on the eastern side of the sun, and there saw certain stars belonging
to the constellation Cancer, where the sun was situate at the time. He
then examined the western side of the sun, and having swept out to a
star which he took to be Zeta Cancri (though he was rather surprised at
its brightness,--but of that more anon) he returned towards the sun,
encountering on his way a star of the fourth magnitude or rather less,
about two degrees to the west of the sun. Close by was the star Theta
Cancri; but Theta was much fainter, and was seen at the same time a
little further west. It is not easy to understand why Watson did not
make comparison between the position of the new star and Theta, instead
of making comparison between the new star, the sun, and the star which
he took to be Zeta. For a comparison with a known object so close as
Theta would have given more satisfactory evidence than a comparison
with objects farther away. However, as he distinctly states in a letter
to Sir G. Airy that the new star was very much brighter than Theta
Cancri, which was seen a little farther to the west, we cannot doubt
that he had sufficient evidence to prove the new star and Theta Cancri
to be distinct orbs.
He adds that there was no appearance of elongation, as might be
expected if the new object were a comet. It had a perceptible disc,
though the magnifying power was only forty five.
The accompanying figure will serve to give a fair idea of the position
of the stranger.
[Illustration: Fig. 1.--Watson's new Planet.]
Now comes the evidence which was at first supposed to be strongly
corroborative of Watson's observation,--the recognition of a star of
about the fourth magnitude, near Theta Cancri, by Professor Louis
Swift, who observed the eclipse from Pike's Peak, in Colorado.
Professor Swift also made some rather unusual arrangements with his
telescope, but they were not altogether so well adapted to advance his
purpose as were Professor Watson's. To prevent the instrument from
swaying he tied what he calls a pole (but what in England I imagine
would be called a stick), ten feet long, about a foot from the eye-end
of the telescope, leaving the other end of this singular appendage
to trail on the ground. (The telescope was set low, Professor Swift
judging, it would seem, that the most comfortable way to observe was
to lie on his back.) As a natural consequence, while he could move his
telescope very readily one way, trailing the stick along, he could not
move it the other way, because the stick's end immediately stuck into
the ground. As the stick was on the west of the telescope, Professor
Swift could move the eye-end eastwards, following the sun's westwardly
motion. Of course the telescope was to have been released from the
stick when totality began, but unfortunately Professor Swift omitted
to do this, so that he had to work during totality with a hampered
telescope.
The following is his account of what he saw:--
'My hampered telescope behaved badly, and no regularity in the sweeps
could be maintained. Almost at once my eye caught two red stars about
three degrees south-west of the sun, with large round and equally
bright discs which I estimated as of the fifth magnitude, appearing
(this was my thought at the time) about as bright in the telescope
as the pole-star does to the naked eye. I then carefully noted their
distance from the sun and from each other, and the direction in which
they pointed, &c., and recorded them in my memory, where, to my mind's
eye, they are still distinctly visible. I then swept southward, not
daring to venture far to the west, for fear I should be unable to get
back again, and soon came upon two stars resembling in every particular
the former two I had found, and, sighting along the outside of the
tube, was surprised to find I was viewing the same objects. Again I
observed them with the utmost care, and then recommenced my sweeps in
another direction; but I soon had them again, and for the third time,
in the field. This was also the last, as a small cloud hindered a final
leave-taking just before the end of totality, as I had intended. I
saw no other star besides these two, not even Delta, so close to the
eastern edge of the sun.'
He adds that the apparent distance between the two bodies was about
one-fourth the sun's diameter. (These are not his words, but convey the
same meaning.)
Again, he adds that, from three careful estimates, he found the two
stars pointed exactly to the sun's centre. He knew one of the two
bodies was Theta; but unfortunately he could not tell which was Theta
and which the new star or planet. 'But,' he says, 'Professor Watson
happily comes to the rescue, and with his means of measuring finds the
planet nearest to the sun.'
Unhappily, however, Professor Watson does not come absolutely to the
rescue here. On the contrary, to use Professor Swift's words in another
part of his letter (and speaking of another matter), 'it is just here
where the trouble begins.' If we construct a little map illustrating
what Professor Swift describes, we get the accompanying arrangement
(fig. 2). It is clearly quite impossible to reconcile this view of the
supposed new planet with Professor Watson's. If three careful estimates
showed Swift the stranger and Theta situated as in fig. 2, it is
absolutely certain that either Watson's observation was very far from
the truth, or else the strange orb he saw was not the same that Swift
saw. On the other hand, if Watson's observation was trustworthy, it is
certain that either Swift's three estimates were inexact or he saw a
different new body. Again, their accounts of the relative brightness of
Theta and the stranger could not possibly be reconciled if we supposed
they were observing the same new planet, for Watson says distinctly
that the stranger was _very much brighter_ than Theta; while Swift
says, with equal distinctness, that the two stars were _equally bright_.
[Illustration: Fig. 2.--Swift's new Planet?]
If we accept both observations, we must consider that the strange orb
seen by Swift was not the nearer to the sun, but the other, for Watson,
in his letter to Sir G. Airy, says that he saw both Theta and his own
new planet, and he could not have overlooked Swift's new planet, if
placed as in fig. 2, whereas if the star there marked as the stranger
were really Theta, Watson might readily enough have overlooked the
other star, as farther away from his newly-discovered planet. According
to this view, the actual arrangement at the time of the eclipse was as
shown in fig. 3.
[Illustration: Fig. 3.--Suggested explanation of Watson's and Swift's
observations.]
But this is not quite all. Professor Watson saw another body, which
in his opinion was a planet. I have already mentioned that he thought
Zeta remarkably bright. It seemed to him a star of nearly the third
magnitude, whereas Zeta Cancri is only of the fifth. Nay, speaking of
the planet near Theta, and of this star which he took for Zeta, he
says, 'they were probably really brighter [than the 4-1/2 and 3-1/2
magnitude respectively], because the illumination of the sky was not
considered in the estimates.' Before he had thoroughly examined the
pencil marks on his card circles, and made the necessary calculations,
he supposed the brighter star to be Zeta, because he did not see the
latter star. But when he examined his result carefully, he found that
the bright star was set (according to his pencil marks) more than
one degree east of Zeta. Writing on August 22, he says, 'The more I
consider the case the more improbable it seems to me that the second
star which I observed, and thought it might be Zeta, was that known
star. I was not certain, in this case, whether the wind had disturbed
the telescope or not. As it had not done so in the case of any other of
six pointings which I recorded, it seems almost certain that the second
was a new star.' It would be easy to understand why Professor Watson
had not seen Zeta, for he only swept as far as the star he mistook for
Zeta, and, as the accompanying figure shows, Zeta was beyond that star
on the west.[6]
Fig. 4 represents the apparent result of the observations made by
Professors Watson and Swift, if all the observations are regarded
as trustworthy. The six stars shown in the figure were probably the
six referred to in the preceding paragraph. The two unnamed ones are
well-known red stars.
[Illustration: Fig. 4.--Showing all the stars observed by Watson and
Swift.]
Let it be noticed, that we cannot reject planet 1, without rejecting
all Watson's observations. We cannot reject planet 2, without rejecting
all Swift's observations. We cannot set this planet to the left of
Theta without throwing doubt on Watson's observations. If Watson swept
over Theta westward without seeing 2, Swift must have made some mistake
as yet unexplained. As for planet 3, if we admit the possibility
that this object really was Zeta, we must admit also the possibility
that the object marked as planet 1 was really Theta, or rather we
should have to do so, were it not that Watson saw Theta also, and (I
suppose) in the same field of view, since he speaks confidently of the
inferiority of Theta in brightness.
It should further be noticed, that though Swift's and Watson's
observations by no means agree in details, they do in reality support
each other (unless Watson should definitely assert that no star as
bright as Theta existed either to the west or to the east of that star,
at the distance indicated by Swift.) For they agree in indicating the
existence of small planets near the sun, such as can only be seen with
the telescope.
On the other hand, it is to be noted that other observers failed to see
any of these bodies, though they looked specially for intra-Mercurial
planets. Thus Professor Hall, of the Washington Observatory, searched
over a larger space than is included in fig. 4, without seeing any
unknown body. But as he also failed to see many known bodies which
should have been seen, it is probable that the search was too hurried
to be trustworthy.
It would be satisfactory to be able to say that any of the supposed
planets might have been Lescarbault's Vulcan. But in reality, I fear,
this cannot have been the case. In the _Times_, I expressed, in an
article dated August 14, 1878, the opinion that the evidence obtained
establishes the existence of the planet which had so long been regarded
as a myth. That opinion was based on a very careful investigation of
the evidence available at the time. But it does not accord with what
has since been learned respecting Watson's observations.
We may dismiss planet 3 at once. If Watson is right about this body
being distinct from Zeta (a point about which, I must confess, I feel
grave doubts), then this must be a planet travelling in an orbit much
wider than we can possibly assign to Vulcan. For even at the distance
of some seven degrees from the sun it showed no sign of gibbosity. If
it had then been at its greatest elongation it would have appeared only
half-full. But with the power Watson was using, which enabled him to
pronounce that the smaller body near Theta showed no elongation, he
would at once have noticed any such peculiarity of shape. He could not
have failed to observe any gibbosity approaching to that of the moon
when three-quarters full. Moreover on July 29 a planet which has its
points of crossing the ecliptic opposite the earth's place on April
3 and October 6, could not appear where Watson saw this body (fully
two degrees from the ecliptic) unless either its orbit were far wider
than that which Leverrier assigned to Vulcan, or else its inclination
far greater. Neither supposition can be reconciled with Lescarbault's
observation.
With regard to planets 1 and 2, the case is equally strong against the
theory that Vulcan was observed. The same reasoning applies to both
these bodies. When I speak therefore of planet 1, it will be understood
that planet 2 also is dealt with. First, as this planet appeared with
a disc appreciably round, it is clear that it must have been near the
point of its orbit farthest from the earth, that is, the point directly
beyond the sun. It was then nearly at its brightest. Yet it appeared as
a fourth-magnitude star only. We have seen that Lescarbault's Vulcan,
even when only half-full, would appear as bright as Mercury at his
brightest, if Lescarbault's account can be accepted in all its details.
Situated as planet 1 was, Vulcan would have shown much more brightly
than an average first-magnitude star. At a very moderate computation it
would have been twice as bright as such a star. But planet 1 appeared
fainter than a fourth-magnitude star. Assume, however, that in reality
it was shining as brightly as an average third-magnitude star. Then it
shone with much less than a twentieth of the lustre Vulcan should have
had, if Lescarbault's estimate were correct. Its diameter then cannot
be greater than a quarter of that which Leverrier assigned to Vulcan
on the strength of Lescarbault's observation. In fact, the apparent
diameter of planet 1, when in transit over the sun's face, could not be
more than a sixteenth of Mercury's in transit, or about two-fifths of a
second,--roughly, about a 5000th part of the sun's apparent diameter.
It is certain that Lescarbault could not have made so considerable a
mistake as this. Nay, it is certain, that with the telescope he used he
could not have seen a spot of this size at all on the sun's face.
It will be seen that Lescarbault's observation still remains
unconfirmed, or rather, to speak more correctly, the doubts which
have been raised respecting Lescarbault's Vulcan are now more than
ever justified. If such a body as he supposed he saw really travels
round the sun within the orbit of Mercury, it is certain that the
observations made last July by those who were specially engaged in
seeking for Vulcan must have been rewarded by a view of that planet.
In July, Lescarbault's Vulcan could not have been invisible, no matter
in what part of his orbit it might be, and the chances would have been
greatly in favour of its appearing as a very bright star, without
telescopic aid.
But on the other hand it seems extremely probable,--in fact, unless
any one be disposed to question the veracity of the observers, it is
certain,--that within the orbit of Mercury there are several small
planets, of which certainly two, and probably three, were seen during
the eclipse of July 29, 1878. All these bodies must be beyond the
range of any except the most powerful telescopes, whether sought for
as bright bodies outside the sun (not eclipsed) or as dark bodies in
transit across the sun's face. The search for such bodies in transit
would in fact be hopeless with any telescope which would not easily
separate double stars one second of arc apart. It is with large
telescopes, then, and under favourable conditions of atmosphere,
locality, and so forth, that the search for intra-Mercurial planets in
transit must in future be conducted. As the observed disturbance of
Mercury's perihelion, and the absence of any corresponding disturbance
of his nodes (the points where he crosses the plane of the earth's
motion) show that the disturbing bodies must form a ring or disc whose
central plane must nearly coincide with the plane of Mercury's path,
the most favourable time for seeing these bodies in transit would
be the first fortnights in May and November; for the earth crosses
the plane of Mercury's orbit on or about May 8 and November 10. I
believe that a search carried out in April, May, and June, and in
October, November, and December, with the express object of discovering
_very_ small planets in transit, could not fail to be quickly
rewarded,--unless the observations made by Watson and Swift are to be
wholly rejected.
[Since this was written, Professor Swift has expressed the opinion
that his planet cannot possibly have been the one seen near Theta
Cancri by Professor Watson,--who it seems saw Theta in the centre
of a large field of view, and must therefore have seen Swift's
planet had that object been placed either as shown in fig. 2 or
fig. 3. Hence Professor Swift considers that both the stars he
himself saw were planets, and that he did not see Theta at all.
The reasoning in the last five paragraphs of the above essay would
not be in the least affected if we adopted Professor Swift's
conclusion, that four and not three intra-Mercurial planets were
detected during the eclipse of July last. Yet later Professor
Peters of Clinton has indicated reasons for believing that while
Watson simply mistook for planets the two fixed stars, Theta
and Zeta Cancri, Professor Swift saw no planets at all. This
interpretation would account fully, though not very satisfactorily,
for all that is mysterious in the two narratives.]
FOOTNOTES:
[Footnote 3: Two observations of Uranus, by Bradley, were discovered
by the late Mr. Breen, and published in No. 1463 of the _Astronomische
Nachrichten_.]
[Footnote 4: Let the student make the following construction if he
entertains any doubt as to the statements made above. Having traced the
orbits of the earth and Uranus from my chart illustrating the article
'Astronomy' in the _Encyc. Brit._, let him describe a circle nearly
twice as large to represent the orbit of Neptune as Bode's law would
give it. Let him first suppose Neptune in conjunction with Uranus in
1820, mark the place of the earth on any given day in 1842, and the
place of the fictitious Neptune; a line joining these points will
indicate the direction of Neptune on the assumptions made. Let him
next make a similar construction on the assumption that conjunction
took place in 1825. (From the way in which the perturbation of Uranus
reached a maximum between 1820 and 1825, it was practically certain
that the disturber was in conjunction with Uranus between those years.)
These two constructions will give limiting directions for Neptune
as viewed from the earth, on the assumption that his orbit has the
dimensions named. He will find that the lines include an angle of a
few degrees only, and that the direction line of the true Neptune is
included between them.]
[Footnote 5: The problem is in reality, at least in the form in which
Lescarbault attacked it, an exceedingly simple one. A solution of the
general problem is given at p. 181 of my treatise on the _Geometry
of Cycloids_. It is, in fact, almost identical with the problem of
determining the distance of a planet from observations made during a
single night.]
[Footnote 6: It may be necessary, perhaps, to explain to some why the
western side is on the right in the little maps illustrating this
paper, and not, as usual with maps, on the left. We are supposed to
look down towards the earth in the case of a terrestrial map, and to
look up from the earth in the case of a celestial map, and naturally
right and left for the former attitude become respectively left and
right for the latter.]
_RESULTS OF THE BRITISH TRANSIT EXPEDITIONS._
Another noteworthy attempt has been made to estimate the distance which
separates our earth from the mighty central orb round which she travels
with her fellow-worlds the planets. In other words, the solar system
itself has been remeasured; for the measurement of any part of the
system is in fact the measurement of the entire system, the proportions
of which, as distinguished from its actual dimensions, have long been
accurately known.
I propose briefly to describe the results which have been obtained
(after some three years of careful examination) from the observations
made by the British parties sent north, south, east, and west to
observe the transit of Venus on December 9, 1874; and then to consider
how these results compare with those which had before been obtained.
First, however, it may be well to remind the reader of the unfavourable
conditions under which the task of measuring our distance from the
remote sun must of necessity be attacked.
Not unfrequently we hear the measurement of the sun's distance, and
the various errors which astronomers have had to correct during the
progress of their efforts to deal with the problem, referred to in
terms which would imply that astronomy had some reason to be ashamed
of labours which are in reality among the most noteworthy achievements
of their science. Because, some twenty years ago, the estimate of 95
million miles, which had for half a century held its ground in our
books of astronomy as the true distance of the sun, was replaced for a
while by an estimate of about 91-1/2 million miles, which has in turn
been displaced for an estimate of about 92-1/3 million miles, it has
been said that astronomy has very little claim to be called the exact
science. It is even supposed by some that astronomy is altogether
at sea respecting the sun's distance--which, if the estimates of
astronomers thus vary in the course of three-quarters of a century, may
in reality, it is thought, be very different from any of the values
hitherto assigned. Others suppose that possibly the sun's distance may
vary, and that the diminution of three or four million miles in the
estimates adopted by astronomers may correspond to an approach of the
earth towards the sun by that amount, an approach which, if continued
at the same rate, would, before many centuries, bring the earth upon
the surface of the sun, to be consumed as fuel perhaps for the warming
of the outer planets, Mars, Jupiter, and the rest.
All these imaginings are mistaken, however. The exactness of astronomy,
as a science, does not depend on the measurement of the sun's distance
or size, any more than the accuracy of a clock as a timekeeper depends
on the exactness with which the hands of the clock are limited to
certain definite lengths. The skill with which astronomy has dealt with
this particular problem of celestial surveying has been great indeed;
and the results, when considered with due reference to the conditions
of the problem, are excellent: but in reality, if astronomers had
failed utterly to form any ideas whatever as to the sun's distance, if
for aught they knew the sun might be less than one million, or more
than a million millions of miles from us, the exactness of astronomy
as a science would be no whit impaired. And, in the second place, no
doubts whatever need be entertained as to the general inference from
astronomical observations that the sun's distance is between 92 and 93
millions of miles. All the measurements made during the last quarter
of a century lie between 90 and 95 millions of miles, and by far the
greater number of those made by the best methods, and under the most
favourable conditions, lie between 91 and 94 millions of miles. All
the very best cluster closely around a distance of 92-1/3 millions of
miles. We are not for the moment, however, concerned with the question
of the exact distance, but with the question whether astronomy has
obtained satisfactory evidence that the sun's distance lies in the
neighbourhood of the distances deduced by the various methods lately
employed. Putting the matter as one of probabilities, as all scientific
statements must be, it may be said as confidently that the sun's
distance lies between 85 millions and 100 millions of miles as that the
sun will rise to-morrow; and the probability that the sun's distance
is less than 90 millions, or greater than 95 millions of miles, is so
small that it may in effect be counted almost as nothing. Thirdly, the
possibility that the earth may be drawing nearer to the sun by three
or four millions of miles in a century may be dismissed entirely from
consideration. For, one of the inevitable consequences of such a change
of distance would be a change in the length of the year by about three
weeks; and so far from the year diminishing by twenty days or so in
length during a century, it has not diminished ten seconds in length
during the last two thousand years. If there has been any change year
by year in the earth's distance from the sun, it is one to be measured
by yards rather than by miles. Astronomers would be well content if
their 'probable error' in estimating the sun's distance could be
measured by thousands of miles; so that any possible approach of the
earth towards the sun would go but a very little way towards accounting
for the discrepancies between the different estimates of the distance,
even if these estimates grew always smaller as time passed, which is
assuredly not the case.