THE TIDES.[44]
Mathematical Astronomy--Lagrange's Theories: how far they are
really True--The Solar System not Made of Rigid Bodies--Kepler's
Laws True to Observation, but not Absolutely True when the Bodies
are not Rigid--The Errors of Observation--The Tides--How the Tides
were Observed--Discovery of the Connection between the Tides and
the Moon--Solar and Lunar Tides--Work done by the Tides--Whence do
the Tides obtain the Power to do the Work?--Tides are Increasing
the Length of the Day--Limit to the Shortness of the Day--Early
History of the Earth-Moon System--Unstable Equilibrium--Ratio of
the Month to the Day--The Future Course of the System--Equality of
the Month and the Day--The Future Critical Epoch--The Constant Face
of the Moon accounted for--The other Side of the Moon--The
Satellites of Mars--Their Remarkable Motions--Have the Tides
Possessed Influence in Moulding the Solar System generally?--Moment
of Momentum--Tides have had little or no Appreciable Effect on the
Orbit of Jupiter--Conclusion.
That the great discoveries of Lagrange on the stability of the planetary
system are correct is in one sense strictly true. No one has ever
ventured to impugn the mathematics of Lagrange. Given the planetary
system in the form which Lagrange assumed and the stability of that
system is assured for all time. There is, however, one assumption which
Lagrange makes, and on which his whole theory was founded: his
assumption is that the planets are _rigid_ bodies.
No doubt our earth seems a rigid body. What can be more solid and
unyielding than the mass of rocks and metals which form the earth, so
far as it is accessible to us? In the wide realms of space the earth is
but as a particle; it surely was a natural and a legitimate assumption
to suppose that that particle was a rigid body. If the earth were
absolutely rigid--if every particle of the earth were absolutely at a
fixed distance from every other particle--if under no stress of forces,
and in no conceivable circumstance, the earth experienced even the
minutest change of form--if the same could be said of the sun and of all
the other planets--then Lagrange's prediction of the eternal duration of
our system must be fulfilled.
But what are the facts of the case? Is the earth really rigid? We know
from experiment that a rigid body in the mathematical sense of the word
does not exist. Rocks are not rigid; steel is not rigid; even a diamond
is not perfectly rigid. The whole earth is far from being rigid even on
the surface, while part of the interior is still, perhaps, more or less
fluid. The earth cannot be called a perfectly rigid body; still less can
the larger bodies of our system be called rigid. Jupiter and Saturn are
perhaps hardly even what could be called solid bodies. The solar system
of Lagrange consisted of a rigid sun and a number of minute rigid
planets; the actual solar system consists of a sun which is in no sense
rigid, and planets which are only partially so.
The question then arises as to whether the discoveries of the great
mathematicians of the last century will apply, not only to the ideal
solar system which they conceived, but to the actual solar system in
which our lot has been cast. There can be no doubt that these
discoveries are approximately true: they are, indeed, so near the
absolute truth, that observation has not yet satisfactorily shown any
departure from them.
But in the present state of science we can no longer overlook the
important questions which arise when we deal with bodies not rigid in
the mathematical sense of the word. Let us, for instance, take the
simplest of the laws to which we have referred, the great law of Kepler,
which asserts that a planet will revolve for ever in an elliptic path of
which the sun is one focus. This is seen to be verified by actual
observation; indeed, it was established by observation before any
theoretical explanation of that movement was propounded. If, however, we
state the matter with a little more precision, we shall find that what
Newton really demonstrated was, that if two _rigid_ particles attract
each other by a law of force which varies with the inverse square of the
distance between the particles, then each of the particles will describe
an ellipse with the common centre of gravity in the focus. The earth is,
to some extent, rigid, and hence it was natural to suppose that the
relative behaviour of the earth and the sun would, to a corresponding
extent, observe the simple elliptic law of Kepler; as a matter of fact,
they do observe it with such fidelity that, if we make allowance for
other causes of disturbance, we cannot, even by most careful
observation, detect the slightest variation in the motion of the earth
arising from its want of rigidity.
There is, however, a subtlety in the investigations of mathematics
which, in this instance at all events, transcends the most delicate
observations which our instruments enable us to make. The principles of
mathematics tell us that though Kepler's laws may be true for bodies
which are absolutely and mathematically rigid, yet that if the sun or
the planets be either wholly, or even in their minutest part, devoid of
perfect rigidity, then Kepler's laws can be no longer true. Do we not
seem here to be in the presence of a contradiction? Observation tells us
that Kepler's laws are true in the planetary system; theory tells us
that these laws cannot be true in the planetary system, because the
bodies in that system are not perfectly rigid. How is this discrepancy
to be removed? Or is there really a discrepancy at all? There is not.
When we say that Kepler's laws have been proved to be true by
observation, we must reflect on the nature of the proofs which are
attainable. We observe the places of the planets with the instruments in
our observatories; these places are measured by the help of our clocks
and of the graduated circles on the instruments. These observations are
no doubt wonderfully accurate; but they do not, they cannot, possess
absolute accuracy in the mathematical sense of the word. We can, for
instance, determine the place of a planet with such precision that it
is certainly not one second of arc wrong; and one second is an extremely
small quantity. A foot-rule placed at a distance of about forty miles
subtends an angle of a second, and it is surely a delicate achievement
to measure the place of a planet, and feel confident that no error
greater than this can have intruded into our result.
When we compare the results of observation with the calculations
conducted on the assumption of the truth of Kepler's laws, and when we
pronounce on the agreement of the observations with the calculations,
there is always a reference, more or less explicit, to the inevitable
errors of the observations. If the calculations and observations agree
so closely that the differences between the two are minute enough to
have arisen in the errors inseparable from the observations, then we are
satisfied with the accordance; for, in fact, no closer agreement is
attainable, or even conceivable. The influence which the want of
rigidity exercises on the fulfilment of the laws of Kepler can be
estimated by calculation; it is found, as might be expected, to be
extremely small--so small, in fact, as to be contained within that
slender margin of error by which observations are liable to be affected.
We are thus not able to discriminate by actual measurement the effects
due to the absence of rigidity; they are inextricably hid among the
small errors of observation.
The argument on which we are to base our researches is really founded on
a very familiar phenomenon. There is no one who has ever visited the
sea-side who is not familiar with that rise and fall of the sea which we
call the tide. Twice every twenty-four hours the sea advances on the
beach to produce high tide; twice every day the sea again retreats to
produce low tide. These tides are not merely confined to the coasts;
they penetrate for miles up the courses of rivers; they periodically
inundate great estuaries. In a maritime country the tides are of the
most profound practical importance; they also possess a significance of
a far less obvious character, which it is our object now to investigate.
These daily pulses of the ocean have long ceased to be a mystery. It
was in the earliest times perceived that there was a connection between
the tides and the moon. Ancient writers, such as Pliny and Aristotle,
have referred to the alliance between the times of high water and the
age of the moon. I think we sometimes do not give the ancient
astronomers as much credit as their shrewdness really entitles them to.
We have all read--we have all been taught--that the moon and the tides
are connected together; but how many of us are in a position to say that
we have actually noticed that connection by direct personal observation?
The first man who studied this matter with sufficient attention to
convince himself and to convince others of its reality must have been a
great philosopher. We know not his name, we know not his nation, we know
not the age in which he lived; but our admiration of his discovery must
be increased by the reflection that he had not the theory of gravitation
to guide him. A philosopher of the present day who had never seen the
sea could still predict the necessity of tides as a consequence of the
law of universal gravitation; but the primitive astronomer, who knew not
of the invisible bond by which all bodies in the universe are drawn
together, made a splendid--indeed, a typical--inductive discovery, when
he ascertained the relation between the moon and the tides.
We can surmise that this discovery, in all probability, first arose from
the observations of experienced navigators. In all matters of entering
port or of leaving port, the state of the tide is of the utmost concern
to the sailor. Even in the open sea he has sometimes to shape his course
in accordance with the currents produced by the tides; or, in guiding
his course by taking soundings, he has always to bear in mind that the
depth varies with the tide. All matters relating to the tide would thus
come under his daily observation. His daily work, the success of his
occupation, the security of his life, depend often on the tides; and
hence he would be solicitous to learn from his observation all that
would be useful to him in the future. To the coasting sailor the
question of the day is the time of high water. That time varies from
day to day; it is an hour or more later to-morrow than to-day, and there
is no very simple rule which can be enunciated. The sailor would
therefore welcome gladly any rule which would guide him in a matter of
such importance. We can make a conjecture as to the manner in which such
a rule was first discovered. Let us suppose that a sailor at Calais, for
example, is making for harbour. He has a beautiful night--the moon is
full; it guides him on his way; he gets safely into harbour; and the
next morning he finds the tide high between 11 and 12.[45] He often
repeats the same voyage, but he finds sometimes a low and inconvenient
tide in the morning. At length, however, it occurs to him that _when he
has a moonlight night_ he has a high tide at 11. This occurs once or
twice: he thinks it but a chance coincidence. It occurs again and again.
At length he finds it always occurs. He tells the rule to other sailors;
they try it too. It is invariably found that when the moon is full, the
high tide always recurs at the same hour at the same place. The
connection between the moon and the tide is thus established, and the
intelligent sailor will naturally compare other phases of the moon with
the times of high water. He finds, for example, that the moon at the
first quarter always gives high water at the same hour of the day; and
finally, he obtains a practical rule, by which, from the state of the
moon, he can at once tell the time when the tide will be high at the
port where his occupation lies. A diligent observer will trace a still
further connection between the moon and the tides; he will observe that
some high tides rise higher than others, that some low tides fall lower
than others. This is a matter of much practical importance. When a
dangerous bar has to be crossed, the sailor will feel much additional
security in knowing that he is carried over it on the top of a spring
tide; or if he has to contend against tidal currents, which in some
places have enormous force, he will naturally prefer for his voyage the
neap tides, in which the strength of these currents is less than usual.
The spring tides and the neap tides will become familiar to him, and he
will perceive that the spring tides occur when the moon is full or
new--or, at all events, that the spring tides are within a certain
constant number of days of the full or new moon. It was, no doubt, by
reasoning such as this, that in primitive times the connection between
the moon and the tides came to be perceived.
It was not, however, until the great discovery of Newton had disclosed
the law of universal gravitation that it became possible to give a
physical explanation of the tides. It was then seen how the moon
attracts the whole earth and every particle of the earth. It was seen
how the fluid particles which form the oceans on the earth were enabled
to obey the attraction in a way that the solid parts could not. When the
moon is overhead it tends to draw the water up, as it were, into a heap
underneath, and thus to give rise to the high tide. The water on the
opposite side of the earth is also affected in a way that might not be
at first anticipated. The moon attracts the solid body of the earth with
greater intensity than it attracts the water at the other side which
lies more distant from it. The earth is thus drawn away from the water,
and there is therefore a tendency to a high tide as well on the side of
the earth away from the moon as on that towards the moon. The low tides
occupy the intermediate positions.
The sun also excites tides on the earth; but owing to the great distance
of the sun, the difference between its attraction on the sea and on the
solid interior of the earth is not so appreciable. The solar tides are
thus smaller than the lunar tides. When the two conspire, they cause a
spring tide; when the solar and lunar tides are opposed, we have the
neap tide.
There are, however, a multitude of circumstances to be taken into
account when we attempt to apply this general reasoning to the
conditions of a particular case. Owing to local peculiarities the tides
vary enormously at the different parts of the coast. In a confined area
like the Mediterranean Sea, the tides have only a comparatively small
range, varying at different places from one foot to a few feet. In
mid-ocean also the tidal rise and fall is not large, amounting, for
instance, to a range of three feet at St. Helena. Near the great
continental masses the tides become very much modified by the coasts. We
find at London a tide of eighteen or nineteen feet; but the most
remarkable tides in the British Islands are those in the Bristol
Channel, where, at Chepstow or Cardiff, there is a rise and fall during
spring tides to the height of thirty-seven or thirty-eight feet, and at
neap tides to a height of twenty-eight or twenty-nine. These tides are
surpassed in magnitude at other parts of the world. The greatest of all
tides are those in the Bay of Fundy, at some parts of which the rise and
fall at spring tides is not less than fifty feet.
The rising and falling of the tide is necessarily attended with the
formation of currents. Such currents are, indeed, well known, and in
some of our great rivers they are of the utmost consequence. These
currents of water can, like water-streams of any other kind, be made to
do useful work. We can, for instance, impound the rising water in a
reservoir, and as the tide falls we can compel the enclosed water to
work a water-wheel before it returns to the sea. We have, indeed, here a
source of actual power; but it is only in very unusual circumstances
that it is found to be economical to use the tides for this purpose. The
question can be submitted to calculation, and the area of the reservoir
can be computed which would retain sufficient water to work a
water-wheel of given horse-power. It can be shown that the area of the
reservoir necessary to impound water enough to produce 100 horse-power
would be 40 acres. The whole question is then reduced to the simple one
of expense: would the construction and the maintenance of this reservoir
be more or less costly than the erection and the maintenance of a
steam-engine of equivalent power? In most cases it would seem that the
latter would be by far the cheaper; at all events, we do not practically
find tidal engines in use, so that the power of the tides is now running
to waste. The economical aspects of the case may, however, be very
profoundly altered at some remote epoch, when our stores of fuel, now
so lavishly expended, give appreciable signs of approaching exhaustion.
The tides are, however, _doing work_ of one kind or another. A tide in a
river estuary will sometimes scour away a bank and carry its materials
elsewhere. We have here work done and energy consumed, just as much as
if the same task had been accomplished by engineers directing the
powerful arms of navvies. We know that work cannot be done without the
consumption of energy in some of its forms; whence, then, comes the
energy which supplies the power of the tides? At a first glance the
answer to this question seems a very obvious one. Have we not said that
the tides are caused by the moon? and must not the energy, therefore, be
derived from the moon? This seems plain enough, but, unfortunately, it
is not true. It is one of those cases by no means infrequent in
Dynamics, where the truth is widely different from that which seems to
be the case. An illustration will perhaps make the matter clearer. When
a rifle is fired, it is the finger of the rifleman that pulls the
trigger; but are we, then, to say that the energy by which the bullet
has been driven off has been supplied by the rifleman? Certainly not;
the energy is, of course, due to the gunpowder, and all the rifleman did
was to provide the means by which the energy stored up in the powder
could be liberated. To a certain extent we may compare this with the
tidal problem; the tides raised by the moon are the originating cause
whereby a certain store of energy is drawn upon and applied to do such
work as the tides are competent to perform. This store of energy,
strange to say, does not lie in the moon; it is in the earth itself.
Indeed, it is extremely remarkable that the moon actually gains energy
from the tides by itself absorbing some of the store which exists in the
earth. This is not put forward as an obvious result; it depends upon a
refined dynamical theorem.
We must clearly understand the nature of this mighty store of energy
from which the tides draw their power, and on which the moon is
permitted to make large and incessant drafts. Let us see in what sense
the earth is said to possess a store of energy. We know that the earth
rotates on its axis once every day. It is this rotation which is the
source of the energy. Let us compare the rotation of the earth with the
rotation of the fly-wheel belonging to a steam-engine. The rotation of
the fly-wheel is really a reservoir, into which the engine pours energy
at each stroke of the piston. The various machines in the mill worked by
the engine merely draw upon the store of energy accumulated in the
fly-wheel. The earth may be likened to a gigantic fly-wheel detached
from the engine, though still connected with the machines in the mill.
From its stupendous dimensions and from its rapid velocity, that great
fly-wheel possesses an enormous store of energy, which must be expended
before the fly-wheel comes to rest. Hence it is that, though the tides
are caused by the moon, yet the energy they require is obtained by
simply appropriating some of the vast supply available from the rotation
of the earth.
There is, however, a distinction of a very fundamental character between
the earth and the fly-wheel of an engine. As the energy is withdrawn
from the fly-wheel and consumed by the various machines in the mill, it
is continually replaced by fresh energy, which flows in from the
exertions of the steam-engine, and thus the velocity of the fly-wheel is
maintained. But the earth is a fly-wheel without the engine. When the
tides draw upon the store of energy and expend it in doing work, that
energy is not replaced. The consequence is irresistible: the energy in
the rotation of the earth must be decreasing. This leads to a
consequence of the utmost significance. If the engine be cut off from
the fly-wheel, then, as everyone knows, the massive fly-wheel may still
give a few rotations, but it will speedily come to rest. A similar
inference must be made with regard to the earth; but its store of energy
is so enormous, in comparison with the demands which are made upon it,
that the earth is able to hold out. Ages of countless duration must
elapse before the energy of the earth's rotation can be completely
exhausted by such drafts as the tides are capable of making.
Nevertheless, it is necessarily true that the energy is decreasing; and
if it be decreasing, then the speed of the earth's rotation must be
surely, if slowly, abating. Now we have arrived at a consequence of the
tides which admits of being stated in the simplest language. If the
speed of rotation be abating, then the length of the day must be
increasing; and hence we are conducted to the following most important
statement: that the _tides are increasing the length of the day_.
To-day is longer than yesterday--to-morrow will be longer than to-day.
The difference is so small that even in the course of ages it can hardly
be said to have been distinctly established by observation. We do not
pretend to say how many centuries have elapsed since the day was even
one second shorter than it is at present; but centuries are not the
units which we employ in tidal evolution. A million years ago it is
quite probable that the divergence of the length of the day from its
present value may have been very considerable. Let us take a glance back
into the profound depths of times past, and see what the tides have to
tell us. If the present order of things has lasted, the day must have
been shorter and shorter the farther we look back into the dim past. The
day is now twenty-four hours; it was once twenty hours, once ten hours;
it was once six hours. How much farther can we go? Once the six hours is
past, we begin to approach a limit which must at some point bound our
retrospect. The shorter the day the more is the earth bulged at the
equator; the more the earth is bulged at the equator the greater is the
strain put upon the materials of the earth by the centrifugal force of
its rotation. If the earth were to go too fast it would be unable to
cohere together; it would separate into pieces, just as a grindstone
driven too rapidly is rent asunder with violence. Here, therefore, we
discern in the remote past a barrier which stops the present argument.
There is a certain critical velocity which is the greatest that the
earth could bear without risk of rupture, but the exact amount of that
velocity is a question not very easy to answer. It depends upon the
nature of the materials of the earth; it depends upon the temperature;
it depends upon the effect of pressure, and on other details not
accurately known to us. An estimate of the critical velocity has,
however, been made, and it has been shown mathematically that the
shortest period of rotation which the earth could have, without flying
into pieces, is about three or four hours. The doctrine of tidal
evolution has thus conducted us to the conclusion that, at some
inconceivably remote epoch, the earth was spinning round its axis in a
period approximating to three or four hours.
We thus learn that we are indebted to the moon for the gradual
elongation of the day from its primitive value up to twenty-four hours.
In obedience to one of the most profound laws of nature, the earth has
reacted on the moon, and the reaction of the earth has taken a tangible
form. It has simply consisted in gradually driving the moon away from
the earth. You may observe that this driving away of the moon resembles
a piece of retaliation on the part of the earth. The consequence of the
retreat of the moon is sufficiently remarkable. The path in which the
moon is revolving has at the present time a radius of 240,000 miles.
This radius must be constantly growing larger, in consequence of the
tides. Provided with this fact, let us now glance back into the past
history of the moon. As the moon's distance is increasing when we look
forwards, so we find it decreasing when we look backwards. The moon must
have been nearer the earth yesterday than it is to-day; the difference
is no doubt inappreciable in years, in centuries, or in thousands of
years; but when we come to millions of years, the moon must have been
significantly closer than it is at present, until at length we find that
its distance, instead of 240,000 miles, has dwindled down to 40,000, to
20,000, to 10,000 miles. Nor need we stop--nor can we stop--until we
find the moon actually close to the earth's surface. If the present laws
of nature have operated long enough, and if there has been no external
interference, then it cannot be doubted that the moon and the earth were
once in immediate proximity. We can, indeed, calculate the period in
which the moon must have been revolving round the earth. The nearer the
moon is to the earth the quicker it must revolve; and at the critical
epoch when the satellite was in immediate proximity to our earth it
must have completed each revolution in about three or four hours.
This has led to one of the most daring speculations which has ever been
made in astronomy. We cannot refrain from enunciating it; but it must be
remembered that it is only a speculation, and to be received with
corresponding reserve. The speculation is intended to answer the
question, What brought the moon into that position, close to the surface
of the earth? We will only say that there is the gravest reason to
believe that the moon was, at some very early period, fractured off from
the earth when the earth was in a soft or plastic condition.
At the beginning of the history we found the earth and the moon close
together. We found that the rate of rotation of the earth was only a few
hours, instead of twenty-four hours. We found that the moon completed
its journey round the primitive earth in exactly the same time as the
primitive earth rotated on its axis, so that the two bodies were then
constantly face to face. Such a state of things formed what a
mathematician would describe as a case of unstable dynamical
equilibrium. It could not last. It may be compared to the case of a
needle balanced on its point; the needle must fall to one side or the
other. In the same way, the moon could not continue to preserve this
position. There were two courses open: the moon must either have fallen
back on the earth, and been reabsorbed into the mass of the earth, or it
must have commenced its outward journey. Which of these courses was the
moon to adopt? We have no means, perhaps, of knowing exactly what it was
which determined the moon to one course rather than to another, but as
to the course which was actually taken there can be no doubt. The fact
that the moon exists shows that it did not return to the earth, but
commenced its outward journey. As the moon recedes from the earth it
must, in conformity with Kepler's laws, require a longer time to
complete its revolution. It has thus happened that, from the original
period of only a few hours, the duration has increased until it has
reached the present number of 656 hours. The rotation of the earth has,
of course, also been modified, in accordance with the retreat of the
moon. Once the moon had commenced to recede, the earth was released from
the obligation which required it constantly to direct the same face to
the moon. When the moon had receded to a certain distance, the earth
would complete the rotation in less time than that required by the moon
for one revolution. Still the moon gets further and further away, and
the duration of the revolution increases to a corresponding extent,
until three, four, or more days (or rotations of the earth) are
identical with the month (or revolution of the moon). Although the
number of days in the month increases, yet we are not to suppose that
the rate of the earth's rotation is increasing; indeed, the contrary is
the fact. The earth's rotation is getting slower, and so is the
revolution of the moon, but the retardation of the moon is greater than
that of the earth. Even though the period of rotation of the earth has
greatly increased from its primitive value, yet the period of the moon
has increased still more, so that it is several times as large as that
of the rotation of the earth. As ages roll on the moon recedes further
and further, its orbit increases, the duration of the revolution
augments, until at length a very noticeable epoch is attained, which is,
in one sense, a culminating point in the career of the moon. At this
epoch the revolution periods of the moon, when measured in rotation
periods of the earth, attain their greatest value. It would seem that
the month was then twenty-nine days. It is not, of course, meant that
the month and the day at that epoch were the month and the day as our
clocks now measure time. Both were shorter then than now. But what we
mean is, that at this epoch the earth rotated twenty-nine times on its
axis while the moon completed one circuit.
This epoch has now been passed. No attempt can be made at present to
evaluate the date of that epoch in our ordinary units of measurement. At
the same time, however, no doubt can be entertained as to the
immeasurable antiquity of the event, in comparison with all historic
records; but whether it is to be reckoned in hundreds of thousands of
years, in millions of years, or in tens of millions of years, must be
left in great degree to conjecture.
This remarkable epoch once passed, we find that the course of events in
the earth-moon system begins to shape itself towards that remarkable
final stage which has points of resemblance to the initial stage. The
moon still continues to revolve in an orbit with a diameter steadily,
though very slowly, growing. The length of the month is accordingly
increasing, and the rotation of the earth being still constantly
retarded, the length of the day is also continually growing. But the
ratio of the length of the month to the length of the day now exhibits a
change. That ratio had gradually increased, from unity at the
commencement, up to the maximum value of somewhere about twenty-nine at
the epoch just referred to. The ratio now begins again to decline, until
we find the earth makes only twenty-eight rotations, instead of
twenty-nine, in one revolution of the moon. The decrease in the ratio
continues until the number twenty-seven expresses the days in the month.
Here, again, we have an epoch which it is impossible for us to pass
without special comment. In all that has hitherto been said we have been
dealing with events in the distant past; and we have at length arrived
at the present state of the earth-moon system. The days at this epoch
are our well-known days, the month is the well-known period of the
revolution of our moon. At the present time the month is about
twenty-seven of our days, and this relation has remained sensibly true
for thousands of years past. It will continue to remain sensibly true
for thousands of years to come, but it will not remain true
indefinitely. It is merely a stage in this grand transformation; it may
possess the attributes of permanence to our ephemeral view, just as the
wings of a gnat seem at rest when illuminated by the electric spark; but
when we contemplate the history with time conceptions sufficiently ample
for astronomy we realise how the present condition of the earth-moon
system can have no greater permanence than any other stage in the
history.
Our narrative must, however, now assume a different form. We have been
speaking of the past; we have been conducted to the present; can we say
anything of the future? Here, again, the tides come to our assistance.
If we have rightly comprehended the truth of dynamics (and who is there
now that can doubt them?), we shall be enabled to make a forecast of the
further changes of the earth-moon system. If there be no interruption
from any external source at present unknown to us, we can predict--in
outline, at all events--the subsequent career of the moon. We can see
how the moon will still follow its outward course. The path in which it
revolves will grow with extreme slowness, but yet it will always grow;
the progress will not be reversed, at all events, before the final stage
of our history has been attained. We shall not now delay to dwell on the
intervening stages; we will rather attempt to sketch the ultimate type
to which our system tends. In the dim future--countless millions of
years to come--this final stage will be approached. The ratio of the
month to the day, whose decline we have already referred to, will
continue to decline. The period of revolution of the moon will grow
longer and longer, but the length of the day will increase much more
rapidly than the increase in the duration of the moon's period. From the
month of twenty-seven days we shall pass to a month of twenty-six days,
and so on, until we shall reach a month of ten days, and, finally, a
month of one day.
Let us clearly understand what we mean by a month of one day. We mean
that the time in which the moon revolves around the earth will be equal
to the time in which the earth rotates around its axis. The length of
this day will, of course, be vastly greater than our day. The only
element of uncertainty in these enquiries arises when we attempt to give
numerical accuracy to the statements. It seems to be as true as the laws
of dynamics that a state of the earth-moon system in which the day and
the month are equal must be ultimately attained; but when we attempt to
state the length of that day we introduce a hazardous element into the
enquiry. In giving any estimate of its length, it must be understood
that the magnitude is stated with great reserve. It may be erroneous to
some extent, though, perhaps, not to any considerable amount. The length
of this great day would seem to be about equal to fifty-seven of our
days. In other words, at some critical time in the excessively distant
future, the earth will take something like 1,400 hours to perform a
rotation, while the moon will complete its journey precisely in the same
time.
We thus see how, in some respects, the first stage of the earth-moon
system and the last stage resemble each other. In each case we have the
day equal to the month. In the first case the day and the month were
only a small fraction of our day; in the last stage the day and the
month are each a large multiple of our day. There is, however, a
profound contrast between the first critical epoch and the last. We have
already mentioned that the first epoch was one of unstability--it could
not last; but this second state is one of dynamical stability. Once that
state has been acquired, it would be permanent, and would endure for
ever if the earth and the moon could be isolated from all external
interference.
There is one special feature which characterises the movement when the
month is equal to the day. A little reflection will show that when this
is the case the earth must constantly direct the same face towards the
moon. If the day be equal to the month, then the earth and moon must
revolve together, as if bound by invisible bands; and whatever
hemisphere of the earth be directed to the moon when this state of
things commences will remain there so long as the day remains equal to
the month.
At this point it is hardly possible to escape being reminded of that
characteristic feature of the moon's motion which has been observed from
all antiquity. We refer, of course, to the fact that the moon at the
present time constantly turns the same face to the earth.
It is incumbent upon astronomers to provide a physical explanation of
this remarkable fact. The moon revolves around our earth once in a
definite number of seconds. If the moon always turns the same face to
the earth, then it is demonstrated that the moon rotates on its axis
once in the same number of seconds also. Now, this would be a
coincidence wildly improbable unless there were some physical cause to
account for it. We have not far to seek for a cause: the tides on the
moon have produced the phenomenon. We now find the moon has a rugged
surface, which testifies to the existence of intense volcanic activity
in former times. Those volcanoes are now silent--the internal fires in
the moon seem to have become exhausted; but there was a time when the
moon must have been a heated and semi-molten mass. There was a time when
the materials of the moon were so hot as to be soft and yielding, and in
that soft and yielding mass the attraction of our earth excited great
tides. We have no historical record of these tides (they were long
anterior to the existence of telescopes, they were probably long
anterior to the existence of the human race), but we know that these
tides once existed by the work they have accomplished, and that work is
seen to-day in the constant face which the moon turns towards the earth.
The gentle rise and fall of the oceans which form our tides present a
picture widely different from the tides by which the moon was once
agitated. The tides on the moon were vastly greater than those of the
earth. They were greater because the weight of the earth is greater than
that of the moon, so that the earth was able to produce much more
powerful tides in the moon than the moon has ever been able to raise on
the earth.
That the moon should bend the same face to the earth depends immediately
upon the condition that the moon shall rotate on its axis in precisely
the same period as that which it requires to revolve around the earth.
The tides are a regulating power of unremitting efficiency to ensure
that this condition shall be observed. If the moon rotated more slowly
than it ought, then the great lava tides would drag the moon round
faster and faster until it attained the desired velocity; and then, but
not till then, they would give the moon peace. Or if the moon were to
rotate faster on its axis than in its orbit, again the tides would come
furiously into play; but this time they would be engaged in retarding
the moon's rotation, until they had reduced the speed of the moon to one
rotation for each revolution.
Can the moon ever escape from the thraldom of the tides? This is not
very easy to answer, but it seems perhaps not impossible that the moon
may, at some future time, be freed from tidal control. It is, indeed,
obvious that the tides, even at present, have not the extremely
stringent control over the moon which they once exercised. We now see no
ocean on the moon, nor do the volcanoes show any trace of molten lava.
There can hardly be tides _on_ the moon, but there may be tides _in_ the
moon. It may be that the interior of the moon is still hot enough to
retain an appreciable degree of fluidity, and if so, the tidal control
would still retain the moon in its grip; but the time will probably
come, if it have not come already, when the moon will be cold to the
centre--cold as the temperature of space. If the materials of the moon
were what a mathematician would call absolutely rigid, there can be no
doubt that the tides could no longer exist, and the moon would be
emancipated from tidal control. It seems impossible to predicate how far
the moon can ever conform to the circumstances of an actual rigid body,
but it may be conceivable that at some future time the tidal control
shall have practically ceased. There would then be no longer any
necessary identity between the period of rotation and that of
revolution. A gleam of hope is thus projected over the astronomy of the
distant future. We know that the time of revolution of the moon is
increasing, and so long as the tidal governor could act, the time of
rotation must increase sympathetically. We have now surmised a state of
things in which the control is absent. There will then be nothing to
prevent the rotation remaining as at present, while the period of
revolution is increasing. The privilege of seeing the other side of the
moon, which has been withheld from all previous astronomers, may thus in
the distant future be granted to their successors.
The tides which the moon raises in the earth act as a brake on the
rotation of the earth. They now constantly tend to bring the period of
rotation of the earth to coincide with the period of revolution of the
moon. As the moon revolves once in twenty-seven days, the earth is at
present going too fast, and consequently the tidal control at the
present moment endeavours to retard the rotation of the earth. The
rotation of the moon long since succumbed to tidal control, but that was
because the moon was comparatively small and the tidal power of the
earth was enormous. But this is the opposite case. The earth is large
and more massive than the moon, the tides raised by the moon are but
small and weak, and the earth has not yet completely succumbed to the
tidal action. But the tides are constant, they never for an instant
relax the effort to control, and they are gradually tending to render
the day and the month coincident, though the progress is a very slow
one.
The theory of the tides leads us to look forward to a remote state of
things, in which the moon revolves around the earth in a period equal to
the day, so that the two bodies shall constantly bend the same face to
each other, provided the tidal control be still able to guide the moon's
rotation. So far as the mutual action of the earth and the moon is
concerned, such an arrangement possesses all the attributes of
permanence. If, however, we venture to project our view to a still more
remote future, we can discern an external cause which must prevent this
mutual accommodation between the earth and the moon from being eternal.
The tides raised by the moon on the earth are so much greater than those
raised by the sun, that we have, in the course of our previous
reasoning, held little account of the sun-raised tides. This is
obviously only an approximate method of dealing with the question. The
influence of the solar tide is appreciable, and its importance
relatively to the lunar tide will gradually increase as the earth and
moon approach the final critical stage. The solar tides will have the
effect of constantly applying a further brake to the rotation of the
earth. It will therefore follow that, after the day and the month have
become equal, a still further retardation awaits the length of the day.
We thus see that in the remote future we shall find the moon revolving
around the earth in a shorter time than that in which the earth rotates
on its axis.
A most instructive corroboration of these views is afforded by the
discovery of the satellites of Mars. The planet Mars is one of the
smaller members of our system. It has a mass which is only the eighth
part of the mass of the earth. A small planet like Mars has much less
energy of rotation to be destroyed than a larger one like the earth. It
may therefore be expected that the small planet will proceed much more
rapidly in its evolution than the large one; we might, therefore,
anticipate that Mars and his satellites have attained a more advanced
stage of their history than is the case with the earth and her
satellite.
When the discovery of the satellites of Mars startled the world, in
1877, there was no feature which created so much amazement as the
periodic time of the interior satellite. We have already pointed out in
Chapter X. how Phobos revolves around Mars in a period of 7 hours 39
minutes. The period of rotation of Mars himself is 24 hours 37 minutes,
and hence we have the fact, unparalleled in the solar system, that the
satellite is actually revolving three times as rapidly as the planet is
rotating. There can hardly be a doubt that the solar tides on Mars have
abated its velocity of rotation in the manner just suggested.
It has always seemed to me that the matter just referred to is one of
the most interesting and instructive in the whole history of astronomy.
We have, first, a very beautiful telescopic discovery of the minute
satellites of Mars, and we have a determination of the anomalous
movement of one of them. We have then found a satisfactory physical
explanation of the cause of this phenomenon, and we have shown it to be
a striking instance of tidal evolution. Finally, we have seen that the
system of Mars and his satellite is really a forecast of the destiny
which, after the lapse of ages, awaits the earth-moon system.
It seems natural to enquire how far the influence of tides can have
contributed towards moulding the planetary orbits. The circumstances are
here very different from those we have encountered in the earth-moon
system. Let us first enunciate the problem in a definite shape. The
solar system consists of the sun in the centre, and of the planets
revolving around the sun. These planets rotate on their axes; and
circulating round some of the planets we have their systems of
satellites. For simplicity, we may suppose all the planets and their
satellites to revolve in the same plane, and the planets to rotate about
axes which are perpendicular to that plane. In the study of the theory
of tidal evolution we must be mainly guided by a profound dynamical
principle known as the conservation of the "moment of momentum." The
proof of this great principle is not here attempted; suffice it to say
that it can be strictly deduced from the laws of motion, and is thus
only second in certainty to the fundamental truths of ordinary geometry
or of algebra. Take, for instance, the giant planet, Jupiter. In one
second he moves around the sun through a certain angle. If we multiply
the mass of Jupiter by that angle, and if we then multiply the product
by the square of the distance from Jupiter to the sun, we obtain a
certain definite amount. A mathematician calls this quantity the
"orbital" moment of momentum of Jupiter.[46] In the same way, if we
multiply the mass of Saturn by the angle through which the planet moves
in one second, and this product by the square of the distance between
the planet and the sun, then we have the orbital moment of momentum of
Saturn. In a similar manner we ascertain the moment of momentum for each
of the other planets due to revolution around the sun. We have also to
define the moment of momentum of the planets around their axes. In one
second Jupiter rotates through a certain angle; we multiply that angle
by the mass of Jupiter, and by the square of a certain line which
depends on his internal constitution: the product forms the "rotational"
moment of momentum. In a similar manner we find the rotational moment of
momentum for each of the other planets. Each satellite revolves through
a certain angle around its primary in one second; we obtain the moment
of momentum of each satellite by multiplying its mass into the angle
described in one second, and then multiplying the product into the
square of the distance of the satellite from its primary. Finally, we
compute the moment of momentum of the sun due to its rotation. This we
obtain by multiplying the angle through which the sun turns in one
second by the whole mass of the sun, and then multiplying the product by
the square of a certain line of prodigious length, which depends upon
the details of the sun's internal structure.
If we have succeeded in explaining what is meant by the moment of
momentum, then the statement of the great law is comparatively simple.
We are, in the first place, to observe that the moment of momentum of
any planet may alter. It would alter if the distance of the planet from
the sun changed, or if the velocity with which the planet rotates upon
its axis changed; so, too, the moment of momentum of the sun may change,
and so may those of the satellites. In the beginning a certain total
quantity of moment of momentum was communicated to our system, and not
one particle of that total can the solar system, as a whole, squander or
alienate. No matter what be the mutual actions of the various bodies of
the system, no matter what perturbations they may undergo--what tides
may be produced, or even what mutual collisions may occur--the great law
of the conservation of moment of momentum must be obeyed. If some bodies
in the solar system be losing moment of momentum, then other bodies in
the system must be gaining, so that the total quantity shall remain
unaltered. This consideration is one of supreme importance in connection
with the tides. The distribution of moment of momentum in the system is
being continually altered by the tides; but, however the tides may ebb
or flow, the total moment of momentum can never alter so long as
influences external to the system are absent.
We must here point out the contrast between the endowment of our system
with energy and with moment of momentum. The mutual actions of our
system, in so far as they produce heat, tend to squander the energy, a
considerable part of which can be thus dissipated and lost; but the
mutual actions have no power of dissipating the moment of momentum.
The total moment of momentum of the solar system being taken to be 100,
this is at present distributed as follows:--
Orbital moment of momentum of Jupiter 60
Orbital moment of momentum of Saturn 24
Orbital moment of momentum of Uranus 6
Orbital moment of momentum of Neptune 8
Rotational moment of momentum of Sun 2
--
100
The contributions of the other items are excessively minute. The orbital
moments of momentum of the few interior planets contain but little more
than one thousandth part of the total amount. The rotational
contributions of all the planets and of their satellites is very much
less, being not more than one sixty-thousandth part of the whole. When,
therefore, we are studying the general effects of tides on the planetary
orbits these trifling matters may be overlooked. We shall, however, find
it desirable to narrow the question still more, and concentrate our
attention on one splendid illustration. Let us take the sun and the
planet Jupiter, and, supposing all other bodies of our system to be
absent, let us discuss the influence of tides produced in Jupiter by the
sun, and of tides in the sun by Jupiter.
It might be hastily thought that, just as the moon was born of the
earth, so the planets were born of the sun, and have gradually receded
by tides into their present condition. We have the means of enquiry
into this question by the figures just given, and we shall show that it
is impossible that Jupiter, or any of the other planets, can ever have
been very much closer to the sun than they are at present. In the case
of Jupiter and the sun we have the moment of momentum made up of three
items. By far the largest of these items is due to the orbital
revolution of Jupiter, the next is due to the sun, the third is due to
the rotation of Jupiter on its axis. We may put them in round numbers as
follows:--
Orbital moment of momentum of Jupiter 600,000
Rotational moment of momentum of Sun 20,000
Rotational moment of momentum of Jupiter 12
The sun produces tides in Jupiter, those tides retard the rotation of
Jupiter. They make Jupiter rotate more and more slowly, therefore the
moment of momentum of Jupiter is decreasing, therefore its present value
of 12 must be decreasing. Even the mighty sun himself may be distracted
by tides. Jupiter raises tides in the sun, those tides retard the motion
of the sun, and therefore the moment of momentum of the sun is
decreasing, and it follows from both causes that the item of 600,000
must be increasing; in other words, the orbital motion of Jupiter must
be increasing, or Jupiter must be receding from the sun. To this extent,
therefore, the sun-Jupiter system is analogous to the earth-moon system.
As the tides on the earth are driving away the moon, so the tides in
Jupiter and the sun are gradually driving the two bodies apart. But
there is a profound difference between the two cases. It can be proved
that the tides produced in Jupiter by the sun are more effective than
those produced in the sun by Jupiter. The contribution of the sun may,
therefore, be at present omitted; so that, practically, the
augmentations of the orbital moment of momentum of Jupiter are now
achieved at the expense of that stored up by Jupiter's rotation. But
what is 12 compared with 600,000. Even when the whole of Jupiter's
rotational moment of momentum and that of his satellites has become
absorbed into the orbital motion, there will hardly be an appreciable
difference in the latter. In ancient days we may indeed suppose that
Jupiter being hotter was larger than at present, and that he had
considerably more rotational moment of momentum. But it is hardly
credible that Jupiter can ever have had one hundred times the moment of
momentum that he has at present. Yet even if 1,200 units of rotational
momentum had been transferred to the orbital motion it would only
correspond with the most trivial difference in the distance of Jupiter
from the sun. We are hence assured that the tides have not appreciably
altered the dimensions of the orbit of Jupiter, or of the other great
planets.
The time will, however, come when the rotation of Jupiter on his axis
will be gradually abated by the influence of the tides. It will then be
found that the moment of momentum of the sun's rotation will be
gradually expended in increasing the orbits of the planets, but as this
reserve only holds about two per cent. of the whole amount in our system
it cannot produce any considerable effect.
The theory of tidal evolution, which in the hands of Professor Darwin
has taught us so much with regard to the past history of the systems of
satellites in the solar system, will doubtless also, as pointed out by
Dr. See, be found to account for the highly eccentric orbits of double
star systems. In the earth-moon system we have two bodies exceedingly
different in bulk, the mass of the earth being about eighty times as
great as that of the moon. But in the case of most double stars we have
to do with two bodies not very different as regards mass. It can be
demonstrated that the orbit must have been originally of slight
eccentricity, but that tidal friction is capable not only of extending,
but also of elongating it. The accelerating force is vastly greater at
periastron (when the two bodies are nearest each other) than at apastron
(when their distance is greatest). At periastron the disturbing force
will, therefore, increase the apastron distance by an enormous amount,
while at apastron it increases the periastron distance by a very small
amount. Thus, while the ellipse is being gradually expanded, the orbit
grows more and more eccentric, until the axial rotations have been
sufficiently reduced by the transfer of axial to orbital moment of
momentum.
And now we must draw this chapter to a close, though there are many
other subjects that might be included. The theory of tidal evolution is,
indeed, one of quite exceptional interest. The earlier mathematicians
expended their labour on the determination of the dynamics of a system
which consisted of rigid bodies. We are indebted to contemporary
mathematicians for opening up celestial mechanics upon the more real
supposition that the bodies are not rigid; in other words, that they are
subject to tides. The mathematical difficulties are enormously enhanced,
but the problem is more true to nature, and has already led to some of
the most remarkable astronomical discoveries made in modern times.
* * * * *
Our Story of the Heavens has now been told. We commenced this work with
some account of the mechanical and optical aids to astronomy; we have
ended it with a brief description of an intellectual method of research
which reveals some of the celestial phenomena that occurred ages before
the human race existed. We have spoken of those objects which are
comparatively near to us, and then, step by step, we have advanced to
the distant nebulae and clusters which seem to lie on the confines of the
visible universe. Yet how little can we see with even our greatest
telescopes, when compared with the whole extent of infinite space! No
matter how vast may be the depth which our instruments have sounded,
there is yet a beyond of infinite extent. Imagine a mighty globe
described in space, a globe of such stupendous dimensions that it shall
include the sun and his system, all the stars and nebulae, and even all
the objects which our finite capacities can imagine. Yet, what ratio
must the volume of this great globe bear to the whole extent of infinite
space? The ratio is infinitely less than that which the water in a
single drop of dew bears to the water in the whole Atlantic Ocean.
APPENDIX.
ASTRONOMICAL QUANTITIES.
THE SUN.
The sun's mean distance from the earth is 92,900,000 miles; his diameter
is 866,000 miles; his mean density, as compared with water, is 1.4; his
ellipticity is insensible; he rotates on his axis in a period between 25
and 26 days.
THE MOON.
The moon's mean distance from the earth is 239,000 miles. The diameter
of the moon is 2,160 miles; and her mean density, as compared with
water, is 3.5. The time of a revolution around the earth is 27.322 days.
THE PLANETS.
___________________________________________________________________________
| |Distance from the Sun in | | Mean | |Density |
| | Millions of Miles. | Periodic |Diameter| Axial |compared|
| |-------------------------| Time | in | Rotation.| with |
| | Mean. | Least.|Greatest.| in Days. | Miles. | | Water. |
|-------+-------+-------+---------+----------+--------+----------+--------|
|Mercury| 36.0| 28.6| 43.3 | 87.969| 3,030 | (?) | 6.85(?)|
|Venus | 67.2| 66.6| 67.5 | 224.70 | 7,700 | (?) | 4.85 |
|Earth | 92.9| 91.1| 94.6 | 365.26 | 7,918 |23 56 4.09| 5.58 |
|Mars | 141 | 128 | 155 | 686.98 | 4,230 |24 37 22.7| 4.01 |
|Jupiter| 483 | 459 | 505 | 4,332.6 | 86,500 | 9 55 -- | 1.38 |
|Saturn | 886 | 834 | 936 |10,759 | 71,000 |10 14 -- | 0.72 |
|Uranus |1,782 |1,700 | 1,860 |30,687 | 31,900 | Unknown | 1.22 |
|Neptune|2,792 |2,760 | 2,810 |60,127 | 34,800 | Unknown | 1.11 |
---------------------------------------------------------------------------
THE SATELLITES OF MARS.
Mean Distance from Periodic Time.
Name. Centre of Mars. hrs. mins. secs.
Phobos 5,800 miles 7 39 14
Deimos 14,500 miles 30 17 54
THE SATELLITES OF JUPITER.
Mean Distance from Periodic Time.
Name. Centre of Jupiter. days. hrs. mins. secs.
New Inner
Satellite
Barnard 112,500 miles 0 11 57 22
I. 261,000 miles 1 18 27 34
II. 415,000 miles 3 13 13 42
III. 664,000 miles 7 3 42 33
IV. 1,167,000 miles 16 16 32 11
THE SATELLITES OF SATURN.
Mean Distance from Periodic Time.
Name. Centre of Saturn. days. hrs. mins. secs.
Mimas 115,000 miles 0 22 37 6
Enceladus 148,000 miles 1 8 53 7
Tethys 183,000 miles 1 21 18 26
Dione 235,000 miles 2 17 41 9
Rhea 329,000 miles 4 12 25 12
Titan 760,000 miles 15 22 41 27
Hyperion 921,000 miles 21 6 38 31
Iapetus 2,215,000 miles 79 7 56 40
THE SATELLITES OF URANUS.
Mean Distance from Periodic Time.
Name. Centre of Uranus. days. hrs. mins. secs.
Ariel 119,000 miles 2 12 29 21
Umbriel 166,000 miles 4 3 27 37
Titania 272,000 miles 8 16 56 30
Oberon 364,000 miles 13 11 7 6
THE SATELLITE OF NEPTUNE.
Mean Distance from Periodic Time.
Name. Centre of Neptune. days. hrs. mins. secs.
Satellite 220,000 miles 5 21 2 44
INDEX.
A
Aberration of light, 503-512;
and the apparent movements of stars, 504, 507;
Bradley's discoveries, 503;
causes, 507-511;
circles of stars, 505-507;
dependent upon the velocity of light, 511;
effect on Draco, 505;
telescopic investigation, 510
Achromatic combination of glasses, 11
Adams, Professor J.C., and the discovery of Neptune, 324-327, 330-332;
and the Ellipse of the Leonids, 386
Aerolite, the Chaco, 398;
the Orgueil, 399
Airy, Sir George, 325
Alban Mount Meteorites, the, 393
Alcor, 438
Aldebaran, 209, 418, 419;
spectrum of, 480;
value of velocity of, 484
Algol, 485, 487
Almagest, the, 7
Alphonsus, 92
Alps, the great valley of the (lunar), 88
Altair, 424
Aluminium in the Sun, 50
Ancients, astronomy of the, 2-7
Andrews, Professor, and basaltic formation at Giant's Causeway, 407
Andromeda, 414;
nebula in, 469, 489
Andromedes, The, shooting star shower, and Biela's comet, 390
Antares, 423
Apennines (lunar), 83
Aphelion, 163
Aquarius, 215, 413
Aquila, or the Eagle, 424
Arago, 326
Archimedes, 88
Arcturus, 358, 480;
value of velocity of, 484
Argelander's Catalogue of Stars, 431, 476
Argus, 481
Ariel, 309, 559
Aristarchus, 90
Aristillus, 88
Aristotle, lunar crater named after him, 88;
credulity respecting his writings, 267;
the Moon and the tides and, 535
Asteroids, 229-244
Astrea, 328
Astronomers of Nineveh, 156
Astronomical quantities, 558
Astronomy, ancient, 2-7;
Galileo's achievements in, 10;
the first phenomenon of, 2
_Athenaeum_, the, and Sir John Herschel's letter on Adams's share
in the discovery of Neptune, 330
Atmosphere, height of the Earth's, 100
Attraction, between the Moon and the Earth, 75;
between the planets, 148;
between the Sun and the planets, 144, 148;
of Jupiter, 248, 249;
producing precession, 498
Auriga, 414, 489
Aurora borealis, 42
Autolycus, 88
Auwers and star distances, 449;
and the irregularity in movement of Sirius, 427
Axis, Polar, 196, 497;
precession and nutation of the Earth's, 492-502
B
Backlund, and Encke's comet, 349, 351
Barnard, Professor E.E., and Saturn, 271, 278, 282;
and Titan, 294;
and the comet of 1892, 355;
and the Milky Way, 475
Beehive, the, 422
Belopolsky, M., and Binaries, 487, 488
Benares meteorite, the, 392
Bessel, and Bradley, 501;
and the distance of 61 Cygni, 446, 448, 449;
and the distances of stars, 442;
and the irregular movements of Sirius, 426;
receives gold medal of Royal Astronomical Society, 442
Betelgeuze, 209, 418, 419, 482;
value of velocity of, 484
Biela's comet, and Sir John
Herschel, 357;
and the Andromedes, 390
Binaries, spectroscopic, 487
Binocular glass, 27
Biot and the L'Aigle meteorites, 392
Bode's law, 230;
list of double stars, 435
Bond, Professor, and Saturn's satellites, 296;
and the nebula in Orion, 469;
and the third ring of Saturn, 280
Booetes, 422
Bradley, and nutation, 501;
and the aberration of light, 503;
his observations of Uranus, 312
Bredichin, Professor, and the tails of comets, 365, 366, 367
Breitenbach iron, the, 397
Bristol Channel, tides in the, 538
Bruennow, Dr., observations on the parallax of 61 Cygni, 449
_Burial of Sir John Moore_, 72
Burnham, Mr., and the orbit of Sirius, 427;
his additions to the known number of double stars, 439
Butler, Bishop, and probability, 460
Butsura meteorite, 397
C
Cadmium in the Sun, 50
Calais, tides at, 536
Calcium in the Sun, 50
Campbell, Mr., and Argus, 481;
and Mars, 223
Canals on Mars, 220
Cancri 20, 154
Cancri, z, 154
Cancri, th, 154
Canis major, 419
Canopus, 422
Cape Observatory, 27
Capella, 414, 480, 487
Carboniferous period, 518
Cardiff, tides at, 538
Cassini, J.D., and double stars, 434;
and Saturn's satellites, 294;
and the rings of Saturn, 278
Cassiopeia, 412
Castor, 420, 487;
a binary star, 437;
revolution of, 437
Catalogues of stars, 310, 311;
Messier's, 529
Catharina, 92
Centauri, a, 422;
Dr. Gill's observations of, 451;
Henderson's measurement of distance of, 442, 451
Ceres, 231, 232, 238;
and meteorites, 404, 405
Chaco meteorite, the, 398
Chacornac, and the lunar crater Schickard, 90
_Challenger_, the cruise of the, and magnetic particles in
the Atlantic, 408
Challis, Professor, 326;
his search for Neptune, 327, 328, 331, 332
Chandler, Mr., and Algol, 485
Charles's Wain, 28
Chepstow, tides at, 538
Cheseaux, discoverer of comet of 1744, 367
Chicago, telescope at Yerkes Observatory, 16
Chladni and the meteorite of Siberia, 392
Chromium in the Sun, 50
Chromosphere, the, 54
Chronometers tested by the Moon, 80
Clairaut and the attraction of planets on comets, 342, 343
Clavius, 91;
and Jupiter's satellites, 267
Clock, astronomical, 23
Clusters, star, 461-464
Cobalt in the Sun, 50
Coggia's comet, 1874, 337
Colour of light and indication of its source, 46
Colours, the seven primary, 45
Columbiad, the, 401
Columbus, 7
Comets, 112, 149, 250, 336;
and the spectroscope, 355;
attraction from planets, 342, 360;
Biela's, 357;
Biela's and the Andromedes, 390;
Clairaut's investigations, 342, 343;
Coggia's, 337;
Common's (1882), 354;
connection of, with shooting star showers, 388;
constitution of, 336;
containing sodium and iron, 356;
Donati's (1858), 353, 358, 366;
eccentricity of, 360;
Encke's, 344-352;
existence of carbon in, 356, 367;
gravitation and, 343, 348;
Halley's investigations about, 341-344;
head or nucleus of, 337;
Lexell's, 370;
mass of, 359;
movements of, 336;
Newton's explanations of, 338;
non-periodic, 353-356;
of 1531, 341;
of 1607, 341;
of 1681, 338, 339;
of 1682, 341;
of 1744 (Cheseaux's), 367;
of 1818, 345;
of 1843, 352;
of 1866, 388;
of 1874, 337;
of 1892, 355;
origin of, 369;
parabolic orbits of, 338-340, 360;
periodic return of, 338-341;
shape of, 336;
size of, 337;
tailless, 370;
tails of, 337, 361;
Bredichin's researches, 365;
Cheseaux's, 367;
composition of, 365, 369;
condensation of, 369;
electricity and, 368;
gradual growth of, 363;
law of direction of, 362;
repelled by the Sun, 364;
repulsive force of, 364, 368;
various types of, 365;
Tebbutt's (1881), 353;
tenuity of, 357
Common, Dr., constructor of reflectors, 21;
and the comet of 1882, 354;
and the nebula in Orion, 469
Cook, Captain, and the transit of Venus, 184
Copeland, Dr., and Schmidt's star, 489;
and the lunar crater, Tycho, 92;
and the spectra of nebula, 473;
and the transit of Venus, 189
Copernicus and Mercury, 156;
confirmation of his theory by the discovery of Jupiter's satellites, 267;
his theory of astronomy, 7;
lunar crater called after him, 89
Copper in the Sun, 50
Cor scorpionis, 423
Corona Borealis, 423, 488
Corona of Sun, during an eclipse, 62-64, 151
Coronium, 64
Cotopaxi and meteorites, 401
Crab, the, 422
Crabtree, and the transit of Venus, 180
Crape ring of Saturn, 281
Craters in the Moon, 83-85, 87-98
Critical velocity, 103, 104, 237
Crown, the, 423
Cryptograph of Huyghens, the, 277
Cygni, b, 439
Cygni 61, annual parallax of, 450;
Bessel's measurement of distance of, 442, 446, 447;
Bruennow's observations of, 449;
distance from the Sun of, 452;
disturbing influence of, 452;
double, 446;
Professor A. Hall's measurement of, 449;
Professor Pritchard's photographic researches concerning, 449;
proper motion of, 446;
Struve's observations of, 448, 449;
velocity of, 452
Cygnus, 424
Cyrillus, 92
Cysat, and the Belt of Orion, 467
D
D line in solar spectrum, 48
Darwin, Professor G.H., and tidal evolution, 531
Dawes, Professor, and Saturn's third ring, 281
Day, length of, and the Moon, 542;
and the tides, 541
Deimos, 226, 558
Denebola, 423
Diffraction, 56
Dione, 559
Dispersion of colours, 47
Distances, astronomical, 558, 559
Doerfel, and comets, 339
Dog star (_see_ Sirius)
Dog, the Little, 420
Donati's comet, 353, 358;
tails, 366
Double stars, 434-440
D Q, 236
Draco, nebula in, 470
Dragon, the, 415
Draper, Professor, and the nebula in Orion, 469
Dunsink Observatory, 12, 184, 447, 449
Dynamical stability, 547;
theory of Newton, 214
Dynamics and the Earth-Moon system, 546
Dynamics, Galileo the founder of, 10
E
Eagle, the, 424
Earth, The, ancient ideas respecting, 3;
annual movement of, and the apparent movement of the stars, 507, 512;
attraction of Jupiter, 319;
attraction of on Encke's comet, 350;
attraction of, on the Leonids, 386;
attraction of Saturn, 319;
attraction of the Moon, 75, 497;
attraction of the Sun, 496;
axial rotation of, 558;
carboniferous period on, 518;
change of climate on, 518;
composition of, 496;
contact of atmosphere of, with meteors, 377-379;
density of, 558;
diameter of, 558;
distance of, from Mars, 213;
distance of, from the Moon, 73, 558;
distance of, from the Sun, 31, 114, 184, 240, 265, 351, 512, 558;
energy from rotation of, 540;
formerly a molten globe, 200, 201;
geological records and, 517;
glacial period on, 518;
gravitation and, 204, 206, 207, 497;
heat in the interior of, 94, 197, 198, 251, 514;
how it is measured, 193-196;
its mass increasing owing to the fall of meteoric matter, 408;
its oceans once vapour, 251;
once in immediate proximity to the Moon, 542;
orbit of, 114;
orbit of, its elliptic form, 139;
path of deranged by Venus and Mars, 319;
periodic time of, 558;
plane of orbit of, 309;
polar axis of, 196, 492-502;
position of, relatively to the Sun and the Moon, 76, 77;
precession and nutation of axis of, 492-502;
radius of, 193, 512;
rotation of, 75, 196, 200, 494, 496;
shape of, 192, 195, 197, 201, 207;
size of, compared with Jupiter, 119,
and with other planets, 119;
size and weight of, compared with those of the Sun, 30,
and Moon, 74, 75;
velocity of, 115, 139, 146, 512,
and periodic time, 143;
volcanic outbreaks on, 197,
and the origin of meteorites, 405;
weight of, 202, 248,
as compared with Saturn, 271, 272
Earthquakes, astronomical instruments disturbed by, 24
Eccentricity of planetary ellipses, 136, 211
Eclipse of Jupiter's satellites, 261, 262, 265-267
Ellipse of the Moon, 77-80;
of the Sun, 53
Eclipses, ancient explanations of, 6;
calculations of the recurrence of, 79, 80
Ecliptic, the, 5, 233;
Pole of the, 493, 500, 505
Electric Light, the, 44
Ellipse, the, 136;
eccentricity of, 137;
focus of, 137;
Kepler's discoveries respecting, 136, 138, 142-144, 505;
the form which the orbit of a planet takes, 136;
the parallactic, 444;
variety of form of, 139
Enceladus, 559
Encke, and the distance of the Sun from the Earth, 147, 184;
his comet, 344-352
Encke's comet, 344-352;
approach to Jupiter of, 349;
and Mercury, 349;
and the Sun, 346;
diminution in periodic time of, 351;
distance from Mercury of, 347;
disturbed by the Earth, 350,
and by Mercury, 348;
irregularities of, 347, 351;
orbit of, 346;
periodical return of, 351;
Von Asten's calculations concerning, 349-350
Energy supplying the tides, 539
Ensisheim meteorite, the, 393
Equatorial diameter, 196, 497;
telescope, 14
Eratosthenes, 89
Eros, 236
Eruptions, 197
Evening star, 109, 169
Eye, structure of the, 10
F
Faculae of the Sun, 37
Fire ball of 1869, 375
Fire balls, 374
"Fixed" stars, 503
Flamsteed, first Astronomer-Royal, 311;
his _Historia Coelestis_, 311
Focus of planetary ellipse, 137-139
Fomalhaut, 413
Fraunhofer, 478
Fraunhofer lines, 48
Fundy, Bay of, tides in, 538
G
Galileo, achievements of, 10;
and Jupiter's satellites, 267;
and Saturn's rings, 273, 274;
and the Pleiades, 418
Galle, Dr., and Neptune, 328-330
Gassendi, and the transit of Mercury, 164;
and the transit of Venus, 178;
lunar crater named after him, 90
Gauss, and the minor planet Ceres, 232
Gemini, constellation of, 303, 420
Geminids, the, 400
Geologists and the lapse of time, 453
Geometers, Oriental, 5
Geometry, cultivation by the ancients of, 6
George III. and Sir W. Herschel, 299, 306
Giant's Causeway, 407
Gill, Dr. D., 27;
and Juno, 243;
and the minor planets, 242;
and the parallax of a Centauri, 451;
and the parallax of Mars, 214
Glacial period, 518
Gravitation, law of, 122-149;
and binary stars, 437;
and precession, 497;
and the Earth's axis, 495, 497, 499;
and the parabolic path of comets, 340;
and the periodical return of comets, 343;
and the weight of the Earth, 203, 204;
illustrated by experiments, 123, 124, 127, 129-132;
its discovery aided by lunar observations, 108, 125;
its influence on the satellites, 149;
its influence on stars, 149;
its influence on tides, 149;
Le Verrier's triumphant proof of, 330;
Newton's discoveries, 125, 126, 147;
on the Moon, 96;
universality amongst the heavenly bodies, 128, 373
Great Bear, 27, 28, 241;
configuration, 410;
double star in the, 438;
positions of, 409, 411
Green, Mr., and Mars, 220
Greenwich Observatory, 26, 311
Griffiths, Mr., and Jupiter, 252
Grimaldi, 90
Grubb, Sir Howard, 14
"Guards," the, 412
_Gulliver's Travels_ and the satellites of Mars, 228
H
Hadley's observations of Saturn, 282
Hall, Professor Asaph, and the satellites of Mars, 225
Halley, and the periodicity of comets, 341-343;
and the transit of Venus, 180
Heat, bearings on astronomy, 513;
in the interior of the Earth, 197-199, 514;
of the Sun, 515-526
Heliometer, the, 243
Helium, 55
Henderson, and the distance of a Centauri, 442, 451
Hercules, star cluster in, 269, 462
Herodotus (lunar crater), 90
Herschel, Caroline, 299, 465
Herschel, Sir John, address to British Association, 328;
address on the presentation of gold medal to Bessel, 443;
and Biela's comet, 357;
and nebulae, 464;
letter to _Athenoeum_ on Adams's share in the discovery of
Neptune, 330
Herschel, Sir W., and double stars, 435, 436;
and Saturn, 279;
and Saturn's satellites, 295;
and the Empress Catherine, 301;
and the movement of solar system towards Lyra, 457;
discovery of satellite of Uranus by, 308, 309;
discovery of Uranus by, 305, 308;
early life of, 299;
friendship with Sir W. Watson of 302;
he makes his own telescopes, 301;
"King's Astronomer," 307;
method of making his telescopes, 302;
musical talent of, 299;
organist of Octagon Chapel, Bath, 300;
pardon for desertion from George III., 299;
passion for astronomy of, 300, 301;
relinquishes musical profession, 307;
sidereal aggregation theory of, 529;
study of the nebulae by, 464-465, 529
Herschelian telescope, 19
_Historia Coelestis_, 311
Hoedi, the, 414
Holmes's, Mr., comet (1892), 355
Horrocks, and the transit of Venus, 179
Howard, Mr., and the Benares meteorite, 392
Huggins, Sir W., 479, 483;
and nebulae, 472
Huyghens, and Saturn's rings, 275-278;
discovers first satellite of Saturn, 293
Hyades, the, 419
Hydrogen in Sirius and Vega, 479;
in the Sun, 50
Hyginus, 93
Hyperion, 559
I
Iapetus, 559
Iberians, the, 3
Inquisition, the, and Galileo, 10
Iris, 242
Iron, dust in the Arctic regions, 408;
in the Sun, 50;
of meteorites, the, 396;
spectrum of, 50
J
Janssen, M., 34, 53;
and the transit of Venus, 177
Juno, 233, 238
Jupiter, ancient study of, 6;
and the Leonids, 386;
attraction of, 248;
axial rotation of, 558;
belts of, 252;
brilliancy of, 257;
composition of, 250;
covered with an atmosphere of clouds, 253, 254;
density of, 558;
diameter of, 247, 558;
distance from the Earth of, 110, 111;
distance from the Sun of, 246, 558;
habitability of, 257;
heat received from the Sun by, 256;
internal heat of, 252, 256, 515;
lack of permanent features of, 253;
lack of solidity of, 248, 253, 254;
moment of momentum of, 554, 555;
occultation of, 255;
orbit of, 114, 115, 246;
path of, perturbed by the attraction of Saturn, 316;
periodic time of, 558;
a planet, or "wanderer," 111;
red spot in 1878, 253;
revolution of, 246;
rotation of, 201, 202;
satellites of, 247, 249, 257-261, 265, 559;
satellites of, and gravitation, 266;
satellites of, and the Copernican theory, 267;
shadow from satellites of, 257;
shape of, 201, 202, 247, 252;
size of, compared with the Earth, 19, 246, 248,
and other planets, 114;
and the Sun, 114;
storms on, 256;
tides on, 555;
weight of, 248, 250,
and Encke's comet, 350
K
Keeler, Professor, and Saturn's ring, 288
Kempf, Dr., and the Sun's velocity, 484
Kepler, and comets, 360;
and laws of planetary motion, 10;
and meteors, 386;
and the orbit of Mars, 209;
explanation of his laws, 147, 148, 533;
his discovery of the shape of the planetary orbits, 136, 138;
his first planetary law, 138;
lunar crater called after him, 90;
prediction of the transit of Venus and Mercury, 163, 178;
second law, 141;
third law, 142
Kids, the, 414
Kirchhoff, and spectrum analysis, 478
Kirkwood, Professor, and the movements of Saturn's satellites, 296
Klinkerfues, Professor, 390
L
Lagrange, and the theory of planetary perturbation, 320-322;
his assumption of planetary rigidity, 531
L'Aigle meteorites, the, 392
Lalande, and Neptune, 332, 333
Landscapes, lunar, 98
Lane, Mr. J. Homer, 522
Laplace, and the nebular theory, 526;
and the satellites of Jupiter, 266;
and the theory of planetary perturbation, 320
Lassell, Mr., and Saturn's eighth satellite, 296;
discovers Neptune's satellite, 334
Law of gravitation (_see_ Gravitation)
Laws of Planetary Motion (_see_ Planetary Motion)
Lead in the Sun, 50
Ledger, Mr., and Mercury, 163
Leibnitz, lunar mountains named after him, 93
Lemonnier, and Uranus, 312
Leo, and shooting stars, 380, 420
Leonids, attractions of planets on, 386;
breadth of stream of, 387;
change of shape of, 383;
decrease of, 385;
enormous number of, 382;
historical records, 383;
length of stream of, 387;
Le Verrier, and the cause of their introduction into the solar
system, 388;
meteor shoal of, 382;
periodic return of, 382;
their connection with comets and Professor, Schiaparelli, 388
Leonis g, value of velocity of, 484
Leverage by equatorial protuberance, 498
Le Verrier, and Mars, 214;
and the discovery of Neptune, 324-332;
and the introduction of the Leonids into the solar system, 388;
and the weight of Mercury, 349
Lexell's comet, 370
Libration, 84
Lick Observatory, 16
Light, aberration of, 503-512;
velocity of, 261, 262, 265, 505, 512
Linne, 87, 94
Lion, the, 420, 421
Little Bear, the, 412
Little Dog, the, 420
Livy, and meteorites, 393
Lloyd, Provost, 407
Lockyer, Sir Norman, and Betelgeuze, 482;
and solar light, 52
London, tides at, 538
Louvain, F. Terby, and Titan, 295
Lowell, Mr., and Mercury, 165
Lunar tides, 548, 549
Lyra, motion of solar system towards, 459
Lyre, the, 424;
Nebula in, 469
Lyrids, the, 400
M
Maedler, and the lunar craters, 88, 90, 91
Magellanic clouds, 463
Magnesium, colour of flame from, 46;
in the Sun, 50
Magnetism, connection with Sun spots, 42
Manganese in the Sun, 50
Maraldi, and the rings of Saturn, 279
Mare crisium, 83;
foecunditatis, 83;
humorum, 83;
imbrium, 83, 98;
nectaris 83;
nubium, 83;
serenitatis, 83;
tranquillitatis, 83;
vaporum, 83
Mars, ancient study of, 6;
appearance of, through the telescope, 218;
atmosphere of, 222;
axial rotation of, 558;
canals on, 220;
density of, 558;
diameter of, 558;
distance, from the Earth of, 213;
distance from the Sun of, 213, 558;
gravitation on, 225;
Le Verrier's discovery of, 214;
life improbable on, 224;
marking on, 218;
movements of, 211-213;
opposition of, 209-211;
orbit of, 116, 209, 210, 213;
orbit of, and the laws of Kepler, 209;
parallax (1877), and Dr. D. Gill, 214;
periodic time of, 558;
a planet or "wanderer," 111;
"Polar Caps" on, 218, 219;
proximity to the Earth of, 110;
rising and setting of, 209;
rotation of, 218;
satellites of, 225-228, 558;
size of compared with other planets, 116, 216;
tides on, 551;
water and ice on, 219, 224
Maximilian, Emperor, 393
Mayer, Tobias, and Uranus, 312
Measurement of the Earth, 193-196
Mediterranean, tides in the, 537
Mercury, ancient study of, 6;
antiquity of its discovery, 155-157;
atmosphere of, 166;
attraction on comets of, 347;
climate of, 163;
comparative proximity to the Earth of, 111;
composition of, 160;
crescent-shaped, 160;
density of, 558;
diameter of, 558;
distance from the Sun of, 151, 558;
habitability of, 163;
movement of, 160, 161;
its elliptic form, 139, 161;
orbit of, 114;
period of revolution of, 161;
periodic appearances of, 158;
periodic time of, 558;
perturbations of, 350;
a planet or "wanderer," 111;
revolution of, 165;
rotation of, and Professor Schiaparelli, 165;
size of, compared with other planets, 116;
surface of, 162;
transit of, 152;
transit of, and Gassendi's observations, 164;
transit of, predicted by Kepler, 163;
velocity of, 162;
weight of, 166, 349
Meridian circle, 22, 24
Messier's Catalogue of Stars, 529
Meteors (_see_ Stars, shooting)
Meteorites, 391;
Alban Mount, 393;
ancient accounts, 392, 393;
Benares, 392;
Butsura, 397;
Chaco, 398;
characteristics of, 397;
Chladni's account of discovery in Siberia, 392;
composition of, 397-399;
Ensisheim (1492), 393;
Hindoo account of, 391;
L'Aigle, 392;
not connected with comets, 400;
not connected with star showers, 400;
Orgueil, 399;
origin, 400-408;
Ovifak, 407;
Rowton, 395-396;
Wold Cottage, 392
Micrometer, 86
Milky Way, 462-3, 474-6
Mimas, 559
Minor planets, 229-244
Mira Ceti, 430, 482
Mizar, 438, 486
Moment of momentum, the, 552-554
Month of one day, 547
Moon, The, absence of air on, 85, 99;
absence of heat on, 95;
agent in causing the tides, 70, 535-537;
ancient discoveries respecting, 5;
apparent size of, 73;
attraction to the Earth of, 75;
brightness of, as compared with that of the Sun, 71;
changes during the month of, 71, 74;
chart of surface of, 81;
craters on, 83, 84, 87-98, 514;
density of, 558;
diameter of, 558;
distance from the Earth of, 73, 75, 568;
eclipses of, 6, 77-80;
illustration of the law of gravitation, 96, 131, 133;
landscapes on, 98;
life impossible on, 99;
measuring heights of mountains, etc., of, 85, 86;
micrometer, 86; motion of, 75;
mountains on, 83, 85, 88, 89, 91, 93;
phases of, 71, 76;
plane of orbit of, 310, 500, 501;
poets and artists and, 72;
pole, 500;
possibility of ejecting meteorites, 402;
possibly fractured off from the earth, 543;
prehistoric tides on, 548, 549;
produces precession, 497-499;
proximity to the Earth of, 73, 75;
receding from the Earth, 545;
relative position of with regard to the Earth and the Sun, 76, 77;
revolution of, round the Earth, 75, 76, 558;
"seas" on, 82, 83;
shadows of, 85;
size of, compared with that of the Earth, 74;
test for chronometers, a, 80;
thraldom of terrestrial tides, 549;
waterless, 100;
weather not a affected by the phases of, 82;
weight of, 74
Motion, laws of planetary, 138, 141, 142, 147, 148
Mountains of the Moon, 83, 85, 93
N
Nasmyth, Mr., and the formation of lunar craters, 95
Natural History Museum, meteorites, 394
_Nautical Almanack_, 189
Neap Tides, 538
Nebula, in Andromeda, 469;
annular, in Lyra, 469;
in Orion, 269, 461, 466-469;
colour of, 468;
magnitude of, 468;
nature of, 467;
planetary, in Draco, 470;
simplest type of a, 528;
various grades of, 528
Nebulae, 464-472;
condensation, 528;
distances of, 464;
double, 470;
Herschel's labours respecting, 464-465, 528, 529;
number of, 466;
planetary, 470;
self-luminous, 464;
smallest greater than the Sun, 464;
spiral, 470
Nebular theory, the, 526
Neptune, 112;
Adams's researches, 324-326, 332;
Challis's observations of, 326-328;
density of, 558;
diameter of, 333, 558;
disc of, 332;
discovery (1846) of, 315;
distance from the Sun of, 334, 558;
Lalande's observations of, 332, 333;
Le Verrier's calculations, 324-332;
moment of momentum of, 554;
orbit of, 117;
periodic time of, 558;
revolution of, 334;
rotation of uncertain, 333;
satellite of, discovered by Mr. Lassell, 559;
size of, compared with other planets, 119;
vaporous atmosphere of, 333;
weight of, 333
Newall, Mr. H.F., and Capella, 487;
and the values of velocity of stars, 483
Newcomb, Professor, 9, 264, 267, 522
Newton, Professor, and meteoric showers, 377, 384
Newton, Sir Isaac, discovery of gravitation verified Kepler's laws, 144;
dynamical theory, 214;
illustrations of his teaching, 144-147;
law of gravitation and, 125, 126, 537;
parabolic path of comets and, 338-340;
reflecting telescope, 19;
weight of the Earth and, 203
Nickel in the Sun, 50
Nineveh, astronomers of, 156
Nordenskjoeld, and the Ovifak meteorite, 407
Nova Cygni, 431;
brilliancy of, 454;
decline of, 455;
distance of, 456;
parallax of, 455
November meteors, 376, 377, 379
Nutation, and Bradley, 501
O
Oberon, 309, 559
Object-glasses, 11, 12, 14, 16, 19
Observatories, 9-28
Observatory, Cape of Good Hope, 27;
Dunsink, 12, 184;
Greenwich, 26, 314;
Lick, 16;
Paris, 22;
Uraniborg, 10;
Vienna, 14;
Washington, 226;
Yerkes, 16
Occultation, 102, 215
Oceanus Procellarum, 83
Opera-glass, 27, 28
Opposition of Mars, 209
Orbital moment of momentum, 552
Orbits of planets, 114, 115, 117;
dimensions, 139-143;
elliptical form, 138-140;
minor planets, 232, 234, 239;
not exactly circles, 135;
of satellites of Uranus, 310;
Sun the common focus, 139
Orgueil meteorite, the, 399
Orion, 4, 418
Orion, belt of, 418, 467;
brilliancy of, 418;
nebula in, 269, 461, 466-469
Orionis, a, 418, 482
Orionis, th, a multiple star, 318, 467
Ovifak meteorite, the, 407
P
Palisa and the minor planets, 234
Pallas, 233, 238
Parabolic path of comets, 338-340
Parallactic ellipse, 444
Parallax, 181, 182, 214, 443;
of stars, 507
Paris telescope, 22, 23
Pegasus, great square of, 413, 414
Peg-top, the, and the rotation of the Earth, 494
Pendulum for determining the force of the Earth's attraction, 205
Penumbra of Sun-spot, 51
Perihelion, 163
Periodic times of planets, 139-143, 558
Periodicity of Sun-spots, 41
Perseids, 400
Perseus, 415, 416, 429;
sword-handle, 462
Perturbation, planetary, 317-324, 346
Perturbations, theory of, 296
Petavius, 93
Peters, Professor, and charts of minor planets, 234;
and the derangement of Sirius, 427
Phases of the Moon, 71, 76
Phobos, 226, 551, 558
Photography, and practical astronomy, 25;
and the distance of 61 Cygni, 449;
Dr. Roberts and the nebula in Andromeda, 469;
Mr. Common and the nebula in Orion, 469;
Sir W. Huggins and the spectra of nebulae, 473
Photosphere, the, 37, 54
Physical nature of the stars, 477
Piazzi, discoverer of the first known minor planet, 203
Pickering, Professor, 218, 220, 255, 265;
and Betelgeuze, 482;
and planetary nebulae, 474;
and Saturn's satellites, 296;
and spectroscopic binaries, 486, 487
Pico, 89
Planetary motion, Kepler's laws of, 138, 141, 142, 147, 148
Planetary nebulae, 470
Planetary perturbation, 317-324
Planets, ancient ideas respecting, 2, 6;
approximate number of, 112;
attract each other, 148, 317;
attracted by comets,360;
Bode's law, 230;
comparative sizes of, 118, 119;
distance of, from the Earth, 109-111;
distance of, from the Sun, 558;
how distinguished from stars, 111;
irregularity of motions of, 317-324;
Lagrange's theory of rigidity of, 531;
light of, derived from the Sun, 113;
minor, 229-244;
orbits of the four giant, 117;
orbits of the four interior, 114;
orbits have their focus in the centre of the Sun, 139;
orbits not exactly circles, 135;
orbits take the form of an ellipse, 136-138;
origin of, as suggested by the nebular theory, 526;
periodic times of, 139-143, 558;
relative distances of, 229;
uniformity of direction in their revolution, 120, 322;
velocity of, 139-142, 144, 146, 237
Plato (lunar crater), 89
Pleiades, 241, 416;
invisible in the summer, 416
Pliny, the tides and the Moon, 535
Plough, the, 28
Pogson, Mr., 390
Pointers in the Great Bear, 28, 411
Polar axis, 196
Polar caps on Mars, 218, 219
Pole, the, distance of from Pole Star lessening, 494;
elevation of, 195;
movement of, 492;
near a Draconis, 494;
near Vega or a Lyra, 494
Pole Star, 194;
belongs to the Little Bear, 412;
distance of, from the pole of the heavens, 412, 492, 494;
position of, 411;
slow motion of, 412
Pollux, 420, 480;
value of velocity of, 484
Pons, and the comet of 1818, 345
Posidonius, 87
Potassium in the Sun, 50
Praesepe, 422
Precession and nutation of the Earth's axis, 492-502
Proctor, and the stars in Argelander's atlas, 476
Prism, the, 45;
its analysing power, 46
Pritchard, Professor, stellar photographic researches of, 449
Procyon, 420;
value of velocity of, 484
Prominences on the Sun, 53-59
Ptolemy, his theory of astronomy, 6;
lunar crater named after him, 92
Q
Quarantids, the, 400
R
Radius of the Earth, 193, 512
Rainbow, the, 45
Ram, the, 420
Reflectors, 19, 21, 25
Refraction by the prism, 45
Refractors, 11, 14, 16
Regulus, 421, 479
Reservoir formed from tidal water, 538
Retina, the, and the telescope, 10, 11
Rhea, 559
Rigel, 418, 420, 480
Rigidity of the planets, 532, 533
Roberts, Dr. Isaac, and the nebula in Andromeda, 469;
and the nebula in Orion, 469
Roemer, and the velocity of light, 261
Romance, planet of, 151-154
Rosse telescope, the, 19, 20, 468, 470
Rotational moment of momentum, 553
Rowland, Professor, and spectral lines, 491
Rowton Siderite, 395
Royal Astronomical Society and Bessel, 442
S
Sappho, 242
Satellites of Jupiter, 249, 250, 257-261, 266, 559;
confirmation of the Copernican theory, 267
Satellites of Mars, 209, 225-228, 551, 558
Satellites of Neptune, 334, 559
Satellites of Saturn, 559;
Bond's discoveries, 296;
Cassini's discoveries, 294;
distances, 559;
Herschel's discoveries, 295;
Huyghens' discovery, 293;
Kirkwood's deduction, 296;
Lassell's deduction, 296;
movements, 296;
origin as suggested by the nebular theory, 526
Satellites of Uranus, 308, 309, 310, 559
Saturn, ancient study of, 6;
attraction on Uranus, 322;
axial rotation of, 558;
beauty of, 209;
comparative proximity to the Earth of, 110;
density of, 558;
diameter of, 271, 558;
distance of, from the Sun, 268, 271, 558;
elliptic path of, 271;
gravitation paramount, 283;
internal heat of, 272, 515;
Leonids and, 386;
low density of, 272;
moment of momentum of, 554;
motion of, 271;
orbit of, 117, 118;
path of, perturbed by the attraction of Jupiter, 316;
periodic time of, 558;
period of revolution of, 269;
picturesqueness of, 291;
position of, in the solar system, 269;
rings of, 269;
rings, Bonds discovery, 280;
rings, Cassini's discovery, 278;
rings, consistency, 286;
rings, Dawes's discovery, 281;
rings, Galileo's discovery, 273, 274;
rings, Hadley's observations, 282;
rings, Herschel's researches, 279;
rings, Huyghens' discovery, 275-278;
rings, Keeler's measurement of the rotation, 288;
rings, Maraldi's researches, 279;
rings, rotation of, 285, 288;
rings, spectrum of, 291;
rings, Trouvelot's drawing, 278;
satellites of, 293, 294, 295, 296, 559;
size of, compared with other planets, 119, 269, 272;
spectrum of, 291;
unequal in appearance to Mars and Venus, 269;
velocity of, 271;
weight of, compared with the Earth, 272
Savary and binary stars, 436
Schaeberle, Mr., and Mars, 224
Scheiner, and the values of velocity of stars, 483;
observations on Sun-spots, 36
Schiaparelli, Professor, and Mars, 220;
and the connection between shooting-star showers and comets, 388;
and the rotation of Mercury, 165
Schickard, 90
Schmidt, and Nova Cygni, 454, 489;
and the crater Linne, 87;
and the Leibnitz Mountains, 93
Schroeter, and the crater Posidonius, 87
Schwabe, and Sun-spots, 40
Seas in the Moon, 82
Secchi, and stellar spectra, 479
Shoal of shooting stars, 377;
dimensions, 377
Shooting stars (_see_ Stars, shooting)
Sickle, the, 421
Sidereal aggregation theory of Sir W. Herschel, 529
Siderite, Rowton, 395
Sinus Iridum, 83
Sirius, change in position of, 425;
companion of, 427, 428;
exceptional lustre of, 110;
irregularities of movement of, 426;
larger than the Sun, 110;
most brilliant star, 419;
periodical appearances of, 157;
proper motion of, 425;
spectrum of, 479;
velocity of, 426;
weight of, 427
Smyth, Professor C.P., 493
Sodium, colour of flame from, 49;
in the Sun, 50
Solar corona, prominences etc. (_see under_ Sun)
Solar system, 107-121;
Copernican exposition of the, 7;
influence of gravitation on, 149;
information respecting, obtained by observing the transit of Venus, 174;
island in the universe, 121;
minor planets, 229-244;
moment of momentum, 554;
movement of, towards Lyra, 457;
origin of, as suggested by the nebular theory, 526;
position of Saturn and Uranus in, 297, 305
South, Sir James, 12
Spectra of stars, 479
Spectro-heliograph, 58
Spectroscope, 43-56;
detection of iron in the Sun by the, 50
Spectroscopic binaries, 487
Spectrum analysis, 47;
dark lines, 49, 50;
gaseous nebulae, 474;
line D, 48, 49
Speculum, the Rosse, 20
Spica, 423, 487
Spider-threads for adjusting the micrometer, 86;
for sighting telescopes, 22
Spots on the Sun, 36-43;
connection with magnetism, 42;
cycles, 41;
duration, 41;
epochs of maximum, 42;
motion, 36;
period of revolution, 40;
Scheiner's observations, 36;
zones in which they occur, 39
Star clusters, 461-464;
in Hercules, 462;
in Perseus, 462
Stars, apparent movements due to precession, nutation, and aberration, 504;
approximate number of, 28;
attraction inappreciable, 316;
catalogues of, 310, 311, 409, 431;
charts of, 325, 328;
circular movement of, 505-507
Stars, distances of, 441;
Bessel's labours, 442-449;
Henderson's labours, 442;
method of measuring, 443-445;
Struve's work, 442, 448, 449;
parallactic ellipse, 444-449
Stars, double, 434;
Bode's list, 435;
Burnham's additions, 439;
Cassini, 434;
Herschel, 435, 436;
measurement, 435, 436;
revolution, 436;
Savary, 436;
shape of orbit, 436;
variation in colour, 438
Stars, elliptic movement of, 506;
gravitation and, 149;
how distinguished from planets, 111;
physical nature of, 477;
probability of their possessing a planetary system, 121;
real and apparent movements of, 504;
really suns, 32, 121
Stars, shooting, attractions of the planets, 386;
connection with comets, 388-390;
countless in number, 372;
dimensions of shoal, 377;
features of, 373;
length of orbit, 387;
orbit, 378;
orbit, gradual change, 386;
period of revolution, 384;
periodic return, 378, 379;
shower of November, 1866, 377, 379-380;
shower of November, 1866, and Professor Adams, 384, 386;
shower of November, 1866, radiation of tracks from Leo, 380;
shower of November, 1872, 389;
showers, 376;
showers and Professor Newton, 377;
track, 377;
transformed into vapour by friction with the Earth's
atmosphere, 374, 376;
velocity, 373, 386
Stars, spectra of, 479;
teaching of ancients respecting, 3;
temperature of, 515;
temporary, 430, 488;
values of velocity of, 484;
variable, 429
Stoney, Dr. G.J., 387
Strontium, flame from, 46;
in the Sun, 50
Struve, Otto, and the distance of Vega, 442, 447;
and the distance of 61 Cygni, 448, 449
Sun, The, and the velocity of light, 265;
apparent size of, as seen from the planets, 117, 118;
as a star, 32;
axial rotation of, 558;
compared with the Earth, 29;
connection of, with the seasons, 4;
corona of, during eclipse, 62-64;
density of, 65, 558;
diameter of, 558;
distance of, from Mars, 213;
distance of, from Saturn, 271;
distance of, from the Earth, 31, 114, 184, 240, 558;
eclipse of, 6, 53;
ellipticity of, 558;
faculae on surface of, 37;
focus of planets' orbits, 138;
gradually parting with its heat, 95;
granules on surface of, 34;
heat of, and its sources, 515-526;
heat of, thrown on Jupiter, 256;
minor planets and, 240;
movement of, towards Lyra, 457;
nebular theory of its heat, 526;
photographed, 34;
precession of the Earth's axis, 497;
prominences of, 53-59;
relation of, to the Moon, 71;
rising and setting of, 2;
rotation of, 40, 201;
size of, 29;
spectrum of, 48;
spots on, 36-43;
spots, connection with magnetism, 42;
storms and convulsions on, 42, 43;
surface of, gaseous matter, 34;
surface of, mottled, 34;
teaching of early astronomers concerning, 3-7;
temperature of, 30, 31, 516;
texture of, 34;
tides on, 530;
velocity of, 484;
weight of, compared with Jupiter, 250, 350;
zodiacal light and, 67;
zones on the surface of, 39
Sunbeam, revelations of a, 44
Swan, the, 424, 439, 445
Sword-handle of Perseus, 462
Syrtis major, 222
T
Taurus, constellation of, 231, 419
Tebbutt's comet, 353
Telescope, construction of the first, 10;
equatorial (Dunsink), 12-14, 185;
Greenwich, 26;
Herschelian, 19;
Lick, 16, 19;
Paris, 22, 23;
reflecting, 19, 21;
refracting, 11, 14;
Rosse, 19, 20, 468, 470;
sighting of a, 23;
structure of the eye illustrates the principle of the, 10;
Vienna, 14-16;
Washington, 226;
Yerkes, 16
Temporary stars, 430, 488
Tethys, 559
Theophilus, 92
Tides, The, actual energy derived from the Earth, 539;
affected by the law of gravitation, 149, 535;
affected by the Moon, 70, 535-537;
at Bay of Fundy, 538;
at Cardiff, 538;
at Chepstow, 538;
at London, 538;
at St. Helena, 538;
excited by the Sun, 537;
formation of currents, 538;
in Bristol Channel, 538;
in Mediterranean, 537;
in mid-ocean, 538;
Jupiter and, 552;
length of the day and, 541;
lunar, 548, 549;
moment of momentum and, 552;
neap, 537;
rotation of the Earth, and revolution of the Moon, 549;
satellites of Mars, 551;
solar, 550;
spring, 537;
variations in, 538;
waste of water power, 538;
work effected, 539
Tin in the Sun, 50
Titan, 294, 295, 559
Titania, 309, 559
Transit of Mercury, 152, 163, 164
Transit of Venus, 152;
Captain Cook, 184;
Copeland's observations of, 189;
Crabtree's observations of, 180;
Gassendi's observations of, 178;
Halley's method, 180, 181;
Horrocks' observations of, 179, 180;
importance of, 173;
Kepler's prediction of, 163;
observations of, at Dunsink, 184-188
Transit of Vulcan, 152-153
Triesnecker, 84, 93
Trouvelot, Mr. L., and Saturn's rings, 278
Tschermak, and the origin of meteorites, 400, 401
Tycho (lunar crater), 91
Tycho Brahe, and the Observatory of Uraniborg, 9, 10, 430
U
Umbra of Sun-spot, 51
Umbriel, 309, 559
Unstable dynamical equilibrium, 543
Uraniborg, Observatory of, 10
Uranus, 112;
attraction of Saturn, 322;
Bradley's observations of, 312;
composition of, 308;
density of, 558;
diameter of, 308, 558;
diameter of orbit of, 305;
disc of, 308;
discovery of, by Herschel, 305, 308;
distance from Sun of, 558;
ellipse of, 313;
first taken for a comet, 304;
Flamsteed's observations of, 311, 312;
formerly regarded as a star, 311, 312;
investigations to discover a planet outside the orbit, 323-324;
irregular motion of, 314, 323;
Lemonnier's observations of, 312;
Leonids and, 386;
Mayer's observations of, 312;
moment of momentum of, 554;
orbit of, 117, 310;
periodic time of, 558;
period of revolution of, 312;
rotation of, 308;
satellites of, 559;
satellites, discovery by Herschel, 308;
satellites, movement nearly circular, 309;
satellites, periodical movements, 309;
satellites, plane of orbits, 309, 310;
size of compared with the Earth, 308;
and with other planets, 119;
subject to another attraction besides the Sun, 314
Ursa major (_see_ Great Bear)
V
Variable Stars, 429
Vega, 414, 423, 424, 479;
Struve's measurement of, 442
Velocity, of light, 261, 262, 265;
of light, laws dependent upon, 511;
of planets, 140-143, 146, 237;
of stars, values of, 483-4
Venus, ancient study of, 6;
aspects of, 171;
atmosphere of, 189;
brilliancy of, 168;
density of, 558;
diameter of, 191, 558;
distance of, from the Sun, 191, 558;
habitability of, 173;
movement of, 168;
neighbour to the Earth, 109;
orbit of, 114, 135;
orbit form of, 139, 191;
periodic time of, 558;
a planet or "wanderer," 111;
rotation of, 191;
shape of, 169;
size of, compared with other planets, 116, 169;
surface of, 171;
transit of, 152, 176-190;
transit, importance of, 173;
transit predicted by Kepler, 163;
velocity and periodic time of, 142, 143, 191;
view of the ancients about, 157
Vesta, 233, 238
Victoria, 242
Vienna telescope, 14-16
Virgo, 423
Vogel and Algol, 485;
and Spica, 486, 487;
and the spectra of the stars, 479, 483
Volcanic origin of meteorites, 400;
outbreaks on the Earth, 197
Von Asten and Encke's comet, 349, 350;
and the distance of the Sun, 351;
and the weight of Mercury, 166
Vortex rings, 469
Vulcan, 152, 153;
and the Sun, 3
W
Wargentin, 90
Watson, Professor, and Mercury, 154
Watson, Sir William, friendship with Herschel, 302
Wave-lengths, 60
Weather, not affected by the Moon, 82
Wilson, Mr. W.E., and the nebula in Orion, 469
Witt, Herr G., and Eros, 236
Wold Cottage meteorite, the, 392
Wright, Thomas, and the Milky Way, 474
Y
"Year of Stars," the, 377
Yerkes Observatory, Chicago, 16
Young, Professor, account of a marvellous Sun-prominence, 42;
and Sun-spots, 38;
observations on magnetic storms, 39
Z
Zeeman, Dr., and spectral lines, 491
Zinc in the Sun, 50
Zodiac, the, 5
Zodiacal light, 67
Zone of minor planets, 234
PRINTED BY CASSELL & COMPANY, LIMITED, LA BELLE SAUVAGE, LONDON, E.C.
FOOTNOTES:
[1] It may, however, be remarked that a star is never _seen_ to set, as,
owing to our atmosphere, it ceases to be visible before it reaches the
horizon.
[2] "Popular Astronomy," p. 66.
[3] _Limb_ is the word used by astronomers to denote the _edge_ or
circumference of the apparent disc of a heavenly body.
[4] "The Sun," p. 119.
[5] It has been frequently stated that the outburst in 1859, witnessed
by Carrington and Hodgson, was immediately followed by an unusually
intense magnetic storm, but the records at Kew and Greenwich show that
the magnetic disturbances on that day were of a very trivial character.
[6] Some ungainly critic has observed that the poet himself seems to
have felt a doubt on the matter, because he has supplemented the dubious
moonbeams by the "lantern dimly burning." The more generous, if somewhat
a sanguine remark has been also made, that "the time will come when the
evidence of this poem will prevail over any astronomical calculations."
[7] This sketch has been copied by permission from the very beautiful
view in Messrs. Nasmyth and Carpenter's book, of which it forms Plate
XI. So have also the other illustrations of lunar scenery in Plates
VIII., IX. The photographs were obtained by Mr. Nasmyth from models
carefully constructed from his drawings to illustrate the features on
the moon. During the last twenty years photography has completely
superseded drawing by eye in the delineation of lunar objects. Long
series of magnificent photographs of lunar scenery have been published
by the Paris and Lick Observatories.
[8] At the British Association's meeting at Cardiff in 1892, Prof.
Copeland exhibited a model of the moon, on which the appearance of the
streaks near full moon was perfectly shown by means of small spheres of
transparent glass attached to the surface.
[9] The duration of an occultation, or, in other words, the length of
time during which the moon hides the star, would be slightly shorter
than the computed time, if the moon had an atmosphere capable of
sensibly refracting the light from the star. But, so far, our
observations do not indicate this with certainty.
[10] I owe my knowledge of this subject to Dr. G. Johnstone Stoney,
F.R.S. There has been some controversy as to who originated the
ingenious and instructive doctrine here sketched.
[11] The space described by a falling body is proportional to the
product of the force and the square of the time. The force varies
inversely as the square of the distance from the earth, so that the
space will vary as the square of the time, and inversely as the square
of the distance. If, therefore, the distance be increased sixty-fold,
the time must also be increased sixty-fold, if the space fallen through
is to remain the same.
[12] See Newcomb's "Popular Astronomy," p. 78.
[13] Recent investigation by Newcomb on the motion of Mercury have led
to the result that the hypothesis of a planet or a ring of very small
planets between the orbit of Mercury and the sun cannot account for the
difference between theory and observation in the movements of Mercury.
Harzer has come to the same result, and has shown that the disturbing
element may possibly be the material of the Solar Corona.
[14] "The Sun: its Planets, and their Satellites." London: 1882 (page
147).
[15] James Gregory, in a book on optics written in 1667, had already
suggested the use of the transit of Venus for this purpose.
[16] _See_ "Astronomy and Astrophysics," No. 128.
[17] _See_ "Astronomy and Astrophysics," No. 128.
[18] This is the curved marking which on Plate XVIII. appears in
longitude 290 deg. and north of (that is, below) the equator. Here, as in
all astronomical drawings, north is at the foot and south at the top.
_See_ above, p. 82 (Chapter III.).
[19] Now Director of the Lick Observatory.
[20] The heliometer is a telescope with its object-glass cut in half
along a diameter. One or both of these halves is movable transversely by
a screw. Each half gives a complete image of the object. The measures
are effected by observing how many turns of the screw convey the image
of the star formed by one half of the object-glass to coincide with the
image of the planet formed by the other.
[21] See "Astronomy and Astrophysics," No. 109.
[22] It is only right to add that some observers believe that, in
exceptional circumstances, points of Jupiter have shown some slight
degree of intrinsic light.
[23] Professor Pickering, of Cambridge, Mass., has, however, effected
the important improvement of measuring the decline of light of the
satellite undergoing eclipse by the photometer. Much additional
precision may be anticipated in the results of such observations.
[24] "Newcomb's Popular Astronomy," p. 336.
[25] _See_ Grant, "History of Physical Astronomy," page 255.
[26] Now Director of the Lick Observatory.
[27] We are here neglecting the orbital motion of Saturn, by which the
whole system is moved towards or from the earth, but as this motion is
common to the ball and the ring, it will not disturb the relative
positions of the three spectra.
[28] According to Prof. Barnard's recent measures, the diameter of Titan
is 2,700 miles. This is the satellite discovered by Huyghens; it is the
sixth in order from the planet.
[29] Extract from "Three Cities of Russia," by C. Piazzi Smyth, vol.
ii., p. 164: "In the year 1796. It then chanced that George III., of
Great Britain, was pleased to send as a present to the Empress Catharine
of Russia a ten-foot reflecting telescope constructed by Sir William
Herschel. Her Majesty immediately desired to try its powers, and
Roumovsky was sent for from the Academy to repair to Tsarskoe-Selo,
where the Court was at the time residing. The telescope was accordingly
unpacked, and for eight long consecutive evenings the Empress employed
herself ardently in observing the moon, planets, and stars; and more
than this, in inquiring into the state of astronomy in her dominions.
Then it was that Roumovsky set before the Imperial view the Academy's
idea of removing their observatory, detailing the necessity for, and the
advantages of, such a proceeding. Graciously did the 'Semiramis of the
North,' the 'Polar Star,' enter into all these particulars, and warmly
approve of the project; but death closed her career within a few weeks
after, and prevented her execution of the design."
[30] _See_ Professor Holden's "Sir William Herschel, his Life and
Works."
[31] Arago says that "Lemonnier's records were the image of chaos."
Bouvard showed to Arago one of the observations of Uranus which was
written on a paper bag that in its time had contained hair-powder.
[32] The first comet of 1884 also suddenly increased in brightness,
while a distinct disc, which hitherto had formed the nucleus, became
transformed into a fine point of light.
[33] The three numbers 12, 1, and 1/4 are nearly inversely proportional
to the atomic weights of hydrogen, hydrocarbon gas, and iron vapour, and
it is for this reason that Bredichin suggested the above-mentioned
composition of the various types of tail. Spectroscopic evidence of the
presence of hydrogen is yet wanting.
[34] This illustration, as well as the figure of the path of the
meteors, has been derived from Dr. G.J. Stoney's interesting lecture on
"The Story of the November Meteors," at the Royal Institution, in 1879.
[35] On the 27th November, 1885, a piece of meteoric iron fell at
Mazapil, in Mexico, during the shower of Andromedes, but whether it
formed part of the swarm is not known. It is, however, to be noticed
that meteorites are said to have fallen on several other occasions at
the end of November.
[36] Hooke had noticed, in 1664, that the star Gamma Arietis was double.
[37] Perhaps if we could view the stars without the intervention of the
atmosphere, blue stars would be more common. The absorption of the
atmosphere specially affects the greenish and bluish colours. Professor
Langley gives us good reason for believing that the sun itself would be
blue if it were not for the effect of the air.
[38] The declination of a star is the arc drawn from the star to the
equator at right angles to the latter.
[39] The distance of 61 Cygni has, however, again been investigated by
Professor Asaph Hall, of Washington, who has obtained a result
considerably less than had been previously supposed; on the other hand,
Professor Pritchard's photographic researches are in confirmation of
Struve's and those obtained at Dunsink.
[40] I am indebted for this drawing to the kindness of Messrs. De la
Rue.
[41] _See_ Chapter XIX., on the mass of Sirius and his satellite.
[42] As the earth carries on the telescope at the rate of 18 miles a
second, and as light moves with the velocity of 180,000 miles a second
very nearly, it follows that the velocity of the telescope is about one
ten-thousandth part of that of light. While the light moves down the
tube 20 feet long, the telescope will therefore have moved the
ten-thousandth part of 20 feet--_i.e._, the fortieth of an inch.
[43] _See_ Newcomb's "Popular Astronomy," p. 508, where the discovery of
this law is attributed to Mr. J. Homer Lane, of Washington. The
contraction theory is due to Helmholtz.
[44] The theory of Tidal Evolution sketched in this chapter is mainly
due to the researches of Professor G.H. Darwin, F.R.S.
[45] The hour varies with the locality: it would be 11.49 at Calais; at
Liverpool, 11.23; at Swansea Bay, 5.56, etc.
[46] Having decided upon the units of mass, of angle, and of distance
which we intend to use for measuring these quantities, then any mass, or
angle, or distance is expressed by a certain definite number. Thus if we
take the mass of the earth as the unit of mass, the angle through which
it moves in a second as the unit of angle, and its distance from the sun
as the unit of distance, we shall find that the similar quantities for
Jupiter are expressed by the numbers 316, 0.0843, and 5.2 respectively.
Hence its orbital moment of momentum is 316 x 0.0843 x (5.2) squared.
End of Project Gutenberg's The Story of the Heavens, by Robert Stawell Ball