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[1] The actual condition of the sun in 1842 may be inferred from the following table, showing the number of spots observed in 1837 the preceding year of maximum disturbance, in 1842, and in 1844 the following year of minimum disturbance; the observer was Schwabe of Dessau:
| Days of observation | Days without spots | New groups observed | |
| 1837 | 168 | 307 | 321 |
| 1842 | 0 | 94 | 111 |
| 1844 | 333 | 68 | 52 |
Only it should be noticed that nearly all the spots seen in the year 1844 belonged to the next period, the time of actual minimum occurring early in 1844.
[2] The following table shows the position occupied by the years 1851 and 1860 in this report, as compared with the year 1848 (maximum next preceding 1851), 1856 (minimum next following 1851) and 1867, minimum next following 1860:—
| Days of observation | Days without spots | New groups observed | |
| 1848 | 278 | 0 | 930 |
| 1851 | 308 | 0 | 141 |
| 1856 | 321 | 193 | 34 |
| 1860 | 332 | 0 | 211 |
| 1867 | 312 | 195 | 25 |
A comparison of the three tables given in these notes and the text will afford some idea of the irregularities existing in the various waves of sun-spots.
SUN-SPOTS AND COMMERCIAL PANICS.
We are not only, it would seem, to regard the sun as the ultimate source of all forms of terrestrial energy, existent or potential, but as regulating in a much more special manner the progress of mundane events. Many years have passed since Sabine, Wolf, and Gauthier asserted that variations in the daily oscillations of the magnetic needle appear to synchronise with the changes taking place in the sun's condition, the oscillations attaining their maximum average range in years when the sun shows most spots, and their minimum range when there are fewest spots. And although it is well known that the Astronomer Royal in England and the President of the Academy of Sciences in France reject this doctrine, it still remains in vogue. True, the average magnetic period appears to be about 10.45 years, while Wolf obtains for the sun-spot period 11.11 years; but believers in the connection between terrestrial magnetic disturbances and sun-spots consider that among the imperfect records of the past condition of the sun Wolf must have lost sight of one particular wave of sun-spots, so to speak. If there have been 24 such waves between 1611 and 1877, when sun-spots were fewest, we get Wolf's period of 11.11 years; if there have been 25 such waves then, taking an admissible estimate for the earliest epoch, we get 10.45 years, the period required to synchronise with the period of terrestrial magnetic changes. The matter must be regarded as still sub judice. This, however, is only one relation out of many now suggested. Displays of the aurora, being unquestionably dependent on the magnetic condition of the earth, would of course be associated with the sun spot period, if the magnetic period is so; and certainly the most remarkable displays of the aurora in recent times have occurred when the sun has shown many spots. Yet this of itself proves nothing more than had been already known—namely, that the last few magnetic periods have nearly synchronised with the last few sun-spot periods. It is rather strange, too, that no auroras are mentioned in the English records for 80 years preceding the aurora of 1716, and in the records of the Paris Academy of Sciences one only—that of 1666, which occurred when sun-spots were fewest. The great aurora of 1723, seen as far south as Bologna, also occurred at the time of minimum solar activity. Here we are not depending on either Wolf's period of 11 years or Brown's of 10½ years; from records of actual observation it is known that in 1666 and 1713 there were no sun-spots. In fact it is worth mentioning that Cassini, writing in 1671, says, 'It is now about 20 years since astronomers have seen any considerable spots on the sun,' a circumstance which throws grave doubt on the law of sun-spot periodicity itself. It is at least certain that the interval from maximum, spot-frequency to maximum, or from minimum to minimum, has sometimes fallen far short of 9 years, and has at others exceeded 18 years.
It appears again that certain meteorological phenomena show a tendency, more or less marked, to run through a ten-year cycle. Thus, from the records of rainfall kept at Oxford it appears that more rain fell under west and south-west winds when sun-spots were largest and most numerous than under south and south-east winds, these last being the more rainy winds when sun-spots were least in size and fewest in number. This is a somewhat recondite relation, and at least proves that earnest search has been made for such cyclic relations as we are considering. But this is not all. When other records were examined, the striking circumstance was discovered that elsewhere, as at St. Petersburg, the state of things observed at Oxford was precisely reversed. At some intermediate point between Oxford and St. Petersburg, no doubt the rainfall under the winds named was equally distributed throughout the spot period. Moreover, as the conditions thus differ at different places, we may assume that they differ also at different times. Such relations appear then to be not only recondite, but complicated.
When we learn that during nearly two entire sun-spot periods cyclones have been somewhat more numerous in the Indian Seas when spots are most numerous than when the sun is without spots, and vice versâ, we recognise the possible existence of cyclic relations better worth knowing than those heretofore mentioned. The evidence is not absolutely decisive; some, indeed, regard it as scarcely trustworthy. Yet there does seem to have been an excess of cyclonic disturbance during the last two periods of great solar disturbance, precisely as there was also an excess of magnetic disturbance during those periods. The excess was scarcely sufficient, however, to justify the rather daring statement made by one observer, that 'the whole question of cyclones is merely a question of solar activity.' We had records of some very remarkable cyclonic disturbances during the years 1876 and 1877, when the sun showed very few spots, the actual minimum of disturbance having probably been reached late in 1877. A prediction that 1877 would be a year of few and slight storms would have proved disastrous if implicit reliance had been placed on it by seamen and travellers.
Rainfall and atmospheric pressure in India have been found to vary in a cyclic manner, of late years at any rate, the periods being generally about 10 or 11 years. The activity of the sun, as shown by the existence of many spots, apparently makes more rainfall at Madras, Najpore, and some other places; while at Calcutta, Bombay, Mysore, and elsewhere it produces a contrary effect. Yet these effects are produced in a somewhat capricious way: for sometimes the year of actual maximum spot frequency is one in which rainfall is below the average (instead of above) at the former stations, and above the average (instead of below) at the latter. It is only by taking averages—and in a somewhat artificial manner—that the relation seems to be indicated on which stress has been laid.
Since Indian famines are directly dependent on defective rainfall, it is natural that during the years over which observation has hitherto extended the connection apparently existing between sun-spots and Indian rainfall should seem also to extend itself to Indian famines. It was equally to be expected that since cyclones have been rather more numerous, for some time past, in years when sun-spots have been most numerous, shipwrecks should also have been somewhat more frequent in such years. Two years ago Mr. Jeula gave some evidence which, in his opinion, indicated such a connection between sun-spots and shipwrecks. He showed that in the four years of fewest spots the mean percentage of losses was 8.64; in four intermediate years the mean percentage was 9.21; in three remaining years of the eleven-year cycle—that is, in three years of greatest spot frequency the mean percentage was 9.53. Some suggested that possibly such events as the American war, which included two of the three years of greatest spot frequency, may have had more effect than sun-spots in increasing the percentage of ships lost; while perhaps, the depression following the commercial panic of 1866 (at a time of fewest sun-spots) may have been almost as effective in reducing the percentage of losses as the diminished area of solar maculation. But others consider that we ought rather to regard the American war as yet another product of the sun's increased activity in 1860–61, and the great commercial panic of 1866 as directly resulting from diminished sun-spots at that time, thus obtaining fresh evidence of the sun's specific influence on terrestrial phenomena instead of explaining away the evidence derived from Lloyd's list of losses.
This leads us to the last, and, in some respects, the most singular suggestion respecting solar influence on mundane events—the idea, namely, that commercial crises synchronise with the sun-spot period, occurring near the time when spots are least in size and fewest in number; or, as Professor Jevons (to whom the definite enunciation of this theory is due) poetically presents the matter, that from 'the sun, which is truly "of this great world both eye and soul," we derive our strength and our weakness, our success and our failure, our elation in commercial mania, and our despondency and ruin in commercial collapse.' We have better opportunities of dealing with this theory than with the others, for we have records of commercial matters extending as far back as the beginning of the eighteenth century. In fact, we have better evidence than Professor Jevons seems to have supposed, for whereas in his discussion of the matter he considers only the probable average of the sun-spot period, we know approximately the epochs themselves at which the maxima and minima of sun spots have occurred since the year 1700. The evidence as presented by Professor Jevons is very striking, though when examined in detail it is rather disappointing. He presents the whole series of decennial crises as follows:—1701? (such query marks are his own), 1711, 1721, 1731–32, 1742 (?), 1752 (?), 1763, 1772–73, 1783, 1793, 1804–5 (?), 1815, 1825, 1836–9 (1837 in the United States), 1847, 1857, 1866 and 1878. The average interval comes out 10.466 years, showing, as Jevons points out, 'almost perfect coincidence with Brown's estimate of the average sun-spot period.' Let us see, however, whether these dates correspond so closely with the years of minimum spot-frequency as to remove all doubt. Taking 5¼ years as the average interval between maximum and minimum sun-spot frequency, we should like to find every crisis occurring within a year or so on either side of the minimum though we should prefer perhaps to find the crisis always following the time of fewest sun-spots, as this would more directly show the depressing effect of a spotless sun. No crisis ought to occur within a year or so of maximum solar disturbance; for that, it should seem, would be fatal to the suggested theory. Taking the commercial crises in order, and comparing them with the known (or approximately known) epochs of maximum and minimum spot frequency, we obtain the following results (we italicize numbers or results unfavourable to the theory):—The doubtful crisis of 1701 followed a spot minimum by three years; the crisis of 1711 preceded a minimum by one year; that of 1721 preceded a minimum by two years; 1731–32, preceded a minimum by one year; 1742 preceded a minimum by three years; 1752 followed a maximum by two years; 1763 followed a maximum by a year and a half; 1772–73 came midway between a maximum and a minimum; 1783 preceded a minimum by nearly two years; 1793 came nearly midway between a maximum and a minimum; 1804–5 coincided with a maximum; 1815 preceded a maximum by two years; 1825 followed a minimum by two years; 1836–39 included the year 1837 of maximum solar activity (that year being the time also when a commercial crisis occurred in the United States); 1847 preceded a maximum by a year and a half; 1866 preceded a minimum by a year; and 1878 followed a minimum by a year. Four favourable cases out of 17 can hardly be considered convincing. If we include cases lying within two years of a minimum, the favourable cases mount up to seven, leaving ten unfavourable ones. It must be remembered, too, that a single decidedly unfavourable case (as 1804, 1815, 1837) does more to disprove such a theory than 20 favourable cases would do towards establishing it. The American panic of 1873, by the way, which occurred when spots were very numerous, decidedly impairs the evidence derived from the crises of 1866 and 1878.
NEW PLANETS NEAR THE SUN.
Perhaps no scientific achievement during the present century has been deemed more marvellous than the discovery of the outermost member (so far as is known) of the sun's family of planets. In many respects, apart from the great difficulty of the mathematical problem involved, the discovery appealed strongly to the imagination. A planet seventeen hundred millions of miles from the sun had been discovered in March, 1781, by a mere accident, though the accident was not one likely to occur to any one but an astronomer constantly studying the star-depths. Engaged in such observation, but with no idea of enlarging the known domain of the sun, Sir W. Herschel perceived the distant planet Uranus. His experienced eye at once recognised the fact that the stranger was not a fixed star. He judged it to be a comet. It was not until several weeks had elapsed that the newly discovered body was proved to be a planet, travelling nearly twice as far away from the sun as Saturn, the remotest planet before known. A century only had elapsed since the theory of gravitation had been established. Yet it was at once perceived how greatly this theory had increased the power of the astronomer to deal with planetary motions. Before a year had passed more was known about the motions of Uranus than had been learned about the motion of any of the old planets during the two thousand years preceding the time of Copernicus. It was possible to calculate in advance the position of the newly discovered planet, to calculate retrogressively the path along which it had been travelling, unseen and unsuspected, during the century preceding its discovery. And now observations which many might have judged to be of little value, came in most usefully. Astronomers since the discovery of the telescope had formed catalogues of the places of many hundreds of stars invisible to the naked eye. Search among the observations by which such catalogues had been formed, revealed the fact that Uranus had been seen and catalogued as a fixed star twenty-one several times! Flamsteed had seen it five times, each time recording it as a star of the sixth magnitude, so that five of Flamsteed's stars had to be cancelled from his lists. Lemonnier had actually seen Uranus twelve times, and only escaped the honour of discovering the planet (as such) through the most marvellous carelessness, his astronomical papers being, as Arago said, 'a very picture of chaos.' Bradley saw Uranus three times.[3] Mayer saw the planet once only.
It was from the study of the movements of Uranus as thus seen, combined with the planet's progress after its discovery, that mathematicians first began to suspect the existence of some unknown disturbing body. The observations preceding the discovery of the planet range over an interval of ninety years and a few months, the earliest observation used being one made by Flamsteed on December 23, 1690. There is something very strange in the thought that science was able thus to deal with the motions of a planet for nearly a century before the planet was known. Astronomy calculated in the first place where the planet had been during that time; and then, from records made by departed observers, who had had no suspicion of the real nature of the body they were observing, Astronomy corrected her calculations, and deduced more rigorously the true nature of the new planet's motions.
But still stranger and more impressive is the thought that from researches such as these, Astronomy should be able to infer the existence of a planet a thousand million miles further away than Uranus itself. How amazing it would have seemed to Flamsteed, for example, if on that winter evening in 1693, when he first observed Uranus, he had been told that the orb which he was entering in his lists as a star of the sixth magnitude was not a star at all, and that the observation he was then making would help astronomers a century and a half later to discover an orb a hundred times larger than the earth, and travelling thirty times farther away from the sun.
Even more surprising, however, than any of the incidents which preceded the discovery of Neptune was this achievement itself. That a planet so remote as to be quite invisible to the naked eye, never approaching our own earth within less than twenty-six hundred millions of miles, never even approaching Uranus within less than nine hundred and fifty millions of miles, should be detected by means of those particular perturbations (among many others) which it produced upon a planet not yet known for three-quarters of a century, seemed indeed surprising. Yet even this was not all. As if to turn a wonderful achievement into a miracle of combined skill and good fortune, came the announcement that, after all, the planet discovered in the spot to which Adams and Leverrier pointed was not the planet of their calculations, but travelled in an orbit four or five hundred millions of miles nearer to the sun than the orbit which had been assigned to the unknown body. Many were led to suppose that nothing but a most marvellous accident had rewarded with such singular success the calculations of Adams and Leverrier. Others were even more surprised to learn that the new planet departed strangely from the law of distances which all the other planets of the solar system seemed to obey. For according to that law (called Bode's law) the distance of Neptune, instead of being about thirty times, should have been thirty-nine times the earth's distance from the sun.
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 5–⅓ and 7–⅓ 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 12–⅕ 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 2½ 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.
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.
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.
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.
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 4½ and 3½ 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.
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.]
