FOOTNOTES:

The moon possesses for us a unique interest. She in all probability shared the origin of the earth; she perhaps prefigures its decay. She is at present its minister and companion. Her existence, so far as we can see, serves no other purpose than to illuminate the darkness of terrestrial nights, and to measure, by swiftly-recurring and conspicuous changes of aspect, the long span of terrestrial time. Inquiries stimulated by visible dependence, and aided by relatively close vicinity, have resulted in a wonderfully minute acquaintance with the features of the single lunar hemisphere open to our inspection.

Selenography, in the modern sense, is little more than a hundred years old. It originated with the publication in 1791 of Schröter'sSelenotopographische Fragmente.[914]Not but that the lunar surface had already been diligently studied, chiefly by Hevelius, Cassini, Riccioli, and Tobias Mayer; the idea, however, of investigating the moon's physical condition, and detecting symptoms of the activity there of natural forces through minute topographical inquiry, first obtained effect at Lilienthal. Schröter's delineations, accordingly, imperfect though they were, afforded a starting-point for acomparativestudy of the superficial features of our satellite.

The first of the curious objects which he named "rills" was noted by him in 1787. Before 1801 he had found eleven; Lohrmann added 75; Mädler 55; Schmidt published in 1866 a catalogue of 425, of which 278 had been detected by himself;[915]and he eventually brought the number up to nearly 1,000. They are, then, a very persistent lunar feature, though wholly without terrestrial analogue. There is no difference of opinion as to their nature. They are quite obviously clefts in a rocky surface, 100 to 500 yards deep, usually a couple of miles across, and pursuing straight, curved, or branching tracks up to 150 miles in length. As regards their origin, the most probable view is that they are fissures produced in cooling; but Neison inclines to consider them rather as dried watercourses.[916]

On February 24, 1792, Schröter perceived what he took to be distinct traces of a lunar twilight, and continued to observe them during nine consecutive years.[917]They indicated, he thought, the presence of a shallow atmosphere, about 29 times more tenuous than our own. Bessel, on the other hand, considered that the only way of "saving" a lunar atmosphere was to deny it any refractive power, the sharpness and suddenness of star-occultations negativing the possibility of gaseous surroundings of greater density (admitting an extreme supposition) than 1/500 that of terrestrial air.[918]Newcomb places the maximum at 1/400. Sir John Herschel concluded "the non-existence of any atmosphere at the moon's edge having 1/1980 part of the density of the earth's atmosphere."[919]

This decision was fully borne out by Sir William Huggins's spectroscopic observation of the disappearance behind the moon's limb of the small star ε Piscium, January 4, 1865.[920]Not the slightestsign of selective absorption or unequal refraction was discernible. The entire spectrum went out at once, as if a slide had suddenly dropped over it. The spectroscope has uniformly told the same tale; for M. Thollon's observation during the total solar eclipse at Sohag of a supposed thickening at the moon's rim, of certain dark lines in the solar spectrum, is now acknowledged to have been illusory. Moonlight, analysed with the prism, is found to be pure reflected sunlight, diminished inquantity, owing to the low reflective capability of the lunar surface, to less than one-fifth its incident intensity, but wholly unmodified inquality.

Nevertheless, the diameter of the moon appeared from the Greenwich observations discussed by Airy in 1865[921]to be 4′ smaller than when directly measured; and the effect would be explicable by refraction in a lunar atmosphere 2,000 times thinner than our own at the sea-level. But the difference was probably illusory. It resulted in part, if not wholly, from the visual enlargement by irradiation of the bright disc of the moon. Professor Comstock, employing the 16-inch Clark equatoreal of the Washburn Observatory, found in 1897 the refractive displacements of occulted stars so trifling as to preclude the existence of a permanent lunar atmosphere of much more than 1/5000 the density of the terrestrial envelope.[922]The possibility, however, was admitted that, on the illuminated side of the moon, temporary exhalations of aqueous vapour might arise from ice-strata evaporated by sun-heat. Meantime, some renewed evidence of actual crepuscular gleams on the moon had been gathered by MM. Paul and Prosper Henry of the Paris Observatory, as well as by Mr. W. H. Pickering, in the pure air of Arequipa, at an altitude of 8,000 feet above the sea.[923]An occultation of Jupiter, too, observed by him August 12, 1892,[924]was attended with a slight flattening of the planet's disc through the effect, it was supposed, of lunar refraction—but of refraction in an atmosphere possessing, at the most, 1/4000 the density at the sea-level of terrestrial air, and capable of holding in equilibrium no more than 1/250 of an inch of mercury. Yet this small barometric value corresponds, Mr. Pickering remarks, "to a pressure of hundreds of tons per square mile of the lunar surface." The compression downward of gaseous strata on the moon should, in any case, proceed very gradually, owing to the slight power of lunar gravity,[925]and they might hence play an important part in the economy of our satellite while evading spectroscopic and other tests. Thus—asMr. Ranyard remarked[926]—the cliffs and pinnacles of the moon bear witness, by their unworn condition, to the efficiency of atmospheric protection against meteoric bombardment; and Mr. Pickering shows that it could be afforded by such a tenuous envelope as that postulated by him.

The first to emulate Schröter's selenographical zeal was Wilhelm Gotthelf Lohrmann, a land-surveyor of Dresden, who, in 1824, published four out of twenty-five sections of the first scientifically executed lunar chart, on a scale of 37-1/2 inches to a lunar diameter. His sight, however, began to fail three years later, and he died in 1840, leaving materials from which the work was completed and published in 1878 by Dr. Julius Schmidt, late director of the Athens Observatory. Much had been done in the interim. Beer and Mädler began at Berlin in 1830 their great trigonometrical survey of the lunar surface, as yet neither revised nor superseded. A map, issued in four parts, 1834-36, on nearly the same scale as Lohrmann's, but more detailed and authoritative, embodied the results. It was succeeded, in 1837, by a descriptive volume bearing the imposing title,Der Mond; oder allgemeine vergleichende Selenographie. This summation of knowledge in that branch, though in truth leaving many questions open, had an air of finality which tended to discourage further inquiry.[927]It gave form to a reaction against the sanguine views entertained by Hevelius, Schröter, Herschel and Gruithuisen as to the possibilities of agreeable residence on the moon, and relegated the "Selenites," one of whose cities Schröter thought he had discovered, and of whose festal processions Gruithuisen had not despaired of becoming a spectator, to the shadowy land of the Ivory Gate. All examples of change in lunar formations were, moreover, dismissed as illusory. The light contained in the work was, in short, a "dry light," not stimulating to the imagination. "A mixture of a lie," Bacon shrewdly remarks, "doth ever add pleasure." For many years, accordingly, Schmidt had the field of selenography almost to himself.

Reviving interest in the subject was at once excited and displayed by the appointment, in 1864, of a Lunar Committee of the British Association. The indirect were of greater value than the direct fruits of its labours. An English school of selenography rose into importance. Popularity was gained for the subject by the diffusion of works conspicuous for ingenuity and research. Nasmyth's and Carpenter's beautifully illustrated volume (1874) was succeeded, after two years, by a still more weighty contribution to lunar science in Mr. Neison's well-known book, accompanied by a map, based on the survey of Beer and Mädler, but adding some 500measures of positions, besides the representation of several thousand new objects. With Schmidt'sCharte der Gebirge der Mondes, Germany once more took the lead. This splendid delineation, built upon Lohrmann's foundation, embraced the detail contained in upwards of 3,000 original drawings, representing the labour of thirty-four years. No less than 32,856 craters are represented in it, on a scale of seventy-five inches to a diameter. An additional help to lunar inquiries was provided at the same time in this country by the establishment, through the initiative of the late Mr. W. R. Birt, of the Selenographical Society.

But the strongest incentive to diligence in studying the rugged features of our celestial helpmate has been the idea of probable or actual variation in them. A change always seems to the inquisitive intellect of man like a breach in the defences of Nature's secrets, through which it may hope to make its way to the citadel. What is desirable easily becomes credible; and thus statements and rumours of lunar convulsions have successively, during the last hundred years, obtained credence, and successively, on closer investigation, been rejected. The subject is one as to which illusion is peculiarly easy. Our view of the moon's surface is a bird's-eye view. Its conformation reveals itself indirectly through irregularities in the distribution of light and darkness. The forms of its elevations and depressions can be inferred only from the shapes of the black, unmitigated shadows cast by them. But these shapes are in a state of perpetual and bewildering fluctuation, partly through changes in the angle of illumination, partly through changes in our point of view, caused by what are called the moon's "librations."[928]The result is, that no single observation can beexactlyrepeated by the same observer, since identical conditions recur only after the lapse of a great number of years.

Local peculiarities of surface, besides, are liable to produce perplexing effects. The reflection of earth-light at a particular angle from certain bright summits completely, though temporarily, deceived Herschel into the belief that he had witnessed, in 1783 and 1787, volcanic outbursts on the dark side of the moon. The persistent recurrence, indeed, of similar appearances under circumstances less amenable to explanation inclined Webb to the viewthat effusions of native light actually occur.[929]More cogent proofs must, however, be adduced before a fact so intrinsically improbable can be admitted as true.

But from the publication of Beer and Mädler's work until 1866, the received opinion was that no genuine sign of activity had ever been seen, or was likely to be seen, on our satellite; that her face was a stereotyped page, a fixed and irrevisable record of the past. A profound sensation, accordingly, was produced by Schmidt's announcement, in October, 1866, that the crater "Linné," in the Mare Serenitatis, had disappeared,[930]effaced, as it was supposed, by an igneous outflow. The case seemed undeniable, and is still dubious. Linné had been known to Lohrmann and Mädler, 1822-32, as a deep crater, five or six miles in diameter, the third largest in the dusky plain known as the "Mare Serenitatis"; and Schmidt had observed and drawn it, 1840-43, under a practically identical aspect. Now it appears under high light as a whitish spot, in the centre of which, as the rays begin to fall obliquely, a pit, scarcely two miles across, emerges into view.[931]The crateral character of this comparatively minute depression was detected by Father Secchi, February 11, 1867.

This is not all. Schröter's description of Linné, as seen by him November 5, 1788, tallies quite closely with modern observation;[932]while its inconspicuousness in 1797 is shown by its omission from Russell's lunar globe and maps.[933]We are thus driven to adopt one of two suppositions: either Lohrmann, Mädler, and Schmidt were entirely mistaken in the size and importance of Linné, or a real change in its outward semblance supervened during the first half of the century, and has since passed away, perhaps again to recur. The latter hypothesis seems the more probable: and its probability is strengthened by much evidence of actual obscuration or variation of tint in other parts of the lunar surface, more especially on the floor of the great "walled plain" named "Plato."[934]From a re-examination with a 13-inch refractor at Arequipa in 1891-92, of this region, and of the Mare Serenitatis, Mr. W. H. Pickering inclines to the belief that lunar volcanic action, once apparently so potent, is not yet wholly extinct.[935]

An instance of an opposite kind of change was alleged by Dr. Hermann J. Klein of Cologne in March, 1878.[936]In Linné theobliteration of an old crater had been assumed; in "Hyginus N.," the formation of a new crater was asserted. Yet, quite possibly, the same cause may have produced the effects thought to be apparent in both. It is, however, far from certain that any real change has affected the neighbourhood of Hyginus. The novelty of Klein's observation of May 19, 1877, may have consisted simply in the detection of a hitherto unrecognised feature. The region is one of complex formation, consequently of more than ordinary liability to deceptive variations in aspect under rapid and entangled fluctuations of light and shade.[937]Moreover, it seems to be certain, from Messrs. Pratt and Capron's attentive study, that "Hyginus N." is no true crater, but a shallow, saucer-like depression, difficult of clear discernment.[938]Under suitable illumination, nevertheless, it contains, and is marked by, an ample shadow.[939]

In both these controverted instances of change, lunar photography was invoked as a witness; but, notwithstanding the great advances made in the art by De la Rue in this country, by Draper, and, above all, by Rutherford in America, without decisive results. Investigations of the kind began to assume a new aspect in 1890, when Professor Holden organised them at the Lick Observatory.[940]Autographic moon-pictures were no longer taken casually, but on system; and Dr. Weinek's elaborate study, and skilful reproductions of them at Prague,[941]gave them universal value. They were designed to provide materials for an atlas on the scale of Beer and Mädler's, of which some beautiful specimen-plates have been issued. At Paris, in 1894, with the aid of a large "equatoreal coudé," a work of similar character was set on foot by MM. Loewy and Puiseux. Its progress has been marked by the successive publication of five instalments of a splendid atlas, on a scale of about eight feet to the lunar diameter, accompanied by theoretical dissertations, designed to establish a science of "selenology." The moon's formations are thus not only delineated under every variety of light-incidence, but their meaning is sought to be elicited, and their history and mutual relations interpreted.[942]Henceforth, at any rate, the lunar volcanoes can scarcely, without notice taken, breathe hard in their age-long sleep.

Melloni was the first to get undeniable heating effects from moonlight. His experiments, made on Mount Vesuvius early in 1846,[943]were repeated with like result by Zantedeschi at Venice four years later. A rough measure of the intensity of those effects was arrived at by Piazzi Smyth at Guajara, on the Peak of Teneriffe, in 1856. At a distance of fifteen feet from the thermomultiplier, a Price's candle was found to radiate just twice as much heat as the full moon.[944]Then, after thirteen years, in 1869-72, an exact and extensive series of observations on the subject were made by the present Earl of Rosse. The lunar radiations, from the first to the last quarter, displayed, when concentrated with the Parsonstown three-foot mirror, appreciable thermal energy, increasing with the phase, and largely due to "dark heat," distinguished from the quicker-vibrating sort by inability to traverse a plate of glass. This was supposed to indicate an actual heating of the surface, during the long lunar day of 300 hours, to about 500° F.[945](corrected later to 197°),[946]the moon thus acting as a direct radiator no less than as a reflector of heat. But the conclusion was very imperfectly borne out by Dr. Boeddicker's observations with the same instrument and apparatus during the total lunar eclipse of October 4, 1884.[947]This initial opportunity of measuring the heat phases of an eclipsed moon was used with the remarkable result of showing that the heat disappeared almost completely, though not quite simultaneously, with the light. Confirmatory evidence of the extraordinary promptitude with which our satellite parts with heat already to some extent appropriated, was afforded by Professor Langley's bolometric observations at Allegheny of the partial eclipse of September 23, 1885.[948]Yet it is certain that the moon sends us a perceptible quantity of heaton its own account, besides simply throwing back solar radiations. For in February, 1885, Professor Langley succeeded, after many fruitless attempts, in getting measures of a "lunar heat-spectrum." The incredible delicacy of the operation may be judged of from the statement that the sum-total of the thermal energy dispersed by his rock-salt prisms was insufficient to raise a thermometer fully exposed to it one-thousandth of a degree Centigrade! The singular fact was, however, elicited that this almost evanescent spectrum is made up of two superposed spectra, one due to reflection, the other, with a maximum far down in the infra-red, to radiation.[949]The corresponding temperature of the moon's sunlit surface Professor Langleyconsiders to be about that of freezing water.[950]Repeated experiments having failed to get any thermal effects from the dark part of the moon, it was inferred that our satellite "has no internal heat sensible at the surface"; so that the radiations from the lunar soil giving the low maximum in the heat-spectrum, "must be due purely to solar heat which has been absorbed and almost immediately re-radiated." Professor Langley's explorations of the terra incognita of immensely long wave-lengths where lie the unseen heat-emissions from the earth into space, led him to the discovery that these, contrary to the received opinion, are in good part transmissible by our atmosphere, although they are completely intercepted by glass. Another important result of the Allegheny work was the abolition of the anomalous notion of the "temperature of space," fixed by Pouillet at -140° C. For space in itself can have no temperature, and stellar radiation is a negligible quantity. Thus, it is safe to assume "that a perfect thermometer suspended in space at the distance of the earth or moon from the sun, but shielded from its rays, would sensibly indicate the absolute zero,"[951]ordinarily placed at -273° C.

A "Prize Essay on the Distribution of the Moon's Heat" (The Hague), 1891, by Mr. Frank W. Very, who had taken an active part in Professor Langley's long-sustained inquiry, embodies the fruits of its continuation. They show the lunar disc to be tolerably uniform in thermal power. The brighter parts are also indeed hotter, but not much. The traces perceived of a slight retention of heat by the substances forming the lunar surface, agreed well with the Parsonstown observations of the total eclipse of the moon, January 28, 1888.[952]For they brought out an unmistakable divergence between the heat and light phases. A curious decrease of heat previous to the first touch of the earth's shadow upon the lunar globe remains unexplained, unless it be admissible to suppose the terrestrial atmosphere capable of absorbing heat at an elevation of 190 miles. The probable range of temperature on the moon was discussed by Professor Very in 1898.[953]He concluded it to be very wide. Hotter than boiling water under the sun's vertical rays, the arid surface of our dependent globe must, he found, cool in the 14-day lunar night to about the temperature of liquid air.

Although that fundamental part of astronomy known as "celestialmechanics" lies outside the scope of this work, and we therefore pass over in silence the immense labours of Plana, Damoiseau, Hansen, Delaunay, G. W. Hill, and Airy in reconciling the observed and calculated motions of the moon, there is one slight but significant discrepancy which is of such importance to the physical history of the solar system, that some brief mention must be made of it.

Halley discovered in 1693, by examining the records of ancient eclipses, that the moon was going faster then than 2,000 years previously—so much faster, as to have got ahead of the place in the sky she would otherwise have occupied, by about two of her own diameters. It was one of Laplace's highest triumphs to have found an explanation of this puzzling fact. He showed, in 1787, that it was due to a very slow change in the ovalness of the earth's orbit, tending, during the present age of the world, to render it more nearly circular. The pull of the sun upon the moon is thereby lessened; the counter-pull of the earth gets the upper hand; and our satellite, drawn nearer to us by something less than an inch each year,[954]proportionately quickens her pace. Many thousands of years hence the process will be reversed; the terrestrial orbit will close in at the sides, the lunar orbit will open out under the growing stress of solar gravity, and our celestial chronometer will lose instead of gaining time.

This is all quite true as Laplace put it; but it is not enough. Adams, the virtual discoverer of Neptune, found with surprise in 1853 that the received account of the matter was "essentially incomplete," and explained, when the requisite correction was introduced, only half the observed acceleration.[955]What was to be done with the remaining half? Here Delaunay, the eminent French mathematical astronomer, unhappily drowned at Cherbourg in 1872 by the capsizing of a pleasure-boat, came to the rescue.[956]

It is obvious to anyone who considers the subject a little attentively, that the tides must act to some extent as a friction-brake upon the rotating earth. In other words, they must bring about an almost infinitely slow lengthening of the day. For the two masses of water piled up by lunar influence on the hither and farther sides of our globe, strive, as it were, to detach themselves from the unity of the terrestrial spheroid, and to follow the movements of the moon. The moon, accordingly, holds themagainstthe whirling earth, which revolves like a shaft in a fixed collar, slowlylosing motion and gaining heat, eventually dissipated through space.[957]This must go on (so far as we can see) until the periods of the earth's rotation and of the moon's revolution coincide. Nay, the process will be continued—should our oceans survive so long—by the feebler tide-raising power of the sun, ceasing only when day and night cease to alternate, when one side of our planet is plunged in perpetual darkness and the other seared by unchanging light.

Here, then, we have the secret of the moon's turning always the same face towards the earth. It is that in primeval times, when the moon was liquid or plastic, an earth-raised tidal wave rapidly and forcibly reduced her rotation to its present exact agreement with her period of revolution. This was divined by Kant[958]nearly a century before the necessity for such a mode of action presented itself to any other thinker. In a weekly paper published at Königsberg in 1754, the modern doctrine of "tidal friction" was clearly outlined by him, both as regards its effects actually in progress on the rotation of the earth, and as regards its effects already consummated on the rotation of the moon—the whole forming a preliminary attempt at what he called a "natural history" of the heavens. His sagacious suggestion, however, remained entirely unnoticed until revived—it would seem independently—by Julius Robert Mayer in 1848;[959]while similar, and probably original, conclusions were reached by William Ferrel of Allensville, Kentucky, in 1858.[960]

Delaunay was not then the inventor or discoverer of tidal friction; he merely displayed it as an effective cause of change. He showed reason for believing that its action in checking the earth's rotation, far from being, as Ferrel had supposed, completely neutralised by the contraction of the globe through cooling, was a fact to be reckoned with in computing the movements, as well as in speculating on the history, of the heavenly bodies. The outstanding acceleration of the moon was thus at once explained. It was explained as apparent only—the reflection of a real lengthening, by one second in 100,000 years, of the day. But on this point the last word has not yet been spoken.

Professor Newcomb undertook in 1870 the onerous task of investigating the errors of Hansen's Lunar Tables as compared withobservations prior to 1750. The results, published in 1878,[961]proved somewhat perplexing. They tend, in general, to reduce the amount of acceleration left unaccounted for by Laplace's gravitational theory, and proportionately to diminish the importance of the part played by tidal friction. But, in order to bring about this diminution, and at the same time conciliate Alexandrian and Arabian observations, it is necessary to rejectas totalthe ancient solar eclipses known as those of Thales and Larissa. This may be a necessary, but it must be admitted to be a hazardous expedient. Its upshot was to indicate a possibility that the observed and calculated values of the moon's acceleration might after all prove to be identical; and the small outstanding discrepancy was still further diminished by Tisserand's investigation, differently conducted, of the same Arabian eclipses discussed by Newcomb.[962]The necessity of having recourse to a lengthening day is then less pressing than it seemed some time ago; and the effect, if perceptible in the moon's motion, should, M. Tisserand remarked, be proportionately so in the motions of all the other heavenly bodies. The presence of the apparent general acceleration that should ensue can be tested with most promise of success, according to the same authority, by delicate comparisons of past and future transits of Mercury.

Newcomb further showed that small residual irregularities are still found in the movements of our satellite, inexplicable either by any known gravitational influence, or by anyuniformvalue that could be assigned to secular acceleration.[963]If set down to the account of imperfections in the "time-keeping" of the earth, it could only be on the arbitrary supposition of fluctuations in its rate of going themselves needing explanation. This, it is true, might be found in very slight changes of figure,[964]not altogether unlikely to occur. But into this cloudy and speculative region astronomers for the present decline to penetrate. They prefer, if possible, to deal only with calculable causes, and thus to preserve for their "most perfect of sciences" its special prerogative of assured prediction.

FOOTNOTES:[796]Neueste Beyträge zur Erweiterung der Sternkunde, Bd. iii., p. 14 (1800).[797]Ibid., p. 24.[798]Phil. Trans., vol. xciii., p. 215.[799]Mem. Roy. Astr. Soc., vol. vi., p. 116.[800]Month. Not., vol. xix., pp. 11, 25.[801]Ibid., vol. xxxviii., p. 398.[802]Am. Jour. of Sc., vol. xvi., p. 124.[803]Wash. Obs.for 1876, Part ii., p. 34.[804]Pop. Astr., vol. ii., p. 168;Astr. Jour., No. 335.[805]Astr. and Astrophysics, vol. xiii., p. 866.[806]Ibid., p. 867.[807]Month. Not., vol. xxiv., p. 18.[808]Ibid., vol. xxiii., p. 234 (Challis).[809]Untersuchungen über die Spectra der Planeten, p. 9.[810]Sirius, vol. vii., p. 131.[811]Potsdam Publ., No. 30;Astr. Nach., No. 3,171; Frost,Astr. and Astrophysics, vol. xii., p. 619.[812]Zöllner and Winnecke made it=O·13,Astr. Nach., No. 2,245.[813]Neueste Beyträge, Bd. iii., p. 50.[814]Astr. Jahrbuch, 1804, pp. 97-102.[815]Webb,Celestial Objects, p. 46 (4th ed.).[816]L'Astronomie, t. ii., p. 141.[817]Observations sur les Planètes Vénus et Mercure, p. 87.[818]Observatory, vol. vi., p. 40.[819]Atti dell' Accad. dei Lincei, t. v. ii., p. 283, 1889;Astr. Nach., No. 2,944.[820]Astr. Nach.No. 2,479.[821]Memoirs Amer. Acad., vol. xii., No. 4, p. 464.[822]Hist. de l'Astr., p. 682.[823]Comptes Rendus, t. xlix., p. 379.[824]Comptes Rendus, t. l., p. 40.[825]Ibid., p. 46.[826]Astr. Nach., Nos. 1,248 and 1,281.[827]Comptes Rendus, t. lxxxiii., pp. 510, 561.[828]Handbuch der Mathematik, Bd. ii., p. 327.[829]Comptes Rendus, t. lxxxiii., p. 721.[830]Nature, vol. xviii., pp. 461, 495, 539.[831]Oppolzer,Astr. Nach., No. 2,239.[832]Ibid., Nos. 2,253-4 (C. H. F. Peters).[833]Ibid., Nos. 2,263 and 2,277. See also Tisserand inAnn. Bur. des Long., 1882, p. 729.[834]See J. Bauschinger'sUntersuchungen(1884), summarised inBull. Astr., t. i., p. 506, andAstr. Nach., No. 2,594. Newcomb finds the anomalous motion of the perihelion to be even larger (43′ instead of 38′) than Leverrier made it.Month. Not., February, 1884, p. 187. Harzer's attempt to account for it inAstr. Nach., No. 3,030, is more ingenious than successful.[835]Jour. des Sçavans, December, 1667, p. 122.[836]Élémens d'Astr., p. 525. Cf. Chandler,Pop. Astr., February, 1897, p. 393.[837]Beobachtungen über die sehr beträchtlichen Gebirge und Rotation der Venus, 1792, p. 35. Schröter's final result in 1811 was 23h. 21m. 7·977s.Monat. Corr., Bd. xxv., p. 367.[838]Astr. Nach., No. 404.[839]Rendiconti del R. Istituto Lombardo, t. xxiii., serie ii.[840]Astr. Nach., No. 3,304.[841]Bothkamp Beobachtungen, Heft ii., p. 120.[842]Comptes Rendus, t. cxi., p. 542; t. cxxii., p. 395.[843]Month. Not., vol. lvii., p. 402;Astr. Nach., No. 3,406.[844]Mem. Spettroscopisti Italiani, t. xxv., p. 93;Nature, vol. liii., p. 306.[845]Astr. Nach., No. 3,329.[846]Ibid.[847]Bull. de l'Acad. de Belgique, t. xxi., p. 452, 1891.[848]Observations sur les Planètes Vénus et Mercure, 1892.[849]Astr. Nach., No. 3,300.[850]Ibid., No. 3,332.[851]Ibid., No. 3,314.[852]Ibid., No. 3,170.[853]Ibid., No. 3,641. The velocity of a point on the equator of Venus, if Brenner's period of 23h. 57m. were exact, would be 0·28 miles per second; but the displacements due to this rate would be doubled by reflection.[854]Novæ Observationes, p. 92.[855]Mém. de l'Ac., 1700, p. 296.[856]Phil. Trans., vol. lxxxiii., p. 201.[857]Webb,Cel. Objects, p. 58.[858]Month. Not., vol. xlii., p. 111.[859]Bull. Ac. de Bruxelles, t. xliii., p. 22.[860]Phil. Trans., vol. lxxxii., p. 309;Aphroditographische Fragmente, p. 85 (1796).[861]Astr. Nach., No. 679.[862]Month. Not., vol. xiv., p. 169.[863]Ibid., vol. xxiv., p. 25.[864]Am. Jour. of Sc., vol. xliii., p. 129 (2d ser.); vol. ix., p. 47 (3d ser.).[865]Astroph. Jour., vol. ix., p. 284.[866]Month. Not., vol. xxxvi., p. 347.[867]Old and New Astronomy, p. 448.[868]Hist. Phys. Astr., p. 431.[869]Mem. Roy. Astr. Soc., vol. xlvii., pp. 77, 84.[870]Astr. Reg., vol. xiii., p. 132.[871]L'Astronomie, t. ii., p. 27;Astr. Nach., No. 2,021;Am. Jour. of Sc., vol. xxv., p. 430.[872]Mem. Spettr. Ital., Dicembre, 1882;Am. Jour. of Sc., vol. xxv., p. 328.[873]Comptes Rendus, t. cxvi., p. 288.[874]Vogel,Spectra der Planeten, p. 15.[875]Nature, vol. xix., p. 23.[876]Nova Acta Acad. Naturæ Curiosorum, Bd. x., 239.[877]Astr. Jahrbuch, 1809, p. 164.[878]Month Not., vol. xliii., p. 331.[879]Report Brit. Ass., 1873, p. 407. The paper contains a valuable record of observations of the phenomenon.[880]Photom. Untersuchungen, p. 301.[881]Bothkamp Beobachtungen, Heft ii., p. 126.[882]Astr. Nach., No. 2,818.[883]Mémoires de l'Acad. de Bruxelles, t. xlix., No. 5, 4to;Astr. Nach., No. 2,809;f.Schorr,Der Venusmond, 1875.[884]Phil. Trans., 1839, 1841, 1842.[885]Delaunay objected (Comptes Rendus, t. lxvii., p. 65) that the viscosity of the contained liquid (of which Hopkins took no account) would, where the movements were so excessively slow as those of the earth's axis, almost certainly cause it to behave like a solid. Lord Kelvin, however (Report Brit. Ass., 1876, ii., p. 1), considered Hopkins's argument valid as regards the comparatively quick solar semi-annual and lunar fortnightly nutations.[886]Phil. Trans., cliii., p. 573.[887]Report Brit. Ass., 1868, p. 494.[888]Ibid., 1882, p. 474.[889]Albrecht,Astr. Nach., No. 3,131.[890]Astr. Jour., Nos. 248, 249.[891]Ibid., No. 258.[892]Month. Not., vol. lii., p. 336.[893]Astr. Nach., No. 3,097;Phil. Trans., vol. clxxxvi., A., p. 469;Proc. Roy. Soc., vol. lix.[894]See Chandler's searching investigations,Astr. Jour., Nos. 329, 344, 351, 392, 402, 406, 412, 446, 489, 490, 494, 495.[895]Rees,Pop. Astr., No. 74, 1900.[896]Nature, vol. lxi., p. 447; see also A. V. Bäcklund,Astr. Nach., No. 3,787.[897]Trans. Geol. Soc., vol. iii. (2d ser.), p. 293.[898]See hisTreatise on Astronomy, p. 199 (1833).[899]Phil. Mag., vol. xxviii. (4th ser.), p. 121.[900]Climate and Time, 1875;Discussions on Climate and Cosmology, 1885.[901]See for a popular account of the theory, Sir R. Ball'sThe Cause of an Ice Age, 1892.[902]See A. Woeikof,Phil. Mag., vol. xxi., p. 223.[903]The Ice Age in North America, London, 1890.[904]Phil. Trans., vol. lxviii., p. 783.[905]Comptes Rendus, t. lxxvi., p. 954.[906]Potsdam Publ., Nos. 22, 23.[907]Phil. Trans., vol. clxxxii., p. 565;Adams Prize Essay for 1893.[908]Denkschriften Akad. der Wiss. Wien, Bd. lxiv.; quoted by Poynting.Nature, vol. lxii., p. 404.[909]Report on the Geodetic Survey of S. Africa, 1894.[910]Nature, vol. lxii., p. 622; Hollis,Observatory, vol. xxiii., p. 337; Poincaré,Comptes Rendus, July 23, 1900.[911]Astr. Nach., No. 2,228.[912]Young'sGen. Astr., p. 601.[913]Astr. Constants, p. 195.[914]The second volume was published at Göttingen in 1802.[915]Ueber Rillen auf dem Monde, p. 13.Cf. The Moon, by T. Gwyn Elger, p. 20. W. H. Pickering,Harvard Annals, vol. xxxii., p. 249.[916]The Moon, p. 73.[917]Selen. Fragm., Th. ii., p. 399.[918]Astr. Nach., No. 263 (1834);Pop. Vorl., pp. 615-620 (1838).[919]Outlines of Astr., par. 431.[920]Month. Not., vol. xxv., p. 61.[921]Month. Not., vol. xxv., p. 264.[922]Astroph. Jour., vol. vi., p. 422.[923]Harvard Annals, vol. xxxii., p. 81.[924]Astr. and Astrophysics, vol. xi., p. 778.[925]Neison,The Moon, p. 25.[926]Knowledge, vol. xvii., p. 85.[927]Neison,The Moon, p. 104.[928]The combination of a uniform rotational with an unequal orbital movement causes a slight swaying of the moon's globe, now east, now west, by which we are able to see round the edges of the averted hemisphere. There is also a "parallactic" libration, depending on the earth's rotation; and a species of nodding movement—the "libration in latitude"—is produced by the inclination of the moon's axis to her orbit, and by her changes of position with regard to the terrestrial equator. Altogether, about 2/11 of theinvisibleside come into view.[929]Cel. Objects, p. 58 (4th ed.).[930]Astr. Nach., No. 1,631.[931]Cf. Leo Brenner,Naturwiss. Wochenschrift, January 13, 1895;Jour. Brit. Astr. Ass., vol. v., pp. 29, 222.[932]Respighi,Les Mondes, t. xiv., p. 294; Huggins,Month. Not., vol. xxvii., p. 298.[933]Birt,Ibid., p. 95.[934]Report Brit. Ass., 1872, p. 245.[935]Observatory, vol. xv., p. 250.[936]Astr. Reg., vol. xvi., p. 265;Astr. Nach., No. 2,275.[937]Lindsay and Copeland,Month. Not., vol. xxxix., p. 195.[938]Observatory, vols. ii., p. 296; iv., p. 373. N. E. Green (Astr. Reg., vol. xvii., p. 144) concluded the object a mere "spot of colour," dark under oblique light.[939]Webb,Cel. Objects, p. 101.[940]Publ. Lick Observatory, vol. iii., p. 7.[941]Ibid., p. 21; Mee,Knowledge, vol. xviii., p. 135.[942]Comptes Rendus, t. cxxii., p. 967;Bull. Astr., August, 1899;Ann. Bureau des Long., 1898;Nature, vols. lii., p. 439; lvi., p. 280; lix., p. 304; lx., p. 491;Astroph. Jour.vol. vi., p. 51.[943]Comptes Rendus, t. xxii., p. 541.[944]Phil. Trans., vol. cxlviii., p. 502.[945]Proc. Roy. Soc., vol. xvii., p. 443.[946]Phil. Trans., vol. clxiii., p. 623.[947]Trans. R. Dublin Soc., vol. iii., p. 321.[948]Science, vol. vii., p. 9.[949]Amer. Jour. of Science, vol. xxxviii., p. 428.[950]"The Temperature of the Moon,"Memoirs National Acad. of Sciences, vol. iv., p. 193, 1889.[951]Temperature of the Moon, p. iii.; see also App. ii., p. 206.[952]Trans. R. Dublin Soc., vol. iv., p. 481, 1891; Rosse,Proc. Roy. Institution, May 31, 1895.[953]Astroph. Jour., vol. viii., pp. 199, 265.[954]Airy,Observatory, vol. iii., p. 420.[955]Phil. Trans., vol. cxliii., p. 397;Proc. Roy. Soc., vol. vi., p. 321.[956]Comptes Rendus, t. lxi., p. 1023.[957]Professor Darwin calculated that the heat generated by tidal friction in the course of lengthening the earth's period of rotation from 23 to 24 hours, equalled 23 million times the amount of its present annual loss by cooling.Nature, vol. xxxiv., p. 422.[958]Sämmtl. Werke(ed. 1839), Th. vi., pp. 5-12. See also C. J. Monro's useful indications inNature, vol. vii., p. 241.[959]Dynamik des Himmels, p. 40.[960]Gould'sAstr. Jour., vol. iii., p. 138.[961]Wash. Obs.for 1875, vol. xxii., App. ii.[962]Comptes Rendus, t. cxiii., p. 669;Annuaire, Paris, 1892.[963]Newcomb,Pop. Astr.(4th ed.), p. 101.[964]Sir W. Thomson,Report Brit. Ass., 1876, p. 12.

[796]Neueste Beyträge zur Erweiterung der Sternkunde, Bd. iii., p. 14 (1800).

[796]Neueste Beyträge zur Erweiterung der Sternkunde, Bd. iii., p. 14 (1800).

[797]Ibid., p. 24.

[797]Ibid., p. 24.

[798]Phil. Trans., vol. xciii., p. 215.

[798]Phil. Trans., vol. xciii., p. 215.

[799]Mem. Roy. Astr. Soc., vol. vi., p. 116.

[799]Mem. Roy. Astr. Soc., vol. vi., p. 116.

[800]Month. Not., vol. xix., pp. 11, 25.

[800]Month. Not., vol. xix., pp. 11, 25.

[801]Ibid., vol. xxxviii., p. 398.

[801]Ibid., vol. xxxviii., p. 398.

[802]Am. Jour. of Sc., vol. xvi., p. 124.

[802]Am. Jour. of Sc., vol. xvi., p. 124.

[803]Wash. Obs.for 1876, Part ii., p. 34.

[803]Wash. Obs.for 1876, Part ii., p. 34.

[804]Pop. Astr., vol. ii., p. 168;Astr. Jour., No. 335.

[804]Pop. Astr., vol. ii., p. 168;Astr. Jour., No. 335.

[805]Astr. and Astrophysics, vol. xiii., p. 866.

[805]Astr. and Astrophysics, vol. xiii., p. 866.

[806]Ibid., p. 867.

[806]Ibid., p. 867.

[807]Month. Not., vol. xxiv., p. 18.

[807]Month. Not., vol. xxiv., p. 18.

[808]Ibid., vol. xxiii., p. 234 (Challis).

[808]Ibid., vol. xxiii., p. 234 (Challis).

[809]Untersuchungen über die Spectra der Planeten, p. 9.

[809]Untersuchungen über die Spectra der Planeten, p. 9.

[810]Sirius, vol. vii., p. 131.

[810]Sirius, vol. vii., p. 131.

[811]Potsdam Publ., No. 30;Astr. Nach., No. 3,171; Frost,Astr. and Astrophysics, vol. xii., p. 619.

[811]Potsdam Publ., No. 30;Astr. Nach., No. 3,171; Frost,Astr. and Astrophysics, vol. xii., p. 619.

[812]Zöllner and Winnecke made it=O·13,Astr. Nach., No. 2,245.

[812]Zöllner and Winnecke made it=O·13,Astr. Nach., No. 2,245.

[813]Neueste Beyträge, Bd. iii., p. 50.

[813]Neueste Beyträge, Bd. iii., p. 50.

[814]Astr. Jahrbuch, 1804, pp. 97-102.

[814]Astr. Jahrbuch, 1804, pp. 97-102.

[815]Webb,Celestial Objects, p. 46 (4th ed.).

[815]Webb,Celestial Objects, p. 46 (4th ed.).

[816]L'Astronomie, t. ii., p. 141.

[816]L'Astronomie, t. ii., p. 141.

[817]Observations sur les Planètes Vénus et Mercure, p. 87.

[817]Observations sur les Planètes Vénus et Mercure, p. 87.

[818]Observatory, vol. vi., p. 40.

[818]Observatory, vol. vi., p. 40.

[819]Atti dell' Accad. dei Lincei, t. v. ii., p. 283, 1889;Astr. Nach., No. 2,944.

[819]Atti dell' Accad. dei Lincei, t. v. ii., p. 283, 1889;Astr. Nach., No. 2,944.

[820]Astr. Nach.No. 2,479.

[820]Astr. Nach.No. 2,479.

[821]Memoirs Amer. Acad., vol. xii., No. 4, p. 464.

[821]Memoirs Amer. Acad., vol. xii., No. 4, p. 464.

[822]Hist. de l'Astr., p. 682.

[822]Hist. de l'Astr., p. 682.

[823]Comptes Rendus, t. xlix., p. 379.

[823]Comptes Rendus, t. xlix., p. 379.

[824]Comptes Rendus, t. l., p. 40.

[824]Comptes Rendus, t. l., p. 40.

[825]Ibid., p. 46.

[825]Ibid., p. 46.

[826]Astr. Nach., Nos. 1,248 and 1,281.

[826]Astr. Nach., Nos. 1,248 and 1,281.

[827]Comptes Rendus, t. lxxxiii., pp. 510, 561.

[827]Comptes Rendus, t. lxxxiii., pp. 510, 561.

[828]Handbuch der Mathematik, Bd. ii., p. 327.

[828]Handbuch der Mathematik, Bd. ii., p. 327.

[829]Comptes Rendus, t. lxxxiii., p. 721.

[829]Comptes Rendus, t. lxxxiii., p. 721.

[830]Nature, vol. xviii., pp. 461, 495, 539.

[830]Nature, vol. xviii., pp. 461, 495, 539.

[831]Oppolzer,Astr. Nach., No. 2,239.

[831]Oppolzer,Astr. Nach., No. 2,239.

[832]Ibid., Nos. 2,253-4 (C. H. F. Peters).

[832]Ibid., Nos. 2,253-4 (C. H. F. Peters).

[833]Ibid., Nos. 2,263 and 2,277. See also Tisserand inAnn. Bur. des Long., 1882, p. 729.

[833]Ibid., Nos. 2,263 and 2,277. See also Tisserand inAnn. Bur. des Long., 1882, p. 729.

[834]See J. Bauschinger'sUntersuchungen(1884), summarised inBull. Astr., t. i., p. 506, andAstr. Nach., No. 2,594. Newcomb finds the anomalous motion of the perihelion to be even larger (43′ instead of 38′) than Leverrier made it.Month. Not., February, 1884, p. 187. Harzer's attempt to account for it inAstr. Nach., No. 3,030, is more ingenious than successful.

[834]See J. Bauschinger'sUntersuchungen(1884), summarised inBull. Astr., t. i., p. 506, andAstr. Nach., No. 2,594. Newcomb finds the anomalous motion of the perihelion to be even larger (43′ instead of 38′) than Leverrier made it.Month. Not., February, 1884, p. 187. Harzer's attempt to account for it inAstr. Nach., No. 3,030, is more ingenious than successful.

[835]Jour. des Sçavans, December, 1667, p. 122.

[835]Jour. des Sçavans, December, 1667, p. 122.

[836]Élémens d'Astr., p. 525. Cf. Chandler,Pop. Astr., February, 1897, p. 393.

[836]Élémens d'Astr., p. 525. Cf. Chandler,Pop. Astr., February, 1897, p. 393.

[837]Beobachtungen über die sehr beträchtlichen Gebirge und Rotation der Venus, 1792, p. 35. Schröter's final result in 1811 was 23h. 21m. 7·977s.Monat. Corr., Bd. xxv., p. 367.

[837]Beobachtungen über die sehr beträchtlichen Gebirge und Rotation der Venus, 1792, p. 35. Schröter's final result in 1811 was 23h. 21m. 7·977s.Monat. Corr., Bd. xxv., p. 367.

[838]Astr. Nach., No. 404.

[838]Astr. Nach., No. 404.

[839]Rendiconti del R. Istituto Lombardo, t. xxiii., serie ii.

[839]Rendiconti del R. Istituto Lombardo, t. xxiii., serie ii.

[840]Astr. Nach., No. 3,304.

[840]Astr. Nach., No. 3,304.

[841]Bothkamp Beobachtungen, Heft ii., p. 120.

[841]Bothkamp Beobachtungen, Heft ii., p. 120.

[842]Comptes Rendus, t. cxi., p. 542; t. cxxii., p. 395.

[842]Comptes Rendus, t. cxi., p. 542; t. cxxii., p. 395.

[843]Month. Not., vol. lvii., p. 402;Astr. Nach., No. 3,406.

[843]Month. Not., vol. lvii., p. 402;Astr. Nach., No. 3,406.

[844]Mem. Spettroscopisti Italiani, t. xxv., p. 93;Nature, vol. liii., p. 306.

[844]Mem. Spettroscopisti Italiani, t. xxv., p. 93;Nature, vol. liii., p. 306.

[845]Astr. Nach., No. 3,329.

[845]Astr. Nach., No. 3,329.

[846]Ibid.

[846]Ibid.

[847]Bull. de l'Acad. de Belgique, t. xxi., p. 452, 1891.

[847]Bull. de l'Acad. de Belgique, t. xxi., p. 452, 1891.

[848]Observations sur les Planètes Vénus et Mercure, 1892.

[848]Observations sur les Planètes Vénus et Mercure, 1892.

[849]Astr. Nach., No. 3,300.

[849]Astr. Nach., No. 3,300.

[850]Ibid., No. 3,332.

[850]Ibid., No. 3,332.

[851]Ibid., No. 3,314.

[851]Ibid., No. 3,314.

[852]Ibid., No. 3,170.

[852]Ibid., No. 3,170.

[853]Ibid., No. 3,641. The velocity of a point on the equator of Venus, if Brenner's period of 23h. 57m. were exact, would be 0·28 miles per second; but the displacements due to this rate would be doubled by reflection.

[853]Ibid., No. 3,641. The velocity of a point on the equator of Venus, if Brenner's period of 23h. 57m. were exact, would be 0·28 miles per second; but the displacements due to this rate would be doubled by reflection.

[854]Novæ Observationes, p. 92.

[854]Novæ Observationes, p. 92.

[855]Mém. de l'Ac., 1700, p. 296.

[855]Mém. de l'Ac., 1700, p. 296.

[856]Phil. Trans., vol. lxxxiii., p. 201.

[856]Phil. Trans., vol. lxxxiii., p. 201.

[857]Webb,Cel. Objects, p. 58.

[857]Webb,Cel. Objects, p. 58.

[858]Month. Not., vol. xlii., p. 111.

[858]Month. Not., vol. xlii., p. 111.

[859]Bull. Ac. de Bruxelles, t. xliii., p. 22.

[859]Bull. Ac. de Bruxelles, t. xliii., p. 22.

[860]Phil. Trans., vol. lxxxii., p. 309;Aphroditographische Fragmente, p. 85 (1796).

[860]Phil. Trans., vol. lxxxii., p. 309;Aphroditographische Fragmente, p. 85 (1796).

[861]Astr. Nach., No. 679.

[861]Astr. Nach., No. 679.

[862]Month. Not., vol. xiv., p. 169.

[862]Month. Not., vol. xiv., p. 169.

[863]Ibid., vol. xxiv., p. 25.

[863]Ibid., vol. xxiv., p. 25.

[864]Am. Jour. of Sc., vol. xliii., p. 129 (2d ser.); vol. ix., p. 47 (3d ser.).

[864]Am. Jour. of Sc., vol. xliii., p. 129 (2d ser.); vol. ix., p. 47 (3d ser.).

[865]Astroph. Jour., vol. ix., p. 284.

[865]Astroph. Jour., vol. ix., p. 284.

[866]Month. Not., vol. xxxvi., p. 347.

[866]Month. Not., vol. xxxvi., p. 347.

[867]Old and New Astronomy, p. 448.

[867]Old and New Astronomy, p. 448.

[868]Hist. Phys. Astr., p. 431.

[868]Hist. Phys. Astr., p. 431.

[869]Mem. Roy. Astr. Soc., vol. xlvii., pp. 77, 84.

[869]Mem. Roy. Astr. Soc., vol. xlvii., pp. 77, 84.

[870]Astr. Reg., vol. xiii., p. 132.

[870]Astr. Reg., vol. xiii., p. 132.

[871]L'Astronomie, t. ii., p. 27;Astr. Nach., No. 2,021;Am. Jour. of Sc., vol. xxv., p. 430.

[871]L'Astronomie, t. ii., p. 27;Astr. Nach., No. 2,021;Am. Jour. of Sc., vol. xxv., p. 430.

[872]Mem. Spettr. Ital., Dicembre, 1882;Am. Jour. of Sc., vol. xxv., p. 328.

[872]Mem. Spettr. Ital., Dicembre, 1882;Am. Jour. of Sc., vol. xxv., p. 328.

[873]Comptes Rendus, t. cxvi., p. 288.

[873]Comptes Rendus, t. cxvi., p. 288.

[874]Vogel,Spectra der Planeten, p. 15.

[874]Vogel,Spectra der Planeten, p. 15.

[875]Nature, vol. xix., p. 23.

[875]Nature, vol. xix., p. 23.

[876]Nova Acta Acad. Naturæ Curiosorum, Bd. x., 239.

[876]Nova Acta Acad. Naturæ Curiosorum, Bd. x., 239.

[877]Astr. Jahrbuch, 1809, p. 164.

[877]Astr. Jahrbuch, 1809, p. 164.

[878]Month Not., vol. xliii., p. 331.

[878]Month Not., vol. xliii., p. 331.

[879]Report Brit. Ass., 1873, p. 407. The paper contains a valuable record of observations of the phenomenon.

[879]Report Brit. Ass., 1873, p. 407. The paper contains a valuable record of observations of the phenomenon.

[880]Photom. Untersuchungen, p. 301.

[880]Photom. Untersuchungen, p. 301.

[881]Bothkamp Beobachtungen, Heft ii., p. 126.

[881]Bothkamp Beobachtungen, Heft ii., p. 126.

[882]Astr. Nach., No. 2,818.

[882]Astr. Nach., No. 2,818.

[883]Mémoires de l'Acad. de Bruxelles, t. xlix., No. 5, 4to;Astr. Nach., No. 2,809;f.Schorr,Der Venusmond, 1875.

[883]Mémoires de l'Acad. de Bruxelles, t. xlix., No. 5, 4to;Astr. Nach., No. 2,809;f.Schorr,Der Venusmond, 1875.

[884]Phil. Trans., 1839, 1841, 1842.

[884]Phil. Trans., 1839, 1841, 1842.

[885]Delaunay objected (Comptes Rendus, t. lxvii., p. 65) that the viscosity of the contained liquid (of which Hopkins took no account) would, where the movements were so excessively slow as those of the earth's axis, almost certainly cause it to behave like a solid. Lord Kelvin, however (Report Brit. Ass., 1876, ii., p. 1), considered Hopkins's argument valid as regards the comparatively quick solar semi-annual and lunar fortnightly nutations.

[885]Delaunay objected (Comptes Rendus, t. lxvii., p. 65) that the viscosity of the contained liquid (of which Hopkins took no account) would, where the movements were so excessively slow as those of the earth's axis, almost certainly cause it to behave like a solid. Lord Kelvin, however (Report Brit. Ass., 1876, ii., p. 1), considered Hopkins's argument valid as regards the comparatively quick solar semi-annual and lunar fortnightly nutations.

[886]Phil. Trans., cliii., p. 573.

[886]Phil. Trans., cliii., p. 573.

[887]Report Brit. Ass., 1868, p. 494.

[887]Report Brit. Ass., 1868, p. 494.

[888]Ibid., 1882, p. 474.

[888]Ibid., 1882, p. 474.

[889]Albrecht,Astr. Nach., No. 3,131.

[889]Albrecht,Astr. Nach., No. 3,131.

[890]Astr. Jour., Nos. 248, 249.

[890]Astr. Jour., Nos. 248, 249.

[891]Ibid., No. 258.

[891]Ibid., No. 258.

[892]Month. Not., vol. lii., p. 336.

[892]Month. Not., vol. lii., p. 336.

[893]Astr. Nach., No. 3,097;Phil. Trans., vol. clxxxvi., A., p. 469;Proc. Roy. Soc., vol. lix.

[893]Astr. Nach., No. 3,097;Phil. Trans., vol. clxxxvi., A., p. 469;Proc. Roy. Soc., vol. lix.

[894]See Chandler's searching investigations,Astr. Jour., Nos. 329, 344, 351, 392, 402, 406, 412, 446, 489, 490, 494, 495.

[894]See Chandler's searching investigations,Astr. Jour., Nos. 329, 344, 351, 392, 402, 406, 412, 446, 489, 490, 494, 495.

[895]Rees,Pop. Astr., No. 74, 1900.

[895]Rees,Pop. Astr., No. 74, 1900.

[896]Nature, vol. lxi., p. 447; see also A. V. Bäcklund,Astr. Nach., No. 3,787.

[896]Nature, vol. lxi., p. 447; see also A. V. Bäcklund,Astr. Nach., No. 3,787.

[897]Trans. Geol. Soc., vol. iii. (2d ser.), p. 293.

[897]Trans. Geol. Soc., vol. iii. (2d ser.), p. 293.

[898]See hisTreatise on Astronomy, p. 199 (1833).

[898]See hisTreatise on Astronomy, p. 199 (1833).

[899]Phil. Mag., vol. xxviii. (4th ser.), p. 121.

[899]Phil. Mag., vol. xxviii. (4th ser.), p. 121.

[900]Climate and Time, 1875;Discussions on Climate and Cosmology, 1885.

[900]Climate and Time, 1875;Discussions on Climate and Cosmology, 1885.

[901]See for a popular account of the theory, Sir R. Ball'sThe Cause of an Ice Age, 1892.

[901]See for a popular account of the theory, Sir R. Ball'sThe Cause of an Ice Age, 1892.

[902]See A. Woeikof,Phil. Mag., vol. xxi., p. 223.

[902]See A. Woeikof,Phil. Mag., vol. xxi., p. 223.

[903]The Ice Age in North America, London, 1890.

[903]The Ice Age in North America, London, 1890.

[904]Phil. Trans., vol. lxviii., p. 783.

[904]Phil. Trans., vol. lxviii., p. 783.

[905]Comptes Rendus, t. lxxvi., p. 954.

[905]Comptes Rendus, t. lxxvi., p. 954.

[906]Potsdam Publ., Nos. 22, 23.

[906]Potsdam Publ., Nos. 22, 23.

[907]Phil. Trans., vol. clxxxii., p. 565;Adams Prize Essay for 1893.

[907]Phil. Trans., vol. clxxxii., p. 565;Adams Prize Essay for 1893.

[908]Denkschriften Akad. der Wiss. Wien, Bd. lxiv.; quoted by Poynting.Nature, vol. lxii., p. 404.

[908]Denkschriften Akad. der Wiss. Wien, Bd. lxiv.; quoted by Poynting.Nature, vol. lxii., p. 404.

[909]Report on the Geodetic Survey of S. Africa, 1894.

[909]Report on the Geodetic Survey of S. Africa, 1894.

[910]Nature, vol. lxii., p. 622; Hollis,Observatory, vol. xxiii., p. 337; Poincaré,Comptes Rendus, July 23, 1900.

[910]Nature, vol. lxii., p. 622; Hollis,Observatory, vol. xxiii., p. 337; Poincaré,Comptes Rendus, July 23, 1900.

[911]Astr. Nach., No. 2,228.

[911]Astr. Nach., No. 2,228.

[912]Young'sGen. Astr., p. 601.

[912]Young'sGen. Astr., p. 601.

[913]Astr. Constants, p. 195.

[913]Astr. Constants, p. 195.

[914]The second volume was published at Göttingen in 1802.

[914]The second volume was published at Göttingen in 1802.

[915]Ueber Rillen auf dem Monde, p. 13.Cf. The Moon, by T. Gwyn Elger, p. 20. W. H. Pickering,Harvard Annals, vol. xxxii., p. 249.

[915]Ueber Rillen auf dem Monde, p. 13.Cf. The Moon, by T. Gwyn Elger, p. 20. W. H. Pickering,Harvard Annals, vol. xxxii., p. 249.

[916]The Moon, p. 73.

[916]The Moon, p. 73.

[917]Selen. Fragm., Th. ii., p. 399.

[917]Selen. Fragm., Th. ii., p. 399.

[918]Astr. Nach., No. 263 (1834);Pop. Vorl., pp. 615-620 (1838).

[918]Astr. Nach., No. 263 (1834);Pop. Vorl., pp. 615-620 (1838).

[919]Outlines of Astr., par. 431.

[919]Outlines of Astr., par. 431.

[920]Month. Not., vol. xxv., p. 61.

[920]Month. Not., vol. xxv., p. 61.

[921]Month. Not., vol. xxv., p. 264.

[921]Month. Not., vol. xxv., p. 264.

[922]Astroph. Jour., vol. vi., p. 422.

[922]Astroph. Jour., vol. vi., p. 422.

[923]Harvard Annals, vol. xxxii., p. 81.

[923]Harvard Annals, vol. xxxii., p. 81.

[924]Astr. and Astrophysics, vol. xi., p. 778.

[924]Astr. and Astrophysics, vol. xi., p. 778.

[925]Neison,The Moon, p. 25.

[925]Neison,The Moon, p. 25.

[926]Knowledge, vol. xvii., p. 85.

[926]Knowledge, vol. xvii., p. 85.

[927]Neison,The Moon, p. 104.

[927]Neison,The Moon, p. 104.

[928]The combination of a uniform rotational with an unequal orbital movement causes a slight swaying of the moon's globe, now east, now west, by which we are able to see round the edges of the averted hemisphere. There is also a "parallactic" libration, depending on the earth's rotation; and a species of nodding movement—the "libration in latitude"—is produced by the inclination of the moon's axis to her orbit, and by her changes of position with regard to the terrestrial equator. Altogether, about 2/11 of theinvisibleside come into view.

[928]The combination of a uniform rotational with an unequal orbital movement causes a slight swaying of the moon's globe, now east, now west, by which we are able to see round the edges of the averted hemisphere. There is also a "parallactic" libration, depending on the earth's rotation; and a species of nodding movement—the "libration in latitude"—is produced by the inclination of the moon's axis to her orbit, and by her changes of position with regard to the terrestrial equator. Altogether, about 2/11 of theinvisibleside come into view.

[929]Cel. Objects, p. 58 (4th ed.).

[929]Cel. Objects, p. 58 (4th ed.).

[930]Astr. Nach., No. 1,631.

[930]Astr. Nach., No. 1,631.

[931]Cf. Leo Brenner,Naturwiss. Wochenschrift, January 13, 1895;Jour. Brit. Astr. Ass., vol. v., pp. 29, 222.

[931]Cf. Leo Brenner,Naturwiss. Wochenschrift, January 13, 1895;Jour. Brit. Astr. Ass., vol. v., pp. 29, 222.

[932]Respighi,Les Mondes, t. xiv., p. 294; Huggins,Month. Not., vol. xxvii., p. 298.

[932]Respighi,Les Mondes, t. xiv., p. 294; Huggins,Month. Not., vol. xxvii., p. 298.

[933]Birt,Ibid., p. 95.

[933]Birt,Ibid., p. 95.

[934]Report Brit. Ass., 1872, p. 245.

[934]Report Brit. Ass., 1872, p. 245.

[935]Observatory, vol. xv., p. 250.

[935]Observatory, vol. xv., p. 250.

[936]Astr. Reg., vol. xvi., p. 265;Astr. Nach., No. 2,275.

[936]Astr. Reg., vol. xvi., p. 265;Astr. Nach., No. 2,275.

[937]Lindsay and Copeland,Month. Not., vol. xxxix., p. 195.

[937]Lindsay and Copeland,Month. Not., vol. xxxix., p. 195.

[938]Observatory, vols. ii., p. 296; iv., p. 373. N. E. Green (Astr. Reg., vol. xvii., p. 144) concluded the object a mere "spot of colour," dark under oblique light.

[938]Observatory, vols. ii., p. 296; iv., p. 373. N. E. Green (Astr. Reg., vol. xvii., p. 144) concluded the object a mere "spot of colour," dark under oblique light.

[939]Webb,Cel. Objects, p. 101.

[939]Webb,Cel. Objects, p. 101.

[940]Publ. Lick Observatory, vol. iii., p. 7.

[940]Publ. Lick Observatory, vol. iii., p. 7.

[941]Ibid., p. 21; Mee,Knowledge, vol. xviii., p. 135.

[941]Ibid., p. 21; Mee,Knowledge, vol. xviii., p. 135.

[942]Comptes Rendus, t. cxxii., p. 967;Bull. Astr., August, 1899;Ann. Bureau des Long., 1898;Nature, vols. lii., p. 439; lvi., p. 280; lix., p. 304; lx., p. 491;Astroph. Jour.vol. vi., p. 51.

[942]Comptes Rendus, t. cxxii., p. 967;Bull. Astr., August, 1899;Ann. Bureau des Long., 1898;Nature, vols. lii., p. 439; lvi., p. 280; lix., p. 304; lx., p. 491;Astroph. Jour.vol. vi., p. 51.

[943]Comptes Rendus, t. xxii., p. 541.

[943]Comptes Rendus, t. xxii., p. 541.

[944]Phil. Trans., vol. cxlviii., p. 502.

[944]Phil. Trans., vol. cxlviii., p. 502.

[945]Proc. Roy. Soc., vol. xvii., p. 443.

[945]Proc. Roy. Soc., vol. xvii., p. 443.

[946]Phil. Trans., vol. clxiii., p. 623.

[946]Phil. Trans., vol. clxiii., p. 623.

[947]Trans. R. Dublin Soc., vol. iii., p. 321.

[947]Trans. R. Dublin Soc., vol. iii., p. 321.

[948]Science, vol. vii., p. 9.

[948]Science, vol. vii., p. 9.

[949]Amer. Jour. of Science, vol. xxxviii., p. 428.

[949]Amer. Jour. of Science, vol. xxxviii., p. 428.

[950]"The Temperature of the Moon,"Memoirs National Acad. of Sciences, vol. iv., p. 193, 1889.

[950]"The Temperature of the Moon,"Memoirs National Acad. of Sciences, vol. iv., p. 193, 1889.

[951]Temperature of the Moon, p. iii.; see also App. ii., p. 206.

[951]Temperature of the Moon, p. iii.; see also App. ii., p. 206.

[952]Trans. R. Dublin Soc., vol. iv., p. 481, 1891; Rosse,Proc. Roy. Institution, May 31, 1895.

[952]Trans. R. Dublin Soc., vol. iv., p. 481, 1891; Rosse,Proc. Roy. Institution, May 31, 1895.

[953]Astroph. Jour., vol. viii., pp. 199, 265.

[953]Astroph. Jour., vol. viii., pp. 199, 265.

[954]Airy,Observatory, vol. iii., p. 420.

[954]Airy,Observatory, vol. iii., p. 420.

[955]Phil. Trans., vol. cxliii., p. 397;Proc. Roy. Soc., vol. vi., p. 321.

[955]Phil. Trans., vol. cxliii., p. 397;Proc. Roy. Soc., vol. vi., p. 321.

[956]Comptes Rendus, t. lxi., p. 1023.

[956]Comptes Rendus, t. lxi., p. 1023.

[957]Professor Darwin calculated that the heat generated by tidal friction in the course of lengthening the earth's period of rotation from 23 to 24 hours, equalled 23 million times the amount of its present annual loss by cooling.Nature, vol. xxxiv., p. 422.

[957]Professor Darwin calculated that the heat generated by tidal friction in the course of lengthening the earth's period of rotation from 23 to 24 hours, equalled 23 million times the amount of its present annual loss by cooling.Nature, vol. xxxiv., p. 422.

[958]Sämmtl. Werke(ed. 1839), Th. vi., pp. 5-12. See also C. J. Monro's useful indications inNature, vol. vii., p. 241.

[958]Sämmtl. Werke(ed. 1839), Th. vi., pp. 5-12. See also C. J. Monro's useful indications inNature, vol. vii., p. 241.

[959]Dynamik des Himmels, p. 40.

[959]Dynamik des Himmels, p. 40.

[960]Gould'sAstr. Jour., vol. iii., p. 138.

[960]Gould'sAstr. Jour., vol. iii., p. 138.

[961]Wash. Obs.for 1875, vol. xxii., App. ii.

[961]Wash. Obs.for 1875, vol. xxii., App. ii.

[962]Comptes Rendus, t. cxiii., p. 669;Annuaire, Paris, 1892.

[962]Comptes Rendus, t. cxiii., p. 669;Annuaire, Paris, 1892.

[963]Newcomb,Pop. Astr.(4th ed.), p. 101.

[963]Newcomb,Pop. Astr.(4th ed.), p. 101.

[964]Sir W. Thomson,Report Brit. Ass., 1876, p. 12.

[964]Sir W. Thomson,Report Brit. Ass., 1876, p. 12.


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