I propose in the present lecture to give some account of various theories which have been designed to describe the processes of change by which the bodies of the solar system and the stellar universe may be conceived as having reached their present configurations and general physical states. Such theories consist of attempts to trace back into the remote past the history of the solar system and of other configurations which we observe telescopically and with the aid of the spectroscope on the assumption that the physical laws by means of which we describe the present motions of bodies and their thermal and other physical changes are adequate to describe what we conceive to have happened in the immense periods of time which we must assume in accordance with those laws to have elapsed since the primeval conditions postulated by such cosmical theories. This assumption involves a considerable element of speculation because our knowledge of the range of applicability of physical laws is determined and limited by observations of the special physical processes which we can actually observe only during strictly limited intervals of time; and these laws can only hypothetically be extended to embrace processes going on under conditions widely different and during immense periods of time.
An examination of the bodies of the solar system reveals certain striking uniformities within that system. In the first place the eight great planets Mercury Venus the Earth Mars Jupiter Saturn Uranus and Neptune all revolve in the same direction round the sun; their orbits are all nearly in the same plane and are all approximately ellipses with small eccentricities that is nearly circular. The same statement holds good of the minor planets or asteroids some 900 in number which have been discovered in the solar system. These facts are sufficient to suggest that the uniformity in the orbits of the bodies of the solar system may be represented as the result of some process of formation from a common origin. But these facts do not stand alone. The planets rotate round their axes in the same direction and their satellites with certain exceptions rotate round the primaries in nearly circular orbits nearly in the same plane and in the same direction. Jupiter and Saturn each has a system of satellites forming systems like the system of the sun and planets but on smaller scales. It appears that the exceptional cases arise on the outermost parts of the solar system and the outermost parts of the systems of Jupiter and Saturn. Thus Neptune has only one satellite and this has retrograde motion; that is its direction of revolution is in the opposite direction to that of the great majority of the satellites and of all the planets. Uranus has four satellites whose orbits are all highly inclined to the ecliptic; Saturn has nine satellites of which the outermost has retrograde motion; and its orbit has a large eccentricity. Of the nine satellites of Jupiter the two outermost have retrograde motion. Thus in each case the deviation from uniformity attaches to the planets or satellites which are at the outermost distance from the sun or the primary.
In 1772 it was pointed out by Titius a Professor at Wittenberg that the distances of the six planets at that time known from the sun were very approximately represented by numbers which increase according to a very simple law; but that there was one interruption the planet that should in accordance with the law have its orbit between that of Mars and that of Jupiter not being known to exist. The matter was taken up by Bode of Berlin who suggested that an unknown planet remained to be discovered which would occupy the vacant place in the table of distances indicated by the law of Titius which has since been known as Bode's law. The discovery of the planet Uranus was made about this time and it appeared that its distance from the sun was in fair conformity with the law. This discovery lent further weight to the prediction that a planet would be found to occupy the vacant place and this prediction was ultimately verified in an unexpected manner. A number of small planets or asteroids were discovered in the space between the orbits of Mars and Jupiter the first of these being discovered on the first day of the nineteenth century by Piazzi a Professor at Palermo. The idea then presented itself that these asteroids were fragments of a single planet which had been broken in pieces by an explosion. It was indeed shown that three of these asteroids really conformed closely to Bode's law. Since that time the number of asteroids observed in the region between the orbits of Mars and Jupiter has steadily increased until some 900 of them have been found but the notion that they are all fragments of one original planet is for various reasons regarded as untenable. Nevertheless the discovery is remarkable as the first instance of a successful prediction of the existence of bodies which had at the time not been observed. The story of the still more remarkable verification of the prediction made by J. C. Adams and Leverrier that a planet would be found outside the orbit of Uranus has often been told. This discovery of the planet Neptune was predicted mainly as the result of observation that the motion of the planet Uranus exhibited disturbances which could only be accounted for on the hypothesis that they were due to an unobserved planet at greater distance from the sun. Whereas the prediction which led to the discovery of the first asteroids was inspired by the purely empirical rule known as Bode's law in the prediction which led to the discovery of Neptune that law was only employed to afford ground for a probable value of the distance of the planet from the sun; calculations based upon the law of gravitation taken in conjunction with the data afforded by the irregularities in the motion of Uranus forming the chief basis of the prediction.
After this survey of some of the main features of the solar system and of the considerable degree of the regularities in its structure I now turn to the consideration of the theories that have been proposed as to the mode in which it has been evolved and in particular to the celebrated Nebular hypothesis first suggested by the Philosopher Immanuel Kant and developed more precisely by Laplace.
Kant's speculation as to the origin of the heavenly bodies was published in 1755 in his Allgemeine Naturgeschichte und Theorie des Himmels and was applied by him not only to the solar system but to the stellar universe. He supposed the solar system to have been developed from an initial condition in which a cold nebula at rest consisted of a vast mass of evenly diffused particles. This nebula he supposed to commence to concentrate under the mutual gravitation of its parts and to become hot in doing so owing to the consequent compression. He made the quite arbitrary and unwarranted assumption that this process would give rise to a rotation of the whole mass. He assumed further that the matter would concentrate into rings which would be in rotation and he illustrated this by the case of the rotating rings of Saturn which he regarded as giving evidence of the correctness of his views. He supposed that in course of time these rings would become unstable and would form planets by a process of agglomeration; thus leading to a system of planets revolving round the densest and hottest core the sun. The satellites he supposed to be formed by a repetition of similar processes on a smaller scale as the planets gradually contracted under their own gravitation.
The Nebular hypothesis as we now understand it was first put forward by Laplace in 1796 in his Exposition du Sustéme du Monde. Unlike Kant of whose speculations Laplace appears not to have had any knowledge Laplace limited his theory to the case of the solar system. He assumed as the original form from which the solar system was evolved an immense nebula of a flat or lens-shape consisting of extremely attenuated but gaseous material. Unlike Kant he assumed the nebula to be originally in a state of slow rotation round an axis thus avoiding the dynamical difficulty in Kant's theory as to how the rotation came into being. The mass falls in upon itself owing to the gravitation of its parts and as this occurs the central portion becomes hotter as the whole mass shrinks whilst the outer parts are cooled by radiation at the surface. Since the angular momentum of the mass remains constant in amount the shrinkage of dimensions of the nebula produces a gradual increase in the angular velocity of rotation. It was assumed by Laplace that this increase of angular velocity led to the separation of an outer ring of matter from the main mass. As the shrinkage of the main mass proceeded this process of shedding a ring of matter would be repeated and as the result there would be a central core surrounded by a series of concentric rings all in rotation about a central axis. The planets were then supposed to be formed in the manner indicated by Kant the rings becoming unstable and ultimately forming planets.
In accordance with this theory the rings of Saturn represent a stage in the general process of the formation of planets and of satellites. The theory does not explain why in accordance with dynamical theory the successive rings should become unstable or why the rings of Saturn should form an exception to this instability. It was pointed out by Sir G. H. Darwin that in case a ring became unstable the resulting planet would not be formed on the perimeter of the ring but at its centre of gravity. The fact that a continuous rotating ring of matter would be unstable was established by Maxwell in 1857 who found that the stability of the rings of Saturn could only be accounted for by the supposition that they consist of an aggregation of separate small fragments or a heap of stones.
The highly speculative character of Laplace's theory makes it clear that before it can be accepted as a probable account of the manner in which we may conceive the solar system to have arisen the various stages which it includes must be scrutinized in the light of the principles of Dynamics. The difficulties of a mathematical kind which are involved in an investigation of the forms taken up by rotating masses of tenuous gas of the stability of such forms and in the ascertainment of what happens when the forms become unstable are so great that nearly all the mathematical investigators who have concerned themselves with these questions have found it necessary to treat the nebulae as consisting of homogeneous incompressible fluid. Although the results of these investigations throw some considerable light upon the dynamical possibility of the processes involved in the theory in its original form they cannot be regarded as having an absolutely decisive weight in our judgment of the theory. The details of that theory have received considerable modification at the hands of later investigators but the notion that the solar system originated from a nebulous mass of gas and the conception that increased rotation of that mass owing to shrinkage has been a main factor in the change from the primitive nebula to the present system remain as at least highly probable hypotheses; and they have not been superseded by any other theory.
By later Astronomers the nebular hypothesis has been considered more generally than by Laplace in relation to the idea that stars in general may be conceived to have been formed out of nebulae. The enormous increase of our knowledge of the nature of heavenly bodies due to vastly increased powers of observation in which photography plays an essential part to the employment of the spectroscope not only for the determination of the chemical nature of the composition of the sun stars and nebulae but also of their motions and the discovery that double and multiple stars are extremely numerous in the stellar system have brought Laplace's theory into relation with a number of fundamental problems of cosmology.
After the discovery in 1842 of the mechanical equivalence of heat and motion the attention of Physicists was directed to the question of the means by which the solar radiation of heat and light is maintained. It was pointed out by Mayer that this radiation would have long since ceased if the sun were a body simply cooling or in a state of combustion and without any source of energy from which heat could be obtained. As a source from which the solar radiation might be sustained he advanced the meteoric hypothesis. In accordance with this hypothesis a swarm of meteoric bodies is constantly falling into the sun and by the stoppage of their motion an immense amount of heat is evolved. Mayer calculated that from this source from 4600 to 9200 times as much heat would result as would result from the burning of equal masses of coal. The difficulty of this theory is that the amount of matter which must fall into the sun in order to maintain its radiation must be enormous amounting to a mass equal to that of the moon every half year. So great an accession to the mass of the sun would materially affect the gravitation of the planets towards it producing a diminution in the periods of their revolution round the sun. In the case of the earth Mayer reckoned that this would involve an annual diminution of the length of the year by a not very small fraction of a second; and he postulated an emission of material from the sun to neutralize this continual reinforcement of material from the meteorites Independently of Mayer this theory was advanced by Waterton at the Meeting of the British Association in 1853 and was fully discussed by Lord Kelvin in the following year. Kelvin pointed out that although the influx of meteorites “is the only one of all conceivable causes of solar heat which we know to exist from independent evidence” that source of heat is entirely insufficient. An intraplanetary supply of meteorites would be much too scanty to achieve any perceptible result and it was estimated by Kelvin that a sufficient supply from extra-planetary space would have resulted in a shortening of the year by six weeks since the beginning of the Christian era. This theory of the maintenance of solar heat led to the hypothesis that the earth and planets had been formed by an agglomeration of meteorites which must have been of amount much greater than they at present receive. But the evidence of geological deposits negatives this theory since no considerable parts of these deposits can possibly have been of meteoric origin.
A theory which has been much more widely accepted than the meteoric hypothesis was put forward by Helmholtz in 1854. In accordance with this theory the maintenance of the solar heat and light is due to the shrinkage of the material of which the sun is composed. As the envelope of the sun is continually cooled by radiation a condensation towards the centre occurs which develops heat. In order to provide for the present rate of emission a diminution of the solar diameter by 380 feet a year would suffice and in five million years the sun would have shrunk to less than half its present bulk. Helmholtz estimated that radiation may have gone on at its present intensity for about twenty-two million years an estimate which geologists find insufficient. This theory is in accordance with Laplace's view that the material of which the sun is composed was once diffused through an immense portion of space and has gradually been condensed with the production of heat to the present dimensions.
To that part of the nebular theory which relates to the formation of planets many objections have been raised. Among these is the failure to account for the retrograde motion of the satellite of Neptune and of the satellites of Uranus. Again one of the two satellites of Mars revolves round the planet in a shorter time than that of the rotation of the planet round its axis a fact which it is difficult to reconcile with Laplace's views as to the generation of satellites. An objection to the theory of Laplace is that since under gravitation towards the sun the velocity diminishes as the distance from the centre increases the rings could only coalesce into globes with a backward rotation round their axes. Laplace himself was aware of this difficulty which he endeavored to meet by the assumption that the rings had sufficient cohesion to allow them to rotate in one piece as if they were solid. Thus the outer part of a ring would move faster than the inner part and would give rise to planets spinning forwards as is actually the case. It is difficult to conceive that the materials of nebulae can have had the amount of cohesion which is involved in this explanation. To meet these difficulties a theory was propounded by Faye in accordance with which all the planets except Uranus and Neptune were formed in a practically homogeneous nebula before its condensation had formed the sun. This nebula revolved like a solid body with velocity increasing with the distance from the axis. The planets were then formed by agglomeration and consequently their rotation was direct. The sun was subsequently formed by contraction of the nebula and Uranus and Neptune were formed at a time when this contraction was far advanced; in accordance with this theory the order of formation of the planets is the reverse of what it is in accordance with Laplace's theory.
Attention was called to a factor of great importance in connection with the origin of satellites by the investigations of Sir G. H. Darwin on the effects of tidal action between the Earth and the Moon. The moon by producing tides in the ocean which act as a kind of brake upon the rotation of the earth round its axis produces a very slow lengthening of the day and this effect must have been much greater than it is at present when the earth was liquid or plastic. A precisely similar effect was produced by the tidal action of the earth on the moon. The result of this tidal action in the case of the moon is the present state of the rotation of the moon round its axis in the same period as its rotation round the earth so that it always shows the same half of its surface to the earth. Darwin proved that a consequence of the tidal action of the moon on the earth in accordance with the laws of Dynamics is that the moon must slowly recede from the earth while its time of rotation round the earth is very slowly increased. He showed that the ultimate result will be that the day and the month will become equal to one another each being then about 1400 hours a state of tidal equilibrium being then reached with the moon at much greater distance from the earth than at present. If this process be traced back from the present time at some epoch not less than 54 million years ago the length of the day was between 2 and 2½ hours; the moon was then almost in contact with the earth and rotated round the earth in the same period as that of the earth round its axis. The period of rotation of the moon round the earth when they were nearly in contact was in accordance with Kepler's law between 2 and 2½ hours. It can be shown mathematically that the most rapid period of rotation of a fluid mass of spheroidal shape of density equal to the earth's average density which is consistent with stability is two hours and twenty minutes. It was consequently suggested that the moon was generated by the separation of a mass from the earth owing to instability due to too rapid rotation of the earth a breakage into two masses being the consequence. That the general character of the changes in the rotation of the earth and in the length of the month is in accordance with the laws of Dynamics is not open to doubt but serious criticism has been directed to the theory that the initial stage of this process is connected with the genesis of the moon. It was pointed out that when the moon was very near the earth a disruptive strain would act on the moon sufficient to prevent it holding together as one continuous mass; to meet this objection Darwin suggested that at that time the moon may have been an aggregation of separate masses. But it would appear that the effect of tidal action would have caused a dispersion of these separate masses and to this objection there does not appear to be any adequate answer so that this part of Darwin's theory cannot be regarded as established.
The questions were discussed by Darwin whether satellites of the other planets in the solar system could have originated in the same manner as the moon and whether the present relations between the primaries and their satellites could be accounted for as effects of tidal friction. The answers to both questions were in the negative. The circumstances in these cases are different from those of the earth and moon in the important respect that the ratio of the mass of the moon to that of the earth is much greater than the ratio of the mass of any other satellite to that of its primary. Consequently tidal friction has been a much more important factor in determining the relations of the earth and moon than in any other case in the solar system. Darwin showed that satellites such as those of Jupiter Saturn or Mars in all probability never revolved round the primaries in much smaller orbits than at present; thus in these cases no such great tides ever existed as were raised on the earth when the moon's orbit was much smaller than at present. Darwin also considered the effect which the friction of the tides raised on the planets by the sun may be taken to have had in altering the periods of their orbits and their distances from the sun. He showed that no large effects upon the planetary orbits can have arisen from the solar tides and thus that the planets cannot have arisen by separation of portions of the plastic mass of the sun in a manner similar to that by which he supposed the moon to have been detached from the earth. This removes one possible alternative to Laplace's theory of the formation of the planets. It was however pointed out by Roche in 1872 that the tides produced on the planets by the sun may have been a decisive factor in relation to the formation of satellites. According to Darwin's view a satellite will be formed when the rotation of a fluid or plastic mass comes to exceed a certain magnitude when the figure becomes unstable. There would then be no production of a satellite in case the solar tidal friction were sufficient to prevent the attainment of this critical angular velocity of rotation; this may be held to account for the fact that Mercury and Venus have no satellites their nearness to the sun involving a large effect of solar tides in reducing what would otherwise have been their greatly increased periods of rotation as their masses contracted. In the case of the earth and the outer planets the friction of the solar tides may be supposed not to have been sufficient to prevent the instability arising owing to too rapid rotation and thus to have prevented the formation of satellites by division into two parts.
It was formerly supposed that our solar system was typical of what was regarded as the ordinary state of things in the universe; that in fact every star was a sun with its attendant satellites forming for each star a system with a character resembling our solar system. The discovery of the existence in the heavens of a large number of binary stars has modified this view since it has exhibited the existence of systems of a character differing widely from the solar system. When William Herschel commenced his great exploration of the heavenly bodies his attention was early directed to double stars that is pairs of stars apparently very close to one another. At first he shared the general opinion that the connection between such a pair was purely optical; that in fact they might be simply two stars at widely different distances but of which the directions happened to be nearly the same. But he was later led to the conclusion that in a very considerable number of cases double stars really consist of binary combinations in which the two stars rotate round one another. In several cases the periods of these rotations were determined. It has since been shown that such binary combinations exist in large numbers. Of the nineteen stars which are at the present time nearest to us it is definitely known that eight no less than 42 per cent of the whole are binary stars. A scrutiny of various parts of the heavens makes it probable that not less than one-third of all the stars that can be observed are binaries. As long ago as 1764 it was observed by John Goodricke a deaf mute that the brilliancy of the star Algol was subject to periodic variation and he suggested that this phenomenon was due to periodic eclipses by an invisible companion star. The correctness of this theory was verified in 1889 when it was proved that the star was moving in an orbit of such a character as would result from gravitation with a dark companion star by which it would be partially eclipsed. By means of the spectroscope it has been proved that many stars which are single in appearance really consist of two stars in orbital motion round one another. It was from the first surmised that the motions of the stars in a binary combination are such as would be in accordance with the law of gravitation and that this is actually the case has been established in a number of instances. The first of such cases of gravitating binaries was ascertained in 1827 by Savary of Paris who proved that for a bin at star in the Great Bear the orbits of the components were ellipses with a period of 58 1⁄4 years in full accord with the gravitational scheme. In a number of binaries it has been found possible to determine the ratio of the masses of the two stars which form the combination and in all such cases the masses have been found to be not very unequal. It has been found for example that in the visual binaries in which the ratio of the masses is pretty accurately determined one of the stars is never less in mass than one-third the mass of the other star and a similar result has been obtained in the case of nineteen spectroscopic binaries. On the other hand in the solar system the mass of the greatest planet Jupiter is less than a thousandth part of the mass of the sun. It follows that the sun and Jupiter cannot be regarded as forming a binary system similar to the many binary systems which have been observed. Thus a binary star with its attendant planets if such exist forms a system which cannot but be radically different in character from the solar system. Moreover the existence of triple and of multiple systems has been observed. It has been shown that triple systems consist normally of a pair close together with a third star revolving at a distance from the centre of gravity of the pair about ten times the distance of the stars of the pair from one another.
A theory has been worked out by Sir G. H. Darwin which gives at least an indication of the mode in which a double star may be conceived of as generated from a single original mass. The mathematical difficulties of a theory of this kind are so great that they have to be simplified by means of assumptions which are of such a character that the conditions in the mathematical investigation are widely different from what we must assume them to be in actual cases and yet not so widely different that they destroy all the value of the results of the investigation as an indication of what may be conceived to have happened in such actual cases. An actual star consisting of liquid or viscous matter in rotation radiates its heat and shrinks gradually as it cools. Its density will be at any one time very various as we proceed from the outer surface to the interior parts and its average density will increase as the whole mass contracts. Darwin considered what would happen in the case of a mass of liquid which at any one time is homogeneous and incompressible. The shrinkage is assumed to be so slow as to be consistent with this assumption although that shrinkage of course involves an increase of density of the fluid. It has long been known from mathematical investigation that such a mass of liquid in rotation is in relative equilibrium if it have the form of a spheroid with its axis of symmetry as the axis of rotation this axis being the smaller axis of the elliptic sections of the spheroid through that axis. It is further known that this form is a stable one so long as the rate of rotation of the mass is sufficiently slow. As the mass slowly shrinks its rate of rotation increases in accordance with the dynamical principle of the constancy of its angular momentum and the stability of the form gradually diminishes. As it shrinks and the angular velocity of rotation increases its shape changes; in fact it becomes continually more flattened at the poles. When it attains a certain shape in which the equatorial and polar axes are in the ratio of 1000 to 583 the stability entirely disappears; it has reached what has been called by Poincaré a figure of bifurcation a point at which the series of spheroids through which it has passed during the gradual increase of its rate of rotation passes over into a new series of figures of a different kind. This new series of figures consists of a set of ellipsoids with all their axes unequal. As the increase of the rate of rotation proceeds the axes of the equatorial ellipse on the plane perpendicular to the axis of rotation become continually more unequal until when a certain angular velocity has been attained and the longest axis has become about three times the shortest a new figure of bifurcation is reached when the stability of the motion has again disappeared. It had been shown mathematically by Poincaré that the new forms which the liquid will take up after this form of bifurcation is passed will consist of a series of pear-shaped figures in which the figure is blunted at one end and prolonged into a sort of snout at the other end. The question whether these pear-shaped figures are stable is a mathematical problem of great difficulty and the answer given to the question has been different by different investigators. Darwin came himself to the conclusion that they are stable but Liapounoff came to the opposite conclusion and further investigations by Jeans appear to confirm the answer given by Liapounoff. The suggestion made by Darwin was that as the rotation still further increases the inequality between the two parts of the pear becomes accentuated a furrow being formed; and that in the end a new figure of bifurcation is reached after which the mass splits into two parts which separate the subsequent history being that of the two separate masses which represent the two stars in a binary combination. Great doubt is thrown upon the applicability of this theory to the case of the genesis of double stars by the uncertainty as to the stability of the pear-shaped figures but even if the fact that they are unstable be finally admitted they do not wholly lose their importance in connection with theories of cosmogony.
Various mathematical investigations have been carried out in another direction with a view to throwing light upon the double star problem. Instead of attempting to trace out a series of changes in a single continuous mass with a view to the ascertainment whether and under what conditions it may divide into two separate masses as in Darwin's theory the problem has been approached from the other end. In fact the problem of determining the tidal action upon one another of two separate masses rotating round one another without change of relative position has been taken as the starting point. This problem was studied in considerable detail by E. Roche and also by Sir G. H. Darwin. By the former of these investigators the problem was simplified by considering one of the bodies to be a rigid sphere and the series of forms of the other body which was taken to consist of a fluid mass was traced out. It was found that no relative equilibrium of the two masses is possible if the distance of the two bodies from one another is less than a certain minimum depending upon the ratio of their masses so that they cannot rotate in close contact with one another. The more difficult problem connected with the double star question was discussed by Darwin in which both masses are fluid so that each is distorted under the tidal forces generated by the other. As the result of intricate investigations of the stability of the figures of the two rotating masses it appears to be impossible to trace back the states of these masses to a time when they were in contact or nearly so with one another. In fact it appears that in those cases there are no figures which are stable except ellipsoids and spheroids whereas if the masses are to be regarded as coalescing they must pass through forms which are far from being ellipsoidal. When instability is reached it would seem that the whole character of the motion of the system must be changed. These problems are so difficult that no complete solution of them has as yet been obtained. Jeans who has continued the investigations of Poincaré and Darwin in various directions has expressed the opinion that it is highly probable that tidal action may produce systems such as are seen in the solar system and in the systems of Jupiter and Saturn; that increasing rotation may produce systems such as are seen in ordinary binary stars and that the close approach of two stars revolving about one another may produce systems such as Saturn's rings and possibly also the asteroids.
I turn now to some consideration of that part of the theory of Laplace and Kant which has to do with the generation of stars from nebulae. As discerned by the telescope reinforced by the photographic plate there exist nebulae of several distinct forms; some 15000 nebulae have been hitherto investigated. The most frequent of these are the spiral nebulae which consist of a nucleus with two arms emerging from opposite points; these two arms have each a spiral form approximately that of the equiangular spiral. The so-called planetary nebulae are comparatively very few in number; they have an ellipsoidal shape. There are also ring-shaped nebulae and also elongated or spindle-shaped nebulae. Besides these are irregular nebulae such as the great nebula in Orion. All the knowledge we have of nebulae apart from their apparent shapes as disclosed by the telescope has been obtained by analysis of their spectra. In this manner information is obtained in the first place of their chemical constituents. In 1862 Sir W. Huggins and Miller in London and Father Secchi in Rome commenced the work of studying the stars and nebulae by the new means which the spectroscope provided. In 1864 a bright planetary nebula in Draco was found by Huggins to consist of a mass of glowing va pour which showed the characteristic bright line of nitrogen and a fainter line showed itself to be the F line of hydrogen. By 1868 Huggins had examined the spectra of about 70 nebulae about one-third of which turned out to be of a gaseous character and showed the nitrogen line. It was found that all the planetary and annular nebulae as well as the irregular nebulae in the region of the milky way have the character of a glowing va pour. Besides the knowledge of the constitution of stars and nebulae which has been obtained by the use of the spectroscope and has built up the department of stellar chemistry spectroscopic analysis has also been applied to determine the motions of stars and nebulae relatively to the earth in the line of sight. In 1842 Christian Doppler of Prague enunciated the principle that the colour of a luminous body must be changed when the body approaches or recedes from the observer with sufficient velocity to make the change sensible. In an amended form this principle is that the velocity of approach or recess of a star or nebula will exhibit itself by means of a displacement of the lines of the spectrum of the body from the position of the lines of the spectrum of the same substance in the laboratory and that this velocity may be estimated by measuring the amount of this displacement in one direction or the other. This very delicate operation of measurement of displacement was first successfully carried out by Huggins in 1868 in the case of the star Sirius leading to the result that the star is receding from the solar system at the rate of twenty-nine miles a second. A more accurate observation made in 1872 diminished this rate to about twenty miles per second and estimates were made by Huggins for other stars some of which are receding from and others approaching the solar system. Since that time the measurement of such velocities has formed part of the regular work of Astronomers. The earlier observations of nebulae did not disclose any traces of their motion in the line of sight but later observations have shown that the spiral nebulae have very great velocities. For example the Andromeda nebula has been estimated to have a velocity of approach of 300 kms. per second or perhaps somewhat more. Other spiral nebulae have been estimated to have a still greater velocity of recession exceeding 1100 kms. per second. In fact the average velocity of spiral nebulae is some twenty times greater than the average velocity of a star belonging to the system of which the sun is a member. But besides these velocities of nebulae as wholes the spectroscopic method has been applied to detect the rotation of nebulae. A nebula in Virgo was discovered in 1914 by Slipher to be in rotation; and the velocity of rotation has been since estimated to be 330 kms. a second at a distance of 2′ from the centre the velocity increasing proportionally to the distance from the centre. In the cases of other nebulae similar observations have been made but in one case at least the rotation does not appear to be one in which the mass rotates like a rigid body for the angular velocity diminishes with the distance from the centre. The irregular nebulae are found to be almost at rest relatively to the stars of our system and the planetary nebulae have with certain exceptions velocities much smaller than the spiral nebulae. The evidence appears to show that the spiral nebulae are quite outside our system of stars and they are tentatively regarded as island universes each comparable in scale with the system of stars of which the sun is a member.
The opinion that the origin of stars may be traced to nebulae has been very widely held but there has been some considerable difference of opinion as to whether a primitive nebula should be regarded as a mass of gas or as a cloud of dust. Lord Kelvin made the suggestion that a collection of meteoric stones vaporized by collisions would give rise to a gaseous nebula from which a star might be generated by contraction in accordance with the hypothesis of Laplace. The study of stars by the spectroscopic method led to a classification of them into types which were supposed to be indicative of different stages of development after the nebular stage had been passed. Five such successive stages have been distinguished the one first after the formation from nebulae representing the hottest and least dense stars and the last the red stars being the coolest and nearest to extinction. But recent discoveries of H. N. Russell have thrown great doubt not so much upon the theory of the nebular origin of stars as upon the notion that these five spectral types represent the successive ages of stars. There is strong reason to think that a star of the first or hottest type is not at the beginning of its history as a star but half way through it. In accordance with this later view a nebula is or becomes non-luminous and remains so until the mass becomes incandescent as a giant red star. It then passes in order through the successive stages in which it becomes hotter until it becomes of the hottest type and then proceeds in the reverse order until it finally becomes again a red star previously to its extinction. It is thought that only the most massive stars ever go through all the different stages many of them turning back before the type of the hottest star is reached. This is in accordance with the observed fact that all the stars of the hottest type are of exceptionally great mass. Russell's theory is chiefly based upon the evidence afforded by the observed absolute magnitudes of stars. The stars in the three redder and cooler spectral classes were found to fall into two detached groups. In one of these groups the absolute magnitude was found to be nearly independent of spectral type. In the other group consisting of stars of smaller magnitude that magnitude varies with the spectral type being smallest in the reddest type. The stars of these two groups have been called “giant” and “dwarf” stars respectively. A mathematical investigation by Jeans of the changes to be expected in a mass of gas when there is a continual emission of radiation from its surface yields results which are in accordance with Russell's theory.
A new factor has been brought into the discussion of all questions connected with the production and radiation of heat by the recent discovery of the presence of radio-active substances which provide sources of heat that had previously not been recognized. It has been maintained recently that radio-active substances in the interior of the earth may have provided a source of heat of sufficient amount to form an important factor in estimates of the age of the earth based upon the length of time it may have required to cool down to its present condition. The estimates of such age formed by Physicists such as Lord Kelvin which have been regarded by Geologists as inadequate may it is held have to be completely revised when the emission of heat from radio-active substances is taken into account. As regards the effect of radio-active substances in the sun it has been pointed out by Lindemann that the radioactive energy in the sun must be regarded as insignificant in amount compared with the gravitational energy. It is however possible that some more effective means of production of energy of a sub-atomic character perhaps involving the actual destruction of matter may have to be recognized as contributory to the solar radiation. Of the efforts made in connection with the great Science of Geology to give a conceptual account of the mode in which the earth may be regarded as having reached its present condition I am unable to give any account. The few fundamentally important cosmical problems that I have discussed may perhaps afford a sufficient illustration of the highly speculative character of those parts of Natural Science which concern themselves with the ideal reconstruction of the physical conditions of the remote past. It is clear that the scientific theories relating to such matters are tentative and hypothetical in a sense and in a degree which marks them off from theories which refer to short time processes that are capable of verification or refutation of a more direct kind than is possible in the case of theories which have essential reference to immense periods of time. The investigation of cosmical theories involves a completely justifiable attempt by an extension of our conceptions of the actual processes which we can observe to represent such processes as but portions of processes which we conceive to have proceeded during periods belonging to a vastly greater time-span than that of any actual observer. To make the attempt in a certain sense to understand the present by means of the past we are impelled by ineradicable impulses of the human mind. The mental satisfaction obtained by imbedding processes which we can actually observe in long time processes beyond our direct reach is one which we shall never forego. Needless to say when we attempt to push back physical processes ideally as far as may be we involve ourselves in an indefinite regress. Of absolute origins Science knows nothing and we can form no conception. The so-called primordial state such as is postulated in the nebular hypothesis presents a problem which we do not attempt to solve. With some such postulation behind which we do not go every attempt at an historical scientific construction must commence.
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