the star! This means that with any reasonable molecular

velocity, the ejected gas would not form condensations at all. It

would merely scatter into the surrounding space, forming an atmosphere

without any distinct condensations.

Such is the course of events if the stars, like the nebulae before

them, are treated as pure masses of gas. Another alternative must,

however, be considered.

THE FISSION OF LIQUID STARS. We have seen how a gaseous nebula devoid

of rotation would assume a strictly spherical shape under its own

gravitational attraction, while slight rotation would cause it to

flatten into an orange shape, like the earth. The earth also has

assumed this shape on account of its rotation, although its internal

structure is very different from that of a gaseous nebula.

Strict mathematical investigation shews that this flattened-orange

shape must be common to all slowly rotating bodies, regardless of

their internal composition; gases, liquids, and plastic bodies assume

it equally. But the shape of a rapidly rotating body must depend very

greatly on its internal arrangement and constitution, being especially

affected by the extent to which the weight of the body is concentrated

near its centre.

As a consequence of the high compressibility of gases, this central

concentration of weight reaches its extreme limit in a purely

gaseous mass. The opposite extreme is reached in a mass of uniform

incompressible liquid such as water, in which there can be no central

concentration at all. As a mass of this latter type increases its speed

of rotation, the slightly flattened-orange shape merely gives place to

the shape of a more flattened orange. The tendency of a gaseous mass

to form a sharp edge round the equator is entirely absent, and the

cross-section of its figure remains elliptical throughout. At a still

higher speed of rotation, the equator loses its circular shape and it

too becomes elliptical. The figure has now three unequal diameters,

but every cross-section is strictly elliptical; the figure is an

“ellipsoid.” After this, its longest diameter begins to elongate until

the mass, still ellipsoidal in shape, has formed a cigar-shaped figure

with a length nearly three times its shortest diameter.

A new series of events now begins. The mass of liquid gradually

concentrates about two distinct points on its longest diameter, a waist

or furrow forming across its middle. This furrow gets deeper and deeper

until it has cut the body into two distinct detached masses, which now

rotate in orbital motion about one another and form a binary star. The

sequence of events is shewn in fig. 11; diagrams of the final stage as

represented by actual binary stars have already been given on p. 54.

For comparison the sequence of shapes assumed by a rotating mass of

gas is shewn in fig. 12, this being identical with the sequence of

observed nebular shapes which is actually observed, and is illustrated

photographically in Plate XVI (p. 207).

The two chains of configurations shewn in figs. 11 and 12 represent,

it will be remembered, the two extreme cases of a rotating body whose

substance is distributed with complete uniformity, and of a rotating

body whose substance is very highly condensed towards its centre. As

the constitutions of actual astronomical bodies must lie somewhere

between these two extremes, we might naturally expect such a body to

follow a series of configurations intermediate between the two shewn

in figs. 11 and 12. Theory shews that as a matter of fact it does

not. All bodies having less than a certain critical degree of central

condensation follow the sequence shewn in fig. 11, or a sequence

differing only immaterially from this; all bodies having more than

this critical amount of central condensation follow the sequence shewn

in fig. 12. Thus when this critical degree of central condensation

is reached there is a sudden swing over from fig. 11 to fig. 12. In

brief, every rotating body conducts itself either as if it were purely

liquid, or as if it were purely gaseous; there are no intermediate

possibilities.

[Illustration: Fig. 11. The sequence of configurations of a rotating

mass of liquid.]

[Illustration: Fig. 12. The sequence of configurations of a rotating

mass of gas.]

Observational astronomy leaves no room for doubt that a great number of

stars, possibly even all stars, follow the sequence shewn in fig. 11.

No other mechanism, so far as we know, is available for the formation

of the numerous spectroscopic binary systems, in which two constituents

describe small orbits about one another. In these stars, then, the

central condensation of mass must be below the critical amount just

mentioned; to this extent they behave like liquids rather than gases.

We have relied entirely on mathematical analysis in tracing out the

details of the process of fission just described. And we are totally

unable to check our theoretical results by observation. There is not a

single star in the sky of which we can say: here is a star which has

certainly started to break up by fission, and will certainly end as a

binary system. It is perhaps not altogether surprising. The breaking

up process is in all probability of very short duration by comparison

with the lives of the stars, so that in any case we should have to

investigate a great many stars before catching one in the act of

breaking into two.

On the other hand, a star in the act of breaking up ought to be very

easily differentiated from ordinary stars. Mathematical analysis

shews that its interior would be in a state of considerable turmoil,

so that it would hardly be likely to shine with a steady light: it

would be a “variable” star. Further, its condition ought to shew a

progressive change, although it is an open question whether this

would be rapid enough to be detected in a few years of observation.

Finally, if any group or class of stars were suspected of being stars

in process of fission, it ought to be possible to arrange them in an

order corresponding to the extent to which the fissional process had

advanced, and the sequence so formed ought to end with stars in the

physical condition of newly formed binaries.

I have recently suggested that the Cepheid variables, whose unknown

mechanism of light-variation renders such valuable service to the

astronomer, are merely stars in the act of fission. Want of space

prevents our entering here into the intricate question of how far they

exhibit the peculiarities which mathematical analysis requires of

stars in process of fission, but it is easily seen that they satisfy

the three simple tests outlined above. They are certainly variable

stars, and the light-variations of different stars are so similar as

to suggest very strongly that they all arise from the same cause.

The periods of a number of Cepheids are suspected of change, and

Hertzsprung has estimated that the prototype star, δ Cephei, which

has now been observed for 126 years, is decreasing its period of

light-fluctuation at the rate of about a tenth of a second per annum;

thus a million years would reduce its present period of 5⅓ days by

over a day. Finally Dr Otto Struve has found that the sequence of

Cepheids fits almost perfectly on to that of newly formed binaries.

Thus the prospects for the “fission theory” of Cepheid variables seem

hopeful, but the theory must be very thoroughly tested before it can

be accepted, and it cannot be claimed that it has been so far either

tested thoroughly or accepted extensively.

An alternative view, first propounded by Plummer and Shapley, regards

Cepheid variables as pulsating spheres of gas. The behaviour of such

masses of gas has been investigated mathematically by Eddington and

others, but it does not appear that it can be reconciled with the

observed behaviour of Cepheid variables.

THE DEVELOPMENT OF BINARY SYSTEMS

Whatever the process of formation of binary systems may be,

we experience fairly plain sailing in attempting to trace out

the subsequent development of such systems. Three factors are

simultaneously in operation.

TIDAL FRICTION. The first of these three factors, which is only of

brief duration, was designated “tidal friction” by Sir George Darwin,

who first drew attention to it, and investigated the manner of its

operation. When first a rotating mass breaks up and forms a binary

system, the two components are so near that they necessarily raise

tremendous tides on one another; Darwin shewed that these drive the two

bodies apart, and equalise their rates of rotation in so doing. After

these processes have been in operation for millions of years, the rates

of rotation of the two bodies and their rate of revolution about one

another must all become equal, so that each body perpetually turns the

same face to its companion, and the two rotate about one another like

the two masses of a dumb-bell joined by an invisible arm.

Although a sun and planet do not form a binary system in the strict

technical sense, they are necessarily subject to the same forces as

true binary systems. Thus we can see the operation of tidal friction

in the fact that Mercury always turns the same face to the sun, and

that Venus rotates so slowly on its axis that it turns the same face

to the sun day after day, and probably also week after week. As we pass

further out into space the effects of tidal friction rapidly diminish,

but it is probably significant that the nearer planets, Earth and Mars,

have days of about 24 hours each, while the remote planets Jupiter,

Saturn and Uranus each have days of only about 10 hours. The periods of

rotation of Neptune and Pluto are unknown. Apart from these we find, in

a general way, that the further we recede from the sun the more rapidly

the planets rotate, which is precisely the effect that ought to be

produced by tidal friction.

In the same way, tidal friction has in all probability been mainly

responsible for the present configuration of the earth-moon system,

driving the moon away to its present distance from the earth and

causing it always to turn the same face towards us. Tidal friction

must of course still be in operation. The moon is responsible for the

greater part of the tides raised in the oceans of the earth; these,

exerting a pull on the solid earth underneath, slow down its speed of

rotation, with the result that the day is continually lengthening,

and will continue to do so until the earth and moon are rotating and

revolving in complete unison. When, if ever, that time arrives, the

earth will continually turn the same face to the moon, so that the

inhabitants of one of the hemispheres of the earth will never see the

moon at all, while the other side will be lighted by it every night. By

this time the length of the day and the month will be identical, each

being equal to about 47 of our present days. Jeffreys has calculated

that this state of things is likely to be attained after about 50,000

million years.

After this, tidal friction will no longer operate in the sense of

driving the moon further away from the earth. The joint effect of

solar and lunar tides will be to slow down the earth’s rotation still

further, the moon at the same time gradually lessening its distance

from the earth. When it has finally, after unthinkable ages, been

dragged down to within about 12,000 miles of the earth, the tides

raised by the earth in the solid body of the moon will shatter the

latter into fragments (p. 250 below), which will form a system of tiny

satellites revolving around the earth in the same way as the particles

of Saturn’s rings revolve around Saturn, or as the asteroids revolve

around the sun.

We have already noticed how the present arrangement of the earth-moon

system enables us to calculate the earth’s age; Jeffreys estimates that

the system must have taken something of the order of 4000 million years

to reach its present configuration (p. 155).

This period, which seems so long when judged by terrestrial standards,

is only a moment in the life of a star. The components of the true

binary star attain a configuration like that of the earth-moon system

in a brief fraction of their lives, and, passing on, reach in time

the configuration in which each perpetually turns the same face to

the other. Up to now, tidal friction has been driving the masses

ever further apart, but as soon as this stage is attained, the tides

become stationary on both components, so that tidal friction goes out

of operation. Thus the separation produced by tidal friction has now

reached its limit, and, so far as tidal friction is concerned, the two

bodies might rotate in the way just described to all eternity.

LOSS OF WEIGHT. As tidal friction becomes inoperative, a new agency

takes hold. We have calculated that the sun is losing weight at the

rate of 250 million tons a minute, that it has been losing weight at

this rate, or some comparable rate, for millions of millions of years,

and will continue so to do for millions of millions of years yet to

come. The earth is at its present distance from the sun because this

distance is exactly suited to the present weight of the sun. If the

sun’s weight were suddenly reduced to half, its gravitational pull on

the earth would also be reduced to half, and the earth would move to a

greater distance from the sun[22].

[22] Although the details are unimportant, the actual course of events

would be that the earth would begin to describe an elliptic instead of

a circular orbit about the sun, the earth’s _average_ distance being

greater than now.

The sun’s weight is not likely to be suddenly reduced to half, but it

has been reduced by a thousand million tons in the last four minutes,

with the result that its gravitational grip on the earth has been

weakened and the earth has moved out to a wider orbit; at this moment

the radius of the earth’s orbit is greater than it was four minutes

ago. The details can be traced out mathematically with complete

precision. It appears that the earth’s orbit round the sun is not a

circle, or even an ellipse of small eccentricity; it is a spiral curve,

like an uncoiled watch spring. Every year the earth moves a tiny step

further out into the outer cold and darkness; exact calculation shews

that its average distance from the sun increases at the rate of about

a metre (39·37 inches) a century. The effect is of course of precisely

the same kind as we have seen must be produced in the galactic system

by the loss of weight of the stars. The only difference is that in the

galaxy a system of thousands of millions of stars is expanding, whereas

the sun-earth system consists of only two members.

Precisely similar effects must be produced by the loss of weight in the

two components of a binary star. Here both components are radiating

away energy, and so are simultaneously losing weight. Detailed

calculation shews that they must continually recede from one another,

but that the shape of their orbit will undergo no change.

Neither separately nor in combination do the two effects just described

explain either the shapes or the sizes of the observed orbits of binary

stars as a whole. To interpret these we must call on yet a third

agency, the gravitational forces from passing stars. We have already

seen how these account for the statistical distribution of orbits which

is actually observed.

The combination of all three agencies, tidal friction, extending over

millions of years, loss of weight, extending over millions of millions

of years, and disturbance from passing stars, extending over a similar

period, is responsible for the evolution of binary star systems. Their

aggregate effect is to widen the distance between the two stars, while

at the same time knocking the orbit out of shape.

SUBDIVISION. While these changes are going on in the orbital

arrangement of a binary system, the two components are themselves

changing their physical condition on account of their continual loss

of weight, and, as with the parent stars, this loss of weight will

generally result in a shrinkage in the size of the star. The shrinkage

of either component of the system causes its shape to run through the

sequence of configurations we have already enumerated, and if the

shrinkage continues for long enough, the component may end by further

dividing into two separate masses. Either or both of the constituents

of a binary system may subdivide into binary sub-systems in this way,

resulting in a system of either three or four stars. H. N. Russell

has shewn mathematically that when a binary system _P_, _Q_ divides

into a triple system, _P_, _q_, _qʹ_, through _Q_ breaking up into two

constituents _q_, _qʹ_, the distance between _q_ and _qʹ_ cannot be

more than about a fifth of the original distance _PQ_. This theoretical

law is well confirmed by observation. Fig. 13 shews a typical multiple

system, and we notice that the separations in each of the various

sub-systems are all quite small in comparison with those of the main

systems.

[Illustration: Fig. 13. A typical multiple star.]

The development of the hypothetical primitive chaos has now been traced

through five generations of astronomical bodies,

_chaos—nebulae—stars—binary systems—sub-systems_,

to which a sixth generation must be added if the stars of the

sub-system happen to fission further, as, for instance, they have done

in the star shewn in fig. 13. The genealogy of the stars begins with a

vast tenuous nebula filling all space; the last generation consists of

small, shrunken, dying stars with no capacity for further subdivision.

The genealogy has been traced out primarily on theoretical grounds

alone, but we need have no doubts as to its general accuracy, since

observation confirms it repeatedly and at almost every step. Indeed it

is hardly too much to say that the evolutionary sequence could have

been discovered almost equally well from observational evidence alone,

except for the hypothetical primaeval chaos, about which, from the

nature of the case, observation cannot have anything to say.

THE ORIGIN OF THE SOLAR SYSTEM

Almost all observed astronomical formations can be placed in the

evolutionary sequence we have just discussed, either with fair

certainty or with reasonable plausibility, except for one outstanding

and conspicuous exception—the Solar System. Cosmogony came into

being as an attempt to discover the origin of the solar system. The

reasons why it limited its efforts to this particular problem are

chronological; in the early days of cosmogony, astronomy was barely

conscious of anything outside the solar system. The sketch just given

of the findings of modern scientific cosmogony has been remarkable

in that it has exhibited cosmogony taking us a tour round the whole

universe, explaining the origin and life-history of practically every

object we encounter on this tour, and then becoming speechless when

it is brought back home and confronted with its birthplace, the solar

system.

LAPLACE’S NEBULAR HYPOTHESIS. The first serious scientific cosmogony

was that embodied in the famous Nebular Hypothesis of Laplace. In 1755

Kant had pictured a primaeval chaos condensing into spinning nebulae,

and, identifying one of these nebulae with the sun, had imagined the

planets to be formed by the solidification of masses of gas shed from

the nebula, much in the way in which we have supposed the stars to be

born. In 1796, Laplace advanced similar ideas, which he developed

in detail with a mathematical precision quite beyond the capacities

of Kant. He shewed how, as its shrinkage made it spin ever faster

and faster, a rotating mass of gas would flatten out, develop the

lenticular form we have already discussed (fig. 3 of Plate XVI), and

then proceed to eject matter in its equatorial plane, or rather to

leave it behind as the shrinkage of the main mass continued. At this

stage it would look somewhat like the nebulae shewn in figs. 4 and 5

of Plate XVI, although Laplace, being unacquainted with nebulae of

this type, adduced Saturn surrounded by its rings as an example of the

formation to be expected at this stage (Plate XXIV, p. 250). Laplace

imagined that the fringe of abandoned gas would then condense and

form a single planet. As the main mass shrunk further, more gas was

abandoned in the equatorial plane, which in due course condensed into

another planet, and so on, until the sun left off shrinking and no

more planets were born. A repetition of the same process, but on a far

smaller scale, resulted in the satellites being born out of the planets.

That the hypothesis is _prima facie_ plausible, is evident from its

having survived, and indeed been generally accepted, for nearly

a century before it encountered any serious opposition. Recently

criticisms have accumulated, of so vital a nature as to make it clear

that the hypothesis must be abandoned.

The sun, according to Laplace, broke up and gave birth to planets

through excess of rotation. Yet both theory and observation indicate

quite clearly the fate in store for a star which rotates too fast

for safety; it does not found a family, but merely bursts, like an

overdriven fly-wheel, into parts of nearly equal size. Spectroscopic

binary and multiple systems are the relics of stars which have broken

up through excess of rotation, and they do not in the least resemble

the solar system.

Again, the principle of “conservation of angular momentum” requires

that the rotation of the primaeval sun shall persist in the rotation of

the present sun, and in the revolutions of the planets around it. On

adding together the contributions from all of these, we obtain a total

which ought to represent the angular momentum of the primaeval sun. In

strictness a further contribution ought to be added on account of the

weight of all the radiation which the sun has emitted since the planets

were born. We can calculate the amount of this contribution, because we

know the age of the earth with tolerable accuracy, but it proves to be

entirely negligible.

The total angular momentum of the primaeval sun can be calculated with

very fair accuracy, because more than 95 per cent. of the total angular

momentum of the present solar system resides in the orbital motion of

Jupiter. This contribution can be calculated with great exactness, so

that some uncertainty in the minor contributions which make up the

remaining 5 per cent. can have but little influence on the total.

When this total is calculated the startling fact emerges that the

primaeval sun cannot have had enough rotation to cause break-up at

all. Clearly the sun is very far from being broken up by its present

rotation. Flattening of figure is the first step towards break-up,

and the sun’s figure is so little flattened by its present rotation

that the most refined measurements have so far failed to detect

any flattening at all. On adding the further angular momentum now

represented in the motions of Jupiter and all the other members of the

solar system, we arrive at a primaeval sun rotating about as fast as

Jupiter now rotates, and shewing about the same degree of flattening

of figure as Jupiter—enough to measure quite easily in a telescope, or

even to detect with the eye alone, but nothing like enough to cause

break-up.

The sun is hardly likely to have altered much since its planets were

born, for the intervening 2000 million years or so represent but a

minute fraction of the sun’s total life. If, however, we imagine it

to have shrunk appreciably in the interval, then the available amount

of angular momentum would have been even more unable to break up the

large primaeval sun than it is to break up the present shrunken sun.

Whichever way we look at it, we reach the conclusion that the sun

cannot have broken up, as Laplace imagined, through excess of rotation;

indeed it can never have possessed more than a quite tiny fraction of

the amount of rotation needed to break it up.

A third objection is of a somewhat different character. Laplace was a

very great mathematician, and there was nothing the matter with his

abstract mathematical theory, so far as it went. More refined modern

analysis has confirmed it at every step, and observation does the

same, as photographs of rotating nebulae (Plate XVI) bear witness.

These photographs exhibit a process taking place before our eyes,

which is essentially identical with that imagined by Laplace, except

for a colossal difference of scale. Everything happens qualitatively

as Laplace imagined, but on a scale incomparably grander than he ever

dreamed of. In these photographs the primitive nebula is not a single

sun in the making, but contains substance sufficient to form hundreds

of millions of suns; the condensations do not form puny planets of the

size of our earth, but are themselves suns; they are not eight or so in

number, but must be counted in millions.

We may ask why the same thing cannot happen on the smaller scale

imagined by Laplace—for are not the conclusions of mathematics

applicable independently of the size of the body with which we are

dealing? The answer has in effect been given already (p. 218).

Everything happens on the smaller scale according to plan until we

come to the formation of the condensations; here the question of scale

proves to be vital. We have seen (p. 196) how the molecules which form

the sun have condensed into a star because of their great number; the

molecules in a room do not condense into anything at all because they

are too few. In the same way, the molecules left behind by the slow

shrinkage of a sun (assuming this for the moment to rotate rapidly

enough to leave molecules behind) would not condense, because at any

instant there would be too few of them available for condensation. They

would be shed by driblets, and a driblet of gas does not condense but

scatters into space. A mathematical calculation decides the question

definitely, and the decision is entirely adverse to the hypothesis of

Laplace. Apart from minor details, the process imagined by Laplace

explains the birth of suns out of nebulae; it cannot explain the birth

of planets out of suns.

SECOND BODY THEORIES. Laplace imagined his sun to be alone in space,

even its nearest neighbours being too remote to influence it in any

way. It was the natural supposition to make; we have already remarked

how exceedingly rare an event it must be for two stars to approach near

enough to influence one another. Yet no possible mode of evolution of

a star which remains alone in space seems able to explain the origin

of the solar system. As far back as 1750, Buffon had suggested that the

solar system might have been produced through the disruption of the

sun by another body, which he described as a “comet.” In propounding

his Nebular Hypothesis, Laplace mentioned Buffon’s idea, but dismissed

it somewhat curtly on the grounds that it seemed unable to account for

the nearly circular orbits of the planets—an ill-founded objection,

as we shall soon see. Yet when we find that a single star cannot of

itself give birth to a solar system, it becomes natural to investigate

what happens on the rare occasions on which the evolution of a star is

directed along other paths by the near approach of a second star.

In 1880, Bickerton of New Zealand, reviving Buffon’s idea, supposed

that the solar system had been formed by the collision of the sun with

another star. He imagined the débris of the collision to form a third

nebulous body, condensations in which formed the planets. He shewed

how the resistance which the planets would encounter as they moved

through the surrounding nebula would gradually make their orbits more

circular, and so account for their present nearly circular shapes. Ten

years earlier, the English writer, R. A. Proctor, had advanced similar

ideas, although with less precision. In 1905 Professors Chamberlin

and Moulton of Chicago advanced a modification of the same ideas,

under the name of the “Planetesimal Hypothesis.” Discarding the idea

of material collision, they supposed that a passing star exerted a

powerful tidal pull on the sun, with the result that the ordinary solar

prominences temporarily attained an extraordinary violence; the ejected

matter was supposed to rise to unusual heights and condense into small

solid bodies, the “planetesimals,” out of the aggregation of which

the planets were ultimately formed. These various theories were all

purely speculative. They have shewn very little capacity either for

surviving the acid test of mathematical analysis, or for explaining the

more salient features of the solar system; none of them, for instance,

explains why the larger planets in the solar system are accompanied by

families of satellites.

Three years before Chamberlin and Moulton advanced their planetesimal

theory, I had speculated as to the possibility of tidal forces breaking

up a star, and generating a solar system. In 1916, I investigated

mathematically what would actually happen when one star raised violent

tidal forces on another. The results I obtained seemed to me to

demolish the planetesimal theory of Chamberlin and Moulton, and led me

to put forward the present-day “Tidal Theory,” which I believe a large

proportion of astronomers now accept as giving the _most probable_

origin of the solar system; it can of course make no claim to finality

or certainty.

TIDAL THEORY. When two stars or other bodies pass close to one another

without collision, the primary effect must be that each raises tides in

the other. The closer the approach, the higher the tides in general,

although something must depend also on the speed with which the bodies

pass one another, because this determines the length of time during

which they influence one another.

It is likely that the two spiral arms which give their name and

characteristic appearance to the spiral nebulae may owe their inception

to a somewhat similar tidal action. Conditions here are different in

that the rotation of the nebulae in any case causes them to emit matter

in their equatorial planes, so that even small tidal forces should then

cause this matter to concentrate in two symmetrical arms. Under stellar

conditions a far closer approach is necessary to draw matter out from

the star, and it is then most likely that there will be two unequal and

dissimilar arms, or possibly only one arm.

[Illustration: PLATE XXII _Mt Wilson Observatory_

Two Nebulae (N.G.C. 4395, 4401) suggestive of Tidal Action]

[Illustration: PLATE XXIII The twin Nebulae N.G.C. 4567-8]

[Illustration: _Mt Wilson Observatory_

The Nebula N.G.C. 7479]

If the approach is very close indeed, the tides may assume an entirely

different aspect from the feeble tides which the sun and moon raise in

our oceans; they may take the exaggerated forms of high mountains of

matter moving over the surface of the star. An even closer approach

may transform these mountains into long arms of gas drawn out from the

body of the star. If, as will generally be the case, the two stars are

of unequal weights, the lesser will in general suffer more disturbance

than the weightier.

THE BIRTH OF PLANETS. The long arm or filament of matter drawn out of

a star by tidal action is at first continuous in its structure, but

analysis shews that it provides a fit subject for the operation of what

we have called “Gravitational Instability.” Condensations begin to

form in this long arm of gas, in the way already described. As before,

the smaller condensations are dissipated, while the larger increase

in intensity until finally the filament breaks up into a number of

detached masses—planets have been born out of the smaller star. The

pairs of nebulae shewn in Plate XXII and the upper half of Plate XXIII

are very probably under one another’s tidal influence, and may serve

to suggest the general nature of the process we are now considering,

although it must be remembered that whatever is happening here is on an

enormously greater scale than that of the solar system—if it were not,

the telescope would be utterly unable to shew it to us.

When the new-born planets first begin to move as separate and

independent bodies, they are acted on by the gravitational pulls of

both stars, and so describe highly complicated orbits. Gradually the

bigger star recedes until its gravitational effect becomes negligible,

and the planets are left describing orbits around the smaller star

alone. If the planets moved in a clear field of empty space, these

orbits would be exact ellipses. But the great cataclysm which has just

occurred must have left all sorts of débris behind. Comets, meteors

and other minor bodies which still survive in the solar system may

represent a small part of it, but probably the main part was left in

the form of dust or gas, so that the new-born planets had at first to

plough their way through a medium which offered some resistance to

their motions. Under these circumstances their orbits would not be

strict ellipses. It can be proved that a resistance of the kind just

described would change the shape of the orbits, and that with the

progress of time they would become more circular, finally becoming

absolutely circular if the medium should last long enough.

The débris of gas and dust would, however, continually be swept up by

the planets and would disappear completely in time, probably leaving

the planetary orbits something short of absolute circles. Assuming that

all this has happened in the solar system, very little of the original

débris can now remain, its last vestiges being probably represented by

the particles of dust which are responsible for the zodiacal light.

Nevertheless, the resisting medium appears to have existed for long

enough to make the orbits, both of the planets and of their satellites,

very nearly circular for the most part.

The exceptional cases are fully as significant as the cases of

conformity. Comparatively elongated orbits still exist in just those

regions where we should expect the primaeval resisting medium to have

been most sparsely spread in space, namely on the outermost confines

of the solar system and of the various satellite system. Pluto, the

outermost planet of all, has a more elongated orbit than any other

planet. Again, in the systems of Jupiter and Saturn, the satellites

with the most elongated orbits are those which are furthest away

from their primaries. In addition to this, a general tendency may be

discerned for elongated orbits to be associated with small weights,

both in planets and their satellites. Mercury, with a weight of only a

twenty-fifth that of the earth, has a quite elongated orbit, as also

to a less degree has Mars with a ninth of the weight of the earth. An

explanation of this has been suggested by Jeffreys. Massive planets

such as Jupiter and Saturn must have collected a large mass of the

resisting medium round them, and carried it through space with them

as a far-reaching envelope. The massive planets would have their

motion checked by the interaction of the whole of this big envelope

with the remainder of the medium, and so would attain circular orbits

more rapidly than the lighter planets which had accumulated envelopes

of very much smaller dimensions. And the same, with the appropriate

modifications, is true of the satellite systems.

Jeffreys has calculated the rate at which planetary orbits would

change their shape under the action of this resisting medium. The

data of the problem are necessarily uncertain, and this uncertainty

naturally affects his conclusions, but his study has yielded a valuable

confirmation of other estimates of the length of time which has elapsed

since the planets were born.

We may next turn our attention to the physical changes which must all

this time be affecting the various planets. The long filament of matter

pulled out of the sun is likely to have been richest in matter in its

middle parts, these parts having been pulled out when the second star

was nearest and its gravitational pull was strongest. Diagrammatically

at least, we may think of this filament as shaped like a cigar—thick

near the middle, thin at the ends—so that when condensations begin to

form, those near the middle are likely to be richer in matter than

those at the ends. This probably explains why the two most massive

planets, Jupiter and Saturn, occupy the middle positions in the

sequence of planets.

[Illustration: Fig. 14. Diagrammatic scheme shewing the birth of

planets out of a cigar-shaped filament of gas. The number of satellites

is indicated under each planet (see p. 243).]

Fig. 14 shews the planets arranged in the order of their distances from

the sun, with their sizes drawn roughly to scale. The thousands of

asteroids whose orbits now fill the space between the orbits of Mars

and Jupiter are represented as a single planet, it being generally

supposed that these asteroids were formed by the break-up of what was

originally a single planet in a way we shall shortly describe.

If we surround the planets by a continuous outline, as in the diagram,

we can reconstruct in imagination the cigar-shaped filament out of

which they were produced, and we see at once how the biggest planets

were produced where matter was most abundant.

The tidal theory which predicts all these features had been propounded,

and its consequences worked out, many years before the new planet Pluto

had been discovered. Valuable support for the theory may thus be found

in the circumstance that Pluto behaves in every way according to the

requirements of the tidal theory.

THE BIRTH OF SATELLITES. We have already noticed how the great

disparity of weight between the sun and planets distinguishes the

sun-planet formation from that of the normal binary star, and so

suggests entirely different origins for the two formations. Exactly the

same disparity repeats itself in the planet-satellite systems. Just

as the parent sun is enormously more massive than its children the

planets, so these in turn are far more massive than their satellite

children. The sun has 1047 times the weight of its most massive planet

and many millions of times the weight of the smallest. In the system

of Saturn the corresponding figures are 4150 and about 16,000,000. The

nearest approach to equality of weights is provided by the earth-moon

system, the earth having only 81 times the weight of the moon. And,

like the planetary system of the sun, the satellite systems of Saturn

and, to a lesser degree, of Jupiter shew a general tendency for the

weights of the various satellites to increase up to a maximum as we

pass outwards from the planet, and then to decrease again. This again

suggests formation out of a cigar-shaped filament with matter occurring

most richly near the middle. In conjunction with the repetition of

the great disparity of weights between primary and secondaries, this

indicates very forcibly that the satellites of the planets must have

been born by the same type of process as had previously resulted in the

birth of their parents.

We can imagine the process in a general way. Immediately after their

birth, the planets must begin to cool down. The largest planets,

Jupiter and Saturn, naturally cool most slowly and the smallest most

rapidly. The latter may lose heat so speedily that they liquefy, and

perhaps even solidify, almost immediately after their birth. While

these events are in progress, the planets are still pursuing somewhat

erratic orbits, in describing which they may pass so near to the sun

that a second series of tidal disruptions occurs. In these the sun

itself plays the _rôle_ originally played by the passing star from

space, the planets playing the part originally taken by the sun.

The sun may now tear long filaments of matter out of the surfaces

of the planets, and these, forming condensations, may give birth to

yet another generation of astronomical bodies, the satellites of the

planets. In some such way the tidal theory imagines the planetary

satellites to have come into being.

Mathematical investigation shews that the more liquid a planet was

at birth, the less likely it would be to be broken up by the still

gaseous sun. If, however, such a break-up occurred, the weights of

primary and satellites would be more nearly equal than if the planet

had been more gaseous. Thus, on passing from wholly gaseous planets to

planets which liquefied at or immediately after their birth, we should

expect at first to find planets with large numbers of relatively small

satellites, and then, after passing through the border-line cases of

planets with small numbers of relatively large satellites, we should

expect to come to planets having no satellites at all.

We have already seen that the big central planets, Jupiter and Saturn,

ought to have remained gaseous for longest and the smaller planets to

have liquefied earliest; we now see that this prediction of theory

exactly describes what is actually found in the solar system. Starting

from Jupiter and Saturn, each with nine relatively small satellites,

we pass Mars with only two satellites, and come to the earth with its

one relatively large satellite, followed by Venus and Mercury which

have no satellites at all. Proceeding in the other direction we leave

Jupiter and Saturn each with their nine tiny satellites, to discover

Uranus with four small satellites and Neptune with one comparatively

big satellite. The number placed under each planet in fig. 14 gives the

number of its satellites. When the numbers are exhibited in this way,

the law and order in the arrangement of the satellite systems becomes

very apparent, and this arrangement is seen to be exactly in accordance

with the prediction of the tidal theory. The cigar-shaped arrangement

applies not only to the sizes of the planets, but also, as it ought, to

the numbers of their satellites.

The earth and Neptune, with only one satellite each, and those

comparatively large ones, form the obvious lines of demarcation between

planets which were originally liquid and those which were originally

gaseous. This leads us to conjecture that Mercury, Venus and Pluto must

have become liquid or solid immediately after birth, that the earth and

Neptune were partly liquid and partly gaseous, and that Mars, Jupiter,

Saturn and Uranus were born gaseous and remained gaseous at least until

after the birth of their families of satellites.

We may perhaps find further evidence confirmatory of the tidal theory

in the circumstance that the weights of Mars and Uranus are abnormally

small for their positions in the sequence of planets. If, as we have

supposed, the planets were all born out of a continuous filament of

matter, the weight of Mars at birth would in all probability have been

intermediate between those of the earth and Jupiter, and the weight of

Uranus intermediate between those of Neptune and Saturn. But if, as

we have already been led to suppose, the two anomalous planets Mars

and Uranus were the two smallest planets to be born in the gaseous

state, they would be likely to lose more of their substance than the

other planets through their outermost layers of molecules dissipating

away into space before they had cooled down into the liquid state. If

Mars and Uranus are supposed to be mere relics of planets which were

initially far more massive than they now are, the anomalies begin

to disappear and the pieces of the puzzle to fit together in a very

satisfactory manner.

ORBITAL PLANES. Every rotating mass, whether gaseous, liquid or solid,

has a definite axis of rotation, and, perpendicular to this, a definite

equatorial plane which divides the mass symmetrically into two exactly

equal and similar halves. When a mass breaks up under its own rotation,

the equatorial plane and the symmetry still persist. Illustrations of

this can be found in any set of photographs of rotating nebulae, as,

for instance, those shewn in Plates XV and XVI. In more humble life

an illustration is provided by the splashes of mud thrown off by a

spinning bicycle-wheel, which all keep in the plane in which the wheel

is spinning.

If the sun’s equatorial plane had proved to be a plane of symmetry

for the solar system, so that the whole system was similarly arranged

as regards the two sides of this plane, it might have been possible

to explain the system as the result of a rotational break-up. But the

sun’s equatorial plane is not a plane of symmetry. The planets do not

move in it, most of them moving in a plane which makes an angle of 5

or 6 degrees with it. In terms of our humble analogy, the splashes of

mud are not flying about in the plane in which the bicycle-wheel is

spinning.

The hypothesis that the planets came into being through a rotational

break-up of the sun fails completely before this fact, but the tidal

theory provides a simple explanation of it at once. The sun is still

rotating much as it was before the planets were born, and so retains

its original equatorial plane. The quite different plane in, or very

close to, which the planets are describing orbits must clearly be the

plane in which the long tidal filament was originally drawn out by the

passing star. Thus the plane in which the outer planets now move must

record the position of the plane in which the two stars, the sun and

the wandering star, the second parent of the sun’s family of children,

described orbits about one another 2000 million years ago. It is the

only clue the latter has left of his identity, and is of course far too

slight to make identification possible after this long lapse of time.

To sum up, we have seen that the normal mechanism by which the greater

part of the universe has been carved out is the birth of successive

generations of astronomical bodies through the action of “gravitational

instability.”

The normal genealogy runs somewhat as follows:

_chaos—nebulae—stars—binary systems—sub-systems_.

Not all stars have passed on to the last two generations; where only

a small amount of rotation was present, a star might well live its

whole life without further subdivision. Our sun would have provided

an instance of this had it not been for the rare accident of the

close approach of a second star. From the interaction of these, two

other generations came into being, still through the mechanism of

gravitational instability. For our solar system, as for any other

similar systems there may be in the sky, the genealogy runs as follows:

_chaos—nebula—sun—planets—satellites_.

Both types of genealogy shew five generations, each born from its

parent through the action of gravitational instability, and between

them the two genealogies include practically all the large size

astronomical objects with which we are acquainted. It is then fair to

say that “gravitational instability” appears to be the agency primarily

responsible for the main architecture of the universe.

ROCHE’S LIMIT. The reign of gravitational instability must end with

the birth of planetary satellites, since gaseous bodies of less weight

than these could not hold together. Even under the most favourable

circumstances their feeble gravitational pulls would be unable to

restrain their outermost molecules from escaping, so that the whole

mass would speedily scatter into space. Yet astronomy provides many

instances of smaller bodies; we have already mentioned the asteroids,

meteors or shooting-stars, and the particles of Saturn’s rings. As

all these are too small to have been born in the gaseous state, we

must suppose them to be the broken-up fragments of larger masses. This

accords with the circumstance that these small bodies as a rule do not

occur individually but in swarms.

The asteroids occur as a single swarm. If these were found scattered

throughout the solar system, their origin might present a difficult

problem. As things are, the whole swarm can be explained quite simply

as the broken fragments of a primaeval planet. Saturn’s rings again

admit of a natural explanation as the fragments of a former shattered

moon of Saturn. Comets, which we have hardly had occasion to mention

so far, are in all probability swarms of minute bodies which are just

held together sufficiently by their mutual gravitational attraction to

describe a common orbit in space. At its apparition in 1909, Halley’s

comet was estimated to reflect as much of the sun’s light as a single

body 25 miles in diameter. Yet its apparent surface was 300,000 times

that of such a body, and was quite transparent. It is difficult to

resist the conclusion that the comet consisted of a widely-spaced swarm

of small bodies, and such a swarm again admits of a simple explanation

as the broken fragments of a single mass.

Shooting-stars, or meteors, also are encountered in swarms. As we

shall see later, the motion of many of these swarms makes it possible

to identify them as broken-up comets. Thus the broken fragments

which compose a comet are identical with the meteors which we see

as shooting-stars when they penetrate into the earth’s atmosphere.

Shapley has estimated that the earth’s atmosphere must catch thousands

of millions of shooting-stars every day, of which at most only one in

a hundred is bright enough to be visible to the naked eye. Generally

they dissolve into vapour before they reach the earth’s surface (see

p. 176); occasionally one is so big that the earth’s atmosphere fails

to dissipate it entirely, and what remains of it strikes the earth as

a solid body—a meteorite. Every shooting-star and meteorite may be

regarded as a miniature comet, consisting of only a single fragment. On

occasions a whole group of fragments, moving in parallel paths at only

small distances apart, may strike the earth’s atmosphere and appear as

a “fireball.” Generally speaking all the small fry of the solar system

move in swarms, and can be naturally interpreted as the broken-up

fragments of larger bodies.

If the meteorites are broken fragments of bodies which were born out

of the sun at the same time as the planets, they must have solidified

at about the same time as the earth, at an epoch which we have placed

at about 2000 million years ago. But if they had been born out of some

other star, the time of their solidification might have been anywhere

up to millions of millions of years ago.

Professor Paneth and two colleagues at Königsberg have recently

estimated the ages of various meteoric stones by methods similar to

those employed to fix the age of the earth (p. 154). They obtain ages

which range from a few million years up to 2900 million years, but

there is nothing beyond this last figure. Not a single stone suggests

an age even approaching millions of millions of years. This provides

very strong evidence that these stones were products of the same

cataclysm as produced the earth, and incidentally provides valuable

confirmation of our previous estimate of the earth’s age.

We can easily see how larger bodies might be broken up into swarms of

meteors. We have supposed the sun to have been broken up, at least

to the extent of ejecting a family of planets, by the tidal pull of

a passing star. What would have happened if the passing star had not

passed, but had come to stay? So long as it remained within a certain

distance of the sun, its tidal forces were pulling the sun to pieces.

We can imagine how a longer visit from it would have resulted in a

greater upheaval in the sun, and the birth of a larger family of

planets. Finally a visit of unlimited duration would have shattered the

sun into fragments.

In 1850 Roche gave a mathematical investigation of this process of

tidal break-up. His discussion dealt only with solid or liquid bodies,

but the underlying mechanism is the same whether the bodies are solid,

liquid or gaseous. We have seen that the smaller of the two bodies

involved in a tidal encounter suffers the most. Roche dealt only with

the case in which one body was very small in comparison with the

other; in such a case the small body was completely broken up, while

the larger one remained unscathed. Roche imagined the small body to

describe an orbit of gradually decreasing size around the big body.

If the two bodies were of equal density, he calculated that the small

body would be broken up as soon as the radius of its orbit fell to 2·45

times the radius of the large body. If the bodies are of different

density the matter is slightly more complicated. We must imagine the

larger body to expand or contract until it has the same average density

as the smaller body; the critical distance is then 2·45 radii of the

larger body in its imaginary expanded or contracted state.

This distance is generally known as Roche’s limit. A satellite can with

safety describe a circular orbit about its primary so long as this

orbit lies beyond Roche’s limit, but it is broken into fragments as

soon as it trespasses within the limit. The following figures confirm

Roche’s mathematical analysis:

Radius of Saturn’s outermost ring 2·30 radii of Saturn

_Roche’s limit_ 2·45 _radii of primary_

Radius of orbit of Saturn’s

innermost satellite 3·11 radii of Saturn

Radius of orbit of Jupiter’s

innermost satellite 2·54 radii of Jupiter

Radius of orbit of Mars’ innermost satellite 2·79 radii of Mars

At the same time they suggest very forcibly that Saturn’s rings are

the broken-up fragments of a former satellite which ventured into the

danger-zone marked out by Roche’s limit. We have seen how our own

moon is destined in time to contract its orbit, until it is finally

drawn within the Roche’s limit surrounding the earth and broken

into fragments. After this the earth will have no moon, but will be

surrounded by rings like Saturn.

We speak of Saturn’s rings in the plural, because two distinct circular

gaps cause an appearance of three detached rings. There is a tendency

to jump to the hasty inference that the rings are the shattered remains

of three distinct satellites, but it is not so. Goldsbrough has

shewn how certain orbits around Saturn are rendered unstable by the

motions of the larger satellites of Saturn, so that no particle could

permanently remain in such an orbit. He has calculated positions for

these unstable orbits, and these are found to agree exactly with the

positions of the observed divisions between the rings. Thus Saturn’s

rings were in all probability produced by the breakage of a single

satellite. The ring of small satellites which our moon will ultimately

form round the earth will contain no divisions, because the earth has

no other moons to render certain orbits unstable.

[Illustration: PLATE XXIV Saturn in 1916]

[Illustration: Saturn in 1917]

[Illustration: _Lowell Observatory_ Saturn in 1921

Saturn and its System of Rings]

Roche’s fundamental idea can be extended in many directions and admits

of varied applications. There must, for instance, be a danger-zone,

marked off by a Roche’s limit, surrounding the sun. The distance of

this danger-zone from the sun depends on the density of the body for

which it is dangerous (p. 249). For a body having the low density of a

comet the distance will be very great indeed. Whatever the distances

of their danger-zones, comets must occasionally pass through them and

become broken up in so doing. Two comets, Biela’s comet (1846) and

Taylor’s comet (1916), were observed actually to break in two while

at about the earth’s distance from the sun, and in 1882 a comet was

seen to divide into four parts. Biela’s comet returned in due course

(1852) in the form of two distinct comets a million and a half miles

apart, since which time neither part of the original comet has been

seen again. The orbit of this comet was identical with that of the

Andromedid meteors, which make a display of shooting-stars in the

earth’s atmosphere on favourable 27ths of November, so that it is

likely that these shooting-stars are the broken remains of Biela’s

comet. Other conspicuous swarms of shooting-stars also move in the

tracks of comets—the Leonids which used to make a magnificent show

every 33 years move in the track of Comet 1866 I, the Perseids in the

track of another Comet (1862 II), and the Aquarids in the track of

Halley’s famous comet. In each case, there can be little doubt that

the shooting-stars are scattered fragments of the comets. Besides this

there are several families of comets whose members follow one another

round and round in the same orbit, as though they had originally formed

a single mass.

In the same way a Roche’s limit must surround the planet Jupiter,

so that comets and other bodies may be broken up through getting

inside the danger-zone marked off by this limit. Jupiter’s innermost

satellite is already perilously near it. But the greatest interest

of this particular danger-zone is that it probably accounts for the

existence of the asteroids. In the early days of the solar system,

when the orbits of the planets were less nearly circular than they

now are, a primaeval planet between Mars and Jupiter may well have

described an orbit so elongated as to take it repeatedly within the

danger-zone of Jupiter. If so, we need look no further for the origin

of the asteroids. It is significant that the average orbit of all the

asteroids agrees almost exactly with that of the planet which Bode’s

law (p. 19) would require to exist between Mars and Jupiter.