GROWTH AND DECAY
226. NATURE OF THE PROBLEM.--To use a common figure of speech, the
universe is alive. We have found it filled with an activity that
manifests itself not only in the motions of the heavenly bodies along
their orbits, but which extends to their minutest parts, the molecules
and atoms, whose vibrations furnish the radiant energy given off by sun
and stars. Some of these activities, such as the motions of the heavenly
bodies in their orbits, seem fitted to be of endless duration; while
others, like the radiation of light and heat, are surely temporary, and
sooner or later must come to an end and be replaced by something
different. The study of things as they are thus leads inevitably to
questions of what has been and what is to be. A sound science should
furnish some account of the universe of yesterday and to-morrow as well
as of to-day, and we need not shrink from such questions, although
answers to them must be vague and in great measure speculative.
The historian of America finds little difficulty with events of the
nineteenth century or even the eighteenth, but the sources of
information about America in the fifteenth century are much less
definite; the tenth century presents almost a blank, and the history of
American mankind in the first century of the Christian era is wholly
unknown. So, as we attempt to look into the past or the future of the
heavens, we must expect to find the mists of obscurity grow denser with
remoter periods until even the vaguest outlines of its development are
lost, and we are compelled to say, beyond this lies the unknown. Our
account of growth and decay in the universe, therefore, can not aspire
to cover the whole duration of things, but must be limited in its scope
to certain chapters whose epochs lie near to the time in which we live,
and even for these we need to bear constantly in mind the logical bases
of such an inquiry and the limitations which they impose upon us.
227. LOGICAL BASES AND LIMITATIONS.--The first of these bases is: An
adequate knowledge of the present universe. Our only hope of reading the
past and future lies in an understanding of the present; not necessarily
a complete knowledge of it, but one which is sound so far as it goes.
Our position is like that of a detective who is called upon to unravel a
mystery or crime, and who must commence with the traces that have been
left behind in its commission. The foot print, the blood stain, the
broken glass must be examined and compared, and fashioned into a theory
of how they came to be; and as a wrong understanding of these elements
is sure to vitiate the theories based upon them, so a false science of
the universe as it now is, will surely give a false account of what it
has been; while a correct but incomplete knowledge of the present does
not wholly bar an understanding of the past, but only puts us in the
position of the detective who correctly understands what he sees but
fails to take note of other facts which might greatly aid him.
The second basis of our inquiry is: The assumed permanence of natural
laws. The law of gravitation certainly held true a century ago as well
as a year ago, and for aught we know to the contrary it may have been a
law of the universe for untold millions of years; but that it has
prevailed for so long a time is a pure assumption, although a necessary
one for our purpose. So with those other laws of mathematics and
mechanics and physics and chemistry to which we must appeal; if there
was ever a time or place in which they did not hold true, that time and
place lie beyond the scope of our inquiry, and are in the domain
inaccessible to scientific research. It is for this reason that science
knows nothing and can know nothing of a creation or an end of the
universe, but considers only its orderly development within limited
periods of time. What kind of a past universe would, under the operation
of known laws, develop into the present one, is the question with which
we have to deal, and of it we may say with Helmholtz: "From the
standpoint of science this is no idle speculation but an inquiry
concerning the limitations of its methods and the scope of its known
laws."
To ferret out the processes by which the heavenly bodies have been
brought to their present condition we seek first of all for lines of
development now in progress which tend to change the existing order of
things into something different, and, having found these, to trace their
effects into both past and future. Any force, however small, or any
process, however slow, may produce great results if it works always and
ceaselessly in the same direction, and it is in these processes, whose
trend is never reversed, that we find a partial clew to both past and
future.
228. THE SUN'S DEVELOPMENT.--The first of these to claim our attention
is the shrinking of the sun's diameter which, as we have seen in Chapter
X, is the means by which the solar output of radiant energy is
maintained from year to year. Its amount, only a few feet per annum, is
far too small to be measured with any telescope; but it is cumulative,
working century after century in the same direction, and, given time
enough, it will produce in the future, and must have produced in the
past, enormous transformations in the sun's bulk and equally significant
changes in its physical condition.
Thus, as we attempt to trace the sun's history into the past, the
farther back we go the greater shall we expect to find its diameter and
the greater the space (volume) through which its molecules are spread.
By reason of this expansion its density must have been less then than
now, and by going far enough back we may even reach a time at which the
density was comparable with what we find in the nebulæ of to-day. If our
ideas of the sun's present mechanism are sound, then, as a necessary
consequence of these, its past career must have been a process of
condensation in which its component particles were year by year packed
closer together by their own attraction for each other. As we have seen
in § 126, this condensation necessarily developed heat, a part of which
was radiated away as fast as produced, while the remainder was stored
up, and served to raise the temperature of the sun to what we find it
now. At the present time this temperature is a chief obstacle to further
shrinkage, and so powerfully opposes the gravitative forces as to
maintain nearly an equilibrium with them, thus causing a very slow rate
of further condensation. But it is not probable that this was always so.
In the early stages of the sun's history, when the temperature was low,
contraction of its bulk must have been more rapid, and attempts have
been made by the mathematicians to measure its rate of progress and to
determine how long a time has been consumed in the development of the
present sun from a primitive nebulous condition in which it filled a
space of greater diameter than Neptune's orbit. Of course, numerical
precision is not to be expected in results of this kind, but, from a
consideration of the greatest amount of heat that could be furnished by
the shrinkage of a mass equal to that of the sun, it seems that the
period of this development is to be measured in tens of millions or
possibly hundreds of millions of years, but almost certainly does not
reach a thousand millions.
229. THE SUN'S FUTURE.--The future duration of the sun as a source of
radiant energy is surely to be measured in far smaller numbers than
these. Its career as a dispenser of light and heat is much more than
half spent, for the shrinkage results in an ever-increasing density,
which makes its gaseous substance approximate more and more toward the
behavior of a liquid or solid, and we recall that these forms of matter
can not by any further condensation restore the heat whose loss through
radiation caused them to contract. They may continue to shrink, but
their temperature must fall, and when the sun's substance becomes too
dense to obey the laws of gaseous matter its surface must cool rapidly
as a consequence of the radiation into surrounding space, and must
congeal into a crust which, although at first incandescent, will
speedily become dark and opaque, cutting off the light of the central
portions, save as it may be rent from time to time by volcanic outbursts
of the still incandescent mass beneath. But such outbursts can be of
short duration only, and its final condition must be that of a dark
body, like the earth or moon, no longer available as a source of radiant
energy. Even before the formation of a solid crust it is quite possible
that the output of light and heat may be seriously diminished by the
formation of dense vapors completely enshrouding it, as is now the case
with Jupiter and Saturn. It is believed that these planets were formerly
incandescent, and at the present time are in a state of development
through which the earth has passed and toward which the sun is moving.
According to Newcomb, the future during which the sun can continue to
furnish light and heat at its present rate is not likely to exceed
10,000,000 years.
This idea of the sun as a developing body whose present state is only
temporary, furnishes a clew to some of the vexing problems of solar
physics. Thus the sun-spot period, the distribution of the spots in
latitude, and the peculiar law of rotation of the sun in different
latitudes, may be, and very probably are, results not of anything now
operating beneath its photosphere, but of something which happened to it
in the remote past--e. g., an unsymmetrical shrinkage or possibly a
collision with some other body. At sea the waves continue to toss long
after the storm which produced them has disappeared, and, according to
the mathematical researches of Wilsing, a profound agitation of the
sun's mass might well require tens of thousands, or even hundreds of
thousands of years to subside, and during this time its effects would be
visible, like the waves, as phenomena for which the actual condition of
things furnishes no apparent cause.
230. THE NEBULAR HYPOTHESIS.--The theory of the sun's progressive
contraction as a necessary result of its radiation of energy is
comparatively modern, but more than a century ago philosophic students
of Nature had been led in quite a different way to the belief that in
the earlier stages of its career the sun must have been an enormously
extended body whose outer portions reached even beyond the orbit of the
remotest planet. Laplace, whose speculations upon this subject have had
a dominant influence during the nineteenth century, has left, in a
popular treatise upon astronomy, an admirable statement of the phenomena
of planetary motion, which suggest and lead up to the nebular theory of
the sun's development, and in presenting this theory we shall follow
substantially his line of thought, but with some freedom of translation
and many omissions.
He says: "To trace out the primitive source of the planetary movements,
we have the following five phenomena: (1) These movements all take place
in the same direction and nearly in the same plane. (2) The movements of
the satellites are in the same direction as those of the planets. (3)
The rotations of the planets and the sun are in the same direction as
the orbital motions and nearly in the same plane. (4) Planets and
satellites alike have nearly circular orbits. (5) The orbits of comets
are wholly unlike these by reason of their great eccentricities and
inclinations to the ecliptic." That these coincidences should be purely
the result of chance seemed to Laplace incredible, and, seeking a cause
for them, he continues: "Whatever its nature may be, since it has
produced or controlled the motions of the planets, it must have reached
out to all these bodies, and, in view of the prodigious distances which
separate them, the cause can have been nothing else than a fluid of
great extent which must have enveloped the sun like an atmosphere. A
consideration of the planetary motions leads us to think that ... the
sun's atmosphere formerly extended far beyond the orbits of all the
planets and has shrunk by degrees to its present dimensions." This is
not very different from the idea developed in § 228 from a consideration
of the sun's radiant energy; but in Laplace's day the possibility of
generating the sun's heat by contraction of its bulk was unknown, and he
was compelled to assume a very high temperature for the primitive
nebulous sun, while we now know that this is unnecessary. Whether the
primitive nebula was hot or cold the shrinkage would take place in much
the same way, and would finally result in a star or sun of very high
temperature, but its development would be slower if it were hot in the
beginning than if it were cold.
But again Laplace: "How did the sun's atmosphere determine the rotations
and revolutions of planets and satellites? If these bodies had been
deeply immersed in this atmosphere its resistance to their motion would
have made them fall into the sun, and we may therefore conjecture that
the planets were formed, one by one, at the outer limits of the solar
atmosphere by the condensation of zones of vapor which were cast off in
the plane of the sun's equator." Here he proceeds to show by an appeal
to dynamical principles that something of this kind must happen, and
that the matter sloughed off by the nebula in the form of a ring,
perhaps comparable to the rings of Saturn or the asteroid zone, would
ultimately condense into a planet, which in its turn might shrink and
cast off rings to produce satellites.
[Illustration: PIERRE SIMON LAPLACE (1749-1827).]
Planets and satellites would then all have similar motions, as noted at
the beginning of this section, since in every case this motion is an
inheritance from a common source, the rotation of the primitive
nebula about its own axis. "All the bodies which circle around a planet
having been thus formed from rings which its atmosphere successively
abandoned as rotation became more and more rapid, this rotation should
take place in less time than is required for the orbital revolution of
any of the bodies which have been cast off, and this holds true for the
sun as compared with the planets."
231. OBJECTIONS TO THE NEBULAR HYPOTHESIS.--In Laplace's time this
slower rate of motion was also supposed to hold true for Saturn's rings
as compared with the rotation of Saturn itself, but, as we have seen in
Chapter XI, this ring is made up of a great number of independent
particles which move at different rates of speed, and comparing, through
Kepler's Third Law, the motion of the inner edge of the ring with the
known periodic time of the satellites, we may find that these particles
must rotate about Saturn more rapidly than the planet turns upon its
axis. Similarly the inner satellite of Mars completes its revolution in
about one third of a Martian day, and we find in cases like this grounds
for objection to the nebular theory. Compare also Laplace's argument
with the peculiar rotations of Uranus, Neptune, and their satellites
(Chapter XI). Do these fortify or weaken his case?
Despite these objections and others equally serious that have been
raised, the nebular theory agrees with the facts of Nature at so many
points that astronomers upon the whole are strongly inclined to accept
its major outlines as being at least an approximation to the course of
development actually followed by the solar system; but at some
points--e. g., the formation of planets and satellites through the
casting off of nebulous rings--the objections are so many and strong as
to call for revision and possibly serious modification of the theory.
One proposed modification, much discussed in recent years, consists in
substituting for the primitive _gaseous_ nebula imagined by Laplace, a
very diffuse cloud of meteoric matter which in the course of its
development would become transformed into the gaseous state by rising
temperature. From this point of view much of the meteoric dust still
scattered throughout the solar system may be only the fragments left
over in fashioning the sun and planets. Chamberlin and Moulton, who have
recently given much attention to this subject, in dissenting from some
of Laplace's views, consider that the primitive nebulous condition must
have been one in which the matter of the system was "so brought together
as to give low mass, high momentum, and irregular distribution to the
outer part, and high mass, low momentum, and sphericity to the central
part," and they suggest a possible oblique collision of a small nebula
with the outer parts of a large one.
232. BODE'S LAW.--We should not leave the theory of Laplace without
noting the light it casts upon one point otherwise obscure--the meaning
of Bode's law (§ 134). This law, stated in mathematical form, makes a
geometrical series, and similar geometrical series apply to the
distances of the satellites of Jupiter and Saturn from these planets.
Now, Roche has shown by the application of physical laws to the
shrinkage of a gaseous body that its radius at any time may be expressed
by means of a certain mathematical formula very similar to Bode's law,
save that it involves the amount of time that has elapsed since the
beginning of the shrinking process. By comparing this formula with the
one corresponding to Bode's law he reaches the conclusion that the
peculiar spacing of the planets expressed by that law means that they
were formed at successive _equal_ intervals of time--i. e., that Mars is
as much older than the earth as the earth is older than Venus, etc. The
failure of Bode's law in the case of Neptune would then imply that the
interval of time between the formation of Neptune and Uranus was shorter
than that which has prevailed for the other planets. But too much
stress should not be placed upon this conclusion. So long as the manner
in which the planets came into being continues an open question,
conclusions about their time of birth must remain of doubtful validity.
233. TIDAL FRICTION BETWEEN EARTH AND MOON.--An important addition to
theories of development within the solar system has been worked out by
Prof. G. H. Darwin, who, starting with certain very simple assumptions
as to the present condition of things in earth and moon, derives from
these, by a strict process of mathematical reasoning, far-reaching
conclusions of great interest and importance. The key to these
conclusions lies in recognition of the fact that through the influence
of the tides (§ 42) there is now in progress and has been in progress
for a very long time, a gradual transfer of motion (moment of momentum)
from the earth to the moon. The earth's motion of rotation is being
slowly destroyed by the friction of the tides, as the motion of a
bicycle is destroyed by the friction of a brake, and, in consequence of
this slowing down, the moon is pushed farther and farther away from the
earth, so that it now moves in a larger orbit than it had some millions
of years ago.
Fig. 24 has been used to illustrate the action of the moon in raising
tides upon the earth, but in accordance with the third law of motion
(§ 36) this action must be accompanied by an equal and contrary reaction
whose nature may readily be seen from the same figure. The moon moves
about its orbit from west to east and the earth rotates about its axis
in the same direction, as shown by the curved arrow in the figure. The
tidal wave, _I_, therefore points a little _in advance_ of the moon's
position in its orbit and by its attraction must tend to pull the moon
ahead in its orbital motion a little faster than it would move if the
whole substance of the earth were placed inside the sphere represented
by the broken circle in the figure. It is true that the tidal wave at
_I´´_ pulls back and tends to neutralize the effect of the wave at _I_,
but on the whole the tidal wave nearer the moon has the stronger
influence, and the moon on the whole moves a very little faster, and by
virtue of this added impetus draws continually a little farther away
from the earth than it would if there were no tides.
234. CONSEQUENCES OF TIDAL FRICTION UPON THE EARTH.--This process of
moving the moon away from the earth is a cumulative one, going on
century after century, and with reference to it the moon's orbit must be
described not as a circle or ellipse, or any other curve which returns
into itself, but as a spiral, like the balance spring of a watch, each
of whose coils is a little larger than the preceding one, although this
excess is, to be sure, very small, because the tides themselves are
small and the tidal influence feeble when compared with the whole
attraction of the earth for the moon. But, given time enough, even this
small force may accomplish great results, and something like 100,000,000
years of past opportunity would have sufficed for the tidal forces to
move the moon from close proximity with the earth out to its present
position.
For millions of years to come, if moon and earth endure so long, the
distance between them must go on increasing, although at an ever slower
rate, since the farther away the moon goes the smaller will be the tides
and the slower the working out of their results. On the other hand, when
the moon was nearer the earth than now, tidal influences must have been
greater and their effects more rapidly produced than at the present
time, particularly if, as seems probable, at some past epoch the earth
was hot and plastic like Jupiter and Saturn. Then, instead of tides in
the water of the sea, such as we now have, the whole substance of the
earth would respond to the moon's attraction in _bodily tides_ of
semi-fluid matter not only higher, but with greater internal friction of
their molecules one upon another, and correspondingly greater effect in
checking the earth's rotation.
But, whether the tide be a bodily one or confined to the waters of the
sea, so long as the moon causes it to flow there will be a certain
amount of friction which will affect the earth much as a brake affects a
revolving wheel, slowing down its motion, and producing thus a longer
day as well as a longer month on account of the moon's increased
distance. Slowing down the earth's rotation is the direct action of the
moon upon the earth. Pushing the moon away is the form in which the
earth's equal and contrary reaction manifests itself.
235. CONSEQUENCES OF TIDAL FRICTION UPON THE MOON.--When the moon was
plastic the earth must have raised in it a bodily tide manifold greater
than the lunar tides upon the earth, and, as we have seen in Chapter IX,
this tide has long since worn out the greater part of the moon's
rotation and brought our satellite to the condition in which it presents
always the same face toward the earth.
These two processes, slowing down the rotation and pushing away the
disturbing body, are inseparable--one requires the other; and it is
worth noting in this connection that when for any reason the tide ceases
to flow, and the tidal wave takes up a permanent position, as it has in
the moon (§ 99), its work is ended, for when there is no motion of the
wave there can be no friction to further reduce the rate of rotation of
the one body, and no reaction to that friction to push away the other.
But this permanent and stationary tidal wave in the moon, or elsewhere,
means that the satellite presents always the same face toward its
planet, moving once about its orbit in the time required for one
revolution upon its axis, and the tide raised by the moon upon the earth
tends to produce here the result long since achieved in our satellite,
to make our day and month of equal length, and to make the earth turn
always the same side toward the moon. But the moon's tidal force is
small compared with that of the earth, and has a vastly greater momentum
to overcome, so that its work upon the earth is not yet complete.
According to Thomson and Tait, the moon must be pushed off another
hundred thousand miles, and the day lengthened out by tidal influence to
seven of our present weeks before the day and the lunar month are made
of equal length, and the moon thereby permanently hidden from one
hemisphere of the earth.
236. THE EARTH-MOON SYSTEM.--Retracing into the past the course of
development of the earth and moon, it is possible to reach back by means
of the mathematical theory of tidal friction to a time at which these
bodies were much nearer to each other than now, but it has not been
found possible to trace out the mode of their separation from one body
into two, as is supposed in the nebular theory. In the earliest part of
their history accessible to mathematical analysis they are distinct
bodies at some considerable distance from each other, with the earth
rotating about an axis more nearly perpendicular to the moon's orbit and
to the ecliptic than is now the case. Starting from such a condition,
the lunar tides, according to Darwin, have been instrumental in tipping
the earth's rotation axis into its present oblique position, and in
determining the eccentricity of the moon's orbit and its position with
respect to the ecliptic as well as the present length of day and month.
337. TIDAL FRICTION UPON THE PLANETS.--The satellites of the outer
planets are equally subject to influences of this kind, and there
appears to be independent evidence that some of them, at least, turn
always the same face toward their respective planets, indicating that
the work of tidal friction has here been accomplished. We saw in Chapter
XI that it is at present an open question whether the inner planets,
Venus and Mercury, do not always turn the same face toward the sun,
their day and year being of equal length. In addition to the direct
observational evidence upon this point, Schiaparelli has sought to show
by an appeal to tidal theory that such is probably the case, at least
for Mercury, since the tidal forces which tend to bring about this
result in that planet are about as great as the forces which have
certainly produced it in the case of the moon and Saturn's satellite,
Japetus. The same line of reasoning would show that every satellite in
the solar system, save possibly the newly discovered ninth satellite of
Saturn, must, as a consequence of tidal friction, turn always the same
face toward its planet.
238. THE SOLAR TIDE.--The sun also raises tides in the earth, and their
influence must be similar in character to that of the lunar tides,
checking the rotation of the earth and thrusting earth and sun apart,
although quantitatively these effects are small compared with those of
the moon. They must, however, continue so long as the solar tide lasts,
possibly until the day and year are made of equal length--i. e., they
may continue long after the lunar tidal influence has ceased to push
earth and moon apart. Should this be the case, a curious inverse effect
will be produced. The day being then longer than the month, the moon
will again raise a tide in the earth which will run around it _from west
to east_, opposite to the course of the present tide, thus tending to
accelerate the earth's rotation, and by its reaction to bring the moon
back toward the earth again, and ultimately to fall upon it.
We may note that an effect of this kind must be in progress now between
Mars and its inner satellite, Phobos, whose time of orbital revolution
is only one third of a Martian day. It seems probable that this
satellite is in the last stages of its existence as an independent body,
and must ultimately fall into Mars.
239. ROCHE'S LIMIT.--In looking forward to such a catastrophe, however,
due regard must be paid to a dynamical principle of a different
character. The moon can never be precipitated upon the earth entire,
since before it reaches us it will have been torn asunder by the excess
of the earth's attraction for the near side of its satellite over that
which it exerts upon the far side. As the result of Roche's mathematical
analysis we are able to assign a limiting distance between any planet
and its satellite within which the satellite, if it turns always the
same face toward the planet, can not come without being broken into
fragments. If we represent the radius of the planet by _r_, and the
quotient obtained by dividing the density of the planet by the density
of the satellite by _q_, then
Roche's limit = 2.44 × r × q^{1/3}.
Thus in the case of earth and moon we find from the densities given in
§ 95, _q_ = 1.65, and with _r_ = 3,963 miles we obtain 11,400 miles as
the nearest approach which the moon could make to the earth without
being broken up by the difference of the earth's attractions for its
opposite sides.
We must observe, however, that Roche's limit takes no account of
molecular forces, the adhesion of one molecule to another, by virtue of
which a stick or stone resists fracture, but is concerned only with the
gravitative forces by which the molecules are attracted toward the
moon's center and toward the earth. Within a stone or rock of moderate
size these gravitative forces are insignificant, and cohesion is the
chief factor in preserving its integrity, but in a large body like the
moon, the case is just reversed, cohesion plays a small part and
gravitation a large one in holding the body together. We may conclude,
therefore, that at a proper distance these forces are capable of
breaking up the moon, or any other large body, into fragments of a size
such that molecular cohesion instead of gravitation is the chief agent
in preserving them from further disintegration.
240. SATURN'S RINGS.--Saturn's rings are of peculiar interest in this
connection. The outer edge of the ring system lies just inside of
Roche's limit for this planet, and we have already seen that the rings
are composed of small fragments independent of each other. Whatever may
have been the process by which the nine satellites of Saturn came into
existence, we have in Roche's limit the explanation why the material of
the ring was not worked up into satellites; the forces exerted by Saturn
would tear into pieces any considerable satellite thus formed and
equally would prevent the formation of one from raw material.
Saturn's rings present the only case within the solar system where
matter is known to be revolving about a planet at a distance less than
Roche's limit, and it is an interesting question whether these rings can
remain as a permanent part of the planet's system or are only a
temporary feature. The drawings of Saturn made two centuries ago agree
among themselves in representing the rings as larger than they now
appear, and there is some reason to suppose that as a consequence of
mutual disturbances--collisions--their momentum is being slowly wasted
so that ultimately they must be precipitated into the planet. But the
direct evidence of such a progress that can be drawn from present data
is too scanty to justify positive conclusions in the matter. On the
other hand, Nolan suggests that in the outer parts of the ring small
satellites might be formed whose tidal influence upon Saturn would
suffice to push them away from the ring beyond Roche's limit, and that
the very small inner satellites of Saturn may have been thus formed at
the expense of the ring.
The inner satellite of Mars is very close to Roche's limit for that
planet, and, as we have seen above, must be approaching still nearer to
the danger line.
241. THE MOON'S DEVELOPMENT.--The fine series of photographs of the moon
obtained within the last few years at Paris, have been used by the
astronomers of that observatory for a minute study of the lunar
formations, much as geologists study the surface of the earth to
determine something about the manner in which it was formed. Their
conclusions are, in general, that at some past time the moon was a hot
and fluid body which, as it cooled and condensed, formed a solid crust
whose further shrinkage compressed the liquid nucleus and led to a long
series of fractures in the crust and outbursts of liquid matter, whose
latest and feeblest stages produced the lunar craters, while traces of
the earlier ones, connected with a general settling of the crust,
although nearly obliterated, are still preserved in certain large but
vague features of the lunar topography, such as the distribution of the
seas, etc. They find also in certain markings of the surface what they
consider convincing evidence of the existence in past times of a lunar
atmosphere. But this seems doubtful, since the force of gravity at the
moon's surface is so small that an atmosphere similar to that of the
earth, even though placed upon the moon, could not permanently endure,
but would be lost by the gradual escape of its molecules into the
surrounding space.
The molecules of a gas are quite independent one of another, and are in
a state of ceaseless agitation, each one darting to and fro, colliding
with its neighbors or with whatever else opposes its forward motion, and
traveling with velocities which, on the average, amount to a good many
hundreds of feet per second, although in the case of any individual
molecule they may be much less or much greater than the average value,
an occasional molecule having possibly a velocity several times as great
as the average. In the upper regions of our own atmosphere, if one of
these swiftly moving particles of oxygen or nitrogen were headed away
from the earth with a velocity of seven miles per second, the whole
attractive power of the earth would be insufficient to check its motion,
and it would therefore, unless stopped by some collision, escape from
the earth and return no more. But, since this velocity of seven miles
per second is more than thirty times as great as the average velocity of
the molecules of air, it must be very seldom indeed that one is found to
move so swiftly, and the loss of the earth's atmosphere by leakage of
this sort is insignificant. But upon the moon, or any other body where
the force of gravity is small, conditions are quite different, and in
our satellite a velocity of little more than one mile per second would
suffice to carry a molecule away from the outer limits of its
atmosphere. This velocity, only five times the average, would be
frequently attained, particularly in former times when the moon's
temperature was high, for then the average velocity of all the molecules
would be considerably increased, and the amount of leakage might become,
and probably would become, a serious matter, steadily depleting the
moon's atmosphere and leading finally to its present state of
exhaustion. It is possible that the moon may at one time have had an
atmosphere, but if so it could have been only a temporary possession,
and the same line of reasoning may be applied to the asteroids and to
most of the satellites of the solar system, and also, though in less
degree, to the smaller planets, Mercury and Mars.
242. STELLAR DEVELOPMENT.--We have already considered in this chapter
the line of development followed by one star, the sun, and treating this
as a typical case, it is commonly believed that the life history of a
star, in so far as it lies within our reach, begins with a condition in
which its matter is widely diffused, and presumably at a low
temperature. Contracting in bulk under the influence of its own
gravitative forces, the star's temperature rises to a maximum, and then
falls off in later stages until the body ceases to shine and passes over
to the list of dark stars whose existence can only be detected in
exceptional cases, such as are noted in Chapter XIII. The most
systematic development of this idea is due to Lockyer, who looks upon
all the celestial bodies--sun, moon and planets, stars, nebulæ, and
comets--as being only collections of meteoric matter in different stages
of development, and who has sought by means of their spectra to classify
these bodies and to determine their stage of advancement. While the
fundamental ideas involved in this "meteoritic hypothesis" are not
seriously controverted, the detailed application of its principles is
open to more question, and for the most part those astronomers who hold
that in the present state of knowledge stellar spectra furnish a key to
a star's age or degree of advancement do not venture beyond broad
general statements.
[Illustration: FIG. 151.--Types of stellar spectra substantially
according to SECCHI.]
243. STELLAR SPECTRA.--Thus the types of stellar spectra shown in Fig.
151 are supposed to illustrate successive stages in the development of
an average star. Type I corresponds to the period in which its
temperature is near the maximum; Type II belongs to a later stage in
which the temperature has commenced to fall; and Type III to the period
immediately preceding extinction.
While human life, or even the duration of the human race, is too short
to permit a single star to be followed through all the stages of its
career, an adequate picture of that development might be obtained by
examining many stars, each at a different stage of progress, and,
following this idea, numerous subdivisions of the types of stellar
spectra shown in Fig. 151 have been proposed in order to represent with
more detail the process of stellar growth and decay; but for the most
part these subdivisions and their interpretation are accepted by
astronomers with much reserve.
It is significant that there are comparatively few stars with spectra of
Type III, for this is what we should expect to find if the development
of a star through the last stages of its visible career occupied but a
small fraction of its total life. From the same point of view the great
number of stars with spectra of the first type would point to a long
duration of this stage of life. The period in which the sun belongs,
represented by Type II, probably has a duration intermediate between the
others. Since most of the variable stars, save those of the Algol class,
have spectra of the third type, we conclude that variability, with its
associated ruddy color and great atmospheric absorption of light, is a
sign of old age and approaching extinction. The Algol or eclipse
variables, on the other hand, having spectra of the first type, are
comparatively young stars, and, as we shall see a little later, the
shortness of their light periods in some measure confirms this
conclusion drawn from their spectra.
We have noted in § 196 that the sun's near neighbors are prevailingly
stars with spectra of the second type, while the Milky Way is mainly
composed of first-type stars, and from this we may now conclude that in
our particular part of the entire celestial space the stars are, as a
rule, somewhat further developed than is the case elsewhere.
244. DOUBLE STARS.--The double stars present special problems of
development growing out of the effects of tidal friction, which must
operate in them much as it does between earth and moon, tending steadily
to increase the distance between the components of such a star. So, too,
in such a system as is shown in Fig. 132, gravity must tend to make each
component of the double star shrink to smaller dimensions, and this
shrinkage must result in faster rotation and increased tidal friction,
which in turn must push the components apart, so that in view of the
small density and close proximity of those particular stars we may
fairly regard a star like [b] Lyræ as in the early stages of its
career and destined with increasing age to lose its variability of
light, since the eclipses which now take place must cease with
increasing distance between the components unless the orbit is turned
exactly edgewise toward the earth. Close proximity and the resulting
shortness of periodic time in a double star seem, therefore, to be
evidence of its youth, and since this shortness of periodic time is
characteristic of both Algol variables and spectroscopic binaries as a
class, we may set them down as being, upon the whole, stars in the early
stages of their career. On the other hand, it is generally true that the
larger the orbit, and the greater the periodic time in the orbit, the
farther is the star advanced in its development.
In his theory of tidal friction, Darwin has pointed out that whenever
the periodic time in the orbit is more than twice as long as the time
required for rotation about the axis, the effect of the tides is to
increase the eccentricity of the orbit, and, following this indication,
See has urged that with increasing distance between the components of a
double star their orbits about the common center of gravity must grow
more and more eccentric, so that we have in the shape of such orbits a
new index of stellar development; the more eccentric the orbit, the
farther advanced are the stars. It is important to note in this
connection that among the double stars whose orbits have been computed
there seems to run a general rule--the larger the orbit the greater is
its eccentricity--a relation which must hold true if tidal friction
operates as above supposed, and which, being found to hold true,
confirms in some degree the criteria of stellar age which are furnished
by the theory of tidal friction.
245. NEBULÆ.--The nebular hypothesis of Laplace has inclined astronomers
to look upon nebulæ in general as material destined to be worked up into
stars, but which is now in a very crude and undeveloped stage. Their
great bulk and small density seem also to indicate that gravitation has
not yet produced in them results at all comparable with what we see in
sun and stars. But even among nebulæ there are to be found very
different stages of development. The irregular nebula, shapeless and
void like that of Orion; the spiral, ring, and planetary nebulæ and the
star cluster, clearly differ in amount of progress toward their final
goal. But it is by no means sure that these several types are different
stages in one line of development; for example, the primitive nebula
which grows into a spiral may never become a ring or planetary nebula,
and _vice versa_. So too there is no reason to suppose that a star
cluster will ever break up into isolated stars such as those whose
relation to each other is shown in Fig. 122.
246. CLASSIFICATION.--Considering the heavenly bodies with respect to
their stage of development, and arranging them in due order, we should
probably find lowest down in the scale of progress the irregular nebulæ
of chaotic appearance such as that represented in Fig. 146. Above these
in point of development stand the spiral, ring, and planetary nebulæ,
although the exact sequence in which they should be arranged remains a
matter of doubt. Still higher up in the scale are star clusters whose
individual members, as well as isolated stars, are to be classified by
means of their spectra, as shown in Fig. 151, where the order of
development of each star is probably from Type I, through II, into III
and beyond, to extinction of its light and the cutting off of most of
its radiant energy. Jupiter and Saturn are to be regarded as stars which
have recently entered this dark stage. The earth is further developed
than these, but it is not so far along as are Mars and Mercury; while
the moon is to be looked upon as the most advanced heavenly body
accessible to our research, having reached a state of decrepitude which
may almost be called death--a stage typical of that toward which all the
others are moving.
Meteors and comets are to be regarded as fragments of celestial matter,
chips, too small to achieve by themselves much progress along the normal
lines of development, but destined sooner or later, by collision with
some larger body, to share thenceforth in its fortunes.
247. STABILITY OF THE UNIVERSE.--It was considered a great achievement
in the mathematical astronomy of a century ago when Laplace showed that
the mutual attractions of sun and planets might indeed produce endless
perturbations in the motions and positions of these bodies, but could
never bring about collisions among them or greatly alter their existing
orbits. But in the proof of this great theorem two influences were
neglected, either of which is fatal to its validity. One of these--tidal
friction--as we have already seen, tends to wreck the systems of
satellites, and the same effect must be produced upon the planets by any
other influence which tends to impede their orbital motion. It is the
inertia of the planet in its forward movement that balances the sun's
attraction, and any diminution of the planet's velocity will give this
attraction the upper hand and must ultimately precipitate the planet
into the sun. The meteoric matter with which the earth comes ceaselessly
into collision must have just this influence, although its effects are
very small, and something of the same kind may come from the medium
which transmits radiant energy through the interstellar spaces.
It seems incredible that the luminiferous ether, which is supposed to
pervade all space, should present absolutely no resistance to the motion
of stars and planets rushing through it with velocities which in many
cases exceed 50,000 miles per hour. If there is a resistance to this
motion, however small, we may extend to the whole visible universe the
words of Thomson and Tait, who say in their great Treatise on Natural
Philosophy, "We have no data in the present state of science for
estimating the relative importance of tidal friction and of the
resistance of the resisting medium through which the earth and moon
move; but, whatever it may be, there can be but one ultimate result for
such a system as that of the sun and planets, if continuing long enough
under existing laws and not disturbed by meeting with other moving
masses in space. That result is the falling together of all into one
mass, which, although rotating for a time, must in the end come to rest
relatively to the surrounding medium."
Compare with this the words of a great poet who in The Tempest puts into
the mouth of Prospero the lines:
"The cloud-capp'd towers, the gorgeous palaces,
The solemn temples, the great globe itself,
Yea, all which it inherit, shall dissolve;
And, like this insubstantial pageant faded,
Leave not a rack behind."
248. THE FUTURE.--In spite of statements like these, it lies beyond the
scope of scientific research to affirm that the visible order of things
will ever come to naught, and the outcome of present tendencies, as
sketched above, may be profoundly modified in ages to come, by
influences of which we are now ignorant. We have already noted that the
farther our speculation extends into either past or future, the more
insecure are its conclusions, and the remoter consequences of present
laws are to be accepted with a corresponding reserve. But the one great
fact which stands out clear in this connection is that of _change_. The
old concept of a universe created in finished form and destined so to
abide until its final dissolution, has passed away from scientific
thought and is replaced by the idea of slow development. A universe
which is ever becoming something else and is never finished, as shadowed
forth by Goethe in the lines:
"Thus work I at the roaring loom of Time,
And weave for Deity a living robe sublime."
APPENDIX
THE GREEK ALPHABET
The Greek letters are so much used by astronomers in connection with the
names of the stars, and for other purposes, that the Greek alphabet is
printed below--not necessarily to be learned, but for convenient
reference:
Greek. Name. English.
[A] [a] Alpha a
[B] [b] Beta b
[G] [g] Gamma g
[D] [d] Delta d
[E] [e] or [e] Epsilon [)e]
[Z] [z] Zeta z
[Ê] [ê] Eta [=e]
[Th] [th] or [th] Theta th
[I] [i] Iota i
[K] [k] Kappa k
[L] [l] Lambda l
[M] [m] Mu m
[N] [n] Nu n
[X] [x] Xi x
[O] [o] Omicron [)o]
[P] [p] Pi p
[R] [r] Rho r
[S] [s] or [s] Sigma s
[T] [t] Tau t
[Y] [y] Upsilon u
[Ph] [ph] Phi ph
[Ch] [ch] Chi ch
[Ps] [ps] Psi ps
[Ô] [ô] Omega [=o]
POPULAR LITERATURE OF ASTRONOMY
The following brief bibliography, while making no pretense at
completeness, may serve as a useful guide to supplementary reading:
_General Treatises_
YOUNG. _General Astronomy._ An admirable general survey of the entire
field.
NEWCOMB. _Popular Astronomy._ The second edition of a German translation
of this work by Engelmann and Vogel is especially valuable.
BALL. _Story of the Heavens._ Somewhat easier reading than either of the
preceding.
CHAMBERS. _Descriptive Astronomy._ An elaborate but elementary work in
three volumes.
LANGLEY. _The New Astronomy._ Treats mainly of the physical condition of
the celestial bodies.
PROCTOR and RANYARD. _Old and New Astronomy._
_Special Treatises_
PROCTOR. _The Moon._ A general treatment of the subject.
NASMYTH and CARPENTER. _The Moon._ An admirably illustrated but
expensive work dealing mainly with the topography and physical
conditions of the moon. There is a cheaper and very good edition in
German.
YOUNG. _The Sun._ International Scientific Series. The most recent and
authoritative treatise on this subject.
PROCTOR. _Other Worlds than Ours._ An account of planets, comets, etc.
NEWTON. _Meteor._ Encyclopædia Britannica.
AIRY. _Gravitation._ A non-mathematical exposition of the laws of
planetary motion.
STOKES. _On Light as a Means of Investigation._ Burnett Lectures. II.
The basis of spectrum analysis.
SCHELLEN. _Spectrum Analysis._
THOMSON (Sir W., Lord KELVIN), _Popular Lectures, etc._ Lectures on the
Tides, The Sun's Heat, etc.
BALL. _Time and Tide._ An exposition of the researches of G. H. Darwin
upon tidal friction.
GORE. _The Visible Universe._ Deals with a class of problems
inadequately treated in most popular astronomies.
DARWIN. _The Tides._ An admirable elementary exposition.
CLERKE. _The System of the Stars._ Stellar astronomy.
NEWCOMB. Chapters on the Stars, in _Popular Science Monthly_ for 1900.
CLERKE. _History of Astronomy during the Nineteenth Century._ An
admirable work.
WOLF. _Geschichte der Astronomie._ München, 1877. An excellent German
work.
A LIST OF STARS FOR TIME OBSERVATIONS
See § 20.
------------------+---------------+------------------+-------------+
NAME. | Magnitude. | Right Ascension. | Declination.|
------------------+---------------+------------------+-------------+
| | | |
| | h. m. | ° |
[b] Ceti | 2 | 0 38.6 | - 18.5 |
[ê] Ceti | 3 | 1 3.6 | - 10.7 |
[a] Ceti | 3 | 2 57.1 | + 3.7 |
[g] Eridani | 3 | 3 53.4 | - 13.8 |
_Aldebaran_ | 1 | 4 30.2 | + 16.3 |
| | | |
_Rigel_ | 0 | 5 9.7 | - 8.3 |
[k] Orionis | 2 | 5 43.0 | - 9.7 |
[b] Canis Majoris | 2 | 6 18.3 | - 17.9 |
_Sirius_ | -1 | 6 40.7 | - 16.6 |
_Procyon_ | 0 | 7 34.1 | + 5.5 |
| | | |
[a] Hydræ | 2 | 9 22.7 | - 8.2 |
_Regulus_ | 1 | 10 3.0 | + 12.5 |
[n] Hydræ | 3 | 10 44.7 | - 15.7 |
[e] Corvi | 3 | 12 5.0 | - 22.1 |
[g] Corvi | 3 | 12 10.7 | - 17.0 |
| | | |
_Spica_ | 1 | 13 19.9 | - 10.6 |
[z] Virginis | 3 | 13 29.6 | - 0.1 |
[a] Libræ | 3 | 14 45.3 | - 15.6 |
[b] Libræ | 3 | 15 11.6 | - 9.0 |
_Antares_ | 1 | 16 23.3 | - 26.2 |
| | | |
[a] Ophiuchi | 2 | 17 30.3 | + 12.6 |
[e] Sagittarii | 2 | 18 17.5 | - 34.4 |
[d] Aquilæ | 3 | 19 20.5 | + 2.9 |
_Altair_ | 1 | 19 45.9 | + 8.6 |
[b] Aquarii | 3 | 21 26.3 | - 6.0 |
| | | |
[a] Aquarii | 3 | 22 0.6 | - 0.8 |
_Fomalhaut_ | 1 | 22 52.1 | - 30.2 |
------------------+---------------+------------------+-------------+
INDEX
The references are to section numbers.
Absorption of starlight, 225.
Absorption spectra, 87.
Accelerating force, 35.
Adjustment of observations, 2.
Albedo of moon, 97.
of Venus, 148.
Algol, 205.
Altitudes, 4, 21.
Andromeda nebula, 214.
Angles, measurement of, 2.
Angular diameter, 7.
Annular eclipse, 64.
Asteroids, 156.
Atmosphere of the earth, 49.
of the moon, 103.
of Jupiter, 139.
of Mars, 153.
Aurora, 51.
Azimuth, 5, 21.
Biela's comet, 181.
Bode's law, 134, 232.
Bredichin's theory of comet tails, 180.
Calendar, O. S. and N. S., 61.
Capture of comets and meteors, 176.
Canals of Mars, 154.
Celestial mechanics, 32.
Changes upon the moon, 108.
Chemical constitution of sun, 116.
of stars, 210.
Chromosphere, the sun's, 124.
Chronology, 59.
Classification of stars, 212.
Clocks and watches, 74.
sidereal clock, 12.
Collisions with comets, 183.
Colors of stars, 209.
Comets, general characteristics, 158-164.
development of, 179, 181.
groups, 177.
orbits, 161.
periodic, 176.
spectra, 182.
tails, 180.
Comets and meteors, relation of, 175.
Conic sections, 38.
Constellations, 184.
Corona, the sun's, 123.
Craters, lunar, 105.
Dark stars, 201.
Day, 52, 62.
Declination, 21.
Development of comet, 179.
of moon, 241.
of nebulæ, 245.
of stars, 242, 244.
of sun, 228.
of universe, 226.
Distribution of stars and nebulæ, 220.
Diurnal motion, 10, 15.
Doppler principle, 89.
Double nebulæ, 215.
Double stars, 198.
development of, 244.
Driving clock, 80.
Earth, atmosphere, 48.
mass, 45.
size and shape, 44.
warming of the earth, 47.
Eclipses, nature of, 63.
annular eclipse, 64.
eclipse limits, 68.
eclipse maps, 70, 71.
number of, in a year, 69.
partial eclipse, 64.
prediction of, 70, 71.
recurrence of, 72.
shadow cone, 64, 66.
total eclipse, 64.
uses of, 73.
Eclipses of Jupiter's satellites, 141.
Eclipse theory of variable stars, 205.
Ecliptic, 26.
obliquity of, 25.
Ellipse, 33.
Epochs for planetary motion, 30.
Energy, radiant, 75.
condensation of, 76.
Epicycle, 32.
Equation of time, 53.
Equator, 16, 21.
Equatorial mounting, 80.
Equinoxes, 25.
Ether, 75.
Evening star, 31.
Faculæ, 122.
Falling bodies, law of, 35.
Finding the stars, 14.
Fraunhofer lines, 87.
Galaxy, 219.
Geography of the sky, 16.
Graphical representation, 6.
Grating, diffraction, 84.
Gravitation, law of, 37.
Harvest moon, 93.
Heat of the sun, 118, 126.
Helmholtz, contraction theory of the sun, 126, 228.
Horizon, 4, 21.
Hour angle, 21.
Hour circle, 21.
Hyperbola, 38.
Japetus, satellite of Saturn, 145.
Jupiter, 136.
atmosphere, 139.
belts, 137.
invisible from fixed stars, 197.
orbit of, 29.
physical condition, 139.
rotation and flattening, 138.
satellites, 140.
surface markings, 137.
Kepler's laws, 33, 111.
Latitude, determination of, 18.
Leap year, 61.
Lenses, 77.
Leonid meteor shower, 172.
perturbations of, 174.
Librations of moon, 98.
Life upon the planets, 157.
Light curves, 205.
Light, nature of, 75.
Light year, 190.
Limits of eclipses, 68.
Longitude, 56.
determination of, 58.
Lunation, 60.
Magnifying power of telescope, 79.
Magnitude, stellar, 9, 186.
Mars, atmosphere, temperature, 150.
canals, 154.
orbit, 30.
polar caps, 152.
rotation, 151.
satellites, 155.
surface markings, 150.
Mass, determination of, 37.
of comets, 164.
of double stars, 200.
of moon, 94.
of planets, 40, 133.
Measurements, accurate, 1.
Mercury, 149.
motion of its perihelion, 43.
orbit of, 30.
Meridian, 19, 21.
Meteors, nature of, 165, 169.
number of, 167.
velocity, 170.
Meteors and comets, relation of, 175.
Meteor showers, radiant, 171.
Leonids, capture of, 172, 173.
perturbations, 174.
Milky Way, 219.
Mira, [o] Ceti, 204.
Mirrors, 77.
Month, 60.
Moon, 91.
albedo, 97.
atmosphere, 103.
changes in, 108.
density, surface gravity, 95.
development of, 241.
harvest moon, 93.
influence upon the earth, 109, 233.
librations, 98.
map of, 101.
mass and size, 94.
motion, 24, 92.
mountains and craters, 104.
phases, 91, 92.
physical condition, 100, 107.
Month, 60.
Morning star, 31.
Motion in line of sight, 89, 193.
Multiple stars, 202.
Names of stars, 8.
Nebulæ, 214.
density, 217.
development of, 245.
motion, 218.
spectra, 216.
types and classes of, 215.
Nebular hypothesis, 230.
objections to, 231.
Neptune, 146.
discovery of, 41.
Newton's laws of motion, 34.
law of gravitation, 37, 43.
Nodes, 39.
relation to eclipses, 67, 71.
Nucleus, of comet, 160.
Objective, of telescope, 78.
Obliquity of ecliptic, 25.
Observations, of stars, 10.
Occultation of stars, 103.
Orbits, of comets, 161.
of double stars, 199.
of moon, 92.
of planets, 28.
Orion nebula, 215.
Parabola, 35, 38, 161.
Parabolic velocity, 38.
Parallax, 114, 188.
Penumbra, 64, 121.
Perihelion, 38.
Periodic comets, 176.
Personal equation, 82.
Perturbations, 39.
of meteors, 174.
Phases, of the moon, 91, 92.
Photography, 81.
of stars, 13.
Photosphere, of sun, 121.
Planets, 26, 133.
distances from the sun, 134.
how to find, 29.
mass, density, size, 133.
motion of, 27, 38.
periodic times of, 30.
Planetary nebulæ, 215.
Pleiades, 16, 215.
Plumb-line apparatus, 11, 18.
Poles, 21.
Precession, 46.
Prisms, 84.
Problem of three bodies, 39.
Prominences, solar, 125.
Proper motions, 191.
Protractor, 2.
Ptolemaic system, 32.
Radiant energy, 75.
Radiant, of meteor shower, 171.
Radius victor, 33.
Reference lines and circles, 17.
Refraction, 50.
Right ascension, 16, 20, 21.
Roche's limit, 239.
Rotation, of earth, 55.
of Mars, 151.
of moon, 99.
of Jupiter, 138.
of Saturn, 144.
of sun, 120, 132.
Saros, 72.
Satellites, of Jupiter, 136, 140.
of Mars, 155.
of Saturn, 145.
Saturn, 142.
ball of, 144.
orbit, 29.
rings, 142.
rotation, 144.
satellites, 145.
Seasons, on the earth, 47.
on Mars, 151.
Shadow cone, 64, 66.
Sidereal time, 20, 54.
Shooting stars, 158. (See Meteor.)
Spectroscope, 84.
Spectroscopic binaries, 203.
Spectrum, 84, 87.
of comets, 182.
of nebulæ, 216.
of stars, 211.
types of, 88.
Spectrum analysis, 85.
Spiral nebulæ, 215.
Standard time, 57.
Stars, 8, 184.
classes of, 212.
clusters, 213.
colors, 209.
dark stars, 201.
development of, 242.
distances from the sun, 188, 196.
distribution of, 220.
double stars, 198, 203.
drift, 194.
magnitudes, 9, 196.
number of, 185.
spectra, 211.
temporary, 208.
variable, 204.
Starlight, absorption of, 225.
Star maps, construction of, 23.
Stellar system, extent of, 223.
Sun's apparent motion, 25.
real motion, 195.
Sun, 110.
chemical composition, 116.
chromosphere, 124.
corona, 123.
distance from the earth, 111.
faculæ, 119, 122.
gaseous constitution, 127.
heat of, 117.
mechanism of, 126.
physical properties, 115-120.
prominences, 125.
rotation, 120, 132.
surface of, 119.
temperature, 118.
Sun spots, 119, 121.
period, 129, 131.
zones, 130.
Telescopes, 78.
equatorial mounting for, 80.
magnifying power of, 79.
Temperature of Jupiter, 139.
of Mars, 152.
of Mercury, 149.
of moon, 107.
of sun, 118.
Temporary stars, 208.
Terminator, 91.
Tenth meter, 75.
Tidal friction, 233-238.
Tides, 42.
Time, sidereal, 20, 54.
solar, 52.
determination of, 20.
equation of, 53.
standard, 57.
Triangulation, 3.
Trifid nebula, 215.
Twilight, 51.
Twinkling, of stars, 48.
Universe, development of, 226.
stability of, 247.
Uranus, 146.
Variable stars, 204.
Velocity, its relation to orbital motion, 38.
Venus, 148.
orbit of, 30.
Vernal equinox, 21, 25.
Vertical circle, 21.
Wave front, 76.
Wave lengths, 75, 86.
Year, 25.
leap year, 61.
sidereal year, 59.
tropical year, 60.
Zenith, 21.
Zodiac, 26.
Zodiacal light, 168.
THE END
End of Project Gutenberg's A Text-Book of Astronomy, by George C. Comstock