frequently happens with a long-matured difficulty, it gave way in three
places at once. Bessel, Henderson, and Struve almost simultaneously
announced a stellar parallax which could reasonably be accepted. Bessel
was a little the earliest, and by far the most accurate. His, indeed,
was the result which commanded confidence, and to him the palm must be
awarded.
He was largely a self-taught student, having begun life in a
counting-house, and having abandoned business for astronomy. But
notwithstanding these disadvantages, he became a highly competent
mathematician as well as a skilful practical astronomer. He was
appointed to superintend the construction of Germany's first great
astronomical observatory, that of Koenigsberg, which, by his system,
zeal, and genius, he rapidly made a place of the first importance.
Struve at Dorpat, Bessel at Koenigsberg, and Henderson at the Cape of
Good Hope--all of them at newly-equipped observatories--were severally
engaged at the same problem.
But the Russian and German observers had the advantage of the work of
one of the most brilliant opticians--I suppose the most brilliant--that
has yet appeared: Fraunhofer, of Munich. An orphan lad, apprenticed to a
maker of looking-glasses, and subject to hard struggles and privations
in early life, he struggled upwards, and ultimately became head of the
optical department of a Munich firm of telescope-makers. Here he
constructed the famous "Dorpat refractor" for Struve, which is still at
work; and designed the "Koenigsberg heliometer" for Bessel. He also made
a long and most skilful research into the solar spectrum, which has
immortalized his name. But his health was broken by early trials, and he
died at the age of thirty-nine, while planning new and still more
important optical achievements.
A heliometer is the most accurate astronomical instrument for relative
measurements of position, as a transit circle is the most accurate for
absolute determinations. It consists of an equatorial telescope with
object-glass cut right across, and each half movable by a sliding
movement one past the other, the amount by which the two halves are
dislocated being read off by a refined method, and the whole instrument
having a multitude of appendages conducive to convenience and accuracy.
Its use is to act as a micrometer or measurer of small distances.[28]
Each half of the object-glass gives a distinct image, which may be
allowed to coincide or may be separated as occasion requires. If it be
the components of a double star that are being examined, each component
will in general be seen double, so that four images will be seen
altogether; but by careful adjustment it will be possible to arrange
that one image of each pair shall be superposed on or coincide with each
other, in which case only three images are visible; the amount of
dislocation of the halves of the object-glass necessary to accomplish
this is what is read off. The adjustment is one that can be performed
with extreme accuracy, and by performing it again and again with all
possible modifications, an extremely accurate determination of the
angular distance between the two components is obtained.
[Illustration: FIG. 92.--Heliometer.]
Bessel determined to apply this beautiful instrument to the problem of
stellar parallax; and he began by considering carefully the kind of star
for which success was most likely. Hitherto the brightest had been most
attended to, but Bessel thought that quickness of proper motion would be
a still better test of nearness. Not that either criterion is conclusive
as to distance, but there was a presumption in favour of either a very
bright or an obviously moving star being nearer than a faint or a
stationary one; and as the "bright" criterion had already been often
applied without result, he decided to try the other. He had already
called attention to a record by Piazzi in 1792 of a double star in
Cygnus whose proper motion was five seconds of arc every year--a motion
which caused this telescopic object, 61 Cygni, to be known as "the
flying star." Its motion is not really very perceptible, for it will
only have traversed one-third of a lunar diameter in the course of a
century; still it was the quickest moving star then known. The position
of this interesting double he compared with two other stars which were
seen simultaneously in the field of the heliometer, by the method I have
described, throughout the whole year 1838; and in the last month of that
year he was able to announce with confidence a distinct though very
small parallax; substantiating it with a mass of detailed evidence which
commanded the assent of astronomers. The amount of it he gave as
one-third of a second. We know now that he was very nearly right, though
modern research makes it more like half a second.[29]
Soon afterwards, Struve announced a quarter of a second as the parallax
of Vega, but that is distinctly too great; and Henderson announced for
[alpha] Centauri (then thought to be a double) a parallax of one
second, which, if correct, would make it quite the nearest of all the
stars, but the result is now believed to be about twice too big.
Knowing the distance of 61 Cygni, we can at once tell its real rate of
travel--at least, its rate across our line of sight: it is rather over
three million miles a day.
Now just consider the smallness of the half second of arc, thus
triumphantly though only approximately measured. It is the angle
subtended by twenty-six feet at a distance of 2,000 miles. If a
telescope planted at New York could be directed to a house in England,
and be then turned so as to set its cross-wire first on one end of an
ordinary room and then on the other end of the same room, it would have
turned through half a second, the angle of greatest stellar parallax.
Or, putting it another way. If the star were as near us as New York is,
the sun, on the same scale, would be nine paces off. As twenty-six feet
is to the distance of New York, so is ninety-two million miles to the
distance of the nearest fixed star.
Suppose you could arrange some sort of telegraphic vehicle able to carry
you from here to New York in the tenth part of a second--_i.e._ in the
time required to drop two inches--such a vehicle would carry you to the
moon in twelve seconds, to the sun in an hour and a quarter. Travelling
thus continually, in twenty-four hours you would leave the last member
of the solar system behind you, and begin your plunge into the depths of
space. How long would it be before you encountered another object? A
month, should you guess? Twenty years you must journey with that
prodigious speed before you reach the nearest star, and then another
twenty years before you reach another. At these awful distances from one
another the stars are scattered in space, and were they not brilliantly
self-luminous and glowing like our sun, they would be hopelessly
invisible.
I have spoken of 61 Cygni as a flying star, but there is another which
goes still quicker, a faint star, 1830 in Groombridge's Catalogue. Its
distance is far greater than that of 61 Cygni, and yet it is seen to
move almost as quickly. Its actual speed is about 200 miles a
second--greater than the whole visible firmament of fifty million stars
can control; and unless the universe is immensely larger than anything
we can see with the most powerful telescopes, or unless there are crowds
of invisible non-luminous stars mixed up with the others, it can only be
a temporary visitor to this frame of things; it is rushing from an
infinite distance to an infinite distance; it is passing through our
visible universe for the first and only time--it will never return. But
so gigantic is the extent of visible space, that even with its amazing
speed of 200 miles every second, this star will take two or three
million years to get out of sight of our present telescopes, and several
thousand years before it gets perceptibly fainter than it is now.
Have we any reason for supposing that the stars we see are all there
are? In other words, have we any reason for supposing all celestial
objects to be sufficiently luminous to be visible? We have every ground
for believing the contrary. Every body in the solar system is dull and
dark except the sun, though probably Jupiter is still red-hot. Why may
not some of the stars be dark too? The genius of Bessel surmised this,
and consistently upheld the doctrine that the astronomy of the future
would have to concern itself with dark and invisible bodies; he preached
"an astronomy of the invisible." Moreover he predicted the presence of
two such dark bodies--one a companion of Sirius, the other of Procyon.
He noticed certain irregularities in the motions of these stars which he
asserted must be caused by their revolving round other bodies in a
period of half a century. He announced in 1844 that both Sirius and
Procyon were double stars, but that their companions, though large, were
dark, and therefore invisible.
No one accepted this view, till Peters, in America, found in 1851 that
the hypothesis accurately explained the anomalous motion of Sirius, and,
in fact, indicated an exact place where the companion ought to be. The
obscure companion of Sirius became now a recognized celestial object,
although it had never been seen, and it was held to revolve round Sirius
in fifty years, and to be about half as big.
In 1862, the firm of Alvan Clark and Sons, of New York, were completing
a magnificent 18-inch refractor, and the younger Clark was trying it on
Sirius, when he said: "Why, father, the star has a companion!" The elder
Clark also looked, and sure enough there was a faint companion due east
of the bright star, and in just the position required by theory. Not
that the Clarks knew anything about the theory. They were keen-sighted
and most skilful instrument-makers, and they made the discovery by
accident. After it had once been seen, it was found that several of the
large telescopes of the world were able to show it. It is half as big,
but it only gives 1/10000th part of the light that Sirius gives. No
doubt it shines partly with a borrowed light and partly with a dull heat
of its own. It is a real planet, but as yet too hot to live on. It will
cool down in time, as our earth has cooled and as Jupiter is cooling,
and no doubt become habitable enough. It does revolve round Sirius in a
period of 49.4 years--almost exactly what Bessel assigned to it.
But Bessel also assigned a dark companion to Procyon. It and its
luminous neighbour are considered to revolve round each other in a
period of forty years, and astronomers feel perfectly assured of its
existence, though at present it has not been seen by man.
LECTURE XV
THE DISCOVERY OF NEPTUNE
We approach to-night perhaps the greatest, certainly the most
conspicuous, triumphs of the theory of gravitation. The explanation by
Newton of the observed facts of the motion of the moon, the way he
accounted for precession and nutation and for the tides, the way in
which Laplace explained every detail of the planetary motions--these
achievements may seem to the professional astronomer equally, if not
more, striking and wonderful; but of the facts to be explained in these
cases the general public are necessarily more or less ignorant, and so
no beauty or thoroughness of treatment appeals to them, nor can excite
their imaginations. But to predict in the solitude of the study, with no
weapons other than pen, ink, and paper, an unknown and enormously
distant world, to calculate its orbit when as yet it had never been
seen, and to be able to say to a practical astronomer, "Point your
telescope in such a direction at such a time, and you will see a new
planet hitherto unknown to man"--this must always appeal to the
imagination with dramatic intensity, and must awaken some interest in
almost the dullest.
Prediction is no novelty in science; and in astronomy least of all is it
a novelty. Thousands of years ago, Thales, and others whose very names
we have forgotten, could predict eclipses with some certainty, though
with only rough accuracy. And many other phenomena were capable of
prediction by accumulated experience. We have seen, for instance (coming
to later times), how a gap between Mars and Jupiter caused a missing
planet to be suspected and looked for, and to be found in a hundred
pieces. We have seen, also, how the abnormal proper-motion of Sirius
suggested to Bessel the existence of an unseen companion. And these last
instances seem to approach very near the same class of prediction as
that of the discovery of Neptune. Wherein, then, lies the difference?
How comes it that some classes of prediction--such as that if you put
your finger in fire it will get burnt--are childishly easy and
commonplace, while others excite in the keenest intellects the highest
feelings of admiration? Mainly, the difference lies, first, in the
grounds on which the prediction is based; second, on the difficulty of
the investigation whereby it is accomplished; third, in the completeness
and the accuracy with which it can be verified. In all these points, the
discovery of Neptune stands out pre-eminently among the verified
predictions of science, and the circumstances surrounding it are of
singular interest.
* * * * *
In 1781, Sir William Herschel discovered the planet Uranus. Now you know
that three distinct observations suffice to determine the orbit of a
planet completely, and that it is well to have the three observations as
far apart as possible so as to minimize the effects of minute but
necessary errors of observation. (See p. 298.) Directly Uranus was
found, therefore, old records of stellar observations were ransacked,
with the object of discovering whether it had ever been unwittingly seen
before. If seen, it had been thought of course to be a star (for it
shines like a star of the sixth magnitude, and can therefore be just
seen without a telescope if one knows precisely where to look for it,
and if one has good sight), but if it had been seen and catalogued as a
star it would have moved from its place, and the catalogue would by that
entry be wrong. The thing to detect, therefore, was errors in the
catalogues: to examine all entries, and see if the stars entered
actually existed, or were any of them missing. If a wrong entry were
discovered, it might of course have been due to some clerical error,
though that is hardly probable considering the care taken over these
things, or it might have been some tailless comet or other, or it might
have been the newly found planet.
So the next thing was to calculate backwards, and see if by any
possibility the planet could have been in that place at that time.
Examined in this way the tabulated observations of Flamsteed showed that
he had unwittingly observed Uranus five distinct times, the first time
in 1690, nearly a century before Herschel discovered its true nature.
But more remarkable still, Le Monnier, of Paris, had observed it eight
times in one month, cataloguing it each time as a different star. If
only he had reduced and compared his observations, he would have
anticipated Herschel by twelve years. As it was, he missed it
altogether. It was seen once by Bradley also. Altogether it had been
seen twenty times.
These old observations of Flamsteed and those of Le Monnier, combined
with those made after Herschel's discovery, were very useful in
determining an exact orbit for the new planet, and its motion was
considered thoroughly known. It was not an _exact_ ellipse, of course:
none of the planets describe _exact_ ellipses--each perturbs all the
rest, and these small perturbations must be taken into account, those of
Jupiter and Saturn being by far the most important.
For a time Uranus seemed to travel regularly and as expected, in the
orbit which had been calculated for it; but early in the present century
it began to be slightly refractory, and by 1820 its actual place showed
quite a distinct discrepancy from its position as calculated with the
aid of the old observations. It was at first thought that this
discrepancy must be due to inaccuracies in the older observations, and
they were accordingly rejected, and tables prepared for the planet based
on the newer and more accurate observations only. But by 1830 it became
apparent that it would not accurately obey even these. The error
amounted to some 20". By 1840 it was as much as 90', or a minute and a
half. This discrepancy is quite distinct, but still it is very small,
and had two objects been in the heavens at once, the actual Uranus and
the theoretical Uranus, no unaided eye could possibly have distinguished
them or detected that they were other than a single star.
[Illustration: FIG. 93.--Perturbations of Uranus.
The chance observations by Flamsteed, by Le Monnier, and others, are
plotted in this diagram, as well as the modern determinations made after
Herschel had discovered the nature of the planet. The decades are laid
off horizontally. Vertical distance represents the difference between
observed and subsequently calculated longitudes--in other words, the
principal perturbations caused by Neptune. To show the scale, a number
of standard things are represented too by lengths measured upwards from
the line of time, viz: the smallest quantity perceptible to the naked
eye,--the maximum angle of aberration, of nutation, and of stellar
parallax; though this last is too small to be properly indicated. The
perturbations are much bigger than these; but compared with what can be
seen without a telescope they are small--the distance between the
component pairs of [epsilon] Lyrae (210") (see fig. 86, page 288), which
a few keen-eyed persons can see as a simple double star, being about
twice the greatest perturbation.]
The diagram shows all the irregularities plotted in the light of our
present knowledge; and, to compare with their amounts, a few standard
things are placed on the same scale, such as the smallest interval
capable of being detected with the unaided eye, the distance of the
component stars in [epsilon] Lyrae, the constants of aberration, of
nutation, and of stellar parallax.
The errors of Uranus therefore, though small, were enormously greater
than things which had certainly been observed; there was an unmistakable
discrepancy between theory and observation. Some cause was evidently at
work on this distant planet, causing it to disagree with its motion as
calculated according to the law of gravitation. Some thought that the
exact law of gravitation did not apply to so distant a body. Others
surmised the presence of some foreign and unknown body, some comet, or
some still more distant planet perhaps, whose gravitative attraction for
Uranus was the cause of the whole difficulty--some perturbations, in
fact, which had not been taken into account because of our ignorance of
the existence of the body which caused them.
But though such an idea was mentioned among astronomers, it was not
regarded with any special favour, and was considered merely as one among
a number of hypotheses which could be suggested as fairly probable.
It is perfectly right not to attach much importance to unelaborated
guesses. Not until the consequences of an hypothesis have been
laboriously worked out--not until it can be shown capable of producing
the effect quantitatively as well as qualitatively--does its statement
rise above the level of a guess, and attain the dignity of a theory. A
later stage still occurs when the theory has been actually and
completely verified by agreement with observation.
Now the errors in the motion of Uranus, _i.e._ the discrepancy
between its observed and calculated longitudes--all known
disturbing causes, such as Jupiter and Saturn, being allowed
for--are as follows (as quoted by Dr. Haughton) in seconds of
arc:--
ANCIENT OBSERVATIONS (casually made, as of a star).
Flamsteed 1690 +61.2
" 1712 +92.7
" 1715 +73.8
Le Monnier 1750 -47.6
Bradley 1753 -39.5
Mayer 1756 -45.7
Le Monnier 1764 -34.9
" 1769 -19.3
" 1771 -2.3
MODERN OBSERVATIONS.
1780 +3.46
1783 +8.45
1786 +12.36
1789 +19.02
1801 +22.21
1810 +23.16
1822 +20.97
1825 +18.16
1828 +10.82
1831 -3.98
1834 -20.80
1837 -42.66
1840 -66.64
These are the numbers plotted in the above diagram (Fig. 92), where
H marks the discovery of the planet and the beginning of its
regular observation.
Something was evidently the matter with the planet. If the law of
gravitation held exactly at so great a distance from the sun, there must
be some perturbing force acting on it besides all those known ones which
had been fully taken into account. Could it be an outer planet? The
question occurred to several, and one or two tried if they could solve
the problem, but were soon stopped by the tremendous difficulties of
calculation.
The ordinary problem of perturbation is difficult enough: Given a
disturbing planet in such and such a position, to find the perturbations
it produces. This problem it was that Laplace worked out in the
_Mecanique Celeste_.
But the inverse problem: Given the perturbations, to find the planet
which causes them--such a problem had never yet been attacked, and by
only a few had its possibility been conceived. Bessel made preparations
for trying what he could do at it in 1840, but he was prevented by fatal
illness.
In 1841 the difficulties of the problem presented by these residual
perturbations of Uranus excited the imagination of a young student, an
undergraduate of St. John's College, Cambridge--John Couch Adams by
name--and he determined to have a try at it as soon as he was through
his Tripos. In January, 1843, he graduated as Senior Wrangler, and
shortly afterwards he set to work. In less than two years he reached a
definite conclusion; and in October, 1845, he wrote to the
Astronomer-Royal, at Greenwich, Professor Airy, saying that the
perturbations of Uranus would be explained by assuming the existence of
an outer planet, which he reckoned was now situated in a specified
latitude and longitude.
We know now that had the Astronomer-Royal put sufficient faith in this
result to point his big telescope to the spot indicated and commence
sweeping for a planet, he would have detected it within 1-3/4 deg. of the
place assigned to it by Mr. Adams. But any one in the position of the
Astronomer-Royal knows that almost every post brings an absurd letter
from some ambitious correspondent or other, some of them having just
discovered perpetual motion, or squared the circle, or proved the earth
flat, or discovered the constitution of the moon, or of ether, or of
electricity; and out of this mass of rubbish it requires great skill and
patience to detect such gems of value as there may be.
Now this letter of Mr. Adams's was indeed a jewel of the first water,
and no doubt bore on its face a very different appearance from the
chaff of which I have spoken; but still Mr. Adams was an unknown man: he
had graduated as Senior Wrangler it is true, but somebody must graduate
as Senior Wrangler every year, and every year by no means produces a
first-rate mathematician. Those behind the scenes, as Professor Airy of
course was, having been a Senior Wrangler himself, knew perfectly well
that the labelling of a young man on taking his degree is much more
worthless as a testimony to his genius and ability than the general
public are apt to suppose.
Was it likely that a young and unknown man should have successfully
solved so extremely difficult a problem? It was altogether unlikely.
Still, he would test him: he would ask for further explanations
concerning some of the perturbations which he himself had specially
noticed, and see if Mr. Adams could explain these also by his
hypothesis. If he could, there might be something in his theory. If he
failed--well, there was an end of it. The questions were not difficult.
They concerned the error of the radius vector. Mr. Adams could have
answered them with perfect ease; but sad to say, though a brilliant
mathematician, he was not a man of business. He did not answer Professor
Airy's letter.