FOOTNOTES:

Tides are of course produced in the sun by the action of the planets, for the sun rotates in twenty-five days or thereabouts, while the planets revolve in much longer periods than that. The principal tide-generating bodies will be Venus and Jupiter; the greater nearness of one rather more than compensating for the greater mass of the other.It may be interesting to tabulate the relative tide-producing powers of the planets on the sun. They are as follows, calling that of the earth 1,000:—Relative Tide-producing Powers of the Planetson the Sun.Mercury1,121Venus2,339Earth1,000Mars304Jupiter2,136Saturn1,033Uranus21Neptune9The power of all of them is very feeble, and by acting on different sides they usually partly neutralize each other's action; but occasionally they get all on one side, and in that case some perceptible effect may be produced; the probable effect seems likely to be a gentle heaving tide in the solar surface, with breaking up of any incipient crust; and such an effect may be considered as evidenced periodically by the great increase in the number of solar spots which then break out.The solar tides are, however, much too small to appreciably push any planet away, hence we are not to suppose that the planets originated by budding from the sun, in contradiction of the nebular hypothesis. Nor is it necessary to assume that the satellites, as a class, originated in the way ours did; though they may have done so. They were more probably secondary rings. Our moon differs from other satellites in being exceptionally large compared with the size of its primary; it is as big as some of the moons of Jupiter and Saturn. The earth is the only one of the small planets that has an appreciable moon, and hence there is nothing forced or unnatural in supposing that it may have had an exceptional history.Evidently, however, tidal phenomena must be taken into consideration in any treatment of the solar system through enormous length of time, and it will probably play a large part in determining its future.

It may be interesting to tabulate the relative tide-producing powers of the planets on the sun. They are as follows, calling that of the earth 1,000:—

Relative Tide-producing Powers of the Planetson the Sun.Mercury1,121Venus2,339Earth1,000Mars304Jupiter2,136Saturn1,033Uranus21Neptune9

The power of all of them is very feeble, and by acting on different sides they usually partly neutralize each other's action; but occasionally they get all on one side, and in that case some perceptible effect may be produced; the probable effect seems likely to be a gentle heaving tide in the solar surface, with breaking up of any incipient crust; and such an effect may be considered as evidenced periodically by the great increase in the number of solar spots which then break out.

The solar tides are, however, much too small to appreciably push any planet away, hence we are not to suppose that the planets originated by budding from the sun, in contradiction of the nebular hypothesis. Nor is it necessary to assume that the satellites, as a class, originated in the way ours did; though they may have done so. They were more probably secondary rings. Our moon differs from other satellites in being exceptionally large compared with the size of its primary; it is as big as some of the moons of Jupiter and Saturn. The earth is the only one of the small planets that has an appreciable moon, and hence there is nothing forced or unnatural in supposing that it may have had an exceptional history.

Evidently, however, tidal phenomena must be taken into consideration in any treatment of the solar system through enormous length of time, and it will probably play a large part in determining its future.

When Laplace and Lagrange investigated the question of the stability or instability of the solar system, they did so on the hypothesis that the bodies composing it were rigid. They reached a grand conclusion—that all the mutual perturbations of the solar system were periodic—that whatever changes were going on would reach a maximum and thenbegin to diminish; then increase again, then diminish, and so on. The system was stable, and its changes were merely like those of a swinging pendulum.

But this conclusion is not final. The hypothesis that the bodies are rigid is not strictly true: and directly tidal deformation is taken into consideration it is perceived to be a potent factor, able in the long run to upset all their calculations. But it is so utterly and inconceivably minute—it only produces an appreciable effect after millions of years—whereas the ordinary perturbations go through their swings in some hundred thousand years or so at the most. Granted it is small, but it is terribly persistent; and it always acts in one direction. Never does it cease: never does it begin to act oppositely and undo what it has done. It is like the perpetual dropping of water. There may be only one drop in a twelvemonth, but leave it long enough, and the hardest stone must be worn away at last.

We have been speaking of millions of years somewhat familiarly; but what, after all, is a million years that we should not speak familiarly of it? It is longer than our lifetime, it is true. To the ephemeral insects whose lifetime is an hour, a year might seem an awful period, the mid-day sun might seem an almost stationary body, the changes of the seasons would be unknown, everything but the most fleeting and rapid changes would appear permanent and at rest. Conversely, if our life-period embraced myriads of æons, things which now seem permanent would then appear as in a perpetual state of flux. A continent would be sometimes dry, sometimes covered with ocean; the stars we now call fixed would be moving visibly before our eyes; the earth would be humming on its axis like a top, and the whole of human history might seem as fleeting as a cloud of breath on a mirror.

Evolution is always a slow process. To evolve such an animal as a greyhound from its remote ancestors, according to Mr. Darwin, needs immense tracts of time; and if the evolution of some feeble animal crawling on the surface of this planet is slow, shall the stately evolution of the planetary orbs themselves be hurried? It may be that we are able to trace the history of the solar system for some thousand million years or so; but for how much longer time must it not have a history—a history, and also a future—entirely beyond our ken?

Those who study the stars have impressed upon them the existence of the most immeasurable distances, which yet are swallowed up as nothing in the infinitude of space. No less are we compelled to recognize the existence of incalculable æons of time, and yet to perceive that these are but as drops in the ocean of eternity.

FOOTNOTES:[1]The following account of Mars's motion is from the excellent small manual of astronomy by Dr. Haughton of Trinity College, Dublin:—(P. 151) "Mars's motion is very unequal; when he first appears in the morning emerging from the rays of the sun, his motion is direct and rapid; it afterwards becomes slower, and he becomes stationary when at an elongation of 137° from the sun; then his motion becomes retrograde, and its velocity increases until he is in opposition to the sun at 180°; at this time the retrograde motion is most rapid, and afterwards diminishes until he is 137° distant from the sun on the other side, when Mars again becomes stationary; his motion then becomes direct, and increases in velocity until it reaches a maximum, when the planet is again in conjunction with the sun. The retrograde motion of this planet lasts for 73 days: and its arc of retrogradation is 16°."[2]It is not so easy to plot the path of the sun among the stars by direct observation, as it is to plot the path of a planet; because sun and stars are not visible together. Hipparchus used the moon as an intermediary; since sun and moon are visible together, and also moon and stars.[3]This is, however, by no means the whole of the matter. The motion is not a simple circle nor has it a readily specifiable period. There are several disturbing causes. All that is given here is a first rough approximation.[4]The proof is easy, and ought to occur in books on solid geometry. By a "regular" solid is meant one with all its faces, edges, angles, &c., absolutely alike: it is of these perfectly symmetrical bodies that there are only five. Crystalline forms are practically infinite in number.[5]Best known to us by his Christian name, as so many others of that time are known,e.g.Raphael Sanzio, Dante Alighieri, Michael Angelo Buonarotti. The rule is not universal. Tasso and Ariosto are surnames.[6]It would seem that the fact that all bodies of every material tend to fall at the same rate is still not clearly known. Confusion is introduced by the resistance of the air. But a little thought should make it clear that the effect of the air is a mere disturbance, to be eliminated as far as possible, since the atmosphere has nothing to do with gravitation. The old fashioned "guinea and feather experiment" illustrates that in a vacuum things entirely different in specific gravity or surface drop at the same pace.[7]Karl von Gebler (Galileo), p. 13.[8]It is of course the "silver lining" of clouds that outside observers see.[9]L.U.K.,Life of Galileo, p. 26.[10]Note added September, 1892.News from the Lick Observatory makes a very small fifth satellite not improbable.[11]They remained there till this century. In 1835 they were quietly dropped.[12]It was invented by van Helmont, a Belgian chemist, who died in 1644. He suggested two namesgasandblas, and the first has survived. Blas was, I suppose, fromblasen, to blow, and gas seems to be an attempt to get at the Sanskrit root underlying all such words asgeist.[13]Such as this, among many others:—The duration of a flame under different conditions is well worth determining. A spoonful of warm spirits of wine burnt 116 pulsations. The same spoonful of spirits of wine with addition of one-sixth saltpetre burnt 94 pulsations. With one-sixth common salt, 83; with one-sixth gunpowder, 110; a piece of wax in the middle of the spirit, 87; a piece ofKieselstein, 94; one-sixth water, 86; and with equal parts water, only 4 pulse-beats. This, says Liebig, is given as an example of a "licht-bringende Versuch."[14]Draper,History of Civilization in Europe, vol. ii. p. 259.[15]Professor Knight's series of Philosophical Classics.[16]To explain why the entire system, horse and cart together, move forward, the forces acting on the ground must be attended to.[17]The distance being proportional to thesquareof the time, seep. 82.[18]The following letter, recently unearthed and published inNature, May 12, 1881, seems to me well worth preserving. The feeling of a respiratory interval which it describes is familiar to students during the too few periods of really satisfactory occupation. The early guess concerning atmospheric electricity is typical of his extraordinary instinct for guessing right."London,Dec. 15, 1716."Dear Doctor,—He that in ye mine of knowledge deepest diggeth, hath, like every other miner, ye least breathing time, and must sometimes at least come to terr. alt. for air."In one of these respiratory intervals I now sit down to write to you, my friend."You ask me how, with so much study, I manage to retene my health. Ah, my dear doctor, you have a better opinion of your lazy friend than he hath of himself. Morpheous is my last companion; without 8 or 9 hours of him yr correspondent is not worth one scavenger's peruke. My practices did at ye first hurt my stomach, but now I eat heartily enou' as y' will see when I come down beside you."I have been much amused at ye singularφενόμεναresulting from bringing of a needle into contact with a piece of amber or resin fricated on silke clothe. Ye flame putteth me in mind of sheet lightning on a small—how very small—scale. But I shall in my epistles abjure Philosophy whereof when I come down to Sakly I'll give you enou'. I began to scrawl at 5 mins. from 9 of ye clk. and have in writing consmd. 10 mins. My Ld. Somerset is announced."Farewell, Gd. bless you and help yr sincere friend."Isaac Newton."ToDr. Law, Suffolk."[19]Kepler's laws may be called respectively, the law of path, the law of speed, and the relationship law. By the "mass" of a body is meant the number of pounds or tons in it: the amount of matter it contains. The idea is involved in the popular word "massive."[20]The equation we have to verify isgR2=4π2r3,T2with the data thatr, the moon's distance, is 60 times R, the earth's radius, which is 3,963 miles; while T, the time taken to complete the moon's orbit, is 27 days, 13 hours, 18 minutes, 37 seconds. Hence, suppose we calculate outg, the intensity of terrestrial gravity, from the above equation, we getg=4π2× (60)3=39·92 × 216000 × 3963 miles= 32·92 feet-per-second per second,T2(27 days, 13 hours, &c.)2which is not far wrong.[21]The two motions may be roughly compounded into a single motion, which for a few centuries may without much error be regarded as a conical revolution about a different axis with a different period; and Lieutenant-Colonel Drayson writes books emphasizing this simple fact, under the impression that it is a discovery.[22]Members of the Accademia dei Lyncei, the famous old scientific Society established in the time of Cosmo de Medici—older than our own Royal Society.[23]Newton suspected that the moon really did so oscillate, and so it may have done once; but any real or physical libration, if existing at all, is now extremely minute.[24]An interesting picture in the New Gallery this year (1891), attempting to depict "Earth-rise in Moon-land," unfortunately errs in several particulars. First of all, the earth does not "rise," but is fixed relatively to each place on the moon; and two-fifths of the moon never sees it. Next, the earth would not look like a map of the world with a haze on its edge. Lastly, whatever animal remains the moon may contain would probably be rather in the form of fossils than of skeletons. The skeleton is of course intended as an image of death and desolation. It is a matter of taste: but a skeleton, it seems to me, speaks too recently of life to be as appallingly weird and desolate as a blank stone or ice landscape, unshaded by atmosphere or by any trace of animal or plant life, could be made.[25]Five of Jupiter's revolutions occupy 21,663 days; two of Saturn's revolutions occupy 21,526 days.[26]Excircularityis what is meant by this term. It is called "excentricity" because the foci (not the centre) of an ellipse are regarded as the representatives of the centre of a circle. Their distance from the centre, compared with the radius of the unflattened circle, is called the excentricity.[27]A curve of thenth degree has ½n(n+3) arbitrary constants in its equation, hence this number of points specifically determine it. But special points, like focus or vertex, count as two ordinary ones. Hence three points plus the focus act as five points, and determine a conic or curve of the second degree. Three observations therefore fix an orbit round the sun.[28]Its name suggests a measure of the diameter of the sun's disk, and this is one of its functions; but it can likewise measure planetary and other disks; and in general behaves as the most elaborate and expensive form of micrometer. The Königsberg instrument is shewn in fig. 92.[29]It may be supposed that the terms "minute" and "second" have some necessary connection with time, but they are mere abbreviations forpartes minutæandpartes minutæ secundæ, and consequently may be applied to the subdivision of degrees just as properly as to the subdivision of hours. A "second" of arc means the 3600th part of a degree, just as a second of time means the 3600th part of an hour.[30]A group of flying particles, each one invisible, obstructs light singularly little, even when they are close together, as one can tell by the transparency of showers and snowstorms. The opacity of haze may be due not merely to dust particles, but to little eddies set up by radiation above each particle, so that the air becomes turbulent and of varying density. (See a similar suggestion by Mr. Poynting inNature, vol. 39, p. 323.)[31]The moon ought to be watched during the next great shower, if the line of fire happens to take effect on a visible part of the dark portion.[32]Address to Birmingham Midland Institute, "A Glimpse through the Corridors of Time."

[1]The following account of Mars's motion is from the excellent small manual of astronomy by Dr. Haughton of Trinity College, Dublin:—(P. 151) "Mars's motion is very unequal; when he first appears in the morning emerging from the rays of the sun, his motion is direct and rapid; it afterwards becomes slower, and he becomes stationary when at an elongation of 137° from the sun; then his motion becomes retrograde, and its velocity increases until he is in opposition to the sun at 180°; at this time the retrograde motion is most rapid, and afterwards diminishes until he is 137° distant from the sun on the other side, when Mars again becomes stationary; his motion then becomes direct, and increases in velocity until it reaches a maximum, when the planet is again in conjunction with the sun. The retrograde motion of this planet lasts for 73 days: and its arc of retrogradation is 16°."

[2]It is not so easy to plot the path of the sun among the stars by direct observation, as it is to plot the path of a planet; because sun and stars are not visible together. Hipparchus used the moon as an intermediary; since sun and moon are visible together, and also moon and stars.

[3]This is, however, by no means the whole of the matter. The motion is not a simple circle nor has it a readily specifiable period. There are several disturbing causes. All that is given here is a first rough approximation.

[4]The proof is easy, and ought to occur in books on solid geometry. By a "regular" solid is meant one with all its faces, edges, angles, &c., absolutely alike: it is of these perfectly symmetrical bodies that there are only five. Crystalline forms are practically infinite in number.

[5]Best known to us by his Christian name, as so many others of that time are known,e.g.Raphael Sanzio, Dante Alighieri, Michael Angelo Buonarotti. The rule is not universal. Tasso and Ariosto are surnames.

[6]It would seem that the fact that all bodies of every material tend to fall at the same rate is still not clearly known. Confusion is introduced by the resistance of the air. But a little thought should make it clear that the effect of the air is a mere disturbance, to be eliminated as far as possible, since the atmosphere has nothing to do with gravitation. The old fashioned "guinea and feather experiment" illustrates that in a vacuum things entirely different in specific gravity or surface drop at the same pace.

[7]Karl von Gebler (Galileo), p. 13.

[8]It is of course the "silver lining" of clouds that outside observers see.

[9]L.U.K.,Life of Galileo, p. 26.

[10]Note added September, 1892.News from the Lick Observatory makes a very small fifth satellite not improbable.

[11]They remained there till this century. In 1835 they were quietly dropped.

[12]It was invented by van Helmont, a Belgian chemist, who died in 1644. He suggested two namesgasandblas, and the first has survived. Blas was, I suppose, fromblasen, to blow, and gas seems to be an attempt to get at the Sanskrit root underlying all such words asgeist.

[13]Such as this, among many others:—The duration of a flame under different conditions is well worth determining. A spoonful of warm spirits of wine burnt 116 pulsations. The same spoonful of spirits of wine with addition of one-sixth saltpetre burnt 94 pulsations. With one-sixth common salt, 83; with one-sixth gunpowder, 110; a piece of wax in the middle of the spirit, 87; a piece ofKieselstein, 94; one-sixth water, 86; and with equal parts water, only 4 pulse-beats. This, says Liebig, is given as an example of a "licht-bringende Versuch."

[14]Draper,History of Civilization in Europe, vol. ii. p. 259.

[15]Professor Knight's series of Philosophical Classics.

[16]To explain why the entire system, horse and cart together, move forward, the forces acting on the ground must be attended to.

[17]The distance being proportional to thesquareof the time, seep. 82.

[18]The following letter, recently unearthed and published inNature, May 12, 1881, seems to me well worth preserving. The feeling of a respiratory interval which it describes is familiar to students during the too few periods of really satisfactory occupation. The early guess concerning atmospheric electricity is typical of his extraordinary instinct for guessing right."London,Dec. 15, 1716."Dear Doctor,—He that in ye mine of knowledge deepest diggeth, hath, like every other miner, ye least breathing time, and must sometimes at least come to terr. alt. for air."In one of these respiratory intervals I now sit down to write to you, my friend."You ask me how, with so much study, I manage to retene my health. Ah, my dear doctor, you have a better opinion of your lazy friend than he hath of himself. Morpheous is my last companion; without 8 or 9 hours of him yr correspondent is not worth one scavenger's peruke. My practices did at ye first hurt my stomach, but now I eat heartily enou' as y' will see when I come down beside you."I have been much amused at ye singularφενόμεναresulting from bringing of a needle into contact with a piece of amber or resin fricated on silke clothe. Ye flame putteth me in mind of sheet lightning on a small—how very small—scale. But I shall in my epistles abjure Philosophy whereof when I come down to Sakly I'll give you enou'. I began to scrawl at 5 mins. from 9 of ye clk. and have in writing consmd. 10 mins. My Ld. Somerset is announced."Farewell, Gd. bless you and help yr sincere friend."Isaac Newton."ToDr. Law, Suffolk."

"London,Dec. 15, 1716.

"Dear Doctor,—He that in ye mine of knowledge deepest diggeth, hath, like every other miner, ye least breathing time, and must sometimes at least come to terr. alt. for air.

"In one of these respiratory intervals I now sit down to write to you, my friend.

"You ask me how, with so much study, I manage to retene my health. Ah, my dear doctor, you have a better opinion of your lazy friend than he hath of himself. Morpheous is my last companion; without 8 or 9 hours of him yr correspondent is not worth one scavenger's peruke. My practices did at ye first hurt my stomach, but now I eat heartily enou' as y' will see when I come down beside you.

"I have been much amused at ye singularφενόμεναresulting from bringing of a needle into contact with a piece of amber or resin fricated on silke clothe. Ye flame putteth me in mind of sheet lightning on a small—how very small—scale. But I shall in my epistles abjure Philosophy whereof when I come down to Sakly I'll give you enou'. I began to scrawl at 5 mins. from 9 of ye clk. and have in writing consmd. 10 mins. My Ld. Somerset is announced.

"Farewell, Gd. bless you and help yr sincere friend.

"Isaac Newton.

"ToDr. Law, Suffolk."

[19]Kepler's laws may be called respectively, the law of path, the law of speed, and the relationship law. By the "mass" of a body is meant the number of pounds or tons in it: the amount of matter it contains. The idea is involved in the popular word "massive."

[20]The equation we have to verify isgR2=4π2r3,T2with the data thatr, the moon's distance, is 60 times R, the earth's radius, which is 3,963 miles; while T, the time taken to complete the moon's orbit, is 27 days, 13 hours, 18 minutes, 37 seconds. Hence, suppose we calculate outg, the intensity of terrestrial gravity, from the above equation, we getg=4π2× (60)3=39·92 × 216000 × 3963 miles= 32·92 feet-per-second per second,T2(27 days, 13 hours, &c.)2which is not far wrong.

[20]The equation we have to verify is

gR2=4π2r3,T2

with the data thatr, the moon's distance, is 60 times R, the earth's radius, which is 3,963 miles; while T, the time taken to complete the moon's orbit, is 27 days, 13 hours, 18 minutes, 37 seconds. Hence, suppose we calculate outg, the intensity of terrestrial gravity, from the above equation, we get

g=4π2× (60)3=39·92 × 216000 × 3963 miles= 32·92 feet-per-second per second,T2(27 days, 13 hours, &c.)2

which is not far wrong.

[21]The two motions may be roughly compounded into a single motion, which for a few centuries may without much error be regarded as a conical revolution about a different axis with a different period; and Lieutenant-Colonel Drayson writes books emphasizing this simple fact, under the impression that it is a discovery.

[22]Members of the Accademia dei Lyncei, the famous old scientific Society established in the time of Cosmo de Medici—older than our own Royal Society.

[23]Newton suspected that the moon really did so oscillate, and so it may have done once; but any real or physical libration, if existing at all, is now extremely minute.

[24]An interesting picture in the New Gallery this year (1891), attempting to depict "Earth-rise in Moon-land," unfortunately errs in several particulars. First of all, the earth does not "rise," but is fixed relatively to each place on the moon; and two-fifths of the moon never sees it. Next, the earth would not look like a map of the world with a haze on its edge. Lastly, whatever animal remains the moon may contain would probably be rather in the form of fossils than of skeletons. The skeleton is of course intended as an image of death and desolation. It is a matter of taste: but a skeleton, it seems to me, speaks too recently of life to be as appallingly weird and desolate as a blank stone or ice landscape, unshaded by atmosphere or by any trace of animal or plant life, could be made.

[25]Five of Jupiter's revolutions occupy 21,663 days; two of Saturn's revolutions occupy 21,526 days.

[26]Excircularityis what is meant by this term. It is called "excentricity" because the foci (not the centre) of an ellipse are regarded as the representatives of the centre of a circle. Their distance from the centre, compared with the radius of the unflattened circle, is called the excentricity.

[27]A curve of thenth degree has ½n(n+3) arbitrary constants in its equation, hence this number of points specifically determine it. But special points, like focus or vertex, count as two ordinary ones. Hence three points plus the focus act as five points, and determine a conic or curve of the second degree. Three observations therefore fix an orbit round the sun.

[28]Its name suggests a measure of the diameter of the sun's disk, and this is one of its functions; but it can likewise measure planetary and other disks; and in general behaves as the most elaborate and expensive form of micrometer. The Königsberg instrument is shewn in fig. 92.

[29]It may be supposed that the terms "minute" and "second" have some necessary connection with time, but they are mere abbreviations forpartes minutæandpartes minutæ secundæ, and consequently may be applied to the subdivision of degrees just as properly as to the subdivision of hours. A "second" of arc means the 3600th part of a degree, just as a second of time means the 3600th part of an hour.

[30]A group of flying particles, each one invisible, obstructs light singularly little, even when they are close together, as one can tell by the transparency of showers and snowstorms. The opacity of haze may be due not merely to dust particles, but to little eddies set up by radiation above each particle, so that the air becomes turbulent and of varying density. (See a similar suggestion by Mr. Poynting inNature, vol. 39, p. 323.)

[31]The moon ought to be watched during the next great shower, if the line of fire happens to take effect on a visible part of the dark portion.

[32]Address to Birmingham Midland Institute, "A Glimpse through the Corridors of Time."

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