# A Short History of Astronomy (1898)/Chapter 13

CHAPTER XIII.
THE NINETEENTH CENTURY.
"The greater the sphere of our knowledge, the larger is the surface of its contact with the infinity of our ignorance."
272. The last three chapters have contained some account of progress made in three branches of astronomy which, though they overlap and exercise an important influence on one another, are to a large extent studied by different men and by different methods, and have different aims. The difference is perhaps best realised by thinking of the work of a great master in each department, Bradley, Laplace, and Herschel. So great is the difference that Delambre in his standard history of astronomy all but ignores the work of the great school of mathematical astronomers who were his contemporaries and immediate predecessors, not from any want of appreciation of their importance, but because he regards their work as belonging rather to mathematics than to astronomy; while Bessel (§ 277), in saying that the function of astronomy is "to assign the places on the sky where sun, moon, planets, comets, and stars have been, are, and will be," excludes from its scope nearly everything towards which Herschel's energies were directed.
Current modern practice is, however, more liberal in its use of language than either Delambre or Bessel, and finds it convenient to recognise all three of the subjects or groups of subjects referred to as integral parts of one science.
The mutual relation of gravitational astronomy and what has been for convenience called observational astronomy has been already referred to (chapter x., § 196). It should, however, be noticed that the latter term has in this book hitherto been used chiefly for only one part of the ​astronomical work which concerns itself primarily with observation. Observing played at least as large a part in Herschel's work as in Bradley's, but the aims of the two men were in many ways different. Bradley was interested chiefly in ascertaining as accurately as possible the apparent positions of the fixed stars on the celestial sphere, and the positions and motions of the bodies of the solar system, the former undertaking being in great part subsidiary to the latter. Herschel, on the other hand, though certain of his researches, e.g. into the parallax of the fixed stars and into the motions of the satellites of Uranus, were precisely like some of Bradley's, was far more concerned with questions of the appearances, mutual relations, and structure of the celestial bodies in themselves. This latter branch of astronomy may conveniently be called descriptive astronomy, though the name is not altogether appropriate to inquiries into the physical structure and chemical constitution of celestial bodies which are often put under this head, and which play an important part in the astronomy of the present day.
273. Gravitational astronomy and exact observational astronomy have made steady progress during the nineteenth century, but neither has been revolutionised, and the advances made have been to a great extent of such a nature as to be barely intelligible, still less interesting, to those who are not experts. The account of them to be given in this chapter must therefore necessarily be of the slightest character, and deal either with general tendencies or with isolated results of a less technical character than the rest.
Descriptive astronomy, on the other hand, which can be regarded as being almost as much the creation of Herschel as gravitational astronomy is of Newton, has not only been greatly developed on the lines laid down by its founder, but has received—chiefly through the invention of spectrum analysis (§ 299)—extensions into regions not only unthought of but barely imaginable a century ago. Most of the results of descriptive astronomy—unlike those of the older branches of the subject—are readily intelligible and fairly interesting to those who have but little knowledge of the subject; in particular they are as yet to a considerable extent independent of the mathematical ideas and language ​which dominate so much of astronomy and render it unattractive or inaccessible to many. Moreover, not only can descriptive astronomy be appreciated and studied, but its progress can materially be assisted, by observers who have neither knowledge of higher mathematics nor any elaborate instrumental equipment.
Accordingly, while the successors of Laplace and Bradley have been for the most part astronomers by profession, attached to public observatories or to universities, an immense mass of valuable descriptive work has been done by amateurs who, like Herschel in the earlier part of his career, have had to devote a large part of their energies to professional work of other kinds, and who, though in some cases provided with the best of instruments, have in many others been furnished with only a slender instrumental outfit. For these and other reasons one of the most notable features of nineteenth century astronomy has been a great development, particularly in this country and in the United States, of general interest in the subject, and the establishment of a large number of private observatories devoted almost entirely to the study of special branches of descriptive astronomy. The nineteenth century has accordingly witnessed the acquisition of an unprecedented amount of detailed astronomical knowledge. But the wealth of material thus accumulated has outrun our powers of interpretation, and in a number of cases our knowledge of some particular department of descriptive astronomy consists, on the one hand of an immense series of careful observations, and on the other of one or more highly speculative theories, seldom capable of explaining more than a small portion of the observed facts.
In dealing with the progress of modern descriptive astronomy the proverbial difficulty of seeing the wood on account of the trees is therefore unusually great. To give an account within the limits of a single chapter of even the most important facts added to our knowledge would be a hopeless endeavour; fortunately it would also be superfluous, as they are to be found in many easily accessible textbooks on astronomy, or in treatises on special parts of the subject. All that can be attempted is to give some account of the chief lines on which progress has been made, and to ​indicate some general conclusions which seem to be established on a tolerably secure basis.
274. The progress of exact observation has of course been based very largely on instrumental advances. Not only have great improvements been made in the extremely delicate work of making large lenses, but the graduated circles and other parts of the mounting of a telescope upon which accuracy of measurement depends can also be constructed with far greater exactitude and certainty than at the beginning of the century. New methods of mounting telescopes and of making and recording observations have also been introduced, all contributing to greater accuracy. For certain special problems photography is found to present great advantages as compared with eye-observations, though its most important applications have so far been to descriptive astronomy.
275. The necessity for making allowance for various known sources of errors in observation, and for diminishing as far as possible the effect of errors due to unknown causes, had been recognised even by Tycho Brahe (chapter v., § 110), and had played an important part in the work of Flamsteed and Bradley (chapter x., §§ 198, 218). Some further important steps in this direction were taken in the earlier part of this century. The method of least squares, established independently by two great mathematicians, Adrien Marie Legendre (1752–1833) of Paris and Carl Friedrich Gauss (1777–1855) of Göttingen, was a systematic method of combining observations, which gave slightly different results, in such a way as to be as near the truth as possible. Any ordinary physical measurement, e.g. of a length, however carefully executed, is necessarily imperfect; if the same measurement is made several times, even under almost identical conditions, the results will in general differ slightly; and the question arises of combining these so as to get the most satisfactory result. The common practice in this simple case has long been to take the arithmetical mean or average of the different results. But astronomers have constantly ​to deal with more complicated cases in which two or more unknown quantities have to be determined from observations of different quantities, as, for example, when the elements of the orbit of a planet (chapter xi., § 236) have to be found from observations of the planet's position at different times. The method of least squares gives a rule for dealing with such cases, which was a generalisation of the ordinary, rule of averages for the case of a single unknown quantity; and it was elaborated in such a way as to provide for combining observations of different value, such as observations taken by observers of unequal skill or with different instruments, or under more or less favourable conditions as to weather, etc. It also gives a simple means of testing, by means of their mutual consistency, the value of a series of observations, and comparing their probable accuracy with that of some other series executed under different conditions. The method of least squares and the special case of the "average" can be deduced from a certain assumption as to the general character of the causes which produce the error in question; but the assumption itself cannot be justified a priori; on the other hand, the satisfactory results obtained from the application of the rule to a great variety of problems in astronomy and in physics has shewn that in a large number of cases unknown causes of error must be approximately of the type considered. The method is therefore very widely used in astronomy and physics wherever it is worth while to take trouble to secure the utmost attainable accuracy.
276. Legendre's other contributions to science were almost entirely to branches of mathematics scarcely affecting astronomy. Gauss on the other hand, was for nearly half a century head of the observatory of Göttingen, and though his most brilliant and important work was in pure mathematics, while he carried out some researches of first-rate importance in magnetism and other branches of physics, he also made some further contributions of importance to astronomy. These were for the most part processes of calculation of various kinds required for utilising astronomical observations, the best known being a method of calculating the orbit of a planet from three complete ​observations of its position, which was published in his, Theoria Motus (1809). As we have seen (chapter xi., § 236), the complete determination of a planet's orbit depends on six independent elements: any complete observation of the planet's position in the sky, at any time, gives two quantities, e.g. the right ascension and declination (chapter ii., § 33); hence three complete observations give six equations and are theoretically adequate to determine the elements of the orbit; but it had not hitherto been found necessary to deal with the problem in this form. The orbits of all the planets but Uranus had been worked out gradually by the use of a series of observations extending over centuries; and it was feasible to use observations taken at particular times so chosen that certain elements could be determined without any accurate knowledge of the others; even Uranus had been under observation for a considerable time before its path was determined with anything like accuracy; and in the case of comets not only was a considerable series of observations generally available, but the problem was simplified by the fact that the orbit could be taken to be nearly or quite a parabola instead of an ellipse (chapter ix., § 190). The discovery of the new planet Ceres on January 1st, 1801 (§ 294), and its loss when it had only been observed for a few weeks, presented virtually a new problem in the calculation of an orbit. Gauss applied his new methods—including that of least squares—to the observations available, and with complete success, the planet being rediscovered at the end of the year nearly in the position indicated by his calculations.
277. The theory of the "reduction" of observations (chapter x., § 218) was first systematised and very much improved by Friedrich Wilhelm Bessel (1784-1846), who was for more than thirty years the director of the new Prussian observatory at Königsberg. His first great work was the reduction and publication of Bradley's Greenwich observations (chapter x., § 218). This undertaking involved an elaborate study of such disturbing causes as precession, aberration, and refraction, as well as of the errors of Bradley's instruments. Allowance was made for these on a uniform and systematic plan, and the result was the publication in 1818, ​under the title Fundamenta Astronomiae, of a catalogue of the places of 3,222 stars as they were in 1755. A special problem dealt with in the course of the work was that of refraction. Although the complete theoretical solution was then as now unattainable, Bessel succeeded in constructing a table of refractions which agreed very closely with observation and was presented in such a form that the necessary correction for a star in almost any position could be obtained with very little trouble. His general methods of reduction—published finally in his Tabulae Regiomontanae (1830)—also had the great advantage of arranging the necessary calculations in such a way that they could be performed with very little labour and by an almost mechanical process, such as could easily be carried out by a moderately skilled assistant. In addition to editing Bradley's observations, Bessel undertook a fresh series of observations of his own, executed between the years 1821 and 1833, upon which were based two new catalogues, containing about 62,000 stars, which appeared after his death.
278. The most memorable of Bessel's special pieces of
work was the first definite detection of the parallax of a fixed star. He abandoned the test of brightness as an ​indication of nearness, and selected a star (61 Cygni) which was barely visible to the naked eye but was remarkable for its large proper motion (about 5" per annum); evidently if a star is moving at an assigned rate (in miles per hour) through space, the nearer to the observer it is the more rapid does its motion appear to be, so that apparent rapidity of motion,
Fig. 86—The parallax of 61 Cygni.
like brightness, is a probable but by no means infallible indication of nearness. A modification of Galilei's differential method (chapter vi., § 129, and chapter xii., § 263) being adopted, the angular distance of 61 Cygni from two neighbouring stars, the faintness and immovability of which suggested their great distance in space, was measured at frequent intervals during a year. From the changes in these distances σ a, σ b (in fig. 85), the size of the small ellipse described by σ could be calculated. The result, announced at the end of 1838, was that the star had an annual parallax of about 1/3" (chapter viii., § 161), i.e. that the star was at such distance that the greatest angular distance of the earth from the sun viewed from the star (the angle s σ e in fig. 86, where s is the sun and e the earth) was this insignificant angle. The result was confirmed, with slight alterations, by a fresh investigation of Bessel's in 1839-40, but later work seems to shew that the parallax is a little less than 1/2". With this latter estimate, the apparent size of the earth's path round the sun as seen from the star is the same as that of a halfpenny ​at a distance of rather more than three miles. In other words, the distance of the star is about 400,000 times the distance of the sun, which is itself about 93,000,000 miles. A mile is evidently a very small unit by which to measure such a vast distance; and the practice of expressing such distances by means of the time required by light to perform the journey is often convenient. Travelling at the rate of 186,000 miles per second (§ 283), light takes rather more than six years to reach us from 61 Cygni.
279. Bessel's solution of the great problem which had baffled astronomers ever since the time of Coppernicus was immediately followed by two others. Early in 1839 Thomas Henderson (1798–1844) announced a parallax of nearly 1" for the bright star α Centauri which he had observed at the Cape, and in the following year Friedrich Georg Wilhelm Struve (1793–1864) obtained from observations made at Pulkowa a parallax of 1/4" for Vega; later work has reduced these numbers to 3/4" and 1/10" respectively.
A number of other parallax determinations have subsequently been made. An interesting variation in method was made by the late Professor Charles Pritchard (1808–1893) of Oxford by photographing the star to be examined and its companions, and subsequently measuring the distances on the photograph, instead of measuring the angular distances directly with a micrometer.
At the present time some 50 stars have been ascertained with some reasonable degree of probability to have measurable, if rather uncertain, parallaxes; α Centauri still holds its own as the nearest star, the light-journey from it being about four years. A considerable number of other stars have been examined with negative or highly uncertain results, indicating that their parallaxes are too small to be measured with our present means, and that their distances are correspondingly great.
280. A number of star catalogues and star maps—too numerous to mention separately—have been constructed during this century, marking steady progress in our knowledge of the position of the stars, and providing fresh materials for ascertaining, by comparison of the state of the sky at different epochs, such quantities as the proper motions of the stars and the amount of precession. Among ​the most important is the great catalogue of 324,198 stars in the northern hemisphere known as the Bonn Durchmusterung, published in 1859-62 by Bessel's pupil Friedrich Wilhelm August Argelander ( 1799–1875); this was extended (1875–85) so as to include 133,659 stars in a portion of the southern hemisphere by Eduard Schönfeld (1828–1891); and more recently Dr. Gill has executed at the Cape photographic observations of the remainder of the southern hemisphere, the reduction to the form of a catalogue (the first instalment of which was published in 1896) having been performed by Professor Kapteyn of Groningen. The star places determined in these catalogues do not profess to be the most accurate attainable, and for many purposes it is important to know with the utmost accuracy the positions of a smaller number of stars. The greatest undertaking of this kind, set on foot by the German Astronomical Society in 1867, aims at the construction, by the co-operation of a number of observatories, of catalogues of about 130,000 of the stars contained in the "approximate" catalogues of Argelander and Schönfeld; nearly half of the work has now been published.
The greatest scheme for a survey of the sky yet attempted is the photographic chart, together with a less extensive catalogue to be based on it, the construction of which was decided on at an international congress held at Paris in 1887. The whole sky has been divided between 18 observatories in all parts of the world, from Helsingfors in the north to Melbourne in the south, and each of these is now taking photographs with virtually identical instruments. It is estimated that the complete chart, which is intended to include stars of the 14th magnitude, will contain about 20,000,000 stars, 2,000,000 of which will be catalogued also.
281. One other great problem—that of the distance of the sun—may conveniently be discussed under the head of observational astronomy.
The transits of Venus (chapter x., §§ 202, 227) which occurred in 1874 and 1882 were both extensively observed, ​the old methods of time-observation being supplemented by photography and by direct micrometric measurements of the positions of Venus while transiting.
The method of finding the distance of the sun by means of observation of Mars in opposition (chapter viii., § 161) has been employed on several occasions with considerable success, notably by Dr. Gill at Ascension in 1877. A method originally used by Flamsteed, but revived in 1857 by Sir George Biddell Airy (1801–1892), the late Astronomer Royal, was adopted on this occasion. For the determination of the parallax of a planet observations have to be made from two different positions at a known distance apart; commonly these are taken to be at two different observatories, as far as possible removed from one another in latitude. Airy pointed out that the same object could be attained if only one observatory were used, but observations taken at an interval of some hours, as the rotation of the earth on its axis would in that time produce a known displacement of the observer's position and so provide the necessary base line. The apparent shift of the planet's position could be most easily ascertained by measuring (with the micrometer) its distances from neighbouring fixed stars. This method (known as the diurnal method) has the great advantage, among others, of being simple in application, a single observer and instrument being all that is needed.
The diurnal method has also been applied with great success to certain of the minor planets (§ 294). Revolving as they do between Mars and Jupiter, they are all farther off from us than the former; but there is the compensating advantage that as a minor planet, unlike Mars, is, as a rule, too small to shew any appreciable disc, its angular distance from a neighbouring star is more easily measured. The employment of the minor planets in this way was first suggested by Professor Galle of Berlin in 1872, and recent observations of the minor planets Victoria, Sappho, and Iris in 1888–89, made at a number of observatories under the general direction of Dr. Gill, have led to some of the most satisfactory determinations of the sun's distance.
282. It was known to the mathematical astronomers of the 18th century that the distance of the sun could be obtained from a knowledge of various perturbations of ​members of the solar system; and Laplace had deduced a value of the solar parallax from lunar theory. Improvements in gravitational astronomy and in observation of the planets and moon during the present century have added considerably to the value of these methods. A certain irregularity in the moon's motion known as the parallactic inequality, and another in the motion of the sun, called the lunar equation, due to the displacement of the earth by the attraction of the moon, alike depend on the ratio of the distances of the sun and moon from the earth; if the amount of either of these inequalities can be observed, the distance of the sun can therefore be deduced, that of the moon being known with great accuracy. It was by a virtual application of the first of these methods that Hansen (§ 286) in 1854, in the course of an elaborate investigation of the lunar theory, ascertained that the current value of the sun's distance was decidedly too large, and Leverrier (§ 288) confirmed the correction by the second method in 1858.
Again, certain changes in the orbits of our two neighbours, Venus and Mars, are known to depend upon the ratio of the masses of the sun and earth, and can hence be connected, by gravitational principles, with the quantity sought. Leverrier pointed out in 1861 that the motions of Venus and of Mars, like that of the moon, were inconsistent with the received estimate of the sun's distance, and he subsequently worked out the method more completely and deduced (1872) values of the parallax. The displacements to be observed are very minute, and their accurate determination is by no means easy, but they are both secular (chapter xi., § 242), so that in the course of time they will be capable of very exact measurement. Leverrier's method, which is even now a valuable one, must therefore almost inevitably outstrip all the others which are at present known; it is difficult to imagine, for example, that the transits of Venus due in 2004 and 2012 will have any value for the purpose of the determination of the sun's distance.
283. One other method, in two slightly different forms, has become available during this century. The displacement of a star by aberration (chapter x., § 210) depends ​upon the ratio of the velocity of light to that of the earth in its orbit round the sun; and observations of Jupiter's satellites after the manner of Roemer (chapter viii., § 162) give the light-equation, or time occupied by light in travelling from the sun to the earth. Either of these astronomical quantities—of which aberration is the more accurately known—can be used to determine the velocity of light when the dimensions of the solar system are known, or vice versa. No independent method of determining the velocity of light was known until 1849, when Hippolyte Fizeau (1819–1896) invented and successfully carried out a laboratory method.
New methods have been devised since, and three comparatively recent series of experiments, by M. Cornu in France (1874 and 1876) and by Dr. Michelson (1879) and Professor Newcomb (1880–82) in the United States, agreeing closely with one another, combine to fix the velocity of light at very nearly 186,300 miles (299,800 kilometres) per second; the solar parallax resulting from this by means of aberration is very nearly 8"⋅8.
284. Encke's value of the sun's parallax, 8"⋅571, deduced from the transits of Venus (chapter x., § 227) in 1761 and 1769, and published in 1835, corresponding to a distance of about 95,000,000 miles, was generally accepted till past the middle of the century. Then the gravitational methods of Hansen and Leverrier, the earlier determinations of the velocity of light, and the observations made at the opposition of Mars in 1862, all pointed to a considerably larger value of the parallax; a fresh examination of the 18th century observations shewed that larger values than Encke's could easily be deduced from them; and for some time—from about 1860 onwards—a parallax of nearly 8"⋅95, corresponding to a distance of rather more than 91,000,000 miles, was in common use. Various small errors in the new methods were, however, detected, and the most probable value of the parallax has again increased. Three of the most reliable methods, the diurnal method as applied to Mars in 1877, the same applied to the minor planets in 1888–89, and ​aberration, unite in giving values not differing from 8"⋅80 by more than two or three hundredths of a second. The results of the last transits of Venus, the publication and discussion of which have been spread over a good many years, point to a somewhat larger value of the parallax. Most astronomers appear to agree that a parallax of 8"⋅8, corresponding to a distance of rather less than 93,000,000 miles, represents fairly the available data.
285. The minute accuracy of modern observations is well illustrated by the recent discovery of a variation in the latitude of several observatories. Observations taken at Berlin in 1884–85 indicated a minute variation in the latitude; special series of observations to verify this were set on foot in several European observatories, and subsequently at Honolulu and at Cordoba. A periodic alteration in latitude amounting to about 1/2" emerged as the result. Latitude being defined (chapter x., § 221) as the angle which the vertical at any place makes with the equator, which is the same as the elevation of the pole above the horizon, is consequently altered by any change in the equator, and therefore by an alteration in the position of the earth's poles or the ends of the axis about which it rotates.
Dr. S. C. Chandler succeeded (1891 and subsequently) in shewing that the observations in question could be in great part explained by supposing the earth's axis to undergo a minute change of position in such a way that either pole of the earth describes a circuit round its mean position in about 427 days, never deviating more than some 30 feet from it. It is well known from dynamical theory that a rotating body such as the earth can be displaced in this manner, but that if the earth were perfectly rigid the period should be 306 days instead of 427. The discrepancy between the two numbers has been ingeniously used as a test of the extent to which the earth is capable of yielding—like an elastic solid—to the various forces which tend to strain it.
286. All the great problems of gravitational astronomy have been rediscussed since Laplace's time, and further steps taken towards their solution.
Laplace's treatment of the lunar theory was first developed by Marie Charles Theodore Damoiseau (1768-1846), whose ​Tables de la Lune (1824 and 1828) were for some time in general use.
Some special problems of both lunar and planetary theory were dealt with by Siméon Denis Poisson (1781–1840), who is, however, better known as a writer on other branches of mathematical physics than as an astronomer. A very elaborate and detailed theory of the moon, investigated by the general methods of Laplace, was published by Giovanni Antonio Amadeo Plana (1781–1869) in 1832, but unaccompanied by tables. A general treatment of both lunar and planetary theories, the most complete that had appeared up to that time, by Philippe Gustave Doulcet de Pontécoulant (1795–1874), appeared in 1846, with the title Théorie Analytique du Système du Monde; and an incomplete lunar theory similar to his was published by John William Lubbock (1803–1865) in 1830–34.
A great advance in lunar theory was made by Peter Andreas Hansen (1795–1874) of Gotha, who published in 1838 and 1862–64 the treatises commonly known respectively as the Fundamenta and the Darlegung, and produced in 1857 tables of the moon's motion of such accuracy that the discrepancies between the tables and observations in the century 1750–1850 were never greater than 1" or 2". These tables were at once used for the calculation of the Nautical Almanac and other periodicals of the same kind, and with some modifications have remained in use up to the present day.
A completely new lunar theory—of great mathematical interest and of equal complexity—was published by Charles Delaunay (1816–1872) in 1860 and 1867. Unfortunately the author died before he was able to work out the corresponding tables.
Professor Newcomb of Washington (§ 283) has rendered valuable services to lunar theory—as to other branches of astronomy—by a number of delicate and intricate calculations, the best known being his comparison of Hansen's tables with observation and consequent corrections of the tables.
​New methods of dealing with lunar theory were devised by the late Professor John Couch Adams of Cambridge (1819–1892), and similar methods have been developed by Dr. G. W. Hill of Washington; so far they have not been worked out in detail in such a way as to be available for the calculation of tables, and their interest seems to be at present mathematical rather than practical; but the necessary detailed work is now in progress, and these and allied methods may be expected to lead to a considerable diminution of the present excessive intricacy of lunar theory.
287. One special point in lunar theory may be worth mentioning. The secular acceleration of the moon's mean motion which had perplexed astronomers since its first discovery by Halley (chapter x., § 201) had, as we have seen (chapter xi., § 240), received an explanation in 1787 at the hands of Laplace. Adams, on going through the calculation, found that some quantities omitted by Laplace as unimportant had in reality a very sensible effect on the result, so that a certain quantity expressing the rate of increase of the moon's motion came out to be between 5" and 6", instead of being about 10", as Laplace had found and as observation required. The correction was disputed at first by several of the leading experts, but was confirmed independently by Delaunay and is now accepted. The moon appears in consequence to have a certain very minute increase in speed for which the theory of gravitation affords no explanation. An ingenious though by no means certain explanation was suggested by Delaunay in 1865. It had been noticed by Kant that tidal friction—that is, the friction set up between the solid earth and the ocean as the result of the tidal motion of the latter—would have the effect of checking to some extent the rotation of the earth; but as the effect seemed to be excessively minute and incapable of precise calculation it was generally ignored. An attempt to calculate its amount was, however, made in 1853 by William Ferrel, who also pointed out that, as the period of the earth's rotation—the day—is our fundamental unit of time, a reduction of the earth's rate of rotation involves the lengthening of our unit of time, and consequently produces an apparent increase of speed in all other motions ​measured in terms of this unit. Delaunay, working independently, arrived at like conclusions, and shewed that tidal friction might thus be capable of producing just such an alteration in the moon's motion as had to be explained; if this explanation were accepted the observed motion of the moon would give a measure of the effect of tidal friction. The minuteness of the quantities involved is shewn by the fact that an alteration in the earth's rotation equivalent to the lengthening of the day by 1/10 second in 10,000 years is sufficient to explain the acceleration in question. Moreover it is by no means certain that the usual estimate of the amount of this acceleration—based as it is in part on ancient eclipse observations—is correct, and even then a part of it may conceivably be due to some indirect effect of gravitation even more obscure than that detected by Laplace, or to some other cause hitherto unsuspected.
288. Most of the writers on lunar theory already mentioned have also made contributions to various parts of planetary theory, but some of the most important advances in planetary theory made since the death of Laplace have been due to the French mathematician Urbain Jean Joseph Leverrier (1811-1877), whose methods of determining the distance of the sun have been already referred to (§ 282). His first important astronomical paper (1839) was a discussion of the stability (chapter xi., § 245) of the system formed by the sun and the three largest and most distant planets then known, Jupiter, Saturn, and Uranus. Subsequently he worked out afresh the theory of the motion of the sun and of each of the principal planets, and constructed tables of them, which at once superseded earlier ones, and are now used as the basis of the chief planetary calculations in the Nautical Almanac and most other astronomical almanacs. Leverrier failed to obtain a satisfactory agreement between observation and theory in the case of Mercury, a planet which has always given great trouble to astronomers, and was inclined to explain the discrepancies as due to the influence either of a planet revolving between Mercury and the sun or of a number of smaller bodies analogous to the minor planets (§ 294).
Researches of a more abstract character, connecting planetary theory with some of the most recent advances ​in pure mathematics, have been carried out by Hugo Gyldén (1841–1896), while one of the most eminent pure mathematicians of the day, M. Henri Poincaré of Paris, has recently turned his attention to astronomy, and is engaged in investigations which, though they have at present but little bearing on practical astronomy, seem likely to throw important light on some of the general problems of celestial mechanics.
289. One memorable triumph of gravitational astronomy, the discovery of Neptune, has been described so often and so fully elsewhere that a very brief account will suffice here. Soon after the discovery of Uranus (chapter xii., § 253) it was found that the planet had evidently been observed, though not recognised as a planet, as early as 1690, and on several occasions afterwards.
When the first attempts were made to compute its orbit carefully, it was found impossible satisfactorily to reconcile the earlier with the later observations, and in Bouvard's tables (chapter xi., § 247, note) published in 1821 the earlier observations were rejected. But even this drastic measure did not cure the evil; discrepancies between the observed and calculated places soon appeared and increased year by year. Several explanations were proposed, and more than one astronomer threw out the suggestion that the irregularities might be due to the attraction of a hitherto unknown planet. The first serious attempt to deduce from the irregularities in the motion of Uranus the position of this hypothetical body was made by Adams immediately after taking his degree (1843). By October 1845 he had succeeded in constructing an orbit for the new planet, and in assigning for it a position differing (as we now know) by less than 2° (four times the diameter of the full moon) from its actual position. No telescopic search for it was, however, undertaken. Meanwhile, Leverrier had independently taken up the inquiry, and by August 31st, 1846, he, like Adams, had succeeded in determining the orbit and the position of the disturbing body. On the 23rd of the ​following month Dr. Galle of the Berlin Observatory received from Leverrier a request to search for it, and on the same evening found close to the position given by Leverrier a strange body shewing a small planetary disc, which was soon recognised as a new planet, known now as Neptune.
It may be worth while noticing that the error in the motion of Uranus which led to this remarkable discovery never exceeded 2', a quantity imperceptible to the ordinary eye; so that if two stars were side by side in the sky, one in the true position of Uranus and one in the calculated position as given by Bouvard's tables, an observer of ordinary eyesight would see one star only.
290. The lunar tables of Hansen and Professor Newcomb, and the planetary and solar tables of Leverrier, Professor Newcomb, and Dr. Hill, represent the motions of the bodies dealt with much more accurately than the corresponding tables based on Laplace's work, just as these were in turn much more accurate than those of Euler, Clairaut, and Halley. But the agreement between theory and observation is by no means perfect, and the discrepancies are in many cases greater than can be explained as being due to the necessary imperfections in our observations.
The two most striking cases are perhaps those of Mercury and the moon. Leverrier's explanation of the irregularities of the former (§ 288) has never been fully justified or generally accepted; and the position of the moon as given in the Nautical Almanac and in similar publications is calculated by means of certain corrections to Hansen's tables which were deduced by Professor Newcomb from observation and have no justification in the theory of gravitation.
291. The calculation of the paths of comets has become of some importance during this century owing to the discovery of a number of comets revolving round the sun in comparatively short periods. Halley's comet (chapter xi., § 231) reappeared duly in 1835, passing through its perihelion within a few days of the times predicted by three independent calculators; and it may be confidently expected again about 1910. Four other comets are now known which, like Halley's, revolve in elongated elliptic orbits, completing a revolution in between 70 and 80 years; ​two of these have been seen at two returns, that known as Olbers's comet in 1815 and 1887, and the Pons-Brooks comet in 1812 and 1884. Fourteen other comets with periods varying between 31/3 years (Encke's) and 14 years (Tuttle's), have been seen at more than one return; about a dozen more have periods estimated at less than a century; and 20 or 30 others move in orbits that are decidedly elliptic, though their periods are longer and consequently not known
with much certainty. Altogether the paths of about 230 or 240 comets have been, computed, though many are highly uncertain.
292. In the theory of the tides the first important advance made after the publication of the Mécanique Céleste was the collection of actual tidal observations on a large scale, their interpretation, and their comparison with the results of theory. The pioneers in this direction were Lubbock (§ 286), who presented a series of papers on the subject ​to the Royal Society in 1830–37, and William Whewell (1794–1866), whose papers on the subject appeared between 1833 and 1851. Airy (§ 281), then Astronomer Royal, also published in 1845 an important treatise dealing with the whole subject, and discussing in detail the theory of tides in bodies of water of limited extent and special form. The analysis of tidal observations, a large number of which taken from all parts of the world are now available, has subsequently been carried much further by new methods due to Lord Kelvin and Professor G. H. Darwin. A large quantity of information is thus available as to the way in which tides actually vary in different places and according to different positions of the sun and moon.
Of late years a good deal of attention has been paid to the effect of the attraction of the sun and moon in producing alterations—analogous to oceanic tides—in the earth itself. No body is perfectly rigid, and the forces in question must therefore produce some tidal effect. The problem was first investigated by Lord Kelvin in 1863, subsequently by Professor Darwin and others. Although definite numerical results are hardly attainable as yet, the work so far carried out points to the comparative smallness of these bodily tides and the consequent great rigidity of the earth, a result of interest in connection with geological inquiries into the nature of the interior of the earth.
Some speculations connected with tidal friction are referred to elsewhere (§ 320).
293. The series of propositions as to the stability of the solar system established by Lagrange and Laplace (chapter xi., §§ 244, 245), regarded as abstract propositions mathematically deducible from certain definite assumptions, have been confirmed and extended by later mathematicians such as Poisson and Leverrier; but their claim to give information as to the condition of the actual solar system at an indefinitely distant future time receives much less assent now than formerly. The general trend of scientific thought has been towards the fuller recognition of the merely approximate and probable character of even the best ascertained portions of our knowledge; "exact," "always," and "certain" are words which are disappearing from the scientific vocabulary, except as convenient abbreviations, ​Propositions which profess to be—or are commonly interpreted as being—"exact" and valid throughout all future time are consequently regarded with considerable distrust, unless they are clearly mere abstractions.
In the case of the particular propositions in question the progress of astronomy and physics has thrown a good deal of emphasis on some of the points in which the assumptions required by Lagrange and Laplace are not satisfied by the actual solar system.
It was assumed for the purposes of the stability theorems that the bodies of the solar system are perfectly rigid; in other words, the motions relative to one another of the parts of any one body were ignored. Both the ordinary tides of the ocean and the bodily tides to which modern research has called attention were therefore left out of account. Tidal friction, though at present very minute in amount (§ 287), differs essentially from the perturbations which form the main subject-matter of gravitational astronomy, inasmuch as its action is irreversible. The stability theorems shewed in effect that the ordinary perturbations produced effects which sooner or later compensated one another, so that if a particular motion was accelerated at one time it would be retarded at another; but this is not the case with tidal friction. Tidal action between the earth and the moon, for example, gradually lengthens both the day and the month, and increases the distance between the earth and the moon. Solar tidal action has a similar though smaller effect on the sun and earth. The effect in each case—as far as we can measure it at all—seems to be minute almost beyond imagination, but there is no compensating action tending at any time to reverse the process. And on the whole the energy of the bodies concerned is thereby lessened. Again, modern theories of light and electricity require space to be filled with an "ether" capable of transmitting certain waves; and although there is no direct evidence that it in any way affects the motions of earth or planets, it is difficult to imagine a medium so different from all known forms of ordinary matter as to offer no resistance to a body moving through it. Such resistance would have the effect of slowly bringing the members of the solar system nearer to the sun, and gradually diminishing their times of revolution round ​it. This is again an irreversible tendency for which we know of no compensation.
In fact, from the point of view which Lagrange and Laplace occupied, the solar system appeared like a clock which, though not going quite regularly, but occasionally gaining and occasionally losing, nevertheless required no winding up; whereas modern research emphasises the analogy to a clock which after all is running down, though at an excessively slow rate. Modern study of the sun's heat (§ 319) also indicates an irreversible tendency towards the "running down" of the solar system in another way.
294. Our account of modern descriptive astronomy may conveniently begin with planetary discoveries.
The first day of the 19th century was marked by the discovery of a new planet, known as Ceres. It was seen by Giuseppe Piazzi (1746–1826) as a strange star in a region of the sky which he was engaged in mapping, and soon recognised by its motion as a planet. Its orbit—first calculated by Gauss (§ 276)—shewed it to belong to the space between Mars and Jupiter, which had been noted since the time of Kepler as abnormally large. That a planet should be found in this region was therefore no great surprise; but the discovery by Heinrich Olbers (1758–1840), scarcely a year later (March 1802), of a second body (Pallas), revolving at nearly the same distance from the sun, was wholly unexpected, and revealed an entirely new planetary arrangement. It was an obvious conjecture that if there was room for two planets there was room for more, and two fresh discoveries (Juno in 1804, Vesta in 1807) soon followed.
[To face p. 377.
The four minor planets named were for nearly 40 years the only ones known; then a fifth was discovered in 1845 by Karl Ludwig Hencke (1793–1866) after 15 years of search. Two more were found in 1847, another in 1848, and the number has gone on steadily increasing ever since. The process of discovery has been very much facilitated by improvements in star maps, and latterly by the introduction of photography. In this last method, first used by Dr. Max Wolf of Heidelberg in 1891, a photographic plate is exposed for some hours; any planet present in the region of the sky photographed, having moved sensibly relatively to the stars in this period, is thus detected by the trail which its image leaves on the plate. The annexed figure shews (near the centre) the trail of the minor planet Svea, discovered by Dr. Wolf on March 21st, 1892.
At the end of 1897 no less than 432 minor planets were known, of which 92 had been discovered by a single observer, M. Charlois of Nice, and only nine less by Professor Palisa of Vienna.
The paths of the minor planets practically occupy the whole region between the paths of Mars and Jupiter, though few are near the boundaries; no orbit is more inclined to the ecliptic than that of Pallas, and the eccentricities range from almost zero up to about 1/3.
Fig. 89 shews the orbits of the first two minor planets discovered, as well as of No. 323 (Brucia), which comes nearest to the sun, and of No. 361 (not yet named), ​which goes farthest from it. All the orbits are described in the standard, or west to east, direction. The most interesting characteristic in the distribution of the minor planets, first noted in 1866 by Daniel Kirkwood (1815-1895), is the existence of comparatively clear spaces in the regions where the disturbing action of Jupiter would by Lagrange's
principle (chapter xi., § 243) be most effective: for instance, at a distance from the sun about five-eighths that of Jupiter, a planet would by Kepler's law revolve exactly twice as fast as Jupiter; and accordingly there is a gap among the minor planets at about this distance.
Estimates of the sizes and masses of the minor planets are still very uncertain. The first direct measurements ​of any of the discs which seem reliable are those of Professor E. E. Barnard, made at the Lick Observatory in 1894 and 1895; according to these the three largest minor planets, Ceres, Pallas, and Vesta, have diameters of nearly 500 miles, about 300 and about 250 miles respectively. Their sizes compared with the moon are shewn on the diagram (fig 90). An alternative method—the only one available except for a few of the very largest
of the minor planets—is to measure the amount of light received, and hence to deduce the size, on the assumption that the reflective power is the same as that of some known planet. This method gives diameters of about 300 miles for the brightest and of about a dozen miles for the faintest known.
Leverrier calculated from the perturbations of Mars that the total mass of all known or unknown bodies between Mars and Jupiter could not exceed a fourth that of the earth; but such knowledge of the sizes as we can derive from ​light-observations seems to indicate that the total mass of those at present known is many hundred times less than this limit.
295. Neptune and the minor planets are the only planets which have been discovered during this century, but several satellites have been added to our system.
Barely a fortnight after the discovery of Neptune (1846)
a satellite was detected by William Lassell (1799–1880) at Liverpool. Like the satellites of Uranus, this revolves round its primary from east to west—that is, in the direction contrary to that of all the other known motions of the solar system (certain long-period comets not being counted).
Two years later (September 16th, 1848) William Cranch Bond (1789–1859) discovered, at the Harvard College ​Observatory, an eighth satellite of Saturn, called Hyperion, which was detected independently by Lassell two days afterwards. In the following year Bond discovered that Saturn was accompanied by a third comparatively dark ring—now commonly known as the crape ring—lying immediately inside the bright rings (see fig. 95); and the discovery was made independently a fortnight later by
William Rutter Dawes (1799–1868) in England. Lassell discovered in 1851 two new satellites of Uranus, making a total of four belonging to that planet. The next discoveries were those of two satellites of Mars, known as Deimos and Phobos, by Professor Asaph Hall of Washington on August 11th and 17th, 1877. These are remarkable chiefly for their close proximity to Mars and their extremely rapid motion, the nearer one revolving more rapidly than ​Mars rotates, so that to the Martians it must rise in the west and set in the east. Lastly, Jupiter's system received an addition after nearly three centuries by Professor Barnard's discovery at the Lick Observatory (September 9th, 1892) of
an extremely faint fifth satellite, a good deal nearer to Jupiter than the nearest of Galilei's satellites (chapter vi., § 121).
296. The surfaces of the various planets and satellites have been watched with the utmost care by an army of observers, but the observations have to a large extent remained without satisfactory interpretation, and little is known of the structure or physical condition of the bodies concerned.
297. Mars, being the nearest of the superior planets, is the most favourably situated for observation. The chief markings on its surface—provisionally interpreted as being land and water—are fairly permanent and therefore recognisable; several tolerably consistent maps of the surface have been constructed; and by observation of certain striking features the rotation period has been determined to a fraction of a second. Signor Schiaparelli of Milan detected at the opposition of 1877 a number of intersecting dark lines generally known as canals, and as the result of observations made during the opposition of 1881-82 announced that certain of them appeared doubled, two nearly parallel lines being then seen instead of one. These remarkable observations have been to a great extent confirmed by other observers, but remain unexplained.
The visible surfaces of Jupiter and Saturn appear to be layers of clouds; the low density of each planet (1⋅3 and ⋅7 respectively, that of water being 1 and of the earth 5⋅5), the rapid changes on the surface, and other facts indicate that these planets are to a great extent in a fluid condition, and have a high temperature at a very moderate distance ​below the visible surface. The surface markings are in each case definite enough for the rotation periods to be fixed with some accuracy; though it is clear in the case of Jupiter, and probably also in that of Saturn, that—as with the sun (§ 298)—different parts of the surface move at different rates. Laplace had shewn that Saturn's ring (or rings) could not be, as it appeared, a uniform solid body he rashly inferred—without any complete investigation—that it might be an irregularly weighted solid body. The first important advance was made by James Clerk Maxwell (1831–1879), best known as a writer on electricity and other branches of physics. Maxwell shewed (1857) that the rings could neither be continuous solid bodies nor liquid, but that all the important dynamical conditions would be satisfied if they were made up of a very large number of small solid bodies revolving independently round the sun. The theory thus suggested on mathematical grounds has received a good deal of support from telescopic evidence. The rings thus bear to Saturn a relation having some analogy to that which the minor planets bear to the sun; and Kirkwood pointed out in 1867 that Cassini's division between the two main rings can be explained by the perturbations due to certain of the satellites, just as the corresponding gaps in the minor planets can be explained by the action of Jupiter (§ 294).
The great distance of Uranus and Neptune naturally makes the study of them difficult, and next to nothing is known of the appearance or constitution of either; their rotation periods are wholly uncertain.
[To face p. 385.
298. Telescopic study of the surface of the sun during the century has resulted in an immense accumulation of detailed knowledge of peculiarities of the various markings on the surface. The most interesting results of a general nature are connected with the distribution and periodicity of sun-spots. The earliest telescopists had noticed that the number of spots visible on the sun varied from time to time, but no law of variation was established till 1851, when Heinrich Schwabe of Dessau(1789–1875) published in Humboldt's Cosmos the results of observations of sun-spots carried out during the preceding quarter of a century, shewing that the number of spots visible increased and decreased in a tolerably regular way in a period of about ten years.
Earlier records and later observations have confirmed the general result, the period being now estimated as slightly over 11 years on the average, though subject to considerable fluctuations. A year later (1852) three independent investigators. Sir Edward Sabine (1788–1883) in England, Rudolf Wolf (1816–1893) and Alfred Gaufier (1793–1881) in Switzerland, called attention to the remarkable similarity between the periodic variations of sun-spots and of various magnetic disturbances on the earth. Not only is the period the same, but it almost invariably happens that when spots are most numerous on the sun magnetic disturbances are most noticeable on the earth, and that similarly the times of scarcity of the two sets of phenomena coincide. This wholly unexpected and hitherto quite unexplained relationship has been confirmed by the occurrence on several occasions of decided magnetic disturbances simultaneously with rapid changes on the surface of the sun.
A long series of observations of the position of spots on the sun undertaken by Richard Christopher Carrington (1826–1875) led to the first clear recognition of the difference in the rate of rotation of the different parts of the surface of the sun, the period of rotation being fixed (1859) at about 25 days at the equator, and two and a half days longer half-way between the equator and the poles; while ​in addition spots were seen to have also independent "proper motions." Carrington also established (1858) the scarcity of spots in the immediate neighbourhood of the equator, and confirmed statistically their prevalence in the adjacent regions, and their great scarcity more than about 35° from the equator; and noticed further certain regular changes in the distribution of spots on the sun in the course of the 11-year cycle.
Wilson's theory (chapter xii., § 268) that spots are depressions was confirmed by an extensive series of photographs taken at Kew in 1858–72, shewing a large preponderance of cases of the perspective effect noticed by him; but, on the other hand, Mr. F. Howlett, who has watched the sun for some 35 years and made several thousand drawings of spots, considers (1894) that his observations are decidedly against Wilson's theory. Other observers are divided in opinion.
299. Spectrum analysis, which has played such an important part in recent astronomical work, is essentially a method of ascertaining the nature of a body by a process of sifting or analysing into different components the light received from it.
It was first clearly established by Newton, in 1665–66 (chapter ix., § 168), that ordinary white light, such as sunlight, is composite, and that by passing a beam of sunlight—with proper precautions—through a glass prism it can be decomposed into light of different colours; if the beam so decomposed is received on a screen, it produces a band of colours known as a spectrum, red being at one end and violet at the other.
[To face p. 387.
​that light of a particular colour found at a particular part of the spectrum has a definite wave-length. At the extreme violet end of the spectrum, for example, the wave-length is about fifteen millionths of an inch, at the red end it is about twice as great; from which it follows (§ 283), from the known velocity, of light, that when we look at the red end of a spectrum about 400 billion waves of light enter the eye per second, and twice that number when we look at the other end. Newton's experiment thus shews that a prism sorts out light of a composite nature according to the wavelength of the different kinds of light present. The same thing can be done by substituting for the prism a so-called diffraction-grating, and this is for many purposes superseding the prism. In general it is necessary, to ensure purity in the spectrum and to make it large enough, to admit light through a narrow slit, and to use certain lenses in combination with one or more prisms or a grating; and the arrangement is such that the spectrum is not thrown on to a screen, but either viewed directly by the eye or photographed. The whole apparatus is known as a spectroscope.
The solar spectrum appeared to Newton as a continuous band of colours; but in 1802 William Hyde Wollaston (1766–1828) observed certain dark lines running across the spectrum, which he took to be the boundaries of the natural colours. A few years later (1814–15) the great Munich optician Joseph Fraunhofer (1787–1826) examined the sun's spectrum much more carefully, and discovered about 600 such dark lines, the positions of 324 of which he mapped (see fig. 97). These dark lines are accordingly known as Fraunhofer lines: for purposes of identification Fraunhofer attached certain letters of the alphabet to a few of the most conspicuous; the rest are now generally known by the wavelength of the corresponding kind of light.
It was also gradually discovered that dark bands could be produced artificially in spectra by passing light through various coloured substances; and that, on the other hand, the spectra of certain flames were crossed by various bright lines.
Several attempts were made to explain and to connect these various observations, but the first satisfactory and tolerably complete explanation was given in 1859 by Gustav ​Robert Kirchhoff (1824–1887) of Heidelberg, who at first worked in co-operation with the chemist Bunsen.
Kirchhoff shewed that a luminous solid or liquid—or, as we now know, a highly compressed gas—gives a continuous spectrum; whereas a substance in the gaseous state gives a spectrum consisting of bright lines (with or without a faint continuous spectrum), and these bright lines depend on the particular substance and are characteristic of it. Consequently the presence of a particular substance in the form of gas in a hot body can be inferred from the presence of its characteristic lines in the spectrum of the light. The dark lines in the solar spectrum were explained by the fundamental principle—often known as Kirchhoff's law—that a body's capacity for stopping or absorbing light of a particular wave-length is proportional to its power, under like conditions, of giving out the same light. If, in particular, light from a luminous solid or liquid body, giving a continuous spectrum, passes through a gas, the gas absorbs light of the same wave-length as that which it itself gives out: if the gas gives out more light of these particular wave-lengths than it absorbs, then the spectrum is crossed by the corresponding bright lines; but if it absorbs more than it gives out, then there is a deficiency of light of these wave-lengths and the corresponding parts of the spectrum appear dark that is, the spectrum is crossed by dark lines in the same position as the bright lines in the spectrum of the gas alone. Whether the gas absorbs more or less than it gives out is essentially a question of temperature, so that if light from a hot solid or liquid passes through a gas at a higher temperature a spectrum crossed by bright lines is the result, whereas if the gas is cooler than the body behind it dark lines are seen in the spectrum.
300. The presence of the Fraunhofer lines in the spectrum of the sun shews that sunlight comes from a hot solid or liquid body (or from a highly compressed gas), and that it has passed through cooler gases which have absorbed light of the wave-lengths corresponding to the dark lines. These gases must be either round the sun or in our atmosphere; and it is not difficult to shew that, although some of the Fraunhofer lines are due to our ​atmosphere, the majority cannot be, and are therefore caused by gases in the atmosphere of the sun.
For example, the metal sodium when vaporised gives a spectrum characterised by two nearly coincident bright lines in the yellow part of the spectrum; these agree in position with a pair of dark lines (known as D) in the spectrum of the sun (see fig. 97); Kirchhoff inferred therefore that the atmosphere of the sun contains sodium. By comparison of the dark lines in the spectrum of the sun with the bright lines in the spectra of metals and other substances, their presence or absence in the solar atmosphere can accordingly be ascertained. In the case of iron—which has an extremely complicated spectrum—Kirchhoff succeeded in identifying 60 lines (since increased to more than 2,000) in its spectrum with dark lines in the spectrum of the sun. Some half-dozen other known elements were also identified by Kirchhoff in the sun.
The inquiry into solar chemistry thus started has since been prosecuted with great zeal. Improved methods and increased care have led to the construction of a series of maps of the solar spectrum, beginning with Kirchhoff's own, published in 1861–62, of constantly increasing complexity and accuracy. Knowledge of the spectra of the metals has also been greatly extended. At the present time between 30 and 40 elements have been identified in the sun, the most interesting besides those already mentioned being hydrogen, calcium, magnesium, and carbon.
The first spectroscopic work on the sun dealt only with the light received from the sun as a whole, but it was soon seen that by throwing an image of the sun on to the slit of the spectroscope by means of a telescope the spectrum of a particular part of the sun's surface, such as a spot or a facula, could be obtained; and an immense number of observations of this character have been made.
301. Observations of total eclipses of the sun have shewn that the bright surface of the sun as we ordinarily see it is not the whole, but that outside this there is an envelope of some kind too faint to be seen ordinarily but becoming visible when the intense light of the sun itself is cut off by the moon. A white halo of considerable extent round the eclipsed sun, now called the corona, is referred to by ​Plutarch, and discussed by Kepler (chapter vii., § 145) Several 18th century astronomers noticed a red streak along some portion of the common edge of the sun and moon, and red spots or clouds here and there (cf. chapter x., § 205). But little serious attention was given to the subject till after the total solar eclipse of 1842. Observations made then and at the two following eclipses of 1851 and 1860, in the latter of which years photography was for the first time effectively employed, made it evident that the red streak represented a continuous envelope of some kind surrounding the sun, to which the name of chromosphere has been given, and that the red objects, generally known as prominences, were in general projecting parts of the chromosphere, though sometimes detached from it. At the eclipse of 1868 the spectrum of the prominences and the chromosphere was obtained, and found to be one of bright lines, shewing that they consisted of gas. Immediately afterwards M. Janssen, who was one of the observers of the eclipse, and Sir J. Norman Lockyer independently devised a method whereby it was possible to get the spectrum of a prominence at the edge of the sun's disc in ordinary daylight, without waiting for an eclipse; and a modification introduced by Sir William Huggins in the following year (1869) enabled the form of a prominence to be observed spectroscopically. Recently (1892) Professor G. E. Hale of Chicago has succeeded in obtaining by a photographic process a representation of the whole of the chromosphere and prominences, while the same method gives also photographs of faculae (chapter viii., § 153) on the visible surface of the sun.
The most important lines ordinarily present in the spectrum of the chromosphere are those of hydrogen, two lines (H and K) which have been identified with some difficulty as belonging to calcium, and a yellow line the substance producing which, known as helium, has only recently (1895) been discovered on the earth. But the chromosphere when disturbed and many of the prominences give spectra containing a number of other lines.
The corona has been carefully studied at every solar eclipse during the last 30 years, both with the spectroscope and with the telescope, supplemented by photography, and a number of ingenious theories of its constitution have been propounded; but our present knowledge of its nature hardly goes beyond Professor Young's description of it as "an inconceivably attenuated cloud of gas, fog, and dust, surrounding the sun, formed and shaped by solar forces."
302. The spectroscope also gives information as to certain motions taking place on the sun. It was pointed out in 1842 by Christian Doppler (1803–1853), though in an imperfect and partly erroneous way, that if a luminous body is approaching the observer, or vice versa, the waves of light are as it were crowded together and reach the eye at shorter intervals than if the body were at rest, and that the character of the light is thereby changed. The colour and the position in the spectrum both depend on the interval between one wave and the next, so that if a body giving out light of a particular wave-length, e.g. the blue light corresponding to the F line of hydrogen, is approaching the observer rapidly, the line in the spectrum appears slightly on one side of its usual position, being displaced towards the violet end of the spectrum; whereas if the body is receding the line is, in the same way, displaced in the opposite direction. This result is usually known as Doppler's principle. The effect produced can easily be expressed numerically. If, for example, the body is approaching with a speed equal to 1/1000 that of light, then 1001 waves enter the eye or the spectroscope in the same time in which there would other- wise only be 1000; and there is in consequence a virtual shortening of the wave-length in the ratio of 1001 to 1000. So that if it is found that a line in the spectrum of a body is displaced from its ordinary position in such ​a way that its wave-length is apparently decreased by 1/1000 part, it may be inferred that the body is approaching with the speed just named, or about 186 miles per second, and if the wave-length appears increased by the same amount (the line being displaced towards the red end of the spectrum) the body is receding at the same rate.
Some of the earliest observations of the prominences by Sir J. N. Lockyer (1868), and of spots and other features of the sun by the same and other observers, shewed displacements and distortions of the lines in the spectrum, which were soon seen to be capable of interpretation by this method, and pointed to the existence of violent disturbances in the atmosphere of the sun, velocities as great as 300 miles per second being not unknown. The method has received an interesting confirmation from observations of the spectrum of opposite edges of the sun's disc, of which one is approaching and the other receding owing to the rotation of the sun. Professor Dunér of Upsala has by this process ascertained (1887–89) the rate of rotation of the surface of the sun beyond the regions where spots exist, and therefore outside the limits of observations such as Carrington's (§ 298).
304. More than 200 comets have been seen during the present century; not only have the motions of most of them been observed and their orbits computed (§ 291), but in a large number of cases the appearance and structure of the comet have been carefully observed telescopically, while latterly spectrum analysis and photography have also been employed.
Independent lines of inquiry point to the extremely unsubstantial character of a comet, with the possible exception of the bright central part or nucleus, which is nearly always present. More than once, as in 1767 (chapter xi., § 248), a comet has passed close to some member of the solar system, and has never been ascertained to affect its motion. The mass of a comet is therefore very small, but its bulk or volume, on the other hand, is in general very great, the tail often being millions of miles in length; so that the density must be extremely small. Again, stars have often been observed shining through a comet's tail (as shewn in fig. 99), and even through the head at no great distance from the nucleus, their brightness being only slightly, if at all, affected. Twice at least (1819, 1861) the earth has passed through a comet's tail, but we were so little affected that the fact was only discovered by calculations made after the event. The early observation (chapter iii., § 69) that a comet's tail points away from the sun has been abundantly verified; and from this it follows that very rapid changes in the position of the tail must occur in some cases. For example, the comet of 1843 passed very close to the sun at such a rate that in about two hours it had passed from one side of the sun to the opposite; it was then much too near the sun to be seen, but if it followed the ordinary law its tail, which was unusually long, must have entirely reversed its direction within this short time. It is difficult to avoid the inference that the tail is not a permanent part of the comet, but is a stream of matter driven off from it in some way by the action of the sun, and in this respect comparable with the smoke ​issuing from a chimney. This view is confirmed by the fact that the tail is only developed when the comet approaches the sun, a comet when at a great distance from the sun appearing usually as an indistinct patch of nebulous light, with perhaps a brighter spot representing the nucleus. Again, if the tail be formed by an outpouring of matter from the comet, which only takes place when the comet is near the sun, the more often a comet approaches the sun the more must it waste away; and we find accordingly that the short-period comets, which return to the neighbourhood of the sun at frequent intervals (§ 291), are inconspicuous bodies. The same theory is supported by the shape of the tail. In some cases it is straight, but more commonly it is curved to some extent, and the curvature is then always backwards in relation to the comet's motion. Now by ordinary dynamical principles matter shot off from the head of the comet while it is revolving round the sun would tend, as it were, to lag behind more and more the farther it receded from the head, and an apparent backward curvature of the tail—less or greater according to the speed with which the particles forming the tail were repelled—would be the result. Variations in curvature of the tails of different comets, and the existence of two or more differently curved tails of the same comet, are thus readily explained by supposing them made of different materials, repelled from the comet's head at different speeds.
The first application of the spectroscope to the study of comets was made in 1864 by Giambattista Donati (1826–1873), best known as the discoverer of the magnificent comet of 1858. A spectrum of three bright bands, wider than the ordinary "lines," was obtained, but they were not then identified. Four years later Sir William Huggins obtained a similar spectrum, and identified it with that of a compound of carbon and hydrogen. Nearly every comet examined since then has shewn in its spectrum bright bands indicating the presence of the same or some other hydrocarbon, but in a few cases other substances have also been detected. A comet is therefore in part at least self-luminous, and some of the light which it sends us is that of a glowing gas. It also shines to a considerable extent by reflected sunlight; there is nearly always a ​continuous spectrum, and in a few cases—first in 1881—the spectrum has been distinct enough to shew the Fraunhofer lines crossing it. But the continuous spectrum seems also to be due in part to solid or liquid matter in the comet itself, which is hot enough to be self-luminous.
305. The work of the last 30 or 40 years has established a remarkable relation between comets and the minute bodies which are seen in the form of meteors or shooting stars. Only a few of the more important links in the chain of evidence can, however, be mentioned. Showers of shooting stars, the occurrence of which has been known from quite early times, have been shewn to be due to the passage of the earth through a swarm of bodies revolving in elliptic orbits round the sun. The paths of four such swarms were ascertained with some precision in 1866-67, and found in each case to agree closely with the paths of known comets. And since then a considerable number of other cases of resemblance or identity between the paths of meteor swarms and of comets have been detected. One of the four comets just referred to, known as Biela's, with a period of between six and seven years, was duly seen on several successive returns, but in 1845-46 was observed first to become somewhat distorted in shape, and afterwards to have divided into two distinct comets; at the next return (1852) the pair were again seen; but since then nothing has been seen of either portion. At the end of November in each year the earth almost crosses the path of this comet, and on two occasions (1872, and 1885) it did so nearly at the time when the comet was due at the same spot; if, as seemed likely, the comet had gone to pieces since its last appearance, there seemed a good chance of falling in with some of its remains, and this expectation was fulfilled by the occurrence on both occasions of a meteor shower much more brilliant than that usually observed at the same date.
Biela's comet is not the only comet which has shewn signs of breaking up; Brooks's comet of 1889, which is probably identical with Lexell's (chapter xi., § 248), was found to be accompanied by three smaller companions; as this comet has more than once passed extremely close to Jupiter, a plausible explanation of its breaking up is at once given in the attractive force of the planet. Moreover ​certain systems of comets, the members of which revolve in the same orbit but separated by considerable intervals of time, have also been discovered. Tebbutt's comet of 1881 moves in practically the same path as one seen in 1807, and the great comet of 1880, the great comet of 1882 (shewn in fig. 99), and a third which appeared in 1887, all move in paths closely resembling that of the comet of 1843, while that of 1668 is more doubtfully connected with the same system. And it is difficult to avoid regarding the members of a system as fragments of an earlier comet, which has passed through the stages in which we have actually seen the comets of Biela and Brooks.
Evidence of such different kinds points to an intimate connection between comets and meteors, though it is perhaps still premature to state confidently that meteors are fragments of decayed comets, or that conversely comets are swarms of meteors.
306. Each of the great problems of sidereal astronomy which Herschel formulated and attempted to solve has been elaborately studied by the astronomers of the 19th century. The multiplication of observatories, improvements in telescopes, and the introduction of photography—to mention only three obvious factors of progress—have added enormously to the extent and accuracy of our knowledge of the stars, while the invention of spectrum analysis has thrown an entirely new light on several important problems.
307. Then followed his well-known expedition to the Cape of Good Hope (1833–1838), where he "swept" the southern skies in very much the same way in which his father had explored the regions visible in our latitude. Some 1200 double and multiple stars, and a rather larger number of new nebulae, were discovered and studied, while about 500 known nebulae were re-observed; star-gauging on William Herschel's lines was also carried out on an extensive scale. A number of special observations of interest were made almost incidentally during this survey: the remarkable variable star η Argus and the nebula surrounding it (a modern photograph of which is reproduced in fig. 100), the wonderful collections of nebulae clusters and stars, known as the Nubeculae or Magellanic Clouds, and Halley's comet were studied in turn; and the two faintest satellites of Saturn then known (chapter xii., § 255) were seen again for the first time since the death of their discoverer.
An important investigation of a somewhat different character—that of the amount of heat received from the sun—was also carried out (1837) during Herschel's residence at the Cape; and the result agreed satisfactorily with that of an independent inquiry made at the same time in France by Claude Servais Mathias Pouillet (1791–1868). In both cases the heat received on a given area of the earth in a given time from direct sunshine was measured; and allowance being made for the heat stopped in the atmosphere as the sun's rays passed through it, an estimate was formed of the total amount of heat received annually by the earth from the sun, and hence of the total amount radiated by the sun in all directions, an insignificant fraction of which (one part in 2,000,000,000) is alone intercepted by the earth. But the allowance for the heat intercepted in our atmosphere was necessarily uncertain, and later work, in particular that of Dr. S. P. Langley in 1880–81, shews that it was very much under-estimated by both Herschel and Pouillet. According to Herschel's results, the heat received annually from the sun—including that intercepted in the ​atmosphere—would be sufficient to melt a shell of ice 120 feet thick covering the whole earth; according to Dr. Langley, the thickness would be about 160 feet.
308. With his return to England in 1838 Herschel's career as an observer came to an end; but the working out of the results of his Cape observations, the arrangement and cataloguing of his own and his father's discoveries, provided occupation for many years. A magnificent volume on the Results of Astronomical Observations made during the years 1834–8 at the Cape of Good Hope appeared in 1847; and a catalogue of all known nebulae and clusters, amounting to 5,079, was presented to the Royal Society in 1864, while a corresponding catalogue of more than 10,000 double and multiple stars was never finished, though the materials collected for it were published posthumously in 1879. John Herschel's great catalogue of nebulae has since been revised and enlarged by Dr. Dreyer, the result being a list of 7,840 nebulae and clusters known up to the end of 1887; and a supplementary list of discoveries made in 1888–94 published by the same writer contains 1,529 entries, so that the total number now known is between 9,000 and 10,000, of which more than half have been discovered by the two Herschels.
309. Double stars have been discovered and studied by a number of astronomers besides the Herschels. One of the most indefatigable workers at this subject was the elder Struve (§ 279), who was successively director of the two Russian observatories of Dorpat and Pulkowa. He observed altogether some 2,640 double and multiple stars, measuring in each case with care the length and direction of the line joining the two components, and noting other peculiarities, such as contrasts in colour between the members of a pair. He paid attention only to double stars the two components of which were not more than 32" apart, thus rejecting a good many which William Herschel would have noticed; as the number of known doubles rapidly increased, it was clearly necessary to concentrate attention on those which might with some reasonable degree of ​probability turn out to be genuine binaries (chapter xii., § 264).
In addition to a number of minor papers Struve published three separate books on the subject in 1827, 1837, and 1852. A comparison of his own earlier and later observations, and of both with Herschel's earlier ones, shewed about 100 cases of change of relative positions of two members of a pair, which indicated more or less clearly a motion of revolution, and further results of a like character have been obtained
from a comparison of Struve's observations with those of later observers.
William Herschel's observations of binary systems (chapter xii., § 264) only sufficed to shew that a motion of revolution of some kind appeared to be taking place; it was an obvious conjecture that the two members of a pair ​attracted one another according to the law of gravitation, so that the motion of revolution was to some extent analogous to that of a planet round the sun; if this were the case, then each star of a pair should describe an ellipse (or conceivably some other conic) round the other, or each round the common centre of gravity, in accordance with Kepler's laws, and the apparent path as seen on the sky should be of this nature but in general foreshortened by being projected on to the celestial sphere. The first attempt to shew that this was actually the case was made by Felix Savary (1797–1841) in 1827, the star being ξ Ursae, which was found to be revolving in a period of about 60 years.
Many thousand double stars have been discovered by the Herschels, Struve, and a number of other observers, including several living astronomers, among whom Professor S. W. Burnham of Chicago, who has discovered some 1300, holds a leading place. Among these stars there are about 300 which we have fair reason to regard as binary, but not more than 40 or 50 of the orbits can be regarded as at all satisfactorily known. One of the most satisfactory is that of Savary's star ξ Ursae, which is shewn in fig. 101. Apart from the binaries discovered by the spectroscopic method (§ 314), which form to some extent a distinct class, the periods of revolution which have been computed range between about ten years and several centuries, the longer periods being for the most part decidedly uncertain.
311. The question of the status of nebulae in its simplest form may be said to have been settled by the first application of spectrum analysis. Fraunhofer (§ 299) had seen as early, as 1823 that stars had spectra characterised like that of the sun by dark lines, and more complete investigations made soon after Kirchhoff's discoveries by several astronomers, in particular by Sir William Huggins and by the eminent Jesuit astronomer Angela Secchi (1818–1878), confirmed this result as regards nearly all stars observed.
The first spectrum of a nebula was obtained by Sir William Huggins in 1864, and was seen to consist of three bright lines; by 1868 he had examined 70, and found in about one-third of the cases, including that of the Orion nebula, a similar spectrum of bright lines. In these cases therefore the luminous part of the nebula is gaseous, and Herschel's suggestion of a "shining fluid" was confirmed in the most satisfactory way. In nearly all cases three bright lines are seen, one of which is a hydrogen line, while the other two have not been identified, and in the case of a few of the brighter nebulae some other lines have also been seen. On the other hand, a considerable number of nebulae, including many of those which appear capable of telescopic resolution into star clusters, give a continuous spectrum, so that there is no clear spectroscopic evidence to distinguish them from clusters of stars, since the dark lines seen usually in the spectra of the latter could hardly be expected to be visible in the case of such faint objects as nebulae.
312. Stars have been classified, first by Secchi (1863), afterwards in slightly different ways by others, according to the general arrangement of the dark lines in their spectra; and some attempts have been made to base on these ​differences inferences as to the relative "ages," or at any rate the stages of development, of different stars.
Many of the dark lines in the spectra of stars have been identified, first by Sir William Huggins in 1864, with the lines of known terrestrial elements, such as hydrogen, iron, sodium, calcium; so that a certain identity between the materials of which our own earth is made and that of bodies so remote as the fixed stars is thus established.
In addition to the classes of stars already mentioned, the spectroscope has shewn the existence of an extremely interesting if rather perplexing class of stars, falling into several subdivisions, which seem to form a connecting link between ordinary stars and nebulae, for, though indistinguishable telescopically from ordinary stars, their spectra shew bright lines either periodically or regularly. A good many stars of this class are variable, and several "new" stars which have appeared and faded away of late years have shewn similar characteristics.
313. The first application to the fixed stars of the spectroscopic method (§ 302) of determining motion towards or away from the observer was made by Sir William Huggins in 1868. A minute displacement from its usual position of a dark hydrogen line (F) in the spectrum of Sirius was detected, and interpreted as shewing that the star was receding from the solar system at a considerable speed. A number of other stars were similarly observed in the following year, and the work has been taken up since by a number of other observers, notably at Potsdam under the direction of Professor H. C. Vogel, and at Greenwich.
A number of other cases of both classes of spectroscopic binary stars (as they may conveniently be called) have since been discovered. The upper part of fig. 103 shews the doubling of one of the lines in the spectrum of the double star β Aurigae; and the lower part shews the corresponding part of the spectrum at a time when the line appeared single.
315. Variable stars of different kinds have received a good deal of attention during this century, particularly during the last few years. About 400 stars are now clearly recognised as variable, while in a large number of other cases variability of light has been suspected; except, however, in a few cases, like that of Algol, the causes of variability are still extremely obscure.
316. The study of the relative brightness of stars—a branch of astronomy now generally known as stellar photometry—has also been carried on extensively during the century and has now been put on a scientific basis. The traditional classification of stars into magnitudes, according to their brightness, was almost wholly arbitrary, and decidedly uncertain. As soon as exact quantitative comparisons of stars of different brightness began to be carried out on a considerable scale, the need of a more precise system of classification became felt. John Herschel was one of the pioneers in this direction; he suggested a scale ​capable of precise expression, and agreeing roughly, at any rate as far as naked-eye stars are concerned, with the current usages; while at the Cape he measured carefully the light of a large number of bright stars and classified them on this principle. According to the scale now generally adopted, first suggested in 1856 by Norman Robert Pogson (1829–1891), the light of a star of any magnitude bears a fixed ratio (which is taken to be 2⋅512...) to that of a star of the next magnitude. The number is so chosen that a star of the sixth magnitude—thus defined—is 100 times fainter than one of the first magnitude. Stars of intermediate brightness have magnitudes expressed by fractions which can be at once calculated (according to a simple mathematical rule) when the ratio of the light received from the star to that received from a standard star has been observed.
A good many converging lines of evidence thus point to a greater variety in the arrangement, size, and structure of the bodies with which the telescope makes us acquainted than seemed probable when sidereal astronomy was first seriously studied; they also indicate the probability that these bodies should be regarded as belonging to a single system, even if it be of almost inconceivable complexity, rather than to a number of perfectly distinct systems of a simpler type.
318. Laplace's nebular hypothesis (chapter xi., § 250) was published a little more than a century ago (1796), and has been greatly affected by progress in various departments of astronomical knowledge. Subsequent discoveries of planets and satellites (§§ 294, 295) have marred to some extent the uniformity and symmetry of the motions of the solar system on which Laplace laid so much stress; but it is not impossible to give reasonable explanations of the backward motions of the satellites of the two most distant planets, and of the large eccentricity and inclination of the paths of some of the minor planets, while apart from these exceptions the number of bodies the motions of which have the characteristics which Laplace pointed out has been considerably increased. The case for some sort of common origin of the bodies of the solar system has perhaps in this way gained as much as it has lost. Again, the telescopic evidence which Herschel adduced (chapter xii., § 261) in favour of the existence of certain processes of condensation in nebulae has been strengthened by later evidence of a similar character, and by the various pieces of evidence already referred to which connect nebulae with single stars and with clusters. The differences in the spectra of stars also receive their most satisfactory explanation as representing different stages of condensation of bodies of the same general character.
319. An entirely new contribution to the problem has resulted from certain discoveries as to the nature of heat, culminating in the recognition (about 1840-50) of heat as only one form of what physicists now call energy, which manifests itself also in the motion of bodies, in the ​separation of bodies which attract one another, as well as in various electrical, chemical, and other ways. With this discovery was closely connected the general theory known as the conservation of energy, according to which energy, though capable of many transformations, can neither be increased nor decreased in quantity. A body which, like the sun, is giving out heat and light is accordingly thereby losing energy, and is like a machine doing work; either then it is receiving energy from some other source to compensate this loss or its store of energy is diminishing. But a body which goes on indefinitely giving out heat and light without having its store of energy replenished is exactly analogous to a machine which goes on working indefinitely without any motive power to drive it; and both are alike impossible.
The results obtained by John Herschel and Pouillet in 1836 (§ 307) called attention to the enormous expenditure of the sun in the form of heat, and astronomers thus had to face the problem of explaining how the sun was able to go on radiating heat and light in this way. Neither in the few thousand years of the past covered by historic records, nor in the enormously great periods of which geologists and biologists take account, is there any evidence of any important permanent alteration in the amount of heat and light received annually by the earth from the sun. Any theory of the sun's heat must therefore be able to account for the continual expenditure of heat at something like the present rate for an immense period of time. The obvious explanation of the sun as a furnace deriving its heat from combustion is found to be totally inadequate when put to the test of figures, as the sun could in this way be kept going at most for a few thousand years. The explanation now generally accepted was first given by the great German physicist Hermann von Helmholtz (1821–1894) in a popular lecture in 1854. The sun possesses an immense store of energy in the form of the mutual gravitation of its parts; if from any cause it shrinks, a certain amount of gravitational energy is necessarily lost and takes some other form. In the shrinkage of the sun we have therefore a possible source of energy. The precise amount of energy liberated by a definite amount of shrinkage of the sun depends upon ​the internal distribution of density in the sun, which is uncertain, but making any reasonable assumption as to this we find that the amount of shrinking required to supply the sun's expenditure of heat would only diminish the diameter by a few hundred feet annually, and would therefore be imperceptible with our present telescopic power for centuries, while no earlier records of the sun's size are accurate enough to shew it. It is easy to calculate on the same principles the amount of energy liberated by a body like the sun in shrinking from an indefinitely diffused condition to its present state, and from its present state to one of assigned greater density the result being that we can in this way account for an expenditure of sun-heat at the present rate for a period to be counted in millions of years in either past or future time, while if the rate of expenditure was less in the remote past or becomes less in the future the time is extended to a corresponding extent.
No other cause that has been suggested is competent to account for more than a small fraction of the actual heat-expenditure of the sun; the gravitational theory satisfies all the requirements of astronomy proper, and goes at any rate some way towards meeting the demands of biology and geology.
If then we accept it as provisionally established, we are led to the conclusion that the sun was in the past larger and less condensed than now, and by going sufficiently far back into the past we find it in a condition not unlike the primitive nebula which Laplace presupposed, with the exception that it need not have been hot.
320. A new light has been thrown on the possible development of the earth and moon by Professor G. H. Darwin's study of the effects of tidal friction (cf. § 287 and §§ 292, 293). Since the tides increase the length of the day and month and gradually repel the moon from the earth, it follows that in the past the moon was nearer to the earth than now, and that tidal action was consequently much greater. Following out this clue. Professor Darwin found, by a series of elaborate calculations published in 1879–81, strong evidence of a past time when the moon was close to the earth, revolving round it in the same time ​in which the earth rotated on its axis, which was then a little over two hours. The two bodies, in fact, were moving as if they were connected; it is difficult to avoid the probable inference that at an earlier stage the two really were one, and that the moon is in reality a fragment of the earth driven off from it by the too-rapid spinning of the earth, or otherwise.
Professor Darwin has also examined the possibility of explaining in a similar way the formation of the satellites of the other planets and of the planets themselves from the sun, but the circumstances of the moon-earth system turn out to be exceptional, and tidal influence has been less effective in other cases, though it gives a satisfactory explanation of certain peculiarities of the planets and their satellites. More recently (1892) Dr. See has applied a somewhat similar line of reasoning to explain by means of tidal action the development of double stars from an earlier nebulous condition.
Speaking generally, we may say that the outcome of the 19th century study of the problem of the early history of the solar system has been to discredit the details of Laplace's hypothesis in a variety of ways, but to establish on a firmer basis the general view that the solar system has been formed by some process of condensation out of an earlier very diffused mass bearing a general resemblance to one of the nebulae which the telescope shews us, and that stars other than the sun are not unlikely to have been formed in a somewhat similar way; and, further, the theory of tidal friction supplements this general but vague theory, by giving a rational account of a process which seems to have been the predominant factor in the development of the system formed by our own earth and moon, and to have had at any rate an important influence in a number of other cases.
* ↑ The method was published by Legendre in 1806 and by Gauss in 1809, but it was invented and used by the latter more than 20 years earlier.
* ↑ The figure has to be enormously exaggerated, the angle s σ e as shewn there being about 10°, and therefore about 100,000 times too great.
* ↑ Sir R. S. Ball and the late Professor Pritchard (§ 279) have obtained respectively ⋅47 and ⋅43; the mean of these, ⋅45", may be provisionally accepted as not very far from the truth.
* ↑ An average star of the 14th magnitude is 10,000 times fainter than one of the 4th magnitude, which again is about 150 times less bright than Sirius. See § 316.
* ↑ Newcomb's velocity of light and Nyren's constant of aberration (20"⋅4921) give 8"⋅794; Struve's constant of aberration (20"⋅445), Loewy's (20"⋅447), and Hall's (20"⋅454) each give 8"⋅81.
* ↑ Fundamenta Nova Invesiigationis Orbitae Verae quam Luna perlustrat.
* ↑ Darlegung der theoretischen Berechnung der in den Mondtafeln angewandten Störungen.
* ↑ E.g. in Grant's History of Physical Astronomy, Herschel's Outlines of Astronomy, Miss Clerke's History of Astronomy in the Nineteenth Century, and the memoir by Dr. Glaisher prefixed to the first volume of Adams's Collected Papers.
* ↑ This had been suggested as a possibility by several earlier writers.
* ↑ The discovery of a terrestrial substance with this line in its spectrum has been announced while this book has been passing through the press.
* ↑ Observations made on Mont Blanc under the direction of M. Janssen in 1897 indicate a slightly larger number than Dr. Langley's.
* ↑ Catalogus novus stellarum duplicium, Stellarum duplicium et multiplicium mensurae micrometricae, and Stellarum fixarum imprimis duplicium et multiplicium positiones mediae pro epocha 1830.
* ↑ I.e. 2⋅512... is chosen as being the number the logarithm of which is ⋅4, so that (2⋅512...)$^{5/2}$ = 10.
* ↑ If L be the ratio of the light received from a star to that received from a standard first magnitude star, such as Aldebaran or Altair, then its magnitude m is given by the formula L = (1/2⋅512)$^{m−1}$ = (1/100)$^{m−1/5}$, whence m−1 = −5/2 log L. A star brighter than Aldebaran has a magnitude less than 1, while the magnitude of Sirius, which is about nine times as bright as Aldebaran, is a negative quantity, 1⋅4, according to the Harvard photometry.