successfully searched for without a hundredth part of the labour and
thought actually devoted to his detection. It may sound rather daring
to assert that any fairly good geometrician could have pointed after
less than an hour's calculation, based on the facts known respecting
Uranus in 1842, to a region within which the disturbing planet must
certainly lie,--a region larger considerably no doubt than that to
which Adams and Leverrier pointed, yet a region which a single observer
could have swept over adequately in half-a-dozen favourable evenings,
two such surveys sufficing to discover the disturbing planet. I
believe, however, that no one who examines the evidence will deny
the accuracy of this statement. It was manifest, from the nature of
the perturbations experienced by Uranus, that between 1820 and 1825
Uranus and the unknown body had been in conjunction. From this it
followed that the disturber must be behind Uranus in 1840-1845 by about
one-eighth of a revolution round the sun. With the assumptions made
by Adams and Leverrier, indeed, the position of the stranger in this
respect could have been more closely determined. There could be little
doubt that the disturbing planet must be near the ecliptic. It followed
that the planet must lie somewhere on a strip of the heavens, certainly
not more than ten degrees long and about three degrees broad, but the
probable position of the planet would be indicated as within a strip
four degrees long and two broad.[4] Such a strip could be searched over
effectually in the time I have named above, and the planet would have
been found in it. The larger region (ten degrees long and three broad)
could have been searched over in the same time by two observers. If
indeed the single observer used a telescope powerful enough to detect
the difference of aspect between the disc of Neptune and the point-like
image of a star (the feature by which Galle, it will be remembered,
recognised Neptune), a single night would have sufficed for the search
over the smaller of the above-mentioned regions, and two nights for the
search over the larger. The search over the smaller, as already stated,
would have revealed the disturbing planet.
On the other hand, the astronomer could not determine the direction of
an intra-Mercurial planet within a considerably larger space on the
heavens, while the search over the space within which such a planet was
to be looked for was attended by far more serious difficulties than the
search for Neptune. In fact, it seems as though, even when astronomers
have learned where to look for such a planet, they cannot expect to see
it under ordinary atmospheric conditions when the sun is not eclipsed.
Let us consider the history of the search for an intra-Mercurial planet
from the time when first the idea was suggested that such a planet
exists until the time of its actual discovery--for so it seems we must
regard the observations made during the total eclipse of July, 1878.
On January 2, 1860, M. Leverrier announced, in a paper addressed to
the Academy of Sciences, that the observations of Mercury could not
be reconciled with the received elements of the planet. According to
those elements, the point of Mercury's orbit which lies nearest to the
sun undergoes a certain motion which would carry it entirely round in
about 230,000 years. But to account for the observed motions of Mercury
as determined from twenty-one transits over the sun between the years
1697 and 1848, a slight increase in this motion of the perihelion was
required, an increase, in fact, from 581 seconds of arc in a century
to nearly 585. The result would involve, he showed, an increase in
our estimate of the mass of Venus by a full tenth. But such a change
would necessarily lead to difficulties in other directions; for the
mass of Venus had been determined from observations of changes in the
position of the earth's path, and these changes had been too carefully
determined to be readily regarded as erroneous. 'This result naturally
filled me with inquietude,' said Leverrier later. 'Had I not allowed
some error in the theory to escape me? New researches, in which every
circumstance was taken into account by different methods, ended only in
the conclusion that the theory was correct, but that it did not agree
with the observations.' At last, after long and careful investigation
of the matter, he found that a certain slight change would bring
observation and theory into agreement. All that was necessary was
to assume that matter as yet undiscovered exists in the sun's
neighbourhood. 'Does it consist,' he asked, 'of one or more planets, or
other more minute asteroids, or only of cosmical dust? The theory tells
us nothing on this point.'
Leverrier pointed out that a planet half the size of Mercury between
Mercury and the sun would account for the discrepancy between
observation and theory. But a planet of that size would be a very
conspicuous object at certain times, even when the sun was not
eclipsed; and when favourably placed during eclipses would be a
resplendent orb which would attract the notice of even the most
careless observer. For we must remember that the brightness of a
planet depends in part on its size and its distance from the earth,
and in part on its distance from the sun. A planet half as large as
Mercury would have a diameter about four-fifths of Mercury's, and at
equal distance would present a disc about two-thirds of Mercury's in
apparent size. But supposing the planet to be half as far from the sun
as Mercury (and theory required that the planet should be rather nearer
the sun), its surface would be illuminated four times as brightly as
that of Mercury. Hence, with a disc two-thirds as large as Mercury's,
but illuminated four times as brightly, the planet would shine
nearly three times as brilliantly when seen under equally favourable
conditions during eclipse. In such an inquiry, the mean distance of the
two bodies need not be specially considered. Each planet would be seen
most favourably when in the part of its path remotest from the earth,
so that the planet nearest to the sun would on the whole have the
advantage of any difference due to that cause. For, of course, while
Mercury, being farther from the sun, approaches the earth nearer when
between the earth and sun, he recedes farther from the sun for the same
reason when on the part of his path beyond the sun.
It was perfectly clear that no such planet as Leverrier considered
necessary to reconcile theory and observation exists between the sun
and Mercury's orbit. It appeared necessary, therefore, to assume that
either there must be several smaller planets, or else that a cloud of
cosmical dust surrounds the sun. Now it is to be noticed that in either
case the entire mass of matter between Mercury and the sun must be
greater to produce the observed disturbance than the mass of a single
planet travelling at the outside of the region supposed to be occupied
either by a group of planets or a cloud of meteorites.
Leverrier considered the existence of a ring of small planets afforded
the most probable explanation. He recommended astronomers to search
for such bodies. It is noteworthy that it was in reference to this
suggestion that M. Faye (following a suggestion of Sir J. Herschel's)
proposed that at several observatories, suitably selected, the sun
should be photographed several times every day with a powerful
telescope. 'I have myself,' he says, 'shown how to give these
photographs the value of an astronomical observation by taking two
impressions on the same plate after an interval of two minutes. It will
be sufficient to superpose the transparent negatives of this size taken
at a quarter of an hour's interval, to distinguish immediately the
movable projection of a small planet in the middle of the most complex
groups of small spots.'
It was while Leverrier and Faye were discussing this matter, that news
came of the recognition of an intra-Mercurial planet by Lescarbault,
a doctor residing at Orgères, in the department of Eure et Loire. The
story has been so often told that I am loth to occupy space with it
here. An account is given of the leading incidents in an article called
'The Planets put in Leverrier's Balance,' in my 'Science Byways,'
and a somewhat more detailed narrative in my 'Myths and Marvels of
Astronomy.' Here, it will suffice to give a very slight sketch of this
interesting episode in the history of astronomy.
On January 2, 1860, news reached Leverrier that Lescarbault had on
March 26, 1859, seen a round black spot on the sun's face, and had
watched it travelling across like a planet in transit. It had remained
in view for one hour and a quarter. Leverrier could not understand why
three-quarters of a year had been allowed to elapse before so important
an observation had been published. He went to Orgères with the idea
of exposing a pretender. The interview was a strange one. Leverrier
was stern and, to say the truth, exceedingly rude in his demeanour,
Lescarbault singularly lamb-like. If our chief official astronomer
called uninvited upon some country gentleman who had announced an
astronomical discovery, and behaved as Leverrier did to Lescarbault,
there would most certainly have been trouble; but Lescarbault seems
to have been rather pleased than otherwise. 'So you are the man,'
said Leverrier, looking fiercely at the doctor, 'who pretends to have
seen an intra-Mercurial planet. You have committed a grave offence in
hiding your observation, supposing you really have made it, for nine
months. You are either dishonest or deceived. Tell me at once and
without equivocation what you have seen.' Lescarbault described his
observation. Leverrier asked for his chronometer, and, hearing that
the doctor used only his watch, the companion of his professional
journeys, asked how he could pretend to estimate seconds with an old
watch. Lescarbault showed a silk pendulum 'beating seconds,'--though it
would have been more correct to say 'swinging seconds.' Leverrier then
examined the doctor's telescope, and presently asked for the record
of the observations. Lescarbault produced it, written on a piece of
laudanum-stained paper which at the moment was doing service as a
marker in the _Connaissance des Temps_. Leverrier asked Lescarbault
what distance he had deduced for the new planet. The doctor replied
that he had been unable to deduce any, not being a mathematician: he
had made many attempts, however.[5] Hearing this, Leverrier asked for
the rough draft of these ineffective calculations. 'My rough draft?'
said the doctor. 'Paper is rather scarce with us here. I am a joiner as
well as an astronomer' (we can imagine the expression of Leverrier's
face at this moment); 'I calculate in my workshop, and I write upon the
boards; and when I wish to use them in new calculations, I remove the
old ones by planing.' On adjourning to the carpenter's shop, however,
they found the board with its lines and its numbers in chalk still
unobliterated.
This last piece of evidence, though convincing Leverrier that
Lescarbault was no mathematician, and therefore probably in his eyes
no astronomer, yet satisfied him as to the good faith of the doctor of
Orgères. With a grace and dignity full of kindness, which must have
afforded a singular contrast to his previous manner, he congratulated
Lescarbault on his important discovery. He made some inquiry also at
Orgères, concerning the private character of Lescarbault, and learning
from the village _curé_, the _juge de paix_, and other functionaries,
that he was a skilful physician, he determined to secure some reward
for his labours. At Leverrier's request M. Rouland, the Minister
of Public Instruction, communicated to Napoleon III. the result of
Leverrier's visit, and on January 25 the Emperor bestowed on the
village doctor the decoration of the Legion of Honour.
To return to astronomical facts.
It appears from Lescarbault's observation, that on March 26, 1859, at
about four in the afternoon, a round black spot entered on the sun's
disc. It had a diameter less than one-fourth that of Mercury (which he
had seen in transit with the same telescope and the same magnifying
power on May 8, 1845). The time occupied in the transit of this spot
was about one hour seventeen minutes, and, the chord of transit
being somewhat more than a quarter of the sun's diameter in length,
Lescarbault calculated that the time necessary to describe the sun's
diameter would have been nearly four and a half hours. The inclination
of the body's path to the ecliptic seemed to be rather more than 6
degrees, and was probably comprised between 5-1/3 and 7-1/3 degrees.
From Leverrier's calculations, it appeared that the time of revolution
of the new planet would be 19 days 17 hours, its distance from the
sun about 147, the earth's being taken as 1,000; giving for Mars,
the earth, Venus, Mercury, and Vulcan (as the new planet was named),
the respective distances 1, 524, 1,000, 723, 387, and 147. Leverrier
assigned 12-1/5 degrees as Vulcan's inclination, and the places
where it crosses the ecliptic he considered to be in line with those
occupied by the earth on or about April 3 and October 6. Judging from
Lescarbault's statement respecting the apparent size of the dark spot,
Leverrier concluded that the volume of the stranger must be about
one-seventeenth of Mercury's, the masses being presumably in the same
proportion. Hence he inferred that the new planet would be quite
incompetent to produce the observed change in the orbit of Mercury.
Leverrier further found that the brilliancy of Vulcan when the planet
was furthest from the sun on the sky (about eight degrees) would be
less than that of Mercury when similarly placed in his orbit, and he
hence inferred that Vulcan might readily remain unseen, even during
total eclipse. Here, as it seems to me, Leverrier's reasoning was
erroneous. If Vulcan really has a volume equal to one-seventeenth
of Mercury's, the diameter of Vulcan would be rather less than two
fifths of Mercury's and the disc of Vulcan at the same distance about
two-thirteenths of Mercury's. But Vulcan, being nearer the sun than
Mercury in the ratio of 147 to 387, or say 15 to 39, would be more
brightly illuminated in the ratio of 39 times 39 to 15 times 15, or
nearly as 20 to 3. Hence if we first diminish Mercury's lustre when
at his greatest apparent distance from the sun in the ratio of 2 to
13, and increase the result in the ratio of 20 to 3, we get Vulcan's
lustre when he is at his greatest apparent distance from the sun. The
result is that his lustre should exceed Mercury's in the same degree
that 40 exceeds 39. Or practically, for all the numbers used have been
mere approximations, the inference is that Vulcan and Mercury, if both
seen when at their greatest distance from the sun during eclipse, would
probably shine with equal lustre. But in that case Vulcan would be a
very conspicuous object indeed, at such a time; for Mercury when at his
greatest distance from the sun, or greatest elongation, is a bright
star even on a strongly illuminated twilight sky; moreover, Vulcan,
when at either of his greatest elongations, ought to be visible in full
daylight in a suitably adjusted telescope. For Mercury is well seen
when similarly placed, and even when much nearer to the sun and on the
nearer part of his path where he turns much more of his darkened than
of his illuminated hemisphere towards us. Venus has been seen when
so near the sun that the illuminated portion of her disc is a mere
thread-like sickle of light. Nay, Professor Lyman, of Yale College, in
America, has seen her when so near the sun that she appeared to be a
mere circular thread of light, the completion of the circle being the
best possible proof how exceedingly fine the thread must have been, and
also how small its intrinsic lustre.
This is indeed the chief difficulty in Lescarbault's supposed
observation. If he really saw a body in transit across the sun, moving
at the observed rate, and having anything like the observed diameter,
that body ought to have been seen repeatedly during total eclipses of
the sun, and ought not to have escaped the search which has been made
over and over again near the sun for intra-Mercurial planets. Either we
must reject Lescarbault's narrative absolutely, or we must suppose that
he greatly over-estimated the size of the body he observed.
Another difficulty almost equally important is found to exist when
we consider the circumstances of Lescarbault's supposed discovery.
Suppose the path of Vulcan to be inclined about twelve degrees or
thereabouts to the ecliptic or to the plane in which the earth travels.
Then, as seen from the earth on April 3, and October 6, this path, if
it were a material ring, would appear as a straight line across the
sun's centre, and extending on either side of the sun to a distance
of about 16 sun-breadths. As seen on January 3 and July 5, when it
would have its greatest opening, Vulcan's path would appear as an oval
whose longest axis would be about 32 sun-breadths, while its shortest
would be little more than 6 sun-breadths, the sun of course occupying
the centre of the ellipse, which, where closest to him, would lie
but about 2-1/2 sun-breadths only from the outline of his disc. Now
it is easily seen that the path of Vulcan, changing in this way from
apparent straightness to a long oval (whose breadth is about one-fifth
its length), back to straightness but differently inclined, then to
the same oval as before but opened out the other way, and so back to
its original straightness and inclination, must, for no inconsiderable
portion of the year on either side of April 3 and October 6, intersect
the outline of the sun's disc. From a rough but sufficiently accurate
calculation which I have made, I find that the interval would last
about 36 days at each season, that is, from about March 16 to April 21
in spring, and from about September 18 to about October 24 in autumn.
But during a period of 36 days there would generally be two passages of
Vulcan between the earth and sun, and there would always be one (in any
long period of time two such passages would be five times as common an
event during one of these intervals as a single passage). Consequently
there would be at least two transits of Vulcan every year, and there
would generally be four transits; the average number of transits would
be about eleven in three years. With a wider orbit and a greater
inclination transits would be fewer; but even with the widest orbit and
the greatest inclination that can possibly be allowed, there would be
at least one transit a year on the average.
Now when we remember that, so far as the northern hemisphere is
concerned, the sun is observed on every fine day in almost every
country in Europe and in half the States of the American Union, to
say nothing of observations in Asia, where England and Russia have
several observatories, while in the southern hemisphere there are
many observatories, in Australia, South Africa, and South America (on
both side of the Andes), we see how exceedingly small must be the
chance that Vulcan could escape detection even for a single year.
Far less could Vulcan have escaped all the years which have elapsed
since Lescarbault announced his discovery, to say nothing of all the
observations made by Carrington, Schwabe, and many others, before the
year 1860. If Vulcan really exists, and really has the dimensions and
motions described by Lescarbault, the planet must long ere this have
been repeatedly seen upon the sun's disc by experienced observers.
As a matter of fact, Wolf has collected nineteen observations of dark
bodies unlike spots on the sun, during the interval between 1761 and
1865. But as Professor Newcomb justly points out, with two or three
exceptions, the observers are almost unknown as astronomers. In one
case at least the object seen was certainly not a planet, since
it was described as a cloud-like appearance. 'On the other hand,'
says Newcomb, 'for fifty years past the sun has been constantly and
assiduously observed by such men as Schwabe, Carrington, Secchi, and
Spörer, none of whom have ever recorded anything of the sort. That
planets in such numbers should pass over the solar disc, and be seen by
amateur astronomers, and yet escape all these skilled astronomers, is
beyond all moral probability.'
It must be remembered that an inexperienced observer of the sun might
readily mistake a spot of unusual roundness and darkness for a planet's
disc. The practised observer would perceive peculiarities at once
indicating the object as a spot on the sun; but these peculiarities
would escape the notice of a beginner, or of one using a telescope of
small power. Again, an inexperienced observer is apt to mistake the
change of position which a spot on the sun undergoes on account of the
diurnal motion, for a change of place on the sun's disc. At noon, for
instance, the uppermost point of the sun's disc is the north point;
but in the afternoon the uppermost point is east of the true north
point. Thus a spot which at noon was a short distance below the highest
point of the sun's disc would at two or three be considerably to the
west of the highest point, though it had undergone in the interval no
appreciable change of position on the solar disc. Suppose now that
at two or three in the afternoon clouds come over the sun's face,
and he is not seen again that day. On the morrow the spot may have
disappeared, as solar spots are apt enough to do. The observer, then
(assuming him to be inexperienced like most of those who have described
such spots), would say, I saw at noon a small round spot which in the
course of the next three hours moved over an appreciable arc towards
the west (the right direction, be it remembered, for a planet to cross
the sun's face). An experienced observer would not make such a mistake.
But let one point be carefully noted. An experienced astronomer would
be very apt to forget that such a mistake could be made. He would take
it for granted that the observer who described such a change in a
spot's position meant a real change, not a change due to the diurnal
motion.
Therefore, although Leverrier, Moigno, Hind, and other men of science,
have adopted Lescarbault's account, I hold it to be absolutely certain
that that account is in some respect or other erroneous. Newcomb goes
even farther. He says, it is very certain that if the disturbance of
Mercury is due to a group of planets, 'they are each so small as to be
invisible in transits across the sun. They must also,' he proceeds, 'be
so small as to be invisible during total eclipses of the sun, because
they have always failed to show themselves then.' This remark relates,
of course, to naked-eye vision. As no intra-Mercurial planet had ever
been searched for systematically with the telescope, before the recent
eclipse, there was nothing to prevent astronomers from believing that
a group of planets, visible in the telescope during total eclipse, may
travel between the sun and the path of Mercury.
I proceed at once to consider the evidence afforded during the eclipse
of July, 1878, not discussing further the question of Lescarbault's
Vulcan, because it appears to me so clear that there must have been
some mistake, and because later observations seem to throw clearer
evidence on the matter than any which had been before obtained. Yet it
must be admitted that even now the evidence is not all that could be
desired.
Professor Watson, of Ann Arbor, the discoverer of more than a score of
the small planets which travel between the paths of Mars and Jupiter,
had been searching for an _extra-Neptunian_ planet, when the approach
of the eclipse of July, 1878, suggested the idea that he should return
for a while from those dismal depths which lie beyond the path of
Neptune to seek for a new planet within the glowing region between the
sun and the path of Mercury. The occasion was exceptionally favourable
because of the great height above the sea-level from which the eclipse
could be observed. Accordingly he betook himself to Rawlins, Wyoming,
and prepared for the search by providing his telescope with card
circles in such sort that the place of any observed star could be
recorded by a pencil-mark on these circles, instead of being read off
(with the possibility of error) in the usual way. It is unnecessary
to explain further, because every one who has ever used an equatorial
telescope, or is acquainted with the nature of the instrument, will
at once understand Professor Watson's plan, whereas those unfamiliar
with the instrument, would not gain any insight into the nature of his
plan without much more explanatory matter than could be conveniently
given here, even if any explanation without illustrations could make
the matter clear. Let it suffice to note that, having brought any star
centrally into the telescopic field of view, Professor Watson marked in
pencil where the ends of certain pointers came; and that these marks
served to indicate, after the eclipse was over, the position of the
observed star.