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