It needs only the most elementary conceptions of space, direction
and motion to see that, as the earth makes its vast swing from one
extremity of its orbit to the other, the stars, being fixed, must have
an apparent swing in the opposite direction. The seeming absence of
such a swing was in all ages before our own one of the great stumbling
blocks of astronomy. It was the base on which Ptolemy erected his proof
that the earth was immovable in the center of the celestial sphere. It
was felt by Copernicus to be a great difficulty in the reception of his
system. It led Tycho Brahe to suggest a grotesque combination of the
Ptolemaic and Copernican systems, in which the earth was the center of
motion, round which the sun revolved, carrying the planets with it.
With every improvement in their instruments, astronomers sought to
detect the annual swing of the stars. Each time that increased accuracy
in observations failed to show it, the difficulty in the way of the
Copernican system was heightened. How deep the feeling on the subject
is shown by the enthusiastic title, _Copernicus Triumphans_, given by
Horrebow to the paper in which, from observations by Roemer, he claimed
to have detected the swing. But, alas, critical examination showed
that the supposed inequality was produced by the varying effect of the
warmth of the day and the cold of the night upon the rate of the clock
used by the observer, and not by the motion of the earth.
Hooke, a contemporary of Newton, published an attempt to determine the
parallax of the stars, under the title of “An Attempt to Prove the
Motion of the Earth,” but his work was as great a failure as that of
his predecessors. Had it not been that the proofs of the Copernican
system had accumulated until they became irresistible, these repeated
attempts might have led men to think that perhaps, after all, Ptolemy
and the ancients were somehow in the right.
The difficulty was magnified by the philosophic views of the period. It
was supposed that Nature must economize in the use of space as a farmer
would in the use of valuable land. The ancient astronomers correctly
placed the sphere of the stars outside that of the planets, but did not
suppose it far outside. That Nature would squander her resources by
leaving a vacant space hundreds of thousands of times the extent of
the solar system was supposed contrary to all probability. The actual
infinity of space; the consideration that one had only to enlarge his
conceptions a little to see spaces a thousand times the size of the
solar system look as insignificant as the region of a few yards round a
grain of sand, does not seem to have occurred to anyone.
Considerations drawn from photometry were also lost sight of, because
that art was still undeveloped. Kepler saw that the sun might well be
of the nature of a star; in fact, that the stars were probably suns.
Had he and his contemporaries known that the light of the sun was more
than ten thousand million times that of a bright star, they would have
seen that it must be placed at one hundred thousand times its present
distance to shine as a bright star. If, then, the stars are as bright
as the sun, they must be one hundred thousand times as far away, and
their annual parallax would then have been too small for detection with
the instruments of the time. Such considerations as this would have
removed the real difficulty.
The efforts to discover stellar parallax were, of course, still
continued. Bradley, about 1740, made observations on γ Draconis, which
passed the meridian near his zenith, with an instrument of an accuracy
before unequalled. He thus detected an annual swing of 20″ on each
side of the mean. But this swing did not have the right phase to be
due to the motion of the earth; the star appeared at one or the other
extremity of its swing when it should have been at the middle point,
and _vice versa_. What he saw was really the effect of aberration,
depending on the ratio of the velocity of the earth in its orbit to
the velocity of light. It proved the motion of the earth, but in a
different way from what was expected. All that Bradley could prove was
that the distances of the stars must be hundreds of thousands of times
that of the sun.
An introductory remark on the use of the word parallax may preface a
statement of the results of researches now to be considered.
In a general way, the change of apparent direction of an object arising
from a change in the position of an observer is termed _parallax_. More
especially, the parallax of a star is the difference of its direction
as seen from the sun and from that point of the earth’s orbit from
which the apparent direction will be changed by the greatest amount. It
is equal to the angle subtended by the radius of the earth’s orbit, as
seen from the star. The simplest conception of an arc of one second is
reached by thinking of it as the angle subtended by a short line at a
distance of two hundred and six thousand times its length. To say that
a star has a parallax of 1″ would therefore be the same thing as saying
that it was at a distance of a little more than two hundred thousand
times that of the earth from the sun. A parallax of one-half a second
implies a distance twice as great; one of one-third, three times as
great. A parallax of 0″20 implies a distance of more than a million
times that of our unit of measure.
The first conclusive result as to the extreme minuteness of the
parallax of the brighter stars was reached by Struve, at Dorpat, about
1830. In the high latitude of Dorpat the right ascension of a star
can be determined with great precision, not only at the moment of its
transit over the meridian, but also at transit over the meridian below
the pole, which occurs twelve hours later. He, therefore, selected a
large group of stars which could be observed twice daily in this way
at certain times of the year, and made continuous observations on them
through the year. It was not possible, by this method, to certainly
detect the parallax of any one star. What was aimed at was to determine
the limit of the average parallax of all the stars thus observed. The
conclusion reached was that this limit could not exceed one-tenth of a
second and that the average distance of the group could not, therefore,
be much less than two million times the distance of the sun; if,
perchance, some stars were nearer than this, others were more distant.
By a singular coincidence, success in detecting stellar parallax was
reached by three independent investigators almost at the same time,
observing three different stars.
To Bessel is commonly assigned the credit of having first actually
determined the parallax of a star with such certainty as to place the
result beyond question. The star having the most rapid proper motion on
the celestial sphere, so far as known to Bessel, was 61 Cygni, which
is, however, only of the fifth magnitude. This rapid motion indicated
that it was probably among the stars nearest to us, much nearer, in
fact, than the faint stars by which it is surrounded.
After several futile attempts, he undertook a series of measurements
with a heliometer, the best in his power to make, in August, 1837, and
continued them until October, 1838. The object was to determine, night
after night, the position of 61 Cygni, relative to certain small stars
in its neighborhood. Then he and his assistant, Sluter, made a second
series, which was continued until 1840. All these observations showed
conclusively that the star had a parallax of about 0″.35.
While Bessel was making these observations, Struve, at Dorpat, made
a similar attempt upon Alpha Lyræ. This star, in the high northern
latitude of Dorpat, could be accurately observed throughout almost the
entire year. It is one of the brightest stars near the Pole and has
a sensible proper motion. There was, therefore, reason to believe it
among the nearest of the stars. The observations of Struve extended
from 1835 to August, 1838, and were, therefore, almost simultaneous
with the observations made by Bessel on 61 Cygni. He concluded that the
parallax of Alpha Lyræ was about one-fourth of a second. Subsequent
investigations have, however, made it probable that this result was
about double the true value of the parallax.
The third successful attempt was made by Henderson, of England,
astronomer at the Cape of Good Hope. He found from meridian
observations that the star Alpha Centauri had a parallax of about
1″. This is a double star of the first magnitude, which, being only
30° from the south celestial pole, never rises in our latitudes. Its
nearness to us was indicated not only by its magnitude, but also by its
considerable proper motion.
Although subsequent investigation has shown the parallax of this body
to be less than that found by Henderson, it is, up to the time of
writing, the nearest star whose distance has been ascertained. The
extreme difficulty of detecting movements so slight as those we have
described, when they take six months to go through their phases, will
be obvious to the reader. He would be still more impressed with it
when, looking through a powerful telescope at any star, he sees how it
flickers in consequence of the continual motions going on in the air
through which it is seen and how difficult it must be to fix any point
of reference from which to measure the change of direction.
The latter is the capital difficulty in measuring the parallax. How
shall we know that a star has changed its direction by a fraction of a
second in the course of six months? There must be for this purpose some
standard direction from which we can measure.
The most certain of these standard directions is that of the earth’s
axis of rotation. It is true that this direction varies in the course
of the year, but the amount of the variation is known with great
precision, so that it can be properly allowed for in the reduction
of the observations. The angle between the direction of a star and
that of the earth’s axis, the latter direction being represented by
the celestial pole, can be measured with our meridian instruments. It
is, in fact, the north polar distance of the star, or the complement
of its declination. If, therefore, the astronomer could measure the
declination of a star with great precision throughout the entire year,
he would be able to determine its parallax by a comparison of the
measures. But it is found impossible in practice to make measures of so
long an arc with the necessary precision. The uncertain and changing
effect of the varying seasons and different temperatures of day and
night upon the air and the instrument almost masks the parallax. After
several attempts with the finest instruments, handled with the utmost
skill, to determine stellar parallax from the declinations of the
stars, the method has been practically abandoned.
The method now practiced is that of relative parallax. By this method
the standard direction is that of a small star apparently alongside one
whose parallax is to be measured, but, presumably, so much farther
away that it may be regarded as having no parallax. In this assumption
lies the weak point of the method. Can we be sure that the smaller
stars are really without appreciable parallax? Until recent times it
was generally supposed that the magnitude of the stars afforded the
best index to their relative distances. If the stars were of the same
intrinsic brilliancy, the amount of light received from them would, as
already pointed out, have been inversely as the square of the distance.
Although there was no reason to suppose that any such equality really
existed, it would still remain true that, in the general average, the
brighter stars must be nearer to us than the fainter ones. But when the
proper motions of stars came to be investigated, it was found that the
amount of this motion afforded a better index to the distance than the
magnitude did.
The diversity of actual or linear motion is not so wide as that of
absolute brilliancy. Stars have, therefore, in recent times, been
selected for parallax very largely on account of their proper motion,
without respect to their brightness. It is now considered quite safe to
assume that the small stars without proper motion are so far away that
their parallax is insensible.
Ever since the time of Bessel the experience of practical astronomers
has tended toward the conclusion that the best instrument for delicate
measurements like these is the heliometer. This is an equatorial
telescope of which the object glass is divided along a diameter into
two semicircles, which can slide along each other. Each half of the
object glass forms a separate image of any star at which the telescope
may be pointed. By sliding the two halves along each other, the images
can be brought together or separated to any extent. If there are two
stars in proximity, the image of one star made by one-half of the
glass can be brought into coincidence with that of the other star made
by the other half. The sliding of the two halves to bring about this
coincidence affords a scale of measurement for the angular distance of
the two stars.
The most noteworthy forward steps in improving the heliometer are due
to the celebrated instrument-makers of Hamburg, the Messrs. Repsold,
aided by the suggestions of Dr. David Gill, astronomer at the Cape of
Good Hope. The latter, in connection with his coadjutor, Elkin, made an
equally important step in the art of managing the instrument and hence
in determining the parallax of stars. The best results yet attained are
those of these two observers and of Peter, of Germany.
Yet more recently, Kapteyn, of Holland, has applied what has seemed to
be the unpromising method of differences of right ascension observed
with a meridian circle. This method has also been applied by Flint, at
Madison, Wis. Through the skill of these observers, as well as that
of Brünnow and Ball, in applying the equatorial telescope to the same
purposes, the parallax of nearly 100 stars has been measured with some
approach to precision.
A rival method to that of the heliometer has been discovered in
the photographic telescope. The plan of this instrument, and its
application to such purposes as this, are extremely simple. We point a
telescope at a star and set the clock-work going, so that the telescope
shall remain pointed as exactly as possible in the direction of the
star. We place a sensitized plate in the focus and leave it long enough
to form an image both of the particular star in view and of all the
stars around it. The plate being developed, we have a permanent record
of the relative positions of the stars which can be measured with a
suitable instrument at the observer’s leisure. The advantage of the
method consists in the great number of stars which may be examined for
parallax, and in the rapidity with which the work can be done.
The earliest photographs which have been utilized in this way are those
made by Rutherfurd in New York during the years 1860 to 1875. The
plates taken by him have been measured and discussed principally by
Rees and Jacoby, of Columbia University. Before their work was done,
however, Pritchard, of Oxford, applied the method and published results
in the case of a number of stars.
One of the pressing wants of astronomy at the present time is a
parallactic survey of the heavens for the purpose of discovering all
the stars whose parallax exceeds some definable limit, say 0″1. Such a
survey is possible by photography, and by that only. A commencement,
which may serve as an example of one way of conducting the survey,
has been made by Kapteyn on photographic negatives taken by Donner at
Helsingfors.
These plates cover a square in the Milky Way about two degrees on the
side, extending from 35° 50′ in declination to 36° 50′, and from 20h.
1m. in R. A. to 20h. 10m. 24s. Three plates were used, on each of which
the image of each star is formed twelve times. Three of the twelve
impressions were made at the epoch of maximum parallactic displacement,
six at the minimum six months later, and three at the following
maximum. The parallaxes found on the plates can only be relative to the
general mean of all the other stars, and must therefore be negative as
often as positive. The following positive parallaxes, amounting to 0″1,
came out with some consistency from the measures:
Star, B. D., 3972 Mag. 8.6 R.A. 20h., 2m. 0s. Dec. +35°.5
Par. +0″.11
Star, B. D., 3883 Mag. 7.1 R.A. 20h., 2m. 3s. Dec. +36°.1
Par. +0″.18
Star, B. D., 4003 Mag. 9.2 R.A. 20h., 4m. 58s. Dec. +35°.4
Par. +0″.10
Star, B. D., 3959 Mag. 7.0 R.A. 20h., 9m. 14s. Dec. +36°.3
Par. +0″.10
Against these are to be set negative parallaxes of -0″.09, -0″.08 and
several a little smaller, which are certainly unreal.
The presumption in favor of the actuality of one or more of the above
positive values, which is created by their excess over the negative
values, is offset by the following considerations: The area of the
entire sky is more than 40,000 square degrees, or 10,000 times the area
covered by the Helsingfors plates. We cannot well suppose that there
are 1,000 stars in the sky with a parallax of 0″.10, or more without
violating all the probabilities of the case. The probabilities of the
case are therefore against even one star with such a parallax being
found on the plates. Yet the cases of these four stars are worthy of
further examination, if any of them are found to have a sensible proper
motion.
On an entirely different plan is a survey just concluded by Chase with
the Yale heliometer. It includes such stars having an annual proper
motion of 0″.05 or more as had not already been measured for parallax.
The results, in statistical form, are these: