FOOTNOTES:

Printed by Cassell & Company, Limited, la Belle Sauvage, London, E.C.

FOOTNOTES:[1]It may, however, be remarked that a star is neverseento set, as, owing to our atmosphere, it ceases to be visible before it reaches the horizon.[2]"Popular Astronomy," p. 66.[3]Limbis the word used by astronomers to denote theedgeor circumference of the apparent disc of a heavenly body.[4]"The Sun," p. 119.[5]It has been frequently stated that the outburst in 1859, witnessed by Carrington and Hodgson, was immediately followed by an unusually intense magnetic storm, but the records at Kew and Greenwich show that the magnetic disturbances on that day were of a very trivial character.[6]Some ungainly critic has observed that the poet himself seems to have felt a doubt on the matter, because he has supplemented the dubious moonbeams by the "lantern dimly burning." The more generous, if somewhat a sanguine remark has been also made, that "the time will come when the evidence of this poem will prevail over any astronomical calculations."[7]This sketch has been copied by permission from the very beautiful view in Messrs. Nasmyth and Carpenter's book, of which it formsPlate XI. So have also the other illustrations of lunar scenery inPlates VIII.,IX.The photographs were obtained by Mr. Nasmyth from models carefully constructed from his drawings to illustrate the features on the moon. During the last twenty years photography has completely superseded drawing by eye in the delineation of lunar objects. Long series of magnificent photographs of lunar scenery have been published by the Paris and Lick Observatories.[8]At the British Association's meeting at Cardiff in 1892, Prof. Copeland exhibited a model of the moon, on which the appearance of the streaks near full moon was perfectly shown by means of small spheres of transparent glass attached to the surface.[9]The duration of an occultation, or, in other words, the length of time during which the moon hides the star, would be slightly shorter than the computed time, if the moon had an atmosphere capable of sensibly refracting the light from the star. But, so far, our observations do not indicate this with certainty.[10]I owe my knowledge of this subject to Dr. G. Johnstone Stoney, F.R.S. There has been some controversy as to who originated the ingenious and instructive doctrine here sketched.[11]The space described by a falling body is proportional to the product of the force and the square of the time. The force varies inversely as the square of the distance from the earth, so that the space will vary as the square of the time, and inversely as the square of the distance. If, therefore, the distance be increased sixty-fold, the time must also be increased sixty-fold, if the space fallen through is to remain the same.[12]See Newcomb's "Popular Astronomy," p. 78.[13]Recent investigation by Newcomb on the motion of Mercury have led to the result that the hypothesis of a planet or a ring of very small planets between the orbit of Mercury and the sun cannot account for the difference between theory and observation in the movements of Mercury. Harzer has come to the same result, and has shown that the disturbing element may possibly be the material of the Solar Corona.[14]"The Sun: its Planets, and their Satellites." London: 1882 (page 147).[15]James Gregory, in a book on optics written in 1667, had already suggested the use of the transit of Venus for this purpose.[16]See"Astronomy and Astrophysics," No. 128.[17]See"Astronomy and Astrophysics," No. 128.[18]This is the curved marking which onPlate XVIII.appears in longitude 290° and north of (that is, below) the equator. Here, as in all astronomical drawings, north is at the foot and south at the top.Seeabove, p. 82 (Chapter III.).[19]Now Director of the Lick Observatory.[20]The heliometer is a telescope with its object-glass cut in half along a diameter. One or both of these halves is movable transversely by a screw. Each half gives a complete image of the object. The measures are effected by observing how many turns of the screw convey the image of the star formed by one half of the object-glass to coincide with the image of the planet formed by the other.[21]See "Astronomy and Astrophysics," No. 109.[22]It is only right to add that some observers believe that, in exceptional circumstances, points of Jupiter have shown some slight degree of intrinsic light.[23]Professor Pickering, of Cambridge, Mass., has, however, effected the important improvement of measuring the decline of light of the satellite undergoing eclipse by the photometer. Much additional precision may be anticipated in the results of such observations.[24]"Newcomb's Popular Astronomy," p. 336.[25]SeeGrant, "History of Physical Astronomy," page 255.[26]Now Director of the Lick Observatory.[27]We are here neglecting the orbital motion of Saturn, by which the whole system is moved towards or from the earth, but as this motion is common to the ball and the ring, it will not disturb the relative positions of the three spectra.[28]According to Prof. Barnard's recent measures, the diameter of Titan is 2,700 miles. This is the satellite discovered by Huyghens; it is the sixth in order from the planet.[29]Extract from "Three Cities of Russia," by C. Piazzi Smyth, vol. ii., p. 164: "In the year 1796. It then chanced that George III., of Great Britain, was pleased to send as a present to the Empress Catharine of Russia a ten-foot reflecting telescope constructed by Sir William Herschel. Her Majesty immediately desired to try its powers, and Roumovsky was sent for from the Academy to repair to Tsarskoe-Selo, where the Court was at the time residing. The telescope was accordingly unpacked, and for eight long consecutive evenings the Empress employed herself ardently in observing the moon, planets, and stars; and more than this, in inquiring into the state of astronomy in her dominions. Then it was that Roumovsky set before the Imperial view the Academy's idea of removing their observatory, detailing the necessity for, and the advantages of, such a proceeding. Graciously did the 'Semiramis of the North,' the 'Polar Star,' enter into all these particulars, and warmly approve of the project; but death closed her career within a few weeks after, and prevented her execution of the design."[30]SeeProfessor Holden's "Sir William Herschel, his Life and Works."[31]Arago says that "Lemonnier's records were the image of chaos." Bouvard showed to Arago one of the observations of Uranus which was written on a paper bag that in its time had contained hair-powder.[32]The first comet of 1884 also suddenly increased in brightness, while a distinct disc, which hitherto had formed the nucleus, became transformed into a fine point of light.[33]The three numbers 12, 1, and1⁄4are nearly inversely proportional to the atomic weights of hydrogen, hydrocarbon gas, and iron vapour, and it is for this reason that Bredichin suggested the above-mentioned composition of the various types of tail. Spectroscopic evidence of the presence of hydrogen is yet wanting.[34]This illustration, as well as the figure of the path of the meteors, has been derived from Dr. G.J. Stoney's interesting lecture on "The Story of the November Meteors," at the Royal Institution, in 1879.[35]On the 27th November, 1885, a piece of meteoric iron fell at Mazapil, in Mexico, during the shower of Andromedes, but whether it formed part of the swarm is not known. It is, however, to be noticed that meteorites are said to have fallen on several other occasions at the end of November.[36]Hooke had noticed, in 1664, that the star Gamma Arietis was double.[37]Perhaps if we could view the stars without the intervention of the atmosphere, blue stars would be more common. The absorption of the atmosphere specially affects the greenish and bluish colours. Professor Langley gives us good reason for believing that the sun itself would be blue if it were not for the effect of the air.[38]The declination of a star is the arc drawn from the star to the equator at right angles to the latter.[39]The distance of 61 Cygni has, however, again been investigated by Professor Asaph Hall, of Washington, who has obtained a result considerably less than had been previously supposed; on the other hand, Professor Pritchard's photographic researches are in confirmation of Struve's and those obtained at Dunsink.[40]I am indebted for this drawing to the kindness of Messrs. De la Rue.[41]SeeChapter XIX., on the mass of Sirius and his satellite.[42]As the earth carries on the telescope at the rate of 18 miles a second, and as light moves with the velocity of 180,000 miles a second very nearly, it follows that the velocity of the telescope is about one ten-thousandth part of that of light. While the light moves down the tube 20 feet long, the telescope will therefore have moved the ten-thousandth part of 20 feet—i.e., the fortieth of an inch.[43]SeeNewcomb's "Popular Astronomy," p. 508, where the discovery of this law is attributed to Mr. J. Homer Lane, of Washington. The contraction theory is due to Helmholtz.[44]The theory of Tidal Evolution sketched in this chapter is mainly due to the researches of Professor G.H. Darwin, F.R.S.[45]The hour varies with the locality: it would be 11.49 at Calais; at Liverpool, 11.23; at Swansea Bay, 5.56, etc.[46]Having decided upon the units of mass, of angle, and of distance which we intend to use for measuring these quantities, then any mass, or angle, or distance is expressed by a certain definite number. Thus if we take the mass of the earth as the unit of mass, the angle through which it moves in a second as the unit of angle, and its distance from the sun as the unit of distance, we shall find that the similar quantities for Jupiter are expressed by the numbers 316, 0·0843, and 5·2 respectively. Hence its orbital moment of momentum is 316 × 0·0843 × (5·2)2.

[1]It may, however, be remarked that a star is neverseento set, as, owing to our atmosphere, it ceases to be visible before it reaches the horizon.

[2]"Popular Astronomy," p. 66.

[3]Limbis the word used by astronomers to denote theedgeor circumference of the apparent disc of a heavenly body.

[4]"The Sun," p. 119.

[5]It has been frequently stated that the outburst in 1859, witnessed by Carrington and Hodgson, was immediately followed by an unusually intense magnetic storm, but the records at Kew and Greenwich show that the magnetic disturbances on that day were of a very trivial character.

[6]Some ungainly critic has observed that the poet himself seems to have felt a doubt on the matter, because he has supplemented the dubious moonbeams by the "lantern dimly burning." The more generous, if somewhat a sanguine remark has been also made, that "the time will come when the evidence of this poem will prevail over any astronomical calculations."

[7]This sketch has been copied by permission from the very beautiful view in Messrs. Nasmyth and Carpenter's book, of which it formsPlate XI. So have also the other illustrations of lunar scenery inPlates VIII.,IX.The photographs were obtained by Mr. Nasmyth from models carefully constructed from his drawings to illustrate the features on the moon. During the last twenty years photography has completely superseded drawing by eye in the delineation of lunar objects. Long series of magnificent photographs of lunar scenery have been published by the Paris and Lick Observatories.

[8]At the British Association's meeting at Cardiff in 1892, Prof. Copeland exhibited a model of the moon, on which the appearance of the streaks near full moon was perfectly shown by means of small spheres of transparent glass attached to the surface.

[9]The duration of an occultation, or, in other words, the length of time during which the moon hides the star, would be slightly shorter than the computed time, if the moon had an atmosphere capable of sensibly refracting the light from the star. But, so far, our observations do not indicate this with certainty.

[10]I owe my knowledge of this subject to Dr. G. Johnstone Stoney, F.R.S. There has been some controversy as to who originated the ingenious and instructive doctrine here sketched.

[11]The space described by a falling body is proportional to the product of the force and the square of the time. The force varies inversely as the square of the distance from the earth, so that the space will vary as the square of the time, and inversely as the square of the distance. If, therefore, the distance be increased sixty-fold, the time must also be increased sixty-fold, if the space fallen through is to remain the same.

[12]See Newcomb's "Popular Astronomy," p. 78.

[13]Recent investigation by Newcomb on the motion of Mercury have led to the result that the hypothesis of a planet or a ring of very small planets between the orbit of Mercury and the sun cannot account for the difference between theory and observation in the movements of Mercury. Harzer has come to the same result, and has shown that the disturbing element may possibly be the material of the Solar Corona.

[14]"The Sun: its Planets, and their Satellites." London: 1882 (page 147).

[15]James Gregory, in a book on optics written in 1667, had already suggested the use of the transit of Venus for this purpose.

[16]See"Astronomy and Astrophysics," No. 128.

[17]See"Astronomy and Astrophysics," No. 128.

[18]This is the curved marking which onPlate XVIII.appears in longitude 290° and north of (that is, below) the equator. Here, as in all astronomical drawings, north is at the foot and south at the top.Seeabove, p. 82 (Chapter III.).

[19]Now Director of the Lick Observatory.

[20]The heliometer is a telescope with its object-glass cut in half along a diameter. One or both of these halves is movable transversely by a screw. Each half gives a complete image of the object. The measures are effected by observing how many turns of the screw convey the image of the star formed by one half of the object-glass to coincide with the image of the planet formed by the other.

[21]See "Astronomy and Astrophysics," No. 109.

[22]It is only right to add that some observers believe that, in exceptional circumstances, points of Jupiter have shown some slight degree of intrinsic light.

[23]Professor Pickering, of Cambridge, Mass., has, however, effected the important improvement of measuring the decline of light of the satellite undergoing eclipse by the photometer. Much additional precision may be anticipated in the results of such observations.

[24]"Newcomb's Popular Astronomy," p. 336.

[25]SeeGrant, "History of Physical Astronomy," page 255.

[26]Now Director of the Lick Observatory.

[27]We are here neglecting the orbital motion of Saturn, by which the whole system is moved towards or from the earth, but as this motion is common to the ball and the ring, it will not disturb the relative positions of the three spectra.

[28]According to Prof. Barnard's recent measures, the diameter of Titan is 2,700 miles. This is the satellite discovered by Huyghens; it is the sixth in order from the planet.

[29]Extract from "Three Cities of Russia," by C. Piazzi Smyth, vol. ii., p. 164: "In the year 1796. It then chanced that George III., of Great Britain, was pleased to send as a present to the Empress Catharine of Russia a ten-foot reflecting telescope constructed by Sir William Herschel. Her Majesty immediately desired to try its powers, and Roumovsky was sent for from the Academy to repair to Tsarskoe-Selo, where the Court was at the time residing. The telescope was accordingly unpacked, and for eight long consecutive evenings the Empress employed herself ardently in observing the moon, planets, and stars; and more than this, in inquiring into the state of astronomy in her dominions. Then it was that Roumovsky set before the Imperial view the Academy's idea of removing their observatory, detailing the necessity for, and the advantages of, such a proceeding. Graciously did the 'Semiramis of the North,' the 'Polar Star,' enter into all these particulars, and warmly approve of the project; but death closed her career within a few weeks after, and prevented her execution of the design."

[30]SeeProfessor Holden's "Sir William Herschel, his Life and Works."

[31]Arago says that "Lemonnier's records were the image of chaos." Bouvard showed to Arago one of the observations of Uranus which was written on a paper bag that in its time had contained hair-powder.

[32]The first comet of 1884 also suddenly increased in brightness, while a distinct disc, which hitherto had formed the nucleus, became transformed into a fine point of light.

[33]The three numbers 12, 1, and1⁄4are nearly inversely proportional to the atomic weights of hydrogen, hydrocarbon gas, and iron vapour, and it is for this reason that Bredichin suggested the above-mentioned composition of the various types of tail. Spectroscopic evidence of the presence of hydrogen is yet wanting.

[34]This illustration, as well as the figure of the path of the meteors, has been derived from Dr. G.J. Stoney's interesting lecture on "The Story of the November Meteors," at the Royal Institution, in 1879.

[35]On the 27th November, 1885, a piece of meteoric iron fell at Mazapil, in Mexico, during the shower of Andromedes, but whether it formed part of the swarm is not known. It is, however, to be noticed that meteorites are said to have fallen on several other occasions at the end of November.

[36]Hooke had noticed, in 1664, that the star Gamma Arietis was double.

[37]Perhaps if we could view the stars without the intervention of the atmosphere, blue stars would be more common. The absorption of the atmosphere specially affects the greenish and bluish colours. Professor Langley gives us good reason for believing that the sun itself would be blue if it were not for the effect of the air.

[38]The declination of a star is the arc drawn from the star to the equator at right angles to the latter.

[39]The distance of 61 Cygni has, however, again been investigated by Professor Asaph Hall, of Washington, who has obtained a result considerably less than had been previously supposed; on the other hand, Professor Pritchard's photographic researches are in confirmation of Struve's and those obtained at Dunsink.

[40]I am indebted for this drawing to the kindness of Messrs. De la Rue.

[41]SeeChapter XIX., on the mass of Sirius and his satellite.

[42]As the earth carries on the telescope at the rate of 18 miles a second, and as light moves with the velocity of 180,000 miles a second very nearly, it follows that the velocity of the telescope is about one ten-thousandth part of that of light. While the light moves down the tube 20 feet long, the telescope will therefore have moved the ten-thousandth part of 20 feet—i.e., the fortieth of an inch.

[43]SeeNewcomb's "Popular Astronomy," p. 508, where the discovery of this law is attributed to Mr. J. Homer Lane, of Washington. The contraction theory is due to Helmholtz.

[44]The theory of Tidal Evolution sketched in this chapter is mainly due to the researches of Professor G.H. Darwin, F.R.S.

[45]The hour varies with the locality: it would be 11.49 at Calais; at Liverpool, 11.23; at Swansea Bay, 5.56, etc.

[46]Having decided upon the units of mass, of angle, and of distance which we intend to use for measuring these quantities, then any mass, or angle, or distance is expressed by a certain definite number. Thus if we take the mass of the earth as the unit of mass, the angle through which it moves in a second as the unit of angle, and its distance from the sun as the unit of distance, we shall find that the similar quantities for Jupiter are expressed by the numbers 316, 0·0843, and 5·2 respectively. Hence its orbital moment of momentum is 316 × 0·0843 × (5·2)2.

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