DISTANCE OF THE STARS--THE SUN'S MOTION THROUGH SPACE
In early ages, before any approximate idea was reached of the great
distances of the stars from us, the simple conception of a crystal sphere
to which these luminous points were attached and carried round every day on
an axis near which our pole-star is situated, satisfied the demands for an
explanation of the phenomena. But when Copernicus set forth the true
arrangement of the heavenly bodies, earth and planets alike revolving round
the sun at distances of many millions of miles, and when this scheme was
enforced by the laws of Kepler and the telescopic discoveries of Galileo, a
difficulty arose which astronomers were unable satisfactorily to overcome.
If, said they, the earth revolves round the sun at a distance which cannot
be less (according to Kepler's measurement of the distance of Mars at
opposition) than 13-1/2 millions of miles, then how is it that the nearer
stars are not seen to shift their apparent places when viewed from opposite
sides of this enormous orbit? Copernicus, and after him Kepler and Galileo,
stoutly maintained that it was because the stars were at such an enormous
distance from us that the earth's orbit was a mere point in comparison.
But this seemed wholly incredible, even to the great observer Tycho Brahé,
and hence the Copernican theory was not so generally accepted as it
otherwise would have been.
Galileo always declared that the measurement would some day be made, and he
even suggested the method of effecting it which is now found to be the most
trustworthy. But the sun's distance had to be first measured with greater
accuracy, and that was only done in the latter part of the eighteenth
century by means of transits of Venus; and by later observations with more
perfect instruments it is now pretty well fixed at about 92,780,000 miles,
the limits of error being such that 92-3/4 millions may perhaps be quite as
accurate.
With such an enormous base-line as twice this distance, which is available
by making observations at intervals of about six months when the earth is
at opposite points in its orbit, it seemed certain that some parallax or
displacement of the nearer stars could be found, and many astronomers with
the best instruments devoted themselves to the work. But the difficulties
were enormous, and very few really satisfactory results were obtained till
the latter half of the nineteenth century. About forty stars have now been
measured with tolerable certainty, though of course with a considerable
margin of possible or probable error; and about thirty more, which are
found to have a parallax of one-tenth of a second or less, must be
considered to leave a very large margin of uncertainty.
The two nearest fixed stars are Alpha Centauri and 61 Cygni. The former is
one of the brightest stars in the southern hemisphere, and is about
275,000 times as far from us as the sun. The light from this star will take
4-1/4 years to reach us, and this 'light-journey,' as it is termed, is
generally used by astronomers as an easily remembered mode of recording the
distances of the fixed stars, the distance in miles--in this case about 25
millions of millions--being very cumbrous. The other star, 61 Cygni, is
only of about the fifth magnitude, yet it is the second nearest to us, with
a light-journey of about 7-1/4 years. If we had no other determinations of
distance than these two, the facts would be of the highest importance. They
teach us, first, that magnitude or brightness of a star is no proof of
nearness to us, a fact of which there is much other evidence; and in the
second place, they furnish us with a probable minimum distance of
independent suns from one another, which, in proportion to their sizes,
some being known to be many times larger than our sun, is not more than we
might expect. This remoteness may be partly due to those which were once
nearer together having coalesced under the influence of gravitation.
As this measurement of the distance of the nearer stars should be clearly
understood by every one who wishes to obtain some real comprehension of the
scale of this vast universe of which we form a part, the method now adopted
and found to be most effectual will be briefly explained.
Everyone who is acquainted with the rudiments of trigonometry or
mensuration, knows that an inaccessible distance can be accurately
determined if we can measure a base-line from both ends of which the
inaccessible object can be seen, and if we have a good instrument with
which to measure angles. The accuracy will mainly depend upon our base-line
being not excessively short in comparison with the distance to be measured.
If it is as much as half or even a quarter as long the measurement may be
as accurate as if directly performed over the ground, but if it is only
one-hundredth or one-thousandth part as long, a very small error either in
the length of the base or in the amount of the angles will produce a large
error in the result.
In measuring the distance of the moon, the earth's diameter, or a
considerable portion of it, has served as a base-line. Either two observers
at great distances from each other, or the same observer after an interval
of nine or ten hours, may examine the moon from positions six or seven
thousand miles apart, and by accurate measurements of its angular distance
from a star, or by the time of its passage over the meridian of the place
as observed with a transit instrument, the angular displacement can be
found and the distance determined with very great accuracy, although that
distance is more than thirty times the length of the base. The distance of
the planet Mars when nearest to us has been found in the same way. His
distance from us even when at his nearest point during the most favourable
oppositions is about 36 million miles, or more than four thousand times the
earth's diameter, so that it requires the most delicate observations many
times repeated and with the finest instruments to obtain a tolerably
approximate result. When this is done, by Kepler's law of the fixed
proportion between the distances of planets from the sun and their times of
revolution, the proportionate distance of all the other planets and that
of the sun can be ascertained. This method, however, is not sufficiently
accurate to satisfy astronomers, because upon the sun's distance that of
every other member of the solar system depends. Fortunately there are two
other methods by which this important measurement has been made with much
greater approach to certainty and precision.
[Illustration: Diagram illustrating the transit of Venus.]
The first of these methods is by means of the rare occasions when the
planet Venus passes across the sun's disc as seen from the earth. When this
takes place, observations of the transit, as it is termed, are made at
remote parts of the earth, the distance between which places can of course
easily be calculated from their latitudes and longitudes. The diagram here
given illustrates the simplest mode of determining the sun's distance by
this observation, and the following description from Proctor's _Old and New
Astronomy_ is so clear that I copy it verbally:--'V represents Venus
passing between the Earth E and the Sun S; and we see how an observer at E
will see Venus as at v', while an observer at E' will see her as at v. The
measurement of the distance v v', as compared with the diameter of the
sun's disc, determines the angle v V v' or E V E'; whence the distance E V
can be calculated from the known length of the base-line E E'. For
instance, it is known (from the known proportions of the Solar System as
determined from the times of revolution by Kepler's third law) that E V
bears to V v the proportion 28 to 72, or 7 to 18; whence E E' bears to v v'
the same proportion. Suppose, now, that the distance between the two
stations is known to be 7000 miles, so that v v' is 18,000 miles; and that
v v' is found by accurate measurement to be 1/48 part of the sun's
diameter. Then the sun's diameter, as determined by this observation, is 48
times 18,000 miles, or 864,000 miles; whence from his known apparent size,
which is that of a globe 107-1/3 times farther away from us than its own
diameter, his distance is found to be 92,736,000 miles.'
Of course, there being two observers, the proportion of the distance v v'
to the diameter of the sun's disc cannot be measured directly, but each of
them can measure the apparent angular distance of the planet from the sun's
upper and lower margins as it passes across the disc, and thus the angular
distance between the two lines of transit can be obtained. The distance v
v' can also be found by accurately noting the times of the upper and lower
passage of Venus, which, as the line of transit is considerably shorter in
one than the other, gives by the known properties of the circle the exact
proportion of the distance between them to the sun's diameter; and as this
is found to be the most accurate method, it is the one generally adopted.
For this purpose the stations of the observers are so chosen that the
length of the two chords, v and v', may have a considerable difference,
thus rendering the measurement more easy.
The other method of determining the sun's distance is by the direct
measurement of the velocity of light. This was first done by the French
physicist, Fizeau, in 1849, by the use of rapidly revolving mirrors, as
described in most works on physics. This method has now been brought to
such a decree of perfection that the sun's distance so determined is
considered to be equally trustworthy with that derived from the transits of
Venus. The reason that the determination of the velocity of light leads to
a determination of the sun's distance is, because the time taken by light
to pass from the sun to the earth is independently known to be 8 min.
13-1/3 sec. This was discovered so long ago as 1675 by means of the
eclipses of Jupiter's satellites. These satellites revolve round the planet
in from 1-3/4 to 16 days, and, owing to their moving very nearly in the
plane of the ecliptic and the shadow of Jupiter being so large, the three
which are nearest to the planet are eclipsed at every revolution. This
rapid revolution of the satellites and frequency of the eclipses enabled
their periods of recurrence to be determined with extreme accuracy,
especially after many years of careful observation. It was then found that
when Jupiter was at its farthest distance from the earth the eclipses of
the satellites took place a little more than eight minutes later than the
time calculated from the mean period of revolution, and when the planet was
nearest to us the eclipses occurred the same amount earlier. And when
further observation showed that there was no difference between calculation
and observation when the planet was at its mean distance from us, and that
the error arose and increased exactly in proportion to our varying
distance from it, then it became clear that the only cause adequate to
produce such an effect was, that light had not an infinite velocity but
travelled at a certain fixed rate. This however, though a highly probable
explanation, was not absolutely proved till nearly two centuries later, by
means of two very difficult measurements--that of the actual distance of
the sun from the earth, and that of the actual speed of light in miles per
second; the latter corresponding almost exactly with the speed deduced from
the eclipses of Jupiter's satellites and the sun's distance as measured by
the transits of Venus.
[Illustration: (A) and the last 2 lines of the next paragraph should be
replaced with: one-tenth of an inch long, and from a point (A) 5-3/4
inches from it (accurately 5.72957795 inches) we draw straight lines to
B and C. Then the angle at A is one degree.)]
But this problem of measuring the sun's distance, and through it the
dimensions of the orbits of all the planets of our system, sinks into
insignificance when compared with the enormous difficulties in the way of
the determination of the distance of the stars. As a great many people,
perhaps the majority of the readers of any popular scientific book, have
little knowledge of mathematics and cannot realise what an angle of a
minute or a second really means, a little explanation and illustration of
these terms will not be out of place. An angle of one degree (1°) is the
360th part of a circle (viewed from its centre), the 90th part of a right
angle, the 60th part of either of the angles of an equilateral triangle. To
see exactly how much is an angle of one degree we draw a short line (B C)
one-tenth of an inch long, and from a point we draw straight lines to B
and C. Then the angle at A is one degree.
Now, in all astronomical work, one degree is considered to be quite a large
angle. Even before the invention of the telescope the old observers fixed
the position of the stars and planets to half or a quarter of a degree,
while Mr. Proctor thinks that Tycho Brahé's positions of the stars and
planets were correct to about one or two minutes of arc. But a minute of
arc is obtained by dividing the line B C into sixty equal parts and seeing
the distance between two of these with the naked eye from the point A. But
as very long-sighted people can see very minute objects at 10 or 12 inches
distance, we may double the distance A B, and then making the line B C one
three-hundredth part of an inch long, we shall have the angle of one minute
which Tycho Brahé was perhaps able to measure. How very large an amount a
minute is to the modern astronomer is, however, well shown by the fact that
the maximum difference between the calculated and observed positions of
Uranus, which led Adams and Leverrier to search for and discover Neptune,
was only 1-1/2 minutes, a space so small as to be almost invisible to the
average eye, so that if there had been two planets, one in the calculated,
the other in the observed place, they would have appeared as one to
unassisted vision.
In order now to realise what one second of arc really means, let us look at
the circle here shown, which is as nearly as possible one-tenth of an inch
in diameter--(one-O-tenth of an inch). If we remove this circle to a
distance of 28 feet 8 inches it will subtend an angle of one minute, and we
shall have to place it at a distance of nearly 1730 feet--almost one-third
of a mile--to reduce the angle to one second. But the very nearest to us of
the fixed stars, Alpha Centauri, has a parallax of only three-fourths of a
second; that is, the distance of the earth from the sun--about 92-3/4
millions of miles--would appear no wider, seen from the nearest star, than
does three-fourths of the above small circle at one-third of a mile
distance. To see this circle at all at that distance would require a very
good telescope with a power of at least 100, while to see any small part of
it and to measure the proportion of that part to the whole would need very
brilliant illumination and a large and powerful astronomical telescope.
WHAT IS A MILLION?
But when we have to deal with millions, and even with hundreds and
thousands of millions, there is another difficulty--that few people can
form any clear conception of what a million is. It has been suggested that
in every large school the walls of one room or hall should be devoted to
showing a million at one view. For this purpose it would be necessary to
have a hundred large sheets of paper each about 4 feet 6 inches square,
ruled in quarter inch squares. In each alternate square a round black wafer
or circle should be placed a little over-lapping the square, thus leaving
an equal amount of white space between the black spots. At each tenth spot
a double width should be left so as to separate each hundred spots (10 ×
10). Each sheet would then hold ten thousand spots, which would all be
distinctly visible from the middle of a room 20 feet wide, each horizontal
or vertical row containing a thousand. One hundred such sheets would
contain a million spots, and they would occupy a space 450 feet long in one
row, or 90 feet long in five rows, so that they would entirely cover the
walls of a room, about 30 feet square and 25 feet high, from floor to
ceiling, allowing space for doors but not for windows, the hall or gallery
being lighted from above. Such a hall would be in the highest degree
educational in a country where millions are spoken of so glibly and wasted
so recklessly; while no one can really appreciate modern science, dealing
as it does with the unimaginably great and little, unless he is enabled to
realise by actual vision, and summing up, what a vast number is comprised
in _one_ of those millions, which, in modern astronomy and physics, he has
to deal with not singly only, but by hundreds and thousands or even by
millions. In every considerable town, at all events, a hall or gallery
should have a _million_ thus shown upon its walls. It would in no way
interfere with the walls being covered when required with maps, or
ornamental hangings, or pictures; but when these were removed, the visible
and countable million would remain as a permanent lesson to all visitors;
and I believe that it would have widespread beneficial effects in almost
every department of human thought and action. On a small scale any one can
do this for himself by getting a hundred sheets of engineer's paper ruled
in small squares, and making the spots very small; and even this would be
impressive, but not so much so as on the larger scale.
In order to enable every reader of this volume at once to form some
conception of the number of units in a million, I have made an estimate of
the number of _letters_ contained in it, and I find them to amount to about
420,000--considerably less than half a million. Try and realise, when
reading it, that if every letter were a pound sterling, we waste as many
pounds as there are letters in _two_ such volumes whenever we build a
battleship.
Having thus obtained some real conception of the immensity of a million, we
can better realise what it must be to have every one of the dots above
described, or every one of the letters in two such volumes as this
lengthened out so as to be each a mile long, and even then we should have
reached little more than a hundredth part of the distance from our earth to
the sun. When, by careful consideration of these figures, we have even
partially realised this enormous distance, we may take the next step, which
is, to compare this distance with that of the nearest fixed star. We have
seen that the parallax of that star is three-fourths of a second, an amount
which implies that the star is 271,400 times as far from us as our sun is.
If after _seeing_ what a million is, and knowing that the sun is 92-3/4
times this distance from us in miles--a distance which itself is almost
inconceivable to us--we find that we have to multiply this almost
inconceivable distance 271,400 times--more than a quarter of a million
times--to reach the _nearest_ of the fixed stars, we shall begin to
realise, however imperfectly, how vast is the system of suns around us, and
on what a scale of immensity the material universe, which we see so
gloriously displayed in the starry heavens and the mysterious galaxy, is
constructed.
This somewhat lengthy preliminary discussion is thought necessary in order
that my readers may form some idea of the enormous difficulty of obtaining
any measurement whatever of such distances. I now propose to point out what
the special difficulties are, and how they have been overcome; and thus I
hope to be able to satisfy them that the figures astronomers give us of the
distances of the stars are in no way mere guesses or probabilities, but are
real measurements which, within certain not very wide limits of error, may
be trusted as giving us correct ideas of the magnitude of the visible
universe.
MEASUREMENT OF STELLAR DISTANCES
The fundamental difficulty of this measurement is, of course, that the
distances are so vast that the longest available base-line, the diameter of
the earth's orbit, only subtends an angle of little more than a second from
the nearest star, while for all the rest it is less than one second and
often only a small fraction of it. But this difficulty, great as it is, is
rendered far greater by the fact that there is no fixed point in the
heavens from which to measure, since many of the stars are known to be in
motion, and all are believed to be so in varying degrees, while the sun
itself is now known to be moving among the stars at a rate which is not yet
accurately determined, but in a direction which is fairly well known. As
the various motions of the earth while passing round the sun, though
extremely complex, are very accurately known, it was first attempted to
determine the changed position of stars by observations, many times
repeated at six months' intervals, of the moment of their passage over the
meridian and their distance from the zenith; and then by allowing for all
the known motions of the earth, such as precession of the equinoxes and
nutation of the earth's axis, as well as for refraction and for the
aberration of light, to determine what residual effect was due to the
difference of position from which the star was viewed; and a result was
thus obtained in several cases, though almost always a larger one than has
been found by later observations and by better methods. These earlier
observations, however perfect the instruments and however skilful the
observer, are liable to errors which it seems impossible to avoid. The
instruments themselves are subject in all their parts to expansion and
contraction by changes of temperature; and when these changes are sudden,
one part of the instrument may be affected more than another, and this will
often lead to minute errors which may seriously affect the amount to be
measured when that is so small. Another source of error is due to
atmospheric refraction, which is subject to changes both from hour to hour
and at different seasons. But perhaps most important of all are minute
changes in level of the foundations of the instruments even when they are
carried down to solid rock. Both changes of temperature and changes of
moisture of the soil produce minute alterations of level; while
earth-tremors and slow movements of elevation or depression are now known
to be very frequent. Owing to all these causes, actual measurements of
differences of position at different times of the year, amounting to small
fractions of a second, are found to be too uncertain for the determination
of such minute angles with the required accuracy.
But there is another method which avoids almost all these sources of error,
and this is now generally preferred and adopted for these measurements. It
is, that of measuring the distance between two stars situated apparently
very near each other, one of which has large proper motion, while the other
has none which is measurable. The proper motions of the stars was first
suspected by Halley in 1717, from finding that several stars, whose places
had been given by Hipparchus, 130 B.C., were not in the positions where
they now ought to be; and other observations by the old astronomers,
especially those of occultations of stars by the moon, led to the same
result. Since the time of Halley very accurate observations of the stars
have been made, and in many cases it is found that they move perceptibly
from year to year, while others move so slowly that it is only after forty
or fifty years that the motion can be detected. The greatest proper motions
yet determined amount to between 7" and 8" in a year, while other stars
require twenty, or even fifty or a hundred years to show an equal amount of
displacement. At first it was thought that the brightest stars would have
the largest proper motion, because it was supposed they were nearest to us,
but it was soon found that many small and quite inconspicuous stars moved
as rapidly as the most brilliant, while in many very bright stars no
proper motion at all can be detected. That which moves most rapidly is a
small star of less than the sixth magnitude.
It is a matter of common observation that the motion of things at a
distance cannot be perceived so well as when near, even though the speed
may be the same. If a man is seen on the top of a hill several miles off,
we have to observe him closely for some time before we can be sure whether
he is walking or standing still. But objects so enormously distant as we
now know that the stars are, may be moving at the rate of many miles in a
second and yet require years of observation to detect any movement at all.
The proper motions of nearly a hundred stars have now been ascertained to
be more than one second of arc annually, while a large number have less
than this, and the majority have no perceptible motion, presumably due to
their enormous distance from us. It is therefore not difficult in most
cases to find one or two motionless stars sufficiently close to a star
having a large proper motion (anything more than one-tenth of a second is
so called) to serve as fixed points of measurement. All that is then
required is, to measure with extreme accuracy the angular distance of the
moving from the fixed stars at intervals of six months. The measurements
can be made, however, on every fine night, each one being compared with one
at nearly an interval of six months from it. In this way a hundred or more
measurements of the same star may be made in a year, and the mean of the
whole, allowance being made for proper motion in the interval, will give a
much more accurate result than any single measurement. This kind of
measurement can be made with extreme accuracy when the two stars can be
seen together in the field of the telescope; either by the use of a
micrometer, or by means of an instrument called a heliometer, now often
constructed for the purpose. This is an astronomical telescope of rather
large size, the object glass of which is cut in two straight across the
centre, and the two halves made to slide upon each other by means of an
exceedingly fine and accurate screw-motion, so adjusted and tested as to
measure the angular distance of two objects with extreme accuracy. This is
done by the number of turns of the screw required to bring the two stars
into contact with each other, the image of each one being formed by one of
the halves of the object glass.
But the greatest advantage of this method of determining parallax is, as
Sir John Herschell points out, that it gets rid of all the sources of error
which render the older methods so uncertain and inaccurate. No corrections
are required for precession, nutation, or aberration, since these affect
both stars alike, as is the case also with refraction; while alterations of
level of the instrument have no prejudicial effect, since the measures of
angular distance taken by this method are quite independent of such
movements. A test of the accuracy of the determination of parallax by this
instrument is the very close agreement of different observers, and also
their agreement with the new and perhaps even superior method by
photography. This method was first adopted by Professor Pritchard of the
Oxford Observatory, with a fine reflector of thirteen inches aperture. Its
great advantage is, that all the small stars in the vicinity of the star
whose parallax is sought are shown in their exact positions upon the plate,
and the distances of all of them from it can be very accurately measured,
and by comparing plates taken at six months' intervals, each of these stars
gives a determination of parallax, so that the mean of the whole will lead
to a very accurate result. Should, however, the result from any one of
these stars differ considerably from that derived from the rest, it will be
due in all probability to that star having a proper motion of its own, and
it may therefore be rejected. To illustrate the amount of labour bestowed
by astronomers on this difficult problem, it may be mentioned that for the
photographic measurement of the star 61 Cygni, 330 separate plates were
taken in 1886-7, and on these 30,000 measurements of distances of the pairs
of star-images were made. The result agreed closely with the best previous
determination by Sir Robert Ball, using the micrometer, and the method was
at once admitted by astronomers as being of the greatest value.
Although, as a rule, stars having large proper motions are found to be
comparatively near us, there is no regular proportion between these
quantities, indicating that the rapidity of the motion of the stars varies
greatly. Among fifty stars whose distances have been fairly well
determined, the rate of actual motion varies from one or two up to more
than a hundred miles per second. Among six stars with less than a tenth of
a second of annual proper motion there is one with a parallax of nearly
half a second, and another of one-ninth of a second, so that they are
nearer to us than many stars which move several seconds a year. This may be
due to actual slowness of motion, but is almost certainly caused in part by
their motion being either towards us or away from us, and therefore only
measurable by the spectroscope; and this had not been done when the lists
of parallaxes and proper motions from which these facts are taken were
published. It is evident that the actual direction and rate of motion of a
star cannot be known till this radial movement, as it is termed--that is,
towards or away from us--has been measured; but as this element always
tends to increase the visually observed rate of motion, we cannot, through
its absence, exaggerate the actual motions of the stars.
THE SUN'S MOVEMENT THROUGH SPACE
But there is yet another important factor which affects the apparent
motions of all the stars--the movement of our sun, which, being a star
itself, has a proper motion of its own. This motion was suspected and
sought for by Sir William Herschel a century ago, and he actually
determined the direction of its motion towards a point in the constellation
Hercules, not very far removed from that fixed upon as the average of the
best observations since made. The method of determining this motion is very
simple, but at the same time very difficult. When we are travelling in a
railway carriage near objects pass rapidly out of sight behind us, while
those farther from us remain longer in view, and very distant objects
appear almost stationary for a considerable time. For the same reason, if
our sun is moving in any direction through space, the nearer stars will
appear to travel in an opposite direction to our movement, while the more
distant will remain quite stationary. This movement of the nearest stars is
detected by an examination and comparison of their proper motions, by which
it is found that in one part of the heavens there is a preponderance of the
proper motions in one direction and a deficiency in the opposite direction,
while in the directions at right angles to these the proper motions are not
on the average greater in one direction than in the opposite. But the
proper motions of the stars being themselves so minute, and also so
irregular, it is only by a most elaborate mathematical investigation of the
motions of hundreds or even of thousands of stars, that the direction of
the solar motion can be determined. Till quite recently astronomers were
agreed that the motion was towards a point in Hercules near the
outstretched arm in the figure of that constellation. But the latest
inquiries into this problem, involving the comparison of the motions of
several thousand stars in all parts of the heavens, have led to the
conclusion that the most probable direction of the 'solar apex' (as the
point towards which the sun is moving is termed), is in the adjacent
constellation Lyra, and not far from the brilliant star Vega. This is the
position which Professor Newcomb of Washington thinks most probable, though
there is still room for further investigation. To determine the rate of the
motion is very much more difficult than to fix its direction, because the
distances of so few stars have been determined, and very few indeed of
these lie in the directions best adapted to give accurate results. The best
measurements down to 1890 led to a motion of about 15 miles a second. But
more recently the American astronomer, Campbell, has determined by the
spectroscope the motion in the line of sight of a considerable number of
stars towards and away from the solar apex, and by comparing the average of
these motions, he derives a motion for the sun of about 12-1/2 miles a
second, and this is probably as near as we can yet reach towards the true
amount.
SOME NUMERICAL RESULTS OF THE ABOVE MEASUREMENTS
The measurements of distances and proper motions of a considerable number
of the stars, of the motion of our sun in space (its proper motion),
together with accurate determinations of the comparative brilliancy of the
brightest stars as compared with our sun and with each other, have led to
some very remarkable numerical results which serve as indications of the
scale of magnitude of the stellar universe.
The parallaxes of about fifty stars have now been repeatedly measured with
such consistent results that Professor Newcomb considers them to be fairly
trustworthy, and these vary from one-hundredth to three-quarters of a
second. Three more, all stars of the first magnitude--Rigel, Canopus, and
Alpha Cygni--have no measurable parallax, notwithstanding the
long-continued efforts of many astronomers, affording a striking example of
the fact that brilliancy alone is no test of proximity. Six more stars
have a parallax of only one-fiftieth of a second, and five of these are
either of the first or second magnitudes. Of these nine stars having very
small parallax or none, six are situated in or near to the Milky Way,
another indication of exceeding remoteness, which is further shown by the
fact that they all have a very small proper motion or none at all. These
facts support the conclusion, which had been already reached by astronomers
from a careful study of the distribution of the stars, that the larger
portion of the stars of all magnitudes scattered throughout the Milky Way
or along its borders really belong to the same great system, and may be
said to form a part of it. This is a conclusion of extreme importance
because it teaches us that the grandest of the suns, such as Rigel and
Betelgeuse in the constellation Orion, Antares in the Scorpion, Deneb in
the Swan (Alpha Cygni), and Canopus (Alpha Argus), are in all probability
as far removed from us as are the innumerable minute stars which give the
nebulous or milky appearance to the Galaxy.
It is well to consider for a moment what these facts mean. Professor S.
Newcomb, one of the highest authorities on these problems, tells us that
the long series of measurements to discover the parallax of Canopus, the
brightest star in the southern hemisphere, would have shown a parallax of
one-hundredth of a second, had such existed. Yet the results always seemed
to converge to a mean of 0".000! Suppose, then, we assume the parallax of
this star to be somewhat less than the hundredth of a second--let us say
1/125 of a second. At the distance this gives, light would take almost
exactly 400 years to reach us, so that if we suppose this very brilliant
star to be situated a little on this side of the Galaxy, we must give to
that great luminous circle of stars a distance of about 500 light years. We
shall now perceive the advantage of being able to realise what a million
really is. A person who had once seen a wall-space more than 100 feet long
and 20 feet high completely covered with quarter-inch spots a quarter of an
inch apart; and then tried to imagine every spot to be a mile long and to
be placed end to end in one row, would form a very different conception of
a million miles than those who almost daily _read_ of millions, but are
quite unable to visualise even one of them. Having really seen one million,
we can partially realise the velocity of light, which travels over this
million miles in a little less than 5-1/2 seconds; and yet light takes more
than 4-1/3 years at this inconceivable speed to come to us from the very
_nearest_ of the stars. To realise this still more impressively, let us
take the _distance_ of this nearest star, which is 26 _millions_ of
_millions_ of miles. Let us look in imagination at this large and lofty
hall covered from floor to ceiling with quarter-inch spots--only _one_
million. Let all these be imagined as miles. Then repeat this number of
miles in a straight line, one after the other, as many times as there are
spots in this hall; and even then you have reached only one twenty-sixth
part of the distance to the nearest fixed star! This _million_ times a
_million_ miles has to be repeated twenty-six times to reach the _nearest_
fixed star; and it seems probable that this gives us a good indication of
the distance from each other of at least all the stars down to the sixth
magnitude, perhaps even of a large number of the telescopic stars. But as
we have found that the bright stars of the Milky Way must be at least one
hundred times farther from us than these nearest stars, we have found what
may be termed a minimum distance for that vast star-ring. It may be
immensely farther, but it is hardly possible that it should be anything
less.
THE PROBABLE SIZE OF THE STARS
Having thus obtained an inferior limit for the distance of several stars of
the first magnitude, and their actual brilliancy or light-emission as
compared with our sun having been carefully measured, we have afforded us
some indication of size though perhaps an uncertain one. By these means it
has been found that Rigel gives out about ten thousand times as much light
as our sun, so that if its surface is of the same brightness, it must be a
hundred times the diameter of the sun. But as it is one of the white or
Sirian type of stars it is probably very much more luminous, but even if it
were twenty times brighter it would still have to be twenty-two and a half
times the diameter of the sun; and as the stars of this type are probably
wholly gaseous and much less dense than our sun, this enormous size may not
be far from the truth. It is believed that the Sirian stars generally have
a greater surface brilliancy than our sun. Beta Aurigæ, a star of the
second magnitude but of the Sirian type, is one of the double stars whose
distance has been measured, and this has enabled Mr. Gore to find the mass
of the binary system to be five times that of the sun, and their light one
hundred and seventeen times greater. Even if the density is much less than
the sun's, the intrinsic brilliancy of the surface will be considerably
greater. Another double star, Gamma Leonis, has been found to be three
hundred times more brilliant than the sun if of the same density, but it
would require to be seven times rarer than air to have the extent of
surface needed to give the same amount of light if its surface emitted no
more light than our sun from equal areas.
It is clear, therefore, that many of the stars are much larger than our sun
as well as more luminous; but there are also large numbers of small stars
whose large proper motions, as well as the actual measurement of some,
prove them to be comparatively near to us which yet are only about
one-fiftieth part as bright as the sun. These must, therefore, be either
comparatively small, or if large must be but slightly luminous. In the case
of some double stars it has been proved that the latter is the case; but it
seems probable that others are very much smaller than the average. Up to
the present time no means of determining the size of a star by actual
measurement has been discovered, since their distances are so enormous that
the most powerful telescopes show only a point of light. But now that we
have really measured the distance of a good many stars we are able to
determine an upper limit for their actual dimensions. As the nearest fixed
star, Alpha Centauri, has a parallax of 0".75, this means that if this star
has a diameter as great as our distance from the sun (which is not much
more than a hundred times the sun's diameter) it would be seen to have a
distinct disc about as large as that of Jupiter's first satellite. If it
were even one-tenth of the size supposed it would probably be seen as a
disc in our best modern telescopes. The late Mr. Ranyard remarks that if
the Nebular Hypothesis is true, and our sun once extended as far as the
orbit of Neptune, then, among the millions of visible suns there ought to
be some now to be found in every stage of development. But any sun having a
diameter at all approaching this size, and situated as far off as a hundred
times the distance of Alpha Centauri, would be seen by the Lick telescope
to have a disc half a second in diameter. Hence the fact that there are no
stars with visible discs proves that there are no suns of the required
size, and adds another argument, though not perhaps a strong one, against
the acceptance of the Nebular Hypothesis.