PART II A COUPLE OF CENTURIES' PROGRESS.

NOTES TO LECTURE X

Science during the century after Newton

The Principia published, 1687

Roemer 1644–1710

James Bradley 1692–1762

Clairaut 1713–1765

Euler 1707–1783

D'Alembert 1717–1783

Lagrange 1736–1813

Laplace 1749–1827

William Herschel 1738–1822

Olaus Roemer was born in Jutland, and studied at Copenhagen. Assisted Picard in 1671 to determine the exact position of Tycho's observatory on Huen. Accompanied Picard to Paris, and in 1675 read before the Academy his paper "On Successive Propagation of Light as revealed by a certain inequality in the motion of Jupiter's First Satellite." In 1681 he returned to Copenhagen as Professor of Mathematics and Astronomy, and died in 1710. He invented the transit instrument, mural circle, equatorial mounting for telescopes, and most of the other principal instruments now in use in observatories. He made as many observations as Tycho Brahé, but the records of all but the work of three days were destroyed by a great fire in 1728.

Bradley, Professor of Astronomy at Oxford, discovered the aberration of light in 1729, while examining stars for parallax, and the nutation of the earth's axis in 1748. Was appointed Astronomer-Royal in 1742.

LECTURE X

ROEMER AND BRADLEY AND THE VELOCITY OF LIGHT

At Newton's death England stood pre-eminent among the nations of Europe in the sphere of science. But the pre-eminence did not last long. Two great discoveries were made very soon after his decease, both by Professor Bradley, of Oxford, and then there came a gap. A moderately great man often leaves behind him a school of disciples able to work according to their master's methods, and with a healthy spirit of rivalry which stimulates and encourages them. Newton left, indeed, a school of disciples, but his methods of work were largely unknown to them, and such as were known were too ponderous to be used by ordinary men. Only one fresh result, and that a small one, has ever been attained by other men working according to the methods of the Principia. The methods were studied and commented on in England to the exclusion of all others for nigh a century, and as a consequence no really important work was done.

On the Continent, however, no such system of slavish imitation prevailed. Those methods of Newton's which had been simultaneously discovered by Leibnitz were more thoroughly grasped, modified, extended, and improved. There arose a great school of French and German mathematicians, and the laurels of scientific discovery passed to France and Germany—more especially, perhaps, at this time to France. England has never wholly recovered them. During the present century this country has been favoured with some giants who, as they become distant enough for their true magnitude to be perceived, may possibly stand out as great as any who have ever lived; but for the mass and bulk of scientific work at the present day we have to look to Germany, with its enlightened Government and extensive intellectual development. England, however, is waking up, and what its Government does not do, private enterprise is beginning to accomplish. The establishment of centres of scientific and literary activity in the great towns of England, though at present they are partially encumbered with the supply of education of an exceedingly rudimentary type, is a movement that in the course of another century or so will be seen to be one of the most important and fruitful steps ever taken by this country. On the Continent such centres have long existed; almost every large town is the seat of a University, and they are now liberally endowed. The University of Bologna (where, you may remember, Copernicus learnt mathematics) has recently celebrated its 800th anniversary.

The scientific history of the century after Newton, summarized in the above table of dates, embraces the labours of the great mathematicians Clairaut, Euler, D'Alembert, and especially of Lagrange and Laplace.

But the main work of all these men was hardly pioneering work. It was rather the surveying, and mapping out, and bringing into cultivation, of lands already discovered. Probably Herschel may be justly regarded as the next true pioneer. We shall not, however, properly appreciate the stages through which astronomy has passed, nor shall we be prepared adequately to welcome the discoveries of modern times unless we pay some attention to the intervening age. Moreover, during this era several facts of great moment gradually came into recognition; and the importance of the discovery we have now to speak of can hardly be over-estimated.

Our whole direct knowledge of the planetary and stellar universe, from the early observations of the ancients down to the magnificent discoveries of a Herschel, depends entirely upon our happening to possess a sense of sight. To no other of our senses do any other worlds than our own in the slightest degree appeal. We touch them or hear them never. Consequently, if the human race had happened to be blind, no other world but the one it groped its way upon could ever have been known or imagined by it. The outside universe would have existed, but man would have been entirely and hopelessly ignorant of it. The bare idea of an outside universe beyond the world would have been inconceivable, and might have been scouted as absurd. We do possess the sense of sight; but is it to be supposed that we possess every sense that can be possessed by finite beings? There is not the least ground for such an assumption. It is easy to imagine a deaf race or a blind race: it is not so easy to imagine a race more highly endowed with senses than our own; and yet the sense of smell in animals may give us some aid in thinking of powers of perception which transcend our own in particular directions. If there were a race with higher or other senses than our own, or if the human race should ever in the process of development acquire such extra sense-organs, a whole universe of existent fact might become for the first time perceived by us, and we should look back upon our past state as upon a blind chrysalid form of existence in which we had been unconscious of all this new wealth of perception.

It cannot be too clearly and strongly insisted on and brought home to every mind, that the mode in which the universe strikes us, our view of the universe, our whole idea of matter, and force, and other worlds, and even of consciousness, depends upon the particular set of sense-organs with which we, as men, happen to be endowed. The senses of force, of motion, of sound, of light, of touch, of heat, of taste, and of smell—these we have, and these are the things we primarily know. All else is inference founded upon these sensations. So the world appears to us. But given other sense-organs, and it might appear quite otherwise. What it is actually and truly like, therefore, is quite and for ever beyond us—so long as we are finite beings.

Without eyes, astronomy would be non-existent. Light it is which conveys all the information we possess, or, as it would seem, ever can possess, concerning the outer and greater universe in which this small world forms a speck. Light is the channel, the messenger of information; our eyes, aided by telescopes, spectroscopes, and many other "scopes" that may yet be invented, are the means by which we read the information that light brings.

Light travels from the stars to our eyes: does it come instantaneously? or does it loiter by the way? for if it lingers it is not bringing us information properly up to date—it is only telling us what the state of affairs was when it started on its long journey.

Now, it is evidently a matter of interest to us whether we see the sun as he is now, or only as he was some three hundred years ago. If the information came by express train it would be three hundred years behind date, and the sun might have gone out in the reign of Queen Anne without our being as yet any the wiser. The question, therefore, "At what rate does our messenger travel?" is evidently one of great interest for astronomers, and many have been the attempts made to solve it. Very likely the ancient Greeks pondered over this question, but the earliest writer known to me who seriously discussed the question is Galileo. He suggests a rough experimental means of attacking it. First of all, it plainly comes quicker than sound. This can be perceived by merely watching distant hammering, or by noticing that the flash of a pistol is seen before its report is heard, or by listening to the noise of a flash of lightning. Sound takes five seconds to travel a mile—it has about the same speed as a rifle bullet; but light is much quicker than that.

The rude experiment suggested by Galileo was to send two men with lanterns and screens to two distant watch-towers or neighbouring mountain tops, and to arrange that each was to watch alternate displays and obscurations of the light made by the other, and to imitate them as promptly as possible. Either man, therefore, on obscuring or showing his own light would see the distant glimmer do the same, and would be able to judge if there was any appreciable interval between his own action and the response of the distant light. The experiment was actually tried by the Florentine Academicians,[22] with the result that, as practice improved, the interval became shorter and shorter, so that there was no reason to suppose that there was any real interval at all. Light, in fact, seemed to travel instantaneously.

Well might they have arrived at this result. Even if they had made far more perfect arrangements—for instance, by arranging a looking-glass at one of the stations in which a distant observer might see the reflection of his own lantern, and watch the obscurations and flashings made by himself, without having to depend on the response of human mechanism—even then no interval whatever could have been detected.

If, by some impossibly perfect optical arrangement, a lighthouse here were made visible to us after reflection in a mirror erected at New York, so that the light would have to travel across the Atlantic and back before it could be seen, even then the appearance of the light on removing a shutter, or the eclipse on interposing it, would seem to happen quite instantaneously. There would certainly be an interval: the interval would be the fiftieth part of a second (the time a stone takes to drop 1⁄13th of an inch), but that is too short to be securely detected without mechanism. With mechanism the thing might be managed, for a series of shutters might be arranged like the teeth of a large wheel; so that, when the wheel rotates, eclipses follow one another very rapidly; if then an eye looked through the same opening as that by which the light goes on its way to the distant mirror, a tooth might have moved sufficiently to cover up this space by the time the light returned; in which case the whole would appear dark, for the light would be stopped by a tooth, either at starting or at returning, continually. At higher speeds of rotation some light would reappear, and at lower speeds it would also reappear; by noticing, therefore, the precise speed at which there was constant eclipse the velocity of light could be determined.

Fig. 73.—Diagram of eye looking at a light reflected in a distant mirror through the teeth of a revolving wheel.

This experiment has now been made in a highly refined form by Fizeau, and repeated by M. Cornu with prodigious care and accuracy. But with these recent matters we have no concern at present. It may be instructive to say, however, that if the light had to travel two miles altogether, the wheel would have to possess 450 teeth and to spin 100 times a second (at the risk of flying to pieces) in order that the ray starting through any one of the gaps might be stopped on returning by the adjacent tooth.

Well might the velocity of light be called instantaneous by the early observers. An ordinary experiment seemed (and was) hopeless, and light was supposed to travel at an infinite speed. But a phenomenon was noticed in the heavens by a quick-witted and ingenious Danish astronomer, which was not susceptible of any ordinary explanation, and which he perceived could at once be explained if light had a certain rate of travel—great, indeed, but something short of infinite. This phenomenon was connected with the satellites of Jupiter, and the astronomer's name was Roemer. I will speak first of the observation and then of the man.

Fig. 74.—Fizeau's wheel, shewing the appearance of distant image seen through its teeth. 1st, when stationary, next when revolving at a moderate speed, last when revolving at the high speed just sufficient to cause eclipse.

Jupiter's satellites are visible, precisely as our own moon is, by reason of the shimmer of sunlight which they reflect. But as they revolve round their great planet they plunge into his shadow at one part of their course, and so become eclipsed from sunshine and invisible to us. The moment of disappearance can be sharply observed.

Take the first satellite as an example. The interval between successive eclipses ought to be its period of revolution round Jupiter. Observe this period. It was not uniform. On the average it was 42 hours 47 minutes, but it seemed to depend on the time of year. When Roemer observed in spring it was less, and in autumn it was more than usual. This was evidently a puzzling fact: what on earth can our year have to do with the motion of a moon of Jupiter's? It was probably, therefore, only an apparent change, caused either by our greater or less distance from Jupiter, or else by our greater or less speed of travelling to or from him. Considering it thus, he was led to see that, when the time of revolution seemed longest, we were receding fastest from Jupiter, and when shortest, approaching fastest.

If, then, light took time on its journey, if it travelled progressively, the whole anomaly would be explained.

In a second the earth goes nineteen miles; therefore in 42¾ hours (the time of revolution of Jupiter's first satellite) it goes 2·9 million (say three million) miles. The eclipse happens punctually, but we do not see it till the light conveying the information has travelled the extra three million miles and caught up the earth. Evidently, therefore, by observing how much the apparent time of revolution is lengthened in one part of the earth's orbit and shortened in another, getting all the data accurately, and assuming the truth of our hypothetical explanation, we can calculate the velocity of light. This is what Roemer did.

Now the maximum amount of retardation is just about fifteen seconds. Hence light takes this time to travel three million miles; therefore its velocity is three million divided by fifteen, say 200,000, or, as we now know more exactly, 186,000 miles every second. Note that the delay does not depend on our distance, but on our speed. One can tell this by common-sense as soon as we grasp the general idea of the explanation. A velocity cannot possibly depend on a distance only.

Fig. 75.—Eclipses of one of Jupiter's satellites. A diagram intended to illustrate the dependence of its apparent time of revolution (from eclipse to eclipse) on the motion of the earth; but not illustrating the matter at all well. TT' T'' are successive positions of the earth, while JJ' J'' are corresponding positions of Jupiter.

Roemer's explanation of the anomaly was not accepted by astronomers. It excited some attention, and was discussed, but it was found not obviously applicable to any of the satellites except the first, and not very simply and satisfactorily even to that. I have, of course, given you the theory in its most elementary and simple form. In actual fact a host of disturbing and complicated considerations come in—not so violently disturbing for the first satellite as for the others, because it moves so quickly, but still complicated enough.

The fact is, the real motion of Jupiter's satellites is a most difficult problem. The motion even of our own moon (the lunar theory) is difficult enough: perturbed as its motion is by the sun. You know that Newton said it cost him more labour than all the rest of the Principia. But the motion of Jupiter's satellites is far worse. No one, in fact, has yet worked their theory completely out. They are perturbed by the sun, of course, but they also perturb each other, and Jupiter is far from spherical. The shape of Jupiter, and their mutual attractions, combine to make their motions most peculiar and distracting.

Hence an error in the time of revolution of a satellite was not certainly due to the cause Roemer suggested, unless one could be sure that the inequality was not a real one, unless it could be shown that the theory of gravitation was insufficient to account for it. This had not then been done; so the half-made discovery was shelved, and properly shelved, as a brilliant but unverified speculation. It remained on the shelf for half a century, and was no doubt almost forgotten.

Fig. 76.—A Transit-instrument for the British astronomical expedition, 1874. Shewing in its essential features the simplest form of such an instrument.

Now a word or two about the man. He was a Dane, educated at Copenhagen, and learned in the mathematics. We first hear of him as appointed to assist Picard, the eminent French geodetic surveyor (whose admirable work in determining the length of a degree you remember in connection with Newton), who had come over to Denmark with the object of fixing the exact site of the old and extinct Tychonic observatory in the island of Huen. For of course the knowledge of the exact latitude and longitude of every place whence numerous observations have been taken must be an essential to the full interpretation of those observations. The measurements being finished, young Roemer accompanied Picard to Paris, and here it was, a few years after, that he read his famous paper concerning "An Inequality in the Motion of Jupiter's First Satellite," and its explanation by means of an hypothesis of "the successive propagation of light."

The later years of his life he spent in Copenhagen as a professor in the University and an enthusiastic observer of the heavens,—not a descriptive observer like Herschel, but a measuring observer like Sir George Airy or Tycho Brahé. He was, in fact, a worthy follower of Tycho, and the main work of his life is the development and devising of new and more accurate astronomical instruments. Many of the large and accurate instruments with which a modern observatory is furnished are the invention of this Dane. One of the finest observatories in the world is the Russian one at Pulkowa, and a list of the instruments there reads like an extended catalogue of Roemer's inventions.

He not only invented the instruments, he had them made, being allowed money for the purpose; and he used them vigorously, so that at his death he left great piles of manuscript stored in the national observatory.

Unfortunately this observatory was in the heart of the city, and was thus exposed to a danger from which such places ought to be as far as possible exempt.

Some eighteen years after Roemer's death a great conflagration broke out in Copenhagen, and ruined large portions of the city. The successor to Roemer, Horrebow by name, fled from his house, with such valuables as he possessed, to the observatory, and there went on with his work. But before long the wind shifted, and to his horror he saw the flames coming his way. He packed up his own and his predecessor's manuscript observations in two cases, and prepared to escape with them, but the neighbours had resorted to the observatory as a place of safety, and so choked up the staircase with their property that he was barely able to escape himself, let alone the luggage, and everything was lost.

Fig. 77.—Diagram of equatorially mounted telescope; CE is the polar axis parallel to the axis of the earth; AB the declination axis. The diurnal motion is compensated by motion about the polar axis only, the other being clamped.

Of all the observations, only three days' work remains, and these were carefully discussed by Dr. Galle, of Berlin, in 1845, and their nutriment extracted. These ancient observations are of great use for purposes of comparison with the present state of the heavens, and throw light upon possible changes that are going on. Of course nowadays such a series of observations would be printed and distributed in many libraries, and so made practically indestructible.

Sad as the disaster was to the posthumous fame of the great observer, a considerable compensation was preparing. The very year that the fire occurred in Denmark a quiet philosopher in England was speculating and brooding on a remarkable observation that he had made concerning the apparent motion of certain stars, and he was led thereby to a discovery of the first magnitude concerning the speed of light—a discovery which resuscitated the old theory of Roemer about Jupiter's satellites, and made both it and him immortal.

James Bradley lived a quiet, uneventful, studious life, mainly at Oxford but afterwards at the National Observatory at Greenwich, of which he was third Astronomer-Royal, Flamsteed and Halley having preceded him in that office. He had taken orders, and lectured at Oxford as Savilian Professor. It is said that he pondered his great discovery while pacing the Long Walk at Magdalen College—and a beautiful place it is to meditate in.

Bradley was engaged in making observations to determine if possible the parallax of some of the fixed stars. Parallax means the apparent relative shift of bodies due to a change in the observer's position. It is parallax which we observe when travelling by rail and looking out of window at the distant landscape. Things at different distances are left behind at different apparent rates, and accordingly they seem to move relatively to each other. The most distant objects are least affected; and anything enormously distant, like the moon, is not subject to this effect, but would retain its position however far we travelled, unless we had some extraordinarily precise means of observation.

So with the fixed stars: they were being observed from a moving carriage—viz. the earth—and one moving at the rate of nineteen miles a second. Unless they were infinitely distant, or unless they were all at the same distance, they must show relative apparent motions among themselves. Seen from one point of the earth's orbit, and then in six months from an opposite point, nearly 184 million miles away, surely they must show some difference of aspect.

Remember that the old Copernican difficulty had never been removed. If the earth revolved round the sun, how came it that the fixed stars showed no parallax? The fact still remained a surprise, and the question a challenge. Picard, like other astronomers, supposed that it was only because the methods of observation had not been delicate enough; but now that, since the invention of the telescope and the founding of National Observatories, accuracy hitherto undreamt of was possible, why not attack the problem anew? This, then, he did, watching the stars with great care to see if in six months they showed any change in absolute position with reference to the pole of the heavens; any known secular motion of the pole, such as precession, being allowed for. Already he thought he detected a slight parallax for several stars near the pole, and the subject was exciting much interest.

Bradley determined to attempt the same investigation. He was not destined to succeed in it. Not till the present century was success in that most difficult observation achieved; and even now it cannot be done by the absolute methods then attempted; but, as so often happens, Bradley, in attempting one thing, hit upon another, and, as it happened, one of still greater brilliance and importance. Let us trace the stages of his discovery.

Atmospheric refraction made horizon observations useless for the delicacy of his purpose, so he chose stars near the zenith, particularly one—γ Draconis. This he observed very carefully at different seasons of the year by means of an instrument specially adapted for zenith observations, viz. a zenith sector. The observations were made in conjunction with a friend of his, an amateur astronomer named Molyneux, and they were made at Kew. Molyneux was shortly made First Lord of the Admiralty, or something important of that sort, and gave up frivolous pursuits. So Bradley observed alone. They observed the star accurately early in the month of December, and then intended to wait six months. But from curiosity Bradley observed it again only about a week later. To his surprise, he found that it had already changed its position. He recorded his observation on the back of an old envelope: it was his wont thus to use up odd scraps of paper—he was not, I regret to say, a tidy or methodical person—and this odd piece of paper turned up long afterwards among his manuscripts. It has been photographed and preserved as an historical relic.

Again and again he repeated the observation of the star, and continually found it moving still a little further and further south, an excessively small motion, but still an appreciable one—not to be set down to errors of observation. So it went on till March. It then waited, and after a bit longer began to return, until June. By September it was displaced as much to the north as it had been to the south, and by December it had got back to its original position. It had described, in fact, a small oscillation in the course of the year. The motion affected neighbouring stars in a similar way, and was called an "aberration," or wandering from their true place.

For a long time Bradley pondered over this observation, and over others like them which he also made. He found one group of stars describing small circles, while others at a distance from them were oscillating in straight lines, and all the others were describing ellipses. Unless this state of things were cleared up, accurate astronomy was impossible. The fixed stars!—they were not fixed a bit. To refined and accurate observation, such as was now possible, they were all careering about in little orbits having a reference to the earth's year, besides any proper motion which they might really have of their own, though no such motion was at present known. Not till Herschel was that discovered; not till this extraordinary aberration was allowed for could it be discovered. The effect observed by Bradley and Molyneux must manifestly be only an apparent motion: it was absurd to suppose a real stellar motion regulating itself according to the position of the earth. Parallax could not do it, for that would displace stars relatively among each other—it would not move similarly a set of neighbouring stars.

At length, four years after the observation, the explanation struck him, while in a boat upon the Thames. He noticed the apparent direction of the wind changed whenever the boat started. The wind veered when the boat's motion changed. Of course the cause of this was obvious enough—the speed of the wind and the speed of the boat were compounded, and gave an apparent direction of the wind other than the true direction. But this immediately suggested a cause for what he had observed in the heavens. He had been observing an apparent direction of the stars other than the true direction, because he was observing from a moving vehicle. The real direction was doubtless fixed: the apparent direction veered about with the motion of the earth. It must be that light did not travel instantaneously, but gradually, as Roemer had surmised fifty years ago; and that the motion of the light was compounded with the motion of the earth.

Think of a stream of light or anything else falling on a moving carriage. The carriage will run athwart the stream, the occupants of the carriage will mistake its true direction. A rifle fired through the windows of a railway carriage by a man at rest outside would make its perforations not in the true line of fire unless the train is stationary. If the train is moving, the line joining the holes will point to a place in advance of where the rifle is really located.

So it is with the two glasses of a telescope, the object-glass and eye-piece, which are pierced by the light; an astronomer, applying his eye to the tube and looking for the origin of the disturbance, sees it apparently, but not in its real position—its apparent direction is displaced in the direction of the telescope's motion; by an amount depending on the ratio of the velocity of the earth to the velocity of light, and on the angle between those two directions.

Fig. 78.—Aberration diagram. The light-ray L penetrates the object-glass of the moving telescope at O, but does not reach the eye-piece until the telescope has travelled to the second position. Consequently a moving telescope does not point out the true direction of the light, but aims at a point a little in advance.

But how minute is the displacement! The greatest effect is obtained when the two motions are at right angles to each other, i.e. when the star seen is at right angles to the direction of the earth's motion, but even then it is only 20", or 1⁄180th part of a degree; one-ninetieth of the moon's apparent diameter. It could not be detected without a cross-wire in the telescope, and would only appear as a slight displacement from the centre of the field, supposing the telescope accurately pointed to the true direction.

But if this explanation be true, it at once gives a method of determining the velocity of light. The maximum angle of deviation, represented as a ratio of arc ÷ radius, amounts to

1 – ·0001 = 1

180 × 57⅓ 10,000

(a gradient of 1 foot in two miles). In other words, the velocity of light must be 10,000 times as great as the velocity of the earth in its orbit. This amounts to a speed of 190,000 miles a second—not so very different from what Roemer had reckoned it in order to explain the anomalies of Jupiter's first satellite.

Stars in the direction in which the earth was moving would not be thus affected; there would be nothing in mere approach or recession to alter direction or to make itself in any way visible. Stars at right angles to the earth's line of motion would be most affected, and these would be all displaced by the full amount of 20 seconds of arc. Stars in intermediate directions would be displaced by intermediate amounts.

But the line of the earth's motion is approximately a circle round the sun, hence the direction of its advance is constantly though slowly changing, and in one year it goes through all the points of the compass. The stars, being displaced always in the line of advance, must similarly appear to describe little closed curves, always a quadrant in advance of the earth, completing their orbits once a year. Those near the pole of the ecliptic will describe circles, being always at right angles to the motion. Those in the plane of the ecliptic (near the zodiac) will be sometimes at right angles to the motion, but at other times will be approached or receded from; hence these will oscillate like pendulums once a year; and intermediate stars will have intermediate motions—that is to say, will describe ellipses of varying excentricity, but all completed in a year, and all with the major axis 20". This agreed very closely with what was observed.

The main details were thus clearly and simply explained by the hypothesis of a finite velocity for light, "the successive propagation of light in time." This time there was no room for hesitation, and astronomers hailed the discovery with enthusiasm.

Not yet, however, did Bradley rest. The finite velocity of light explained the major part of the irregularities he had observed, but not the whole. The more carefully he measured the amount of the deviation, the less completely accurate became its explanation.

There clearly was a small outstanding error or discrepancy; the stars were still subject to an unexplained displacement—not, indeed, a displacement that repeated itself every year, but one that went through a cycle of changes in a longer period.

The displacement was only about half that of aberration, and having a longer period was rather more difficult to detect securely. But the major difficulty was the fact that the two sorts of disturbances were co-existent, and the skill of disentangling them, and exhibiting the true and complete cause of each inequality, was very brilliant.

For nineteen years did Bradley observe this minor displacement, and in that time he saw it go through a complete cycle. Its cause was now clear to him; the nineteen-year period suggested the explanation. It is the period in which the moon goes through all her changes—a period known to the ancients as the lunar cycle, or Metonic cycle, and used by them to predict eclipses. It is still used for the first rough approximation to the prediction of eclipses, and to calculate Easter. The "Golden Number" of the Prayer-book is the number of the year in this cycle.

The cause of the second inequality, or apparent periodic motion of the stars, Bradley made out to be a nodding motion of the earth's axis.

The axis of the earth describes its precessional orbit or conical motion every 26,000 years, as had long been known; but superposed upon this great movement have now been detected minute nods, each with a period of nineteen years.

The cause of the nodding is completely accounted for by the theory of gravitation, just as the precession of the equinoxes was. Both disturbances result from the attraction of the moon on the non-spherical earth—on its protuberant equator.

"Nutation" is, in fact, a small perturbation of precession. The motion may be observed in a non-sleeping top. The slow conical motion of the top's slanting axis represents the course of precession. Sometimes this path is loopy, and its little nods correspond to nutation.

The probable existence of some such perturbation had not escaped the sagacity of Newton, and he mentions something about it in the Principia, but thinks it too small to be detected by observation. He was thinking, however, of a solar disturbance rather than a lunar one, and this is certainly very small, though it, too, has now been observed.

Newton was dead before Bradley made these great discoveries, else he would have been greatly pleased to hear of them.

These discoveries of aberration and nutation, says Delambre, the great French historian of science, secure to their author a distinguished place after Hipparchus and Kepler among the astronomers of all ages and all countries.

NOTES TO LECTURE XI

Lagrange and Laplace, both tremendous mathematicians, worked very much in alliance, and completed Newton's work. The Mécanique Céleste contains the higher intricacies of astronomy mathematically worked out according to the theory of gravitation. They proved the solar system to be stable; all its inequalities being periodic, not cumulative. And Laplace suggested the "nebular hypothesis" concerning the origin of sun and planets: a hypothesis previously suggested, and to some extent, elaborated, by Kant.

A list of some of the principal astronomical researches of Lagrange and Laplace:—Libration of the moon. Long inequality of Jupiter and Saturn. Perturbations of Jupiter's satellites. Perturbations of comets. Acceleration of the moon's mean motion. Improved lunar theory. Improvements in the theory of the tides. Periodic changes in the form and obliquity of the earth's orbit. Stability of the solar system considered as an assemblage of rigid bodies subject to gravity.

The two equations which establish the stability of the solar system are:—

Sum (me²√d) = constant, and Sum (m tan²θ√d) = constant;

where m is the mass of each planet, d its mean distance from the sun, e the excentricity of its orbit, and θ the inclination of its plane. However the expressions above formulated may change for individual planets, the sum of them for all the planets remains invariable.

The period of the variations in excentricity of the earth's orbit is 86,000 years; the period of conical revolution of the earth's axis is 25,800 years. About 18,000 years ago the excentricity was at a maximum.

LECTURE XI

LAGRANGE AND LAPLACE—THE STABILITY OF THE SOLAR SYSTEM, AND THE NEBULAR HYPOTHESIS

Laplace was the son of a small farmer or peasant of Normandy. His extraordinary ability was noticed by some wealthy neighbours, and by them he was sent to a good school. From that time his career was one brilliant success, until in the later years of his life his prominence brought him tangibly into contact with the deteriorating influence of politics. Perhaps one ought rather to say trying than deteriorating; for they seem trying to a strong character, deteriorating to a weak one—and unfortunately, Laplace must be classed in this latter category.

It has always been the custom in France for its high scientific men to be conspicuous also in politics. It seems to be now becoming the fashion in this country also, I regret to say.

The life of Laplace is not specially interesting, and I shall not go into it. His brilliant mathematical genius is unquestionable, and almost unrivalled. He is, in fact, generally considered to come in this respect next after Newton. His talents were of a more popular order than those of Lagrange, and accordingly he acquired fame and rank, and rose to the highest dignities. Nevertheless, as a man and a politician he hardly commands our respect, and in time-serving adjustability he is comparable to the redoubtable Vicar of Bray. His scientific insight and genius were however unquestionably of the very highest order, and his work has been invaluable to astronomy.

I will give a short sketch of some of his investigations, so far as they can be made intelligible without overmuch labour. He worked very much in conjunction with Lagrange, a more solid though a less brilliant man, and it is both impossible and unnecessary for us to attempt to apportion respective shares of credit between these two scientific giants, the greatest scientific men that France ever produced.

First comes a research into the libration of the moon. This was discovered by Galileo in his old age at Arcetri, just before his blindness. The moon, as every one knows, keeps the same face to the earth as it revolves round it. In other words, it does not rotate with reference to the earth, though it does rotate with respect to outside bodies. Its libration consists in a sort of oscillation, whereby it shows us now a little more on one side, now a little more on the other, so that altogether we are cognizant of more than one-half of its surface—in fact, altogether of about three-fifths. It is a simple and unimportant matter, easily explained.

The motion of the moon may be analyzed into a rotation about its own axis combined with a revolution about the earth. The speed of the rotation is quite uniform, the speed of the revolution is not quite uniform, because the orbit is not circular but elliptical, and the moon has to travel faster in perigee than in apogee (in accordance with Kepler's second law). The consequence of this is that we see a little too far round the body of the moon, first on one side, then on the other. Hence it appears to oscillate slightly, like a lop-sided fly-wheel whose revolutions have been allowed to die away so that they end in oscillations of small amplitude.[23] Its axis of rotation, too, is not precisely perpendicular to its plane of revolution, and therefore we sometimes see a few hundred miles beyond its north pole, sometimes a similar amount beyond its south. Lastly, there is a sort of parallax effect, owing to the fact that we see the rising moon from one point of view, and the setting moon from a point 8,000 miles distant; and this base-line of the earth's diameter gives us again some extra glimpses. This diurnal or parallactic libration is really more effective than the other two in extending our vision into the space-facing hemisphere of the moon.

These simple matters may as well be understood, but there is nothing in them to dwell upon. The far side of the moon is probably but little worth seeing. Its features are likely to be more blurred with accumulations of meteoric dust than are those of our side, but otherwise they are likely to be of the same general character.

The thing of real interest is the fact that the moon does turn the same face towards us; i.e. has ceased to rotate with respect to the earth (if ever it did so). The stability of this state of things was shown by Lagrange to depend on the shape of the moon. It must be slightly egg-shape, or prolate—extended in the direction of the earth; its earth-pointing diameter being a few hundred feet longer than its visible diameter; a cause slight enough, but nevertheless sufficient to maintain stability, except under the action of a distinct disturbing cause. The prolate or lemon-like shape is caused by the gravitative pull of the earth, balanced by the centrifugal whirl. The two forces balance each other as regards motion, but between them they have strained the moon a trifle out of shape. The moon has yielded as if it were perfectly plastic; in all probability it once was so.

It may be interesting to note for a moment the correlative effect of this aspect of the moon, if we transfer ourselves to its surface in imagination, and look at the earth (cf. Fig. 41). The earth would be like a gigantic moon of four times our moon's diameter, and would go through its phases in regular order. But it would not rise or set: it would be fixed in the sky, and subject only to a minute oscillation to and fro once a month, by reason of the "libration" we have been speaking of. Its aspect, as seen by markings on its surface, would rapidly change, going through a cycle in twenty-four hours; but its permanent features would be usually masked by lawless accumulations of cloud, mainly aggregated in rude belts parallel to the equator. And these cloudy patches would be the most luminous, the whitest portions; for of course it would be their silver lining that we would then be looking on.[24]

Next among the investigations of Lagrange and Laplace we will mention the long inequality of Jupiter and Saturn. Halley had found that Jupiter was continually lagging behind its true place as given by the theory of gravitation; and, on the other hand, that Saturn was being accelerated. The lag on the part of Jupiter amounted to about 34½ minutes in a century. Overhauling ancient observations, however, Halley found signs of the opposite state of things, for when he got far enough back Jupiter was accelerated and Saturn was being retarded.

Here was evidently a case of planetary perturbation, and Laplace and Lagrange undertook the working of it out. They attacked it as a case of the problem of three bodies, viz. the sun, Jupiter, and Saturn; which are so enormously the biggest of the known bodies in the system that insignificant masses like the Earth, Mars, and the rest, may be wholly neglected. They succeeded brilliantly, after a long and complex investigation: succeeded, not in solving the problem of the three bodies, but, by considering their mutual action as perturbations superposed on each other, in explaining the most conspicuous of the observed anomalies of their motion, and in laying the foundation of a general planetary theory.

Fig. 79.—Shewing the three conjunction places in the orbits of Jupiter and Saturn. The two planets are represented as leaving one of the conjunctions where Jupiter was being pulled back and Saturn being pulled forward by their mutual attraction.

One of the facts that plays a large part in the result was known to the old astrologers, viz. that Jupiter and Saturn come into conjunction with a certain triangular symmetry; the whole scheme being called a trigon, and being mentioned several times by Kepler. It happens that five of Jupiter's years very nearly equal two of Saturn's,[25] so that they get very nearly into conjunction three times in every five Jupiter years, but not exactly. The result of this close approach is that periodically one pulls the other on and is itself pulled back; but since the three points progress, it is not always the same planet which gets pulled back. The complete theory shows that in the year 1560 there was no marked perturbation: before that it was in one direction, while afterwards it was in the other direction, and the period of the whole cycle of disturbances is 929 of our years. The solution of this long outstanding puzzle by the theory of gravitation was hailed with the greatest enthusiasm by astronomers, and it established the fame of the two French mathematicians.

Next they attacked the complicated problem of the motions of Jupiter's satellites. They succeeded in obtaining a theory of their motions which represented fact very nearly indeed, and they detected the following curious relationship between the satellites:—The speed of the first satellite + twice the speed of the second is equal to the speed of the third.

They found this, not empirically, after the manner of Kepler, but as a deduction from the law of gravitation; for they go on to show that even if the satellites had not started with this relation they would sooner or later, by mutual perturbation, get themselves into it. One singular consequence of this, and of another quite similar connection between their positions, is that all three satellites can never be eclipsed at once.

The motion of the fourth satellite is less tractable; it does not so readily form an easy system with the others.

After these great successes the two astronomers naturally proceeded to study the mutual perturbations of all other bodies in the solar system. And one very remarkable discovery they made concerning the earth and moon, an account of which will be interesting, though the details and processes of calculation are quite beyond us in a course like this.

Astronomical theory had become so nearly perfect by this time, and observations so accurate, that it was possible to calculate many astronomical events forwards or backwards, over even a thousand years or more, with admirable precision.

Now, Halley had studied some records of ancient eclipses, and had calculated back by means of the lunar theory to see whether the calculation of the time they ought to occur would agree with the record of the time they did occur. To his surprise he found a discrepancy, not a large one, but still one quite noticeable. To state it as we know it now:—An eclipse a century ago happened twelve seconds later than it ought to have happened by theory; two centuries back the error amounted to forty-eight seconds, in three centuries it would be 108 seconds, and so on; the lag depending on the square of the time. By research, and help from scholars, he succeeded in obtaining the records of some very ancient eclipses indeed. One in Egypt towards the end of the tenth century A.D.; another in 201 A.D.; another a little before Christ; and one, the oldest of all of which any authentic record has been preserved, observed by the Chaldæan astronomers in Babylon in the reign of Hezekiah.

Calculating back to this splendid old record of a solar eclipse, over the intervening 2,400 years, the calculated and the observed times were found to disagree by nearly two hours. Pondering over an explanation of the discrepancy, Halley guessed that it must be because the moon's motion was not uniform, it must be going quicker and quicker, gaining twelve seconds each century on its previous gain—a discovery announced by him as "the acceleration of the moon's mean motion." The month was constantly getting shorter.

What was the physical cause of this acceleration according to the theory of gravitation? Many attacked the question, but all failed. This was the problem Laplace set himself to work out. A singular and beautiful result rewarded his efforts.

You know that the earth describes an elliptic orbit round the sun: and that an ellipse is a circle with a certain amount of flattening or "excentricity."[26] Well, Laplace found that the excentricity of the earth's orbit must be changing, getting slightly less; and that this change of excentricity would have an effect upon the length of the month. It would make the moon go quicker.

One can almost see how it comes about. A decrease in excentricity means an increase in mean distance of the earth from the sun. This means to the moon a less solar perturbation. Now one effect of the solar perturbation is to keep the moon's orbit extra large: if the size of its orbit diminishes, its velocity must increase, according to Kepler's third law.

Laplace calculated the amount of acceleration so resulting, and found it ten seconds a century; very nearly what observation required; for, though I have quoted observation as demanding twelve seconds per century, the facts were not then so distinctly and definitely ascertained.

This calculation for a long time seemed thoroughly satisfactory, but it is not the last word on the subject. Quite lately an error has been found in the working, which diminishes the theoretical gravitation-acceleration to six seconds a century instead of ten, thus making it insufficient to agree exactly with fact. The theory of gravitation leaves an outstanding error. (The point is now almost thoroughly understood, and we shall return to it in Lecture XVIII).

But another question arises out of this discussion. I have spoken of the excentricity of the earth's orbit as decreasing. Was it always decreasing? and if so, how far back was it so excentric that at perihelion the earth passed quite near the sun? If it ever did thus pass near the sun, the inference is manifest—the earth must at one time have been thrown off, or been separated off, from the sun.

If a projectile could be fired so fast that it described an orbit round the earth—and the speed of fire to attain this lies between five and seven miles a second (not less than the one, nor more than the other)—it would ever afterwards pass through its point of projection as one point of its elliptic orbit; and its periodic return through that point would be the sign of its origin. Similarly, if a satellite does not come near its central orb, and can be shown never to have been near it, the natural inference is that it has not been born from it, but has originated in some other way.

The question which presented itself in connexion with the variable ellipticity of the earth's orbit was the following:—Had it always been decreasing, so that once it was excentric enough just to graze the sun at perihelion as a projected body would do?

Into the problem thus presented Lagrange threw himself, and he succeeded in showing that no such explanation of the origin of the earth is possible. The excentricity of the orbit, though now decreasing, was not always decreasing; ages ago it was increasing: it passes through periodic changes. Eighteen thousand years ago its excentricity was a maximum; since then it has been diminishing, and will continue to diminish for 25,000 years more, when it will be an almost perfect circle; it will then begin to increase again, and so on. The obliquity of the ecliptic is also changing periodically, but not greatly: the change is less than three degrees.

This research has, or ought to have, the most transcendent interest for geologists and geographers. You know that geologists find traces of extraordinary variations of temperature on the surface of the earth. England was at one time tropical, at another time glacial. Far away north, in Spitzbergen, evidence of the luxuriant vegetation of past ages has been found; and the explanation of these great climatic changes has long been a puzzle. Does not the secular variation in excentricity of the earth's orbit, combined with the precession of the equinoxes, afford a key? And if a key at all, it will be an accurate key, and enable us to calculate back with some precision to the date of the glacial epoch; and again to the time when a tropical flora flourished in what is now northern Europe, i.e. to the date of the Carboniferous era.

This aspect of the subject has recently been taught with vigour and success by Dr. Croll in his book "Climate and Time."

A brief and partial explanation of the matter may be given, because it is a point of some interest and is also one of fair simplicity.

Every one knows that the climatic conditions of winter and summer are inverted in the two hemispheres, and that at present the sun is nearest to us in our (northern) winter. In other words, the earth's axis is inclined so as to tilt its north pole away from the sun at perihelion, or when the earth is at the part of its elliptic orbit nearest the sun's focus; and to tilt it towards the sun at aphelion. The result of this present state of things is to diminish the intensity of the average northern winter and of the average northern summer, and on the other hand to aggravate the extremes of temperature in the southern hemisphere; all other things being equal. Of course other things are not equal, and the distribution of land and sea is a still more powerful climatic agent than is the three million miles or so extra nearness of the sun. But it is supposed that the Antarctic ice-cap is larger than the northern, and increased summer radiation with increased winter cold would account for this.

But the present state of things did not always obtain. The conical movement of the earth's axis (now known by a curious perversion of phrase as "precession") will in the course of 13,000 years or so cause the tilt to be precisely opposite, and then we shall have the more extreme winters and summers instead of the southern hemisphere.

If the change were to occur now, it might not be overpowering, because now the excentricity is moderate. But if it happened some time back, when the excentricity was much greater, a decidedly different arrangement of climate may have resulted. There is no need to say if it happened some time back: it did happen, and accordingly an agent for affecting the distribution of mean temperature on the earth is to hand; though whether it is sufficient to achieve all that has been observed by geologists is a matter of opinion.

Once more, the whole diversity of the seasons depends on the tilt of the earth's axis, the 23° by which it is inclined to a perpendicular to the orbital plane; and this obliquity or tilt is subject to slow fluctuations. Hence there will come eras when all causes combine to produce a maximum extremity of seasons in the northern hemisphere, and other eras when it is the southern hemisphere which is subject to extremes.

But a grander problem still awaited solution—nothing less than the fate of the whole solar system. Here are a number of bodies of various sizes circulating at various rates round one central body, all attracted by it, and all attracting each other, the whole abandoned to the free play of the force of gravitation: what will be the end of it all? Will they ultimately approach and fall into the sun, or will they recede further and further from him, into the cold of space? There is a third possible alternative: may they not alternately approach and recede from him, so as on the whole to maintain a fair approximation to their present distances, without great and violent extremes of temperature either way?

If any one planet of the system were to fall into the sun, more especially if it were a big one like Jupiter or Saturn, the heat produced would be so terrific that life on this earth would be destroyed, even at its present distance; so that we are personally interested in the behaviour of the other planets as well as in the behaviour of our own.

The result of the portentously difficult and profoundly interesting investigation, here sketched in barest outline, is that the solar system is stable: that is to say, that if disturbed a little it will oscillate and return to its old state; whereas if it were unstable the slightest disturbance would tend to accumulate, and would sooner or later bring about a catastrophe. A hanging pendulum is stable, and oscillates about a mean position; its motion is periodic. A top-heavy load balanced on a point is unstable. All the changes of the solar system are periodic, i.e. they repeat themselves at regular intervals, and they never exceed a certain moderate amount.

The period is something enormous. They will not have gone through all their changes until a period of 2,000,000 years has elapsed. This is the period of the planetary oscillation: "a great pendulum of eternity which beats ages as our pendulums beat seconds." Enormous it seems; and yet we have reason to believe that the earth has existed through many such periods.

The two laws of stability discovered and stated by Lagrange and Laplace I can state, though they may be difficult to understand:—

Represent the masses of the several planets by m₁, m₂, &c.; their mean distances from the sun (or radii vectores) by r₁, r₂, &c.; the excentricities of their orbits by e₁, e₂, &c.; and the obliquity of the planes of these orbits, reckoned from a single plane of reference or "invariable plane," by θ₁, θ₂, &c.; then all these quantities (except m) are liable to fluctuate; but, however much they change, an increase for one planet will be accompanied by a decrease for some others; so that, taking all the planets into account, the sum of a set of terms like these, m₁e₂²√r₁ + m₂e₂²√r₂ + &c., will remain always the same. This is summed up briefly in the following statement:

Σ(me²√r) = constant.

That is one law, and the other is like it, but with inclination of orbit instead of excentricity, viz.:

Σ(mθ²√r) = constant.

The value of each of these two constants can at any time be calculated. At present their values are small. Hence they always were and always will be small; being, in fact, invariable. Hence neither e nor r nor θ can ever become infinite, nor can their average value for the system ever become zero.

The planets may share the given amount of total excentricity and obliquity in various proportions between themselves; but even if it were all piled on to one planet it would not be very excessive, unless the planet were so small a one as Mercury; and it would be most improbable that one planet should ever have all the excentricity of the solar system heaped upon itself. The earth, therefore, never has been, nor ever will be, enormously nearer the sun than it is at present: nor can it ever get very much further off. Its changes are small and are periodic—an increase is followed by a decrease, like the swing of a pendulum.

The above two laws have been called the Magna Charta of the solar system, and were long supposed to guarantee its absolute permanence. So far as the theory of gravitation carries us, they do guarantee its permanence; but something more remains to be said on the subject in a future lecture (XVIII).

And now, finally, we come to a sublime speculation, thrown out by Laplace, not as the result of profound calculation, like the results hitherto mentioned, not following certainly from the theory of gravitation, or from any other known theory, and therefore not to be accepted as more than a brilliant hypothesis, to be confirmed or rejected as our knowledge extends. This speculation is the "Nebular hypothesis." Since the time of Laplace the nebular hypothesis has had ups and downs of credence, sometimes being largely believed in, sometimes being almost ignored. At the present time it holds the field with perhaps greater probability of ultimate triumph than has ever before seemed to belong to it—far greater than belonged to it when first propounded.

It had been previously stated clearly and well by the philosopher Kant, who was intensely interested in "the starry heavens" as well as in the "mind of man," and who shewed in connexion with astronomy also a most surprising genius. The hypothesis ought by rights perhaps to be known rather by his name than by that of Laplace.

The data on which it was founded are these:—Every motion in the solar system known at that time took place in one direction, and in one direction only. Thus the planets revolve round the sun, all going the same way round; moons revolve round the planets, still maintaining the same direction of rotation, and all the bodies that were known to rotate on their own axis did so with still the same kind of spin. Moreover, all these motions take place in or near a single plane. The ancients knew that sun moon and planets all keep near to the ecliptic, within a belt known as the zodiac: none strays away into other parts of the sky. Satellites also, and rings, are arranged in or near the same plane; and the plane of diurnal spin, or equator of the different bodies, is but slightly tilted.

Now all this could not be the result of chance. What could have caused it? Is there any connection or common ancestry possible, to account for this strange family likeness? There is no connection now, but there may have been once. Must have been, we may almost say. It is as though they had once been parts of one great mass rotating as a whole; for if such a rotating mass broke up, its parts would retain its direction of rotation. But such a mass, filling all space as far as or beyond Saturn, although containing the materials of the whole solar system in itself, must have been of very rare consistency. Occupying so much bulk it could not have been solid, nor yet liquid, but it might have been gaseous.

Are there any such gigantic rotating masses of gas in the heaven now? Certainly there are; there are the nebulæ. Some of the nebulæ are now known to be gaseous, and some of them at least are in a state of rotation. Laplace could not have known this for certain, but he suspected it. The first distinctly spiral nebula was discovered by the telescope of Lord Rosse; and quite recently a splendid photograph of the great Andromeda nebula, by our townsman, Mr. Isaac Roberts, reveals what was quite unsuspected—and makes it clear that this prodigious mass also is in a state of extensive and majestic whirl.

Very well, then, put this problem:—A vast mass of rotating gas is left to itself to cool for ages and to condense as it cools: how will it behave? A difficult mathematical problem, worthy of being attacked to-day; not yet at all adequately treated. There are those who believe that by the complete treatment of such a problem all the history of the solar system could be evolved.

Fig. 80.—Lord Rosse's drawing of the spiral nebula in Canes Venatici, with the stub marks of the draughtsman unduly emphasised into features by the engraver.

Laplace pictured to himself this mass shrinking and thereby whirling more and more rapidly. A spinning body shrinking in size and retaining its original amount of rotation, as it will unless a brake is applied, must spin more and more rapidly as it shrinks. It has what mathematicians call a constant moment of momentum; and what it loses in leverage, as it shrinks, it gains in speed. The mass is held together by gravitation, every particle attracting every other particle; but since all the particles are describing curved paths, they will tend to fly off tangentially, and only a small excess of the gravitation force over the centrifugal is left to pull the particles in, and slowly to concentrate the nebula. The mutual gravitation of the parts is opposed by the centrifugal force of the whirl. At length a point is reached where the two forces balance. A portion outside a certain line will be in equilibrium; it will be left behind, and the rest must contract without it. A ring is formed, and away goes the inner nucleus contracting further and further towards a centre. After a time another ring will be left behind in the same way, and so on. What happens to these rings? They rotate with the motion they possess when thrown or shrunk off; but will they remain rings? If perfectly regular they may; if there be any irregularity they are liable to break up. They will break into one or two or more large masses, which are ultimately very likely to collide and become one. The revolving body so formed is still a rotating gaseous mass; and it will go on shrinking and cooling and throwing off rings, like the larger nucleus by which it has been abandoned. As any nucleus gets smaller, its rate of rotation increases, and so the rings last thrown off will be spinning faster than those thrown off earliest. The final nucleus or residual central body will be rotating fastest of all.

The nucleus of the whole original mass we now see shrunk up into what we call the sun, which is spinning on its axis once every twenty-five days. The rings successively thrown off by it are now the planets—some large, some small—those last thrown off rotating round him comparatively quickly, those outside much more slowly. The rings thrown off by the planetary gaseous masses as they contracted have now become satellites; except one ring which has remained without breaking up, and is to be seen rotating round Saturn still.

One other similar ring, an abortive attempt at a planet, is also left round the sun (the zone of asteroids).

Such, crudely and baldly, is the famous nebular hypothesis of Laplace. It was first stated, as has been said above, by the philosopher Kant, but it was elaborated into much fuller detail by the greatest of French mathematicians and astronomers.

The contracting masses will condense and generate great quantities of heat by their own shrinkage; they will at a certain stage condense to liquid, and after a time will begin to cool and congeal with a superficial crust, which will get thicker and thicker; but for ages they will remain hot, even after they have become thoroughly solid. The small ones will cool fastest; the big ones will retain their heat for an immense time. Bullets cool quickly, cannon-balls take hours or days to cool, planets take millions of years. Our moon may be nearly cold, but the earth is still warm—indeed, very hot inside. Jupiter is believed by some observers still to glow with a dull red heat; and the high temperature of the much larger and still liquid mass of the sun is apparent to everybody. Not till it begins to scum over will it be perceptibly cooler.

Fig. 81.—Saturn.

Many things are now known concerning heat which were not known to Laplace (in the above paragraph they are only hinted at), and these confirm and strengthen the general features of his hypothesis in a striking way; so do the most recent telescopic discoveries. But fresh possibilities have now occurred to us, tidal phenomena are seen to have an influence then wholly unsuspected, and it will be in a modified and amplified form that the philosopher of next century will still hold to the main features of this famous old Nebular Hypothesis respecting the origin of the sun and planets—the Evolution of the solar system.

NOTES TO LECTURE XII

The subject of stellar astronomy was first opened up by Sir William Herschel, the greatest observing astronomer.

Frederick William Herschel was born in Hanover in 1738, and brought up as a musician. Came to England in 1756. First saw a telescope in 1773. Made a great many himself, and began a survey of the heavens. His sister Caroline, born in 1750, came to England in 1772, and became his devoted assistant to the end of his life. Uranus discovered in 1781. Music finally abandoned next year, and the 40-foot telescope begun. Discovered two moons of Saturn and two of Uranus. Reviewed, described, and gauged all the visible heavens. Discovered and catalogued 2,500 nebulæ and 806 double stars. Speculated concerning the Milky Way, the nebulosity of stars, the origin and growth of solar systems. Discovered that the stars were in motion, not fixed, and that the sun as one of them was journeying towards a point in the constellation Hercules. Died in 1822, eighty-four years old. Caroline Herschel discovered eight comets, and lived on to the age of ninety-eight.

LECTURE XII

HERSCHEL AND THE MOTION OF THE FIXED STARS

We may admit, I think, that, with a few notable exceptions, the work of the great men we have been recently considering was rather to complete and round off the work of Newton, than to strike out new and original lines.

This was the whole tendency of eighteenth century astronomy. It appeared to be getting into an adult and uninteresting stage, wherein everything could be calculated and predicted. Labour and ingenuity, and a severe mathematical training, were necessary to work out the remote consequences of known laws, but nothing fresh seemed likely to turn up. Consequently men's minds began turning in other directions, and we find chemistry and optics largely studied by some of the greatest minds, instead of astronomy.

But before the century closed there was destined to arise one remarkable exception—a man who was comparatively ignorant of that which had been done before—a man unversed in mathematics and the intricacies of science, but who possessed such a real and genuine enthusiasm and love of Nature that he overcame the force of adverse circumstances, and entering the territory of astronomy by a by-path, struck out a new line for himself, and infused into the science a healthy spirit of fresh life and activity.

This man was William Herschel.

"The rise of Herschel," says Miss Clerke, "is the one conspicuous anomaly in the otherwise somewhat quiet and prosy eighteenth century. It proved decisive of the course of events in the nineteenth. It was unexplained by anything that had gone before, yet all that came after hinged upon it. It gave a new direction to effort; it lent a fresh impulse to thought. It opened a channel for the widespread public interest which was gathering towards astronomical subjects to flow in."

Herschel was born at Hanover in 1738, the son of an oboe player in a military regiment. The father was a good musician, and a cultivated man. The mother was a German Frau of the period, a strong, active, business-like woman, of strong character and profound ignorance. Herself unable to write, she set her face against learning and all new-fangled notions. The education of the sons she could not altogether control, though she lamented over it, but the education of her two daughters she strictly limited to cooking, sewing, and household management. These, however, she taught them well.

It was a large family, and William was the fourth child. We need only remember the names of his younger brother Alexander, and of his much younger sister Caroline.

They were all very musical—the youngest boy was once raised upon a table to play the violin at a public performance. The girls were forbidden to learn music by their mother, but their father sometimes taught them a little on the sly. Alexander was besides an ingenious mechanician.

At the age of seventeen, William became oboist to the Hanoverian Guards, shortly before the regiment was ordered to England. Two years later he removed himself from the regiment, with the approval of his parents, though probably without the approbation or consent of the commanding officer, by whom such removal would be regarded as simple desertion, which indeed it was; and George III. long afterwards handed him an official pardon for it.

At the age of nineteen, he was thus launched in England with an outfit of some French, Latin, and English, picked up by himself; some skill in playing the hautboy, the violin, and the organ, as taught by his father; and some good linen and clothing, and an immense stock of energy, provided by his mother.

He lived as musical instructor to one or two militia bands in Yorkshire, and for three years we hear no more than this of him. But, at the end of that time, a noted organist, Dr. Miller, of Durham, who had heard his playing, proposed that he should come and live with him and play at concerts, which he was very glad to do. He next obtained the post of organist at Halifax; and some four or five years later he was invited to become organist at the Octagon Chapel in Bath, and soon led the musical life of that then very fashionable place.

About this time he went on a short visit to his family at Hanover, by all of whom he was very much beloved, especially by his young sister Caroline, who always regarded him as specially her own brother. It is rather pitiful, however, to find that her domestic occupations still unfairly repressed and blighted her life. She says:—

"Of the joys and pleasures which all felt at this long-wished-for meeting with my—let me say my dearest—brother, but a small portion could fall to my share; for with my constant attendance at church and school, besides the time I was employed in doing the drudgery of the scullery, it was but seldom I could make one in the group when the family were assembled together."

While at Bath he wrote many musical pieces—glees, anthems, chants, pieces for the harp, and an orchestral symphony. He taught a large number of pupils, and lived a hard and successful life. After fourteen hours or so spent in teaching and playing, he would retire at night to instruct his mind with a study of mathematics, optics, Italian, or Greek, in all of which he managed to make some progress. He also about this time fell in with some book on astronomy.

In 1763 his father was struck with paralysis, and two years later he died.

William then proposed that Alexander should come over from Hanover and join him at Bath, which was done. Next they wanted to rescue their sister Caroline from her humdrum existence, but this was a more difficult matter. Caroline's journal gives an account of her life at this time that is instructive. Here are a few extracts from it:—

"My father wished to give me something like a polished education, but my mother was particularly determined that it should be a rough, but at the same time a useful one; and nothing further she thought was necessary but to send me two or three months to a sempstress to be taught to make household linen....

"My mother would not consent to my being taught French, ... so all my father could do for me was to indulge me (and please himself) sometimes with a short lesson on the violin, when my mother was either in good humour or out of the way.... She had cause for wishing me not to know more than was necessary for being useful in the family; for it was her certain belief that my brother William would have returned to his country, and my eldest brother not have looked so high, if they had had a little less learning."

However, seven years after the death of their father, William went over to Germany and returned to England in triumph, bringing Caroline with him: she being then twenty-two.

So now began a busy life in Bath. For Caroline the work must have been tremendous. For, besides having to learn singing, she had to learn English. She had, moreover, to keep accounts and do the marketing.

When the season at Bath was over, she hoped to get rather more of her brother William's society; but he was deep in optics and astronomy, used to sleep with the books under his pillow, read them during meals, and scarcely ever thought of anything else.

He was determined to see for himself all the astronomical wonders; and there being a small Gregorian reflector in one of the shops, he hired it. But he was not satisfied with this, and contemplated making a telescope 20 feet long. He wrote to opticians inquiring the price of a mirror suitable, but found there were none so large, and that even the smaller ones were beyond his means. Nothing daunted, he determined to make some for himself. Alexander entered into his plans: tools, hones, polishers, and all sorts of rubbish were imported into the house, to the sister's dismay, who says:—

Fig. 82.—Principle of Newtonian reflector.

"And then, to my sorrow, I saw almost every room turned into a workshop. A cabinet-maker making a tube and stands of all descriptions in a handsomely furnished drawing-room; Alex. putting up a huge turning-machine (which he had brought in the autumn from Bristol, where he used to spend the summer) in a bed-room, for turning patterns, grinding glasses, and turning eye-pieces, &c. At the same time music durst not lie entirely dormant during the summer, and my brother had frequent rehearsals at home."

Finally, in 1774, at the age of thirty-six, he had made himself a 5½-foot telescope, and began to view the heavens. So attached was he to the instrument that he would run from the concert-room between the parts, and take a look at the stars.

He soon began another telescope, and then another. He must have made some dozen different telescopes, always trying to get them bigger and bigger; at last he got a 7-foot and then a 10-foot instrument, and began a systematic survey of the heavens; he also began to communicate his results to the Royal Society.

He now took a larger house, with more room for workshops, and a grass plot for a 20-foot telescope, and still he went on grinding mirrors—literally hundreds of them.

I read another extract from the diary of his sister, who waited on him and obeyed him like a spaniel:—

"My time was taken up with copying music and practising, besides attendance on my brother when polishing, since by way of keeping him alive I was constantly obliged to feed him by putting the victuals by bits into his mouth. This was once the case when, in order to finish a 7-foot mirror, he had not taken his hands from it for sixteen hours together. In general he was never unemployed at meals, but was always at those times contriving or making drawings of whatever came in his mind. Generally I was obliged to read to him whilst he was at the turning-lathe, or polishing mirrors—Don Quixote, Arabian Nights' Entertainments, the novels of Sterne, Fielding, &c.; serving tea and supper without interrupting the work with which he was engaged, ... and sometimes lending a hand. I became, in time, as useful a member of the workshop as a boy might be to his master in the first year of his apprenticeship.... But as I was to take a part the next year in the oratorios, I had, for a whole twelvemonth, two lessons per week from Miss Fleming, the celebrated dancing-mistress, to drill me for a gentlewoman (God knows how she succeeded). So we lived on without interruption. My brother Alex. was absent from Bath for some months every summer, but when at home he took much pleasure in executing some turning or clockmaker's work for his brother."

The music, and the astronomy, and the making of telescopes, all went on together, each at high pressure, and enough done in each to satisfy any ordinary activity. But the Herschels knew no rest. Grinding mirrors by day, concerts and oratorios in the evening, star-gazing at night. It is strange his health could stand it.

The star-gazing, moreover, was no dilettante work; it was based on a serious system—a well thought out plan of observation. It was nothing less than this—to pass the whole heavens steadily and in order through the telescope, noting and describing and recording every object that should be visible, whether previously known or unknown. The operation is called sweeping; but it is not a rapid passage from one object to another, as the term might suggest; it is a most tedious business, and consists in following with the telescope a certain field of view for some minutes, so as to be sure that nothing is missed, then shifting it to the next overlapping field, and watching again. And whatever object appears must be scrutinized anxiously to see what there is peculiar about it. If a star, it may be double, or it may be coloured, or it may be nebulous; or again it may be variable, and so its brightness must be estimated in order to compare with a subsequent observation.

Four distinct times in his life did Herschel thus pass the whole visible heavens under review; and each survey occupied him several years. He discovered double stars, variable stars, nebulæ, and comets; and Mr. William Herschel, of Bath, the amateur astronomer, was gradually emerging from his obscurity, and becoming a known man.

Tuesday, the 13th of March, 1781, is a date memorable in the annals of astronomy. "On this night," he writes to the Royal Society, "in examining the small stars near η Geminorum, I perceived one visibly larger than the rest. Struck with its uncommon appearance, I compared it to η Geminorum and another star, and finding it so much larger than either, I suspected it to be a comet."

The "comet" was immediately observed by professional astronomers, and its orbit was computed by some of them. It was thus found to move in nearly a circle instead of an elongated ellipse, and to be nearly twice as far from the sun as Saturn. It was no comet, it was a new planet; more than 100 times as big as the earth, and nearly twice as far away as Saturn. It was presently christened "Uranus."

This was a most striking discovery, and the news sped over Europe. To understand the interest it excited we must remember that such a discovery was unique. Since the most ancient times of which men had any knowledge, the planets Mercury, Venus, Mars, Jupiter, Saturn, had been known, and there had been no addition to their number. Galileo and others had discovered satellites indeed, but a new primary planet was an entire and utterly unsuspected novelty.

One of the most immediate consequences of the event was the discovery of Herschel himself. The Royal Society made him a Fellow the same year. The University of Oxford dubbed him a doctor; and the King sent for him to bring his telescope and show it at Court. So to London and Windsor he went, taking with him his best telescope. Maskelyne, the then Astronomer-Royal, compared it with the National one at Greenwich, and found Herschel's home-made instrument far the better of the two. He had a stand made after Herschel's pattern, but was so disgusted with his own instrument now that he scarcely thought it worthy of the stand when it was made. At Windsor, George III. was very civil, and Mr. Herschel was in great request to show the ladies of the Court Saturn and other objects of interest. Mr. Herschel exhibited a piece of worldly wisdom under these circumstances, that recalls faintly the behaviour of Tycho Brahé under similar circumstances. The evening when the exhibition was to take place threatened to become cloudy and wet, so Herschel rigged up an artificial Saturn, constructed of card and tissue paper, with a lamp behind it, in the distant wall of a garden; and, when the time came, his new titled friends were regaled with a view of this imitation Saturn through the telescope—the real one not being visible. They went away much pleased.

He stayed hovering between Windsor and Greenwich, and uncertain what was to be the outcome of all this regal patronizing. He writes to his sister that he would much rather be back grinding mirrors at Bath. And she writes begging him to come, for his musical pupils were getting impatient. They had to get the better of their impatience, however, for the King ultimately appointed him astronomer or rather telescope-maker to himself, and so Caroline and the whole household were sent for, and established in a small house at Datchet.

From being a star-gazing musician, Herschel thus became a practical astronomer. Henceforth he lived in his observatory; only on wet and moonlight nights could he be torn away from it. The day-time he devoted to making his long-contemplated 20-foot telescope.

Not yet, however, were all their difficulties removed. The house at Datchet was a tumble-down barn of a place, chosen rather as a workshop and observatory than as a dwelling-house. And the salary allowed him by George III. was scarcely a princely one. It was, as a matter of fact, £200 a year. The idea was that he would earn his living by making telescopes, and so indeed he did. He made altogether some hundreds. Among others, four for the King. But this eternal making of telescopes for other people to use or play with was a weariness to the flesh. What he wanted was to observe, observe, observe.

Sir William Watson, an old friend of his, and of some influence at Court, expressed his mind pretty plainly concerning Herschel's position; and as soon as the King got to understand that there was anything the matter, he immediately offered £2,000 for a gigantic telescope to be made for Herschel's own use. Nothing better did he want in life. The whole army of carpenters and craftsmen resident in Datchet were pressed into the service. Furnaces for the speculum metal were built, stands erected, and the 40-foot telescope fairly begun. It cost £4,000 before it was finished, but the King paid the whole.

Fig. 83.—Herschel's 40-foot telescope.

With it he discovered two more satellites to Saturn (five hitherto had been known), and two moons to his own planet Uranus. These two are now known as Oberon and Titania. They were not seen again till some forty years after, when his son, Sir John Herschel, reobserved them. And in 1847, Mr. Lassell, at his house, "Starfield," near Liverpool, discovered two more, called Ariel and Umbriel, making the number four, as now known. Mr. Lassell also discovered, with a telescope of his own making, an eighth satellite of Saturn—Hyperion—and a satellite to Neptune.

A letter from a foreign astronomer about this period describes Herschel and his sister's method of work:—

"I spent the night of the 6th of January at Herschel's, in Datchet, near Windsor, and had the good luck to hit on a fine evening. He has his 20-foot Newtonian telescope in the open air, and mounted in his garden very simply and conveniently. It is moved by an assistant, who stands below it.... Near the instrument is a clock regulated to sidereal time.... In the room near it sits Herschel's sister, and she has Flamsteed's atlas open before her. As he gives her the word, she writes down the declination and right ascension, and the other circumstances of the observation. In this way Herschel examines the whole sky without omitting the least part. He commonly observes with a magnifying power of one hundred and fifty, and is sure that after four or five years he will have passed in review every object above our horizon. He showed me the book in which his observations up to this time are written, and I am astonished at the great number of them. Each sweep covers 2° 15' in declination, and he lets each star pass at least three times through the field of his telescope, so that it is impossible that anything can escape him. He has already found about 900 double stars, and almost as many nebulæ. I went to bed about one o'clock, and up to that time he had found that night four or five new nebulæ. The thermometer in the garden stood at 13° Fahrenheit; but, in spite of this, Herschel observes the whole night through, except that he stops every three or four hours and goes into the room for a few moments. For some years Herschel has observed the heavens every hour when the weather is clear, and this always in the open air, because he says that the telescope only performs well when it is at the same temperature as the air. He protects himself against the weather by putting on more clothing. He has an excellent constitution, and thinks about nothing else in the world but the celestial bodies. He has promised me in the most cordial way, entirely in the service of astronomy, and without thinking of his own interest, to see to the telescopes I have ordered for European observatories, and he will himself attend to the preparation of the mirrors."

Fig. 84.—William Herschel. From an Original Picture in the Possession of Wm. Watson, M.D., F.R.S. Painted by Abbott. Engraved by Ryder.

In 1783, Herschel married an estimable lady who sympathized with his pursuits. She was the only daughter of a City magnate, so his pecuniary difficulties, such as they were (they were never very troublesome to him), came to an end. They moved now into a more commodious house at Slough. Their one son, afterwards the famous Sir John Herschel, was born some nine years later. But the marriage was rather a blow to his devoted sister: henceforth she lived in lodgings, and went over at night-time to help him observe. For it must be remarked that this family literally turned night into day. Whatever sleep they got was in the day-time. Every fine night without exception was spent in observing: and the quite incredible fierceness of the pursuit is illustrated, as strongly as it can be, by the following sentence out of Caroline's diary, at the time of the move from Datchet to Slough: "The last night at Datchet was spent in sweeping till daylight, and by the next evening the telescope stood ready for observation at Slough."

Caroline was now often allowed to sweep with a small telescope on her own account. In this way she picked up a good many nebulæ in the course of her life, and eight comets, four of which were quite new, and one of which, known since as Encke's comet, has become very famous.

The work they got through between them is something astonishing. He made with his own hands 430 parabolic mirrors for reflecting telescopes, besides a great number of complete instruments. He was forty-two when he began contributing to the Royal Society; yet before he died he had sent them sixty-nine long and elaborate treatises. One of these memoirs is a catalogue of 1000 nebulæ. Fifteen years after he sends in another 1000; and some years later another 500. He also discovered 806 double stars, which he proved were really corrected from the fact that they revolved round each other (p. 309). He lived to see some of them perform half a revolution. For him the stars were not fixed: they moved slowly among themselves. He detected their proper motions. He passed the whole northern firmament in review four distinct times; counted the stars in 3,400 gauge-fields, and estimated the brightness of hundreds of stars. He also measured as accurately as he could their proper motions, devising for this purpose the method which still to this day remains in use.

And what is the outcome of it all? It is not Uranus, nor the satellites, nor even the double stars and the nebulæ considered as mere objects: it is the beginning of a science of the stars.

Fig. 85.—Caroline Herschel. From a Drawing from Life, by George Müller, 1847.

Hitherto the stars had only been observed for nautical and practical purposes. Their times of rising and southing and setting had been noted; they had been treated as a clock or piece of dead mechanism, and as fixed points of reference. All the energies of astronomers had gone out towards the solar system. It was the planets that had been observed. Tycho had observed and tabulated their positions. Kepler had found out some laws of their motion. Galileo had discovered their peculiarities and attendants. Newton and Laplace had perceived every detail of their laws.

But for the stars—the old Ptolemaic system might still have been true. They might still be mere dots in a vast crystalline sphere, all set at about one distance, and subservient to the uses of the earth.

Herschel changed all this. Instead of sameness, he found variety; instead of uniformity of distance, limitless and utterly limitless fields and boundless distances; instead of rest and quiescence, motion and activity; instead of stagnation, life.

Fig. 86.—The double-double star ε Lyræ as seen under three different powers.

Yes, that is what Herschel discovered—the life and activity of the whole visible universe. No longer was our little solar system to be the one object of regard, no longer were its phenomena to be alone interesting to man. With Herschel every star was a solar system. And more than that: he found suns revolving round suns, at distances such as the mind reels at, still obeying the same law of gravitation as pulls an apple from a tree. He tried hard to estimate the distance of the stars from the earth, but there he failed: it was too hopeless a problem. It was solved some time after his death by Bessel, and the distances of many stars are now known but these distances are awful and unspeakable. Our distance from the sun shrinks up into a mere speck—the whole solar system into a mere unit of measurement, to be repeated hundreds of thousands of times before we reach the stars.

Yet their motion is visible—yes, to very accurate measurement quite plain. One star, known as 61 Cygni, was then and is now rushing along at the rate of 100 miles every second. Not that you must imagine that this makes any obvious and apparent change in its position. No, for all ordinary and practical purposes they are still fixed stars; thousands of years will show us no obvious change; "Adam" saw precisely the same constellations as we do: it is only by refined micrometric measurement with high magnifying power that their flight can be detected.