THE DISTANCES OF THE STARS.
Sounding-line for Space--The Labours of Bessel--Meaning of Annual
Parallax--Minuteness of the Parallactic Ellipse Illustrated--The
Case of 61 Cygni--Different Comparison Stars used--The Proper
Motion of the Star--Struve's Investigations--Can they be
Reconciled?--Researches at Dunsink--Conclusion obtained--Accuracy
which such Observations admit Examined--The Proper Motion of 61
Cygni--The Permanence of the Sidereal Heavens--The New Star in
Cygnus--Its History--No Appreciable Parallax--A Mighty Outburst of
Light--The Movement of the Solar System through Space--Herschel's
Discovery--Journey towards Lyra--Probabilities.
We have long known the dimensions of the solar system with more or less
accuracy. Our knowledge includes the distances of the planets and the
comets from the sun, as well as their movements. We have also
considerable knowledge of the diameters and the masses of many of the
different bodies which belong to the solar system. We have long known,
in fact, many details of the isolated group nestled together under the
protection of the sun. The problem for consideration in the present
chapter involves a still grander survey than is required for measures of
our solar system. We propose to carry the sounding-line across the vast
abyss which separates the group of bodies closely associated about our
sun from the other stars which are scattered through the realms of
space. For centuries the great problem of star distance has engaged the
attention of those who have studied the heavens. It would be impossible
to attempt here even an outline of the various researches which have
been made on the subject. In the limited survey which we can make, we
must glance first at the remarkable speculative efforts which have been
directed to the problem, and then we shall refer to those labours which
have introduced the problem into the region of accurate astronomy.
No attempt to solve the problem of the absolute distances of the stars
was successful until many years after Herschel's labours were closed.
Fresh generations of astronomers, armed with fresh appliances, have for
many years pursued the subject with unremitting diligence, but for a
long time the effort seemed hopeless. The distances of the stars were so
great that they could not be ascertained until the utmost refinements of
mechanical skill and the most elaborate methods of mathematical
calculation were brought to converge on the difficulty. At last it was
found that the problem was beginning to yield. A few stars have been
induced to disclose the secret of their distance. We are able to give
some answer to the question--How far are the stars? though it must be
confessed that our reply up to the present moment is both hesitating and
imperfect. Even the little knowledge which has been gained possesses
interest and importance. As often happens in similar cases, the
discovery of the distance of a star was made independently about the
same time by two or three astronomers. The name of Bessel stands out
conspicuously in this memorable chapter of astronomy. Bessel proved
(1840) that the distance of the star known as 61 Cygni was a measurable
quantity. His demonstration possessed such unanswerable logic that
universal assent could not be withheld. Almost simultaneously with the
classical labours of Bessel we have Struve's measurement of the distance
of Vega, and Henderson's determination of the distance of the southern
star a Centauri. Great interest was excited in the astronomical
world by these discoveries, and the Royal Astronomical Society awarded
its gold medal to Bessel. It appropriately devolved on Sir John Herschel
to deliver the address on the occasion of the presentation of the medal:
that address is a most eloquent tribute to the labours of the three
astronomers. We cannot resist quoting the few lines in which Sir John
said:--
"Gentlemen of the Royal Astronomical Society,--I congratulate you
and myself that we have lived to see the great and hitherto
impassable barrier to our excursion into the sidereal universe,
that barrier against which we have chafed so long and so
vainly--_aestuantes angusto limite mundi_--almost simultaneously
overleaped at three different points. It is the greatest and most
glorious triumph which practical astronomy has ever witnessed.
Perhaps I ought not to speak so strongly; perhaps I should hold
some reserve in favour of the bare possibility that it may be all
an illusion, and that future researches, as they have repeatedly
before, so may now fail to substantiate this noble result. But I
confess myself unequal to such prudence under such excitement. Let
us rather accept the joyful omens of the time, and trust that, as
the barrier has begun to yield, it will speedily be effectually
prostrated."
Before proceeding further, it will be convenient to explain briefly how
the distance of a star can be measured. The problem is one of a wholly
different character from that of the sun's distance, which we have
already discussed in these pages. The observations for the determination
of stellar parallax are founded on the familiar truth that the earth
revolves around the sun. We may for our present purpose assume that the
earth revolves in a circular path. The centre of that path is at the
centre of the sun, and the radius of the path is 92,900,000 miles. Owing
to our position on the earth, we observe the stars from a point of view
which is constantly changing. In summer the earth is 185,800,000 miles
distant from the position which it occupied in winter. It follows that
the apparent positions of the stars, as projected on the background of
the sky, must present corresponding changes. We do not now mean that the
actual positions of the stars are really displaced. The changes are only
apparent, and while oblivious of our own motion, which produces the
displacements, we attribute the changes to the stars.
On the diagram in Fig. 93 is an ellipse with certain months--viz.,
January, April, July, October--marked upon its circumference. This
ellipse may be regarded as a miniature picture of the earth's orbit
around the sun. In January the earth is at the spot so marked; in April
it has moved a quarter of the whole journey; and so on round the whole
circle, returning to its original position in the course of one year.
When we look from the position of the earth in January, we see the star
A projected against the point of the sky marked 1. Three months later
the observer with his telescope is carried round to April; but he now
sees the star projected to the position marked 2. Thus, as the observer
moves around the whole orbit in the annual revolution of the earth, so
the star appears to move round in an ellipse on the background of the
sky. In the technical language of astronomers, we speak of this as the
parallactic ellipse, and it is by measuring the major axis of this
ellipse that we determine the distance of the star from the sun. Half of
this major axis, or, what comes to the same thing, the angle which the
radius of the earth's orbit subtends as seen from the star, is called
the star's "annual parallax."
[Illustration: Fig. 93.--The Parallactic Ellipse.]
The figure shows another star, B, more distant from the earth and the
solar system generally than the star previously considered. This star
also describes an elliptic path. We cannot, however, fail to notice that
the parallactic ellipse belonging to B is much smaller than that of A.
The difference in the sizes of the ellipses arises from the different
distances of the stars from the earth. The nearer the star is to the
earth the greater is the ellipse, so that the nearest star in the
heavens will describe the largest ellipse, while the most distant star
will describe the smallest ellipse. We thus see that the distance of the
star is inversely proportional to the size of the ellipse, and if we
measure the angular value of the major axis of the ellipse, then, by an
exceedingly simple mathematical manipulation, the distance of the star
can be expressed as a multiple of a radius of the earth's orbit.
Assuming that radius to be 92,900,000 miles, the distance of the star is
obtained by simple arithmetic. The difficulty in the process arises from
the fact that these ellipses are so small that our micrometers often
fail to detect them.
How shall we adequately describe the extreme minuteness of the
parallactic ellipses in the case of even the nearest stars? In the
technical language of astronomers, we may state that the longest
diameter of the ellipse never subtends an angle of more than one and a
half seconds. In a somewhat more popular manner, we would say that one
thousand times the major axis of the very largest parallactic ellipse
would not be as great as the diameter of the full moon. For a still more
simple illustration, let us endeavour to think of a penny-piece placed
at a distance of two miles. If looked at edgeways it will be linear, if
tilted a little it would be elliptic; but the ellipse would, even at
that distance, be greater than the greatest parallactic ellipse of any
star in the sky. Suppose a sphere described around an observer, with a
radius of two miles. If a penny-piece were placed on this sphere, in
front of each of the stars, every parallactic ellipse would be totally
concealed.
The star in the Swan known as 61 Cygni is not remarkable either for its
size or for its brightness. It is barely visible to the unaided eye, and
there are some thousands of stars which are apparently larger and
brighter. It is, however, a very interesting example of that remarkable
class of objects known as double stars. It consists of two nearly equal
stars close together, and evidently connected by a bond of mutual
attraction. The attention of astronomers is also specially directed
towards the star by its large proper motion. In virtue of that proper
motion, the two components are carried together over the sky at the rate
of five seconds annually. A proper motion of this magnitude is extremely
rare, yet we do not say it is unparalleled, for there are some few stars
which have a proper motion even more rapid; but the remarkable duplex
character of 61 Cygni, combined with the large proper motion, render it
an unique object, at all events, in the northern hemisphere.
When Bessel proposed to undertake the great research with which his name
will be for ever connected, he determined to devote one, or two, or
three years to the continuous observations of one star, with the view of
measuring carefully its parallactic ellipse. How was he to select the
object on which so much labour was to be expended? It was all-important
to choose a star which should prove sufficiently near to reward his
efforts by exhibiting a measurable parallax. Yet he could have but
little more than surmise and analogy as a guide. It occurred to him that
the exceptional features of 61 Cygni afforded the necessary presumption,
and he determined to apply the process of observation to this star. He
devoted the greater part of three years to the work, and succeeded in
discovering its distance from the earth.
Since the date of Sir John Herschel's address, 61 Cygni has received the
devoted and scarcely remitted attention of astronomers. In fact, we
might say that each succeeding generation undertakes a new discussion of
the distance of this star, with the view of confirming or of criticising
the original discovery of Bessel. The diagram here given (Fig. 94) is
intended to illustrate the recent history of 61 Cygni.
When Bessel engaged in his labours, the pair of stars forming the double
were at the point indicated on the diagram by the date 1838. The next
epoch occurred fifteen years later, when Otto Struve undertook his
researches, and the pair of stars had by that time moved to the
position marked 1853. Finally, when the same object was more recently
observed at Dunsink Observatory, the pair had made still another
advance, to the position indicated by the date 1878. Thus, in forty
years this double star had moved over an arc of the heavens upwards of
three minutes in length. The actual path is, indeed, more complicated
than a simple rectilinear movement. The two stars which form the double
have a certain relative velocity, in consequence of their mutual
attraction. It will not, however, be necessary to take this into
account, as the displacement thus arising in the lapse of a single year
is far too minute to produce any inconvenient effect on the parallactic
ellipse.
[Illustration: Fig. 94.--61 Cygni and the Comparison Stars.]
The case of 61 Cygni is, however, exceptional. It is one of our nearest
neighbours in the heavens. We can never find its distance accurately to
one or two billions of miles; but still we have a consciousness that an
uncertainty amounting to twenty billions is too large a percentage of
the whole. We shall presently show that we believe Struve was right,
yet it does not necessarily follow that Bessel was wrong. The apparent
paradox can be easily explained. It would not be easily explained if
Struve had used the _same comparison star_ as Bessel had done; but
Struve's comparison star was different from either of Bessel's, and this
is probably the cause of the discrepancy. It will be recollected that
the essence of the process consists of the comparison of the small
ellipse made by the distant star with the larger ellipse made by the
nearer star. If the two stars were at the same distance, the process
would be wholly inapplicable. In such a case, no matter how near the
stars were to the earth, no parallax could be detected. For the method
to be completely successful, the comparison star should be at least
eight times as far as the principal star. Bearing this in mind, it is
quite possible to reconcile the measures of Bessel with those of Struve.
We need only assume that Bessel's comparison stars are about three times
as far as 61 Cygni, while Struve's comparison star is at least eight or
ten times as far. We may add that, as the comparison stars used by
Bessel are brighter than that of Struve, there really is a presumption
that the latter is the most distant of the three.
We have here a characteristic feature of this method of determining
parallax. Even if all the observations and the reductions of a parallax
series were mathematically correct, we could not with strict propriety
describe the final result as the parallax of one star. It is only the
_difference_ between the parallax of the star and that of the comparison
star. We can therefore only assert that the parallax sought cannot be
less than the quantity determined. Viewed in this manner, the
discrepancy between Struve and Bessel vanishes. Bessel asserted that the
distance of 61 Cygni could not be _more_ than sixty billions of miles.
Struve did not contradict this--nay, he certainly confirmed it--when he
showed that the distance could not be more than forty billions.
Nearly half a century has elapsed since Struve made his observations.
Those observations have certainly been challenged; but they are, on the
whole, confirmed by other investigations. In a critical review of the
subject Auwers showed that Struve's determination is worthy of
considerable confidence. Yet, notwithstanding this authoritative
announcement, the study of 61 Cygni has been repeatedly resumed. Dr.
Bruennow, when Astronomer Royal of Ireland, commenced a series of
observations on the parallax of 61 Cygni, which were continued and
completed by the present writer, his successor. Bruennow chose a fourth
comparison star (marked on the diagram), different from any of those
which had been used by the earlier observers. The method of observing
which Bruennow employed was quite different from that of Struve, though
the filar micrometer was used in both cases. Bruennow sought to determine
the parallactic ellipse by measuring the difference in declination
between 61 Cygni and the comparison star.[38] In the course of a year it
is found that the difference in declination undergoes a periodic change,
and from that change the parallactic ellipse can be computed. In the
first series of observations I measured the difference of declination
between the preceding star of 61 Cygni and the comparison star; in the
second series I took the other component of 61 Cygni and the same
comparison star. We had thus two completely independent determinations
of the parallax resulting from two years' work. The first of these makes
the distance forty billions of miles, and the second makes it almost
exactly the same. There can be no doubt that this work supports Struve's
determination in correction of Bessel's, and therefore we may perhaps
sum up the present state of our knowledge of this question by saying
that the distance of 61 Cygni is much nearer to the forty billions of
miles which Struve found than to the sixty billions which Bessel
found.[39]
It is desirable to give the reader the means of forming his own opinion
as to the quality of the evidence which is available in such researches.
The diagram in Fig. 95 here shown has been constructed with this object.
It is intended to illustrate the second series of observations of
difference of declination which I made at Dunsink. Each of the dots
represents one night's observations. The height of the dot is the
observed difference of declination between 61 (B) Cygni and the
comparison star. The distance along the horizontal line--or the
abscissa, as a mathematician would call it--represents the date. These
observations are grouped more or less regularly in the vicinity of a
certain curve. That curve expresses where the observations should have
been, had they been absolutely perfect. The distances between the dots
and the curve may be regarded as the errors which have been committed in
making the observations.
[Illustration: Fig. 95.--Parallax in Declination of 61 Cygni.]
Perhaps it will be thought that in many cases these errors appear to
have attained very undesirable dimensions. Let us, therefore, hasten to
say that it was precisely for the purpose of setting forth these errors
that this diagram has been shown; we have to exhibit the weakness of the
case no less than its strength. The errors of the observations are not,
however, intrinsically so great as might at first sight be imagined. To
perceive this, it is only necessary to interpret the scale on which this
diagram has been drawn by comparison with familiar standards. The
distance from the very top of the curve to the horizontal line denotes
an angle of only four-tenths of a second. This is about the apparent
diameter of a penny-piece at a distance of _ten miles_! We can now
appraise the true magnitude of the errors which have been made. It will
be noticed that no one of the dots is distant from the curve by much
more than half of the height of the curve. It thus appears that the
greatest error in the whole series of observations amounts to but two or
three tenths of a second. This is equivalent to our having pointed the
telescope to the upper edge of a penny-piece fifteen or twenty miles
off, instead of to the lower edge. This is not a great blunder. A rifle
team whose errors in pointing were more than a hundred times as great
might still easily win every prize at Bisley.
We have entered into the history of 61 Cygni with some detail, because
it is the star whose distance has been most studied. We do not say that
61 Cygni is the nearest of all the stars; it would, indeed, be very rash
to assert that any particular star was the nearest of all the countless
millions in the heavenly host. We certainly know one star which seems
nearer than 61 Cygni; it lies in one of the southern constellations, and
its name is a Centauri. This star is, indeed, of memorable
interest in the history of the subject. Its parallax was first
determined at the Cape of Good Hope by Henderson; subsequent researches
have confirmed his observations, and the elaborate investigations of Dr.
Gill have proved that the parallax of this star is about three-quarters
of a second, so that it is only two-thirds of the distance of 61 Cygni.
61 Cygni arrested our attention, in the first instance, by the
circumstance that it had the large proper motion of five seconds
annually. We have also ascertained that the annual parallax is about
half a second. The combination of these two statements leads to a result
of considerable interest. It teaches us that 61 Cygni must each year
traverse a distance of not less than ten times the radius of the earth's
orbit. Translating this into ordinary figures, we learn that this star
must travel nine hundred and twenty million miles per annum. It must
move between two and three million miles each day, but this can only be
accomplished by maintaining the prodigious velocity of thirty miles per
second. There seems to be no escape from this conclusion. The facts
which we have described, and which are now sufficiently well
established, are inconsistent with the supposition that the velocity of
61 Cygni is less than thirty miles per second; the velocity may be
greater, but less it cannot be.
For the last hundred and fifty years we know that 61 Cygni has been
moving in the same direction and with the same velocity. Prior to the
existence of the telescope we have no observation to guide us; we
cannot, therefore, be absolutely certain as to the earlier history of
this star, yet it is only reasonable to suppose that 61 Cygni has been
moving from remote antiquity with a velocity comparable with that it has
at present. If disturbing influences were entirely absent, there could
be no trace of doubt about the matter. _Some_ disturbing influence,
however, there must be; the only question is whether that disturbing
influence is sufficient to modify seriously the assumption we have made.
A powerful disturbing influence might greatly alter the velocity of the
star; it might deflect the star from its rectilinear course; it might
even force the star to move around a closed orbit. We do not, however,
believe that any disturbing influence of this magnitude need be
contemplated, and there can be no reasonable doubt that 61 Cygni moves
at present in a path very nearly straight, and with a velocity very
nearly uniform.
As the distance of 61 Cygni from the sun is forty billions of miles, and
its velocity is thirty miles a second, it is easy to find how long the
star would take to accomplish a journey equal to its distance from the
sun. The time required will be about 40,000 years. In the last 400,000
years 61 Cygni will have moved over a distance ten times as great as
its present distance from the sun, whatever be the direction of motion.
This star must therefore have been about ten times as far from the earth
400,000 years ago as it is at present. Though this epoch is incredibly
more remote than any historical record, it is perhaps not incomparable
with the duration of the human race; while compared with the vast lapse
of geological time, such periods seem trivial and insignificant.
Geologists have long ago repudiated mere thousands of years; they now
claim millions, and many millions of years, for the performance of
geological phenomena. If the earth has existed for the millions of years
which geologists assert, it becomes reasonable for astronomers to
speculate on the phenomena which have transpired in the heavens in the
lapse of similar ages. By the aid of our knowledge of star distances,
combined with an assumed velocity of thirty miles per second, we can
make the attempt to peer back into the remote past, and show how great
are the changes which our universe seems to have undergone.
In a million years 61 Cygni will apparently have moved through a
distance which is twenty-five times as great as its present distance
from the sun. Whatever be the direction in which 61 Cygni is
moving--whether it be towards the earth or from the earth, to the right
or to the left, it must have been about twenty-five times as far off a
million years ago as it is at present; but even at its present distance
61 Cygni is a small star; were it ten times as far it could only be seen
with a good telescope; were it twenty-five times as far it would barely
be a visible point in our greatest telescopes.
The conclusions arrived at with regard to 61 Cygni may be applied with
varying degrees of emphasis to other stars. We are thus led to the
conclusion that many of the stars with which the heavens are strewn are
apparently in slow motion. But this motion though apparently slow may
really be very rapid. When standing on the sea-shore, and looking at a
steamer on the distant horizon, we can hardly notice that the steamer is
moving. It is true that by looking again in a few minutes we can detect
a change in its place; but the motion of the steamer seems slow. Yet if
we were near the steamer we would find that it was rushing along at the
rate of many miles an hour. It is the distance which causes the
illusion. So it is with the stars: they seem to move slowly because they
are very distant, but were we near them, we could see that in the
majority of cases their motions are a thousand times as fast as the
quickest steamer that ever ploughed the ocean.
It thus appears that the permanence of the sidereal heavens, and the
fixity of the constellations in their relative positions, are only
ephemeral. When we rise to the contemplation of such vast periods of
time as the researches of geology disclose, the durability of the
constellations vanishes! In the lapse of those stupendous ages stars and
constellations gradually dissolve from view, to be replaced by others of
no greater permanence.
It not unfrequently happens that a parallax research proves abortive.
The labour has been finished, the observations are reduced and
discussed, and yet no value of the parallax can be obtained. The
distance of the star is so vast that our base-line, although it is
nearly two hundred millions of miles long, is too short to bear any
appreciable ratio to the distance of the star. Even from such failures,
however, information may often be drawn.
Let me illustrate this by an account derived from my own experience at
Dunsink. We have already mentioned that on the 24th November, 1876, a
well-known astronomer--Dr. Schmidt, of Athens--noticed a new bright star
of the third magnitude in the constellation Cygnus. On the 20th of
November Nova Cygni was invisible. Whether it first burst forth on the
21st, 22nd, or 23rd no one can tell; but on the 24th it was discovered.
Its brilliancy even then seemed to be waning; so, presumably, it was
brightest at some moment between the 20th and 24th of November. The
outbreak must thus have been comparatively sudden, and we know of no
cause which would account for such a phenomenon more simply than a
gigantic collision. The decline in the brilliancy was much more tardy
than its growth, and more than a fortnight passed before the star
relapsed into insignificance--two or three days (or less) for the rise,
two or three weeks for the fall. Yet even two or three weeks was a short
time in which to extinguish so mighty a conflagration. It is
comparatively easy to suggest an explanation of the sudden outbreak; it
is not equally easy to understand how it can have been subdued in a few
weeks. A good-sized iron casting in one of our foundries takes nearly as
much time to cool as sufficed to abate the celestial fires in Nova
Cygni!
On this ground it seemed not unreasonable to suppose that perhaps Nova
Cygni was not really a very extensive conflagration. But, if such were
the case, the star must have been comparatively _near_ to the earth,
since it presented so brilliant a spectacle and attracted so much
attention. It therefore appeared a plausible object for a parallax
research; and consequently a series of observations were made some years
ago at Dunsink. I was at the time too much engaged with other work to
devote very much labour to a research which might, after all, only prove
illusory. I simply made a sufficient number of micrometric measurements
to test whether a _large_ parallax existed. It has been already pointed
out how each star appears to describe a minute parallactic ellipse, in
consequence of the annual motion of the earth, and by measurement of
this ellipse the parallax--and therefore the distance--of the star can
be determined. In ordinary circumstances, when the parallax of a star is
being investigated, it is necessary to measure the position of the star
in its ellipse on many different occasions, distributed over a period of
at least an entire year. The method we adopted was much less laborious.
It was sufficiently accurate to test whether or not Nova Cygni had a
_large_ parallax, though it might not have been delicate enough to
disclose a small parallax. At a certain date, which can be readily
computed, the star is at one end of the parallactic ellipse, and six
months later the star is at the other end. By choosing suitable times in
the year for our observations, we can measure the star in those two
positions when it is most deranged by parallax. It was by observations
of this kind that I sought to detect the parallax of Nova Cygni. Its
distance from a neighbouring star was carefully measured by the
micrometer at the two seasons when, if parallax existed, those distances
should show their greatest discrepancy; but no certain difference
between these distances could be detected. The observations, therefore,
failed to reveal the existence of a parallactic ellipse--or, in other
words, the distance of Nova Cygni was too great to be measured by
observations of this kind.
It is certain that if Nova Cygni had been one of the nearest stars these
observations would not have been abortive. We are therefore entitled to
believe that Nova Cygni must be at least 20,000,000,000,000 miles from
the solar system; and the suggestion that the brilliant outburst was of
small dimensions must, it seems, be abandoned. The intrinsic brightness
of Nova Cygni, when at its best, cannot have been greatly if at all
inferior to the brilliancy of our sun himself. If the sun were withdrawn
from us to the distance of Nova Cygni, it would seemingly have dwindled
down to an object not more brilliant than the variable star. How the
lustre of such a stupendous object declined so rapidly remains,
therefore, a mystery not easy to explain. Have we not said that the
outbreak of brilliancy in this star occurred between the 20th and the
24th of November, 1876? It would be more correct to say that the tidings
of that outbreak reached our system at the time referred to. The real
outbreak must have taken place at least three years previously. Indeed,
at the time that the star excited such commotion in the astronomical
world here, it had already relapsed again into insignificance.
In connection with the subject of the present chapter we have to
consider a great problem which was proposed by Sir William Herschel. He
saw that the stars were animated by proper motion; he saw also that the
sun is a star, one of the countless host of heaven, and he was therefore
led to propound the stupendous question as to whether the sun, like the
other stars which are its peers, was also in motion. Consider all that
this great question involves. The sun has around it a retinue of
planets and their attendant satellites, the comets, and a host of
smaller bodies. The question is, whether all this superb system is
revolving around the sun _at rest_ in the middle, or whether the whole
system--sun, planets, and all--is not moving on bodily through space.
Herschel was the first to solve this noble problem; he discovered that
our sun and the splendid retinue by which it is attended are moving in
space. He not only discovered this, but he ascertained the direction in
which the system was moving, as well as the approximate velocity with
which that movement was probably performed. It has been shown that the
sun and his system is now hastening towards a point of the heavens near
the constellation Lyra. The velocity with which the motion is performed
corresponds to the magnitude of the system; quicker than the swiftest
rifle-bullet that was ever fired, the sun, bearing with it the earth and
all the other planets, is now sweeping onwards. We on the earth
participate in that motion. Every half hour we are something like ten
thousand miles nearer to the constellation of Lyra than we should have
been if the solar system were not animated by this motion. As we are
proceeding at this stupendous rate towards Lyra, it might at first be
supposed that we ought soon to get there; but the distances of the stars
in that neighbourhood seem not less than those of the stars elsewhere,
and we may be certain that the sun and his system must travel at the
present rate for far more than a million years before we have crossed
the abyss between our present position and the frontiers of Lyra. It
must, however, be acknowledged that our estimate of the actual _speed_
with which our solar system is travelling is exceedingly uncertain, but
this does not in the least affect the fact that we are moving in the
direction first approximately indicated by Herschel (_see_ Chapter
XXIII.).
It remains to explain the method of reasoning which Herschel adopted, by
which he was able to make this great discovery. It may sound strange to
hear that the detection of the motion of the sun was not made by looking
at the sun; all the observations of the luminary itself with all the
telescopes in the world would never tell us of that motion, for the
simple reason that the earth, whence our observations must be made,
participates in it. A passenger in the cabin of a ship usually becomes
aware that the ship is moving by the roughness of the sea; but if the
sea be perfectly calm, then, though the tables and chairs in the cabin
are moving as rapidly as the ship, yet we do not see them moving,
because we are also travelling with the ship. If we could not go out of
the cabin, nor look through the windows, we would never know whether the
ship was moving or at rest; nor could we have any idea as to the
direction in which the ship was going, or as to the velocity with which
that motion was performed.
The sun, with his attendant host of planets and satellites, may be
likened to the ship. The planets may revolve around the sun just as the
passengers may move about in the cabin, but as the passengers, by
looking at objects on board, can never tell whither the ship is going,
so we, by merely looking at the sun, or at the other planets or members
of the solar system, can never tell if our system as a whole is in
motion.
The conditions of a perfectly uniform movement along a perfectly calm
sea are not often fulfilled on the waters with which we are acquainted,
but the course of the sun and his system is untroubled by any
disturbance, so that the majestic progress is conducted with absolute
uniformity. We do not feel the motion; and as all the planets are
travelling with us, we can get no information from them as to the common
motion by which the whole system is animated.
The passengers are, however, at once apprised of the ship's motion when
they go on deck, and when they look at the sea surrounding them. Let us
suppose that their voyage is nearly accomplished, that the distant land
appears in sight, and, as evening approaches, the harbour is discerned
into which the ship is to enter. Let us suppose that the harbour has, as
is often the case, a narrow entrance, and that its mouth is indicated by
a lighthouse on each side. When the harbour is still a long way off,
near the horizon, the two lights are seen close together, and now that
the evening has closed in, and the night has become quite dark, these
two lights are all that remain visible. While the ship is still some
miles from its destination the two lights seem close together, but as
the distance decreases the two lights seem to open out; gradually the
ship gets nearer, while the lights are still opening, till finally, when
the ship enters the harbour, instead of the two lights being directly in
front, as at the commencement, one of the lights is passed by on the
right hand, while the other is similarly found on the left. If, then, we
are to discover the motion of the solar system, we must, like the
passenger, look at objects unconnected with our system, and learn our
own motion by their apparent movements. But are there any objects in the
heavens unconnected with our system? If all the stars were like the
earth, merely the appendages of our sun, then we never could discover
whether we were at rest or whether we were in motion: our system might
be in a condition of absolute rest, or it might be hurrying on with an
inconceivably great velocity, for anything we could tell to the
contrary. But the stars do not belong to the system of our sun; they
are, rather, suns themselves, and do not recognise the sway of our sun,
as this earth is obliged to do. The stars will, therefore, act as the
external objects by which we can test whether our system is voyaging
through space.
With the stars as our beacons, what ought we to expect if our system be
really in motion? Remember that when the ship was approaching the
harbour the lights gradually opened out to the right and left. But the
astronomer has also lights by which he can observe the navigation of
that vast craft, our solar system, and these lights will indicate the
path along which he is borne. If our solar system be in motion, we
should expect to find that the stars were gradually spreading away from
that point in the heavens towards which our motion tends. This is
precisely what we do find. The stars in the constellations are gradually
spreading away from a central point near the constellation of Lyra, and
hence we infer that it is towards Lyra that the motion of the solar
system is directed.
There is one great difficulty in the discussion of this question. Have
we not had occasion to observe that the stars themselves are in actual
motion? It seems certain that every star, including the sun himself as a
star, has each an individual motion of its own. The motions of the stars
as we see them are partly apparent as well as partly real; they partly
arise from the actual motion of each star and partly from the motion of
the sun, in which we partake, and which produces an apparent motion of
the star. How are these to be discriminated? Our telescopes and our
observations can never effect this decomposition directly. To accomplish
the analysis, Herschel resorted to certain geometrical methods. His
materials at that time were but scanty, but in his hands they proved
adequate, and he boldly announced his discovery of the movement of the
solar system.
So astounding an announcement demanded the severest test which the most
refined astronomical resources could suggest. There is a certain
powerful and subtle method which astronomers use in the effort to
interpret nature. Bishop Butler has said that probability is the guide
of life. The proper motion of a star has to be decomposed into two
parts, one real and the other apparent. When several stars are taken, we
may conceive an infinite number of ways into which the movements of each
star can be so decomposed. Each one of these conceivable divisions will
have a certain element of probability in its favour. It is the business
of the mathematician to determine the amount of that probability. The
case, then, is as follows:--Among all the various systems one must be
true. We cannot lay our finger for certain on the true one, but we can
take that which has the highest degree of probability in its favour, and
thus follow the precept of Butler to which we have already referred. A
mathematician would describe his process by calling it the method of
least squares. Since Herschel's discovery, one hundred years ago, many
an astronomer using observations of hundreds of stars has attacked the
same problem. Mathematicians have exhausted every refinement which the
theory of probabilities can afford, but only to confirm the truth of
that splendid theory which seems to have been one of the flashes of
Herschel's genius.