Part 5

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.

Thus provided, Professor Watson, so soon as totality began, searched 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.

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_.

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.

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.

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.