Part 4

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 10-1/2 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 5-1/4 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. 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. 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. 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.