Part 4

In some respects the discovery of a planet nearer to the sun than Mercury may seem to many far inferior in interest to the detection of the remote giant Neptune. Between Mercury and the sun there intervenes a mean distance of only thirty-six millions of miles, a distance seeming quite insignificant beside those which have been dealt with in describing the discovery of Uranus and Neptune. Again it is quite certain that any planet between Mercury and the sun must be far inferior to our own earth in size and mass, whereas Neptune exceeds the earth 105 times in size and 17 times in mass. Thus a much smaller region has to be searched over for a much smaller body. Moreover, while mathematical calculation cannot deal nearly so exactly with an intra-Mercurial planet as with Neptune, for there are no perturbations of Mercury which give the slightest information as to the orbital position of his disturber, the part of the heavens occupied by the intra-Mercurial planet is known without calculation, seeing that the planet must always lie within six or seven degrees or so of the sun, and can never be very far from the ecliptic.

Yet in reality the detection of an intra-Mercurial planet is a problem of far greater difficulty than that of such a planet as Neptune, while even now when most astronomers consider that an intra-Mercurial planet has been detected, the determination of its orbit is a problem which seems to present almost insuperable difficulties.

I may remark, indeed, with regard to Neptune, that he might have been 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.