Fig. 101.—Illustration of the Motion of Precession.Fig. 101.—Illustration of the Motion of Precession.
If the earth were subject to no external interference, then the direction of the axis about which it rotates must remain for ever constant; but as the direction of the axis does not remain constant, it is necessary to seek for a disturbing force adequate to the production of the phenomena which are observed. We have invariably found that the dynamical phenomena of astronomy can be accounted for by the law of universal gravitation. It is therefore natural to enquire how far gravitation will render an account of the phenomenon of precession; and to put the matter in its simplest form, let us consider the effect which adistant attracting body can have upon the rotation of the earth.
To answer this question, it becomes necessary to define precisely what we mean by the earth; and as for most purposes of astronomy we regard the earth as a spherical globe, we shall commence with this assumption. It seems also certain that the interior of the earth is, on the whole, heavier than the outer portions. It is therefore reasonable to assume that the density increases as we descend; nor is there any sufficient ground for thinking that the earth is much heavier in one part than at any other part equally remote from the centre. It is therefore usual in such calculations to assume that the earth is formed of concentric spherical shells, each one of which is of uniform density; while the density decreases from each shell to the one exterior thereto.
A globe of this constitution being submitted to the attraction of some external body, let us examine the effects which that external body can produce. Suppose, for instance, the sun attracts a globe of this character, what movements will be the result? The first and most obvious result is that which we have already so frequently discussed, and which is expressed by Kepler's laws: the attraction will compel the earth to revolve around the sun in an elliptic path, of which the sun is in the focus. With this movement we are, however, not at this moment concerned. We must enquire how far the sun's attraction can modify the earth's rotation around its axis. It can be demonstrated that the attraction of the sun would be powerless to derange the rotation of the earth so constituted. This is a result which can be formally proved by mathematical calculation. It is, however, sufficiently obvious that the force of attraction of any distant point on a symmetrical globe must pass through the centre of that globe: and as the sun is only an enormous aggregate of attracting points, it can only produce a corresponding multitude of attractive forces; each of these forces passes through the centre of the earth, and consequently the resultant force which expresses the joint result of all the individual forces must also be directed through the centre of the earth. Aforce of this character, whatever other potent influence it may have, will be powerless to affect the rotation of the earth. If the earth be rotating on an axis, the direction of that axis would be invariably preserved; so that as the earth revolves around the sun, it would still continue to rotate around an axis which always remained parallel to itself. Nor would the attraction of the earth by any other body prove more efficacious than that of the sun. If the earth really were the symmetrical globe we have supposed, then the attraction of the sun and moon, and even the influence of all the planets as well, would never be competent to make the earth's axis of rotation swerve for a single second from its original direction.
We have thus narrowed very closely the search for the cause of the "precession." If the earth were a perfect sphere, precession would be inexplicable. We are therefore forced to seek for an explanation of precession in the fact that the earth is not a perfect sphere. This we have already demonstrated to be the case. We have shown that the equatorial axis of the earth is longer than the polar axis, so that there is a protuberant zone girdling the equator. The attraction of external bodies is able to grasp this protuberance, and thereby force the earth's axis of rotation to change its direction.
There are only two bodies in the universe which sensibly contribute to the precessional movement of the earth's axis: these bodies are the sun and the moon. The shares in which the labour is borne by the sun and the moon are not what might have been expected from a hasty view of the subject. This is a point on which it will be desirable to dwell, as it illustrates a point in the theory of gravitation which is of very considerable importance.
The law of gravitation asserts that the intensity of the attraction which a body can exercise is directly proportional to the mass of that body, and inversely proportional to the square of its distance from the attracted point. We can thus compare the attraction exerted upon the earth by the sun and by the moon. The mass of the sun exceeds the massof the moon in the proportion of about 26,000,000 to 1. On the other hand, the moon is at a distance which, on an average, is about one-386th part of that of the sun. It is thus an easy calculation to show that the efficiency of the sun's attraction on the earth is about 175 times as great as the attraction of the moon. Hence it is, of course, that the earth obeys the supremely important attraction of the sun, and pursues an elliptic path around the sun, bearing the moon as an appendage.
But when we come to that particular effect of attraction which is competent to produce precession, we find that the law by which the efficiency of the attracting body is computed assumes a different form. The measure of efficiency is, in this case, to be found by taking the mass of the body and dividing it by thecubeof the distance. The complete demonstration of this statement must be sought in the formulæ of mathematics, and cannot be introduced into these pages; we may, however, adduce one consideration which will enable the reader in some degree to understand the principle, though without pretending to be a demonstration of its accuracy. It will be obvious that the nearer the disturbing body approaches to the earth the greater is theleverage(if we may use the expression) which is afforded by the protuberance at the equator. The efficiency of a given force will, therefore, on this account alone, increase in the inverse proportion of the distance. The actual intensity of the force itself augments in the inverse square of the distance, and hence the capacity of the attracting body for producing precession will, for a double reason, increase when the distance decreases. Suppose, for example, that the disturbing body is brought to half its original distance from the disturbed body, the leverage is by this means doubled, while the actual intensity of the force is at the same time quadrupled according to the law of gravitation. It will follow that the effect produced in the latter case must be eight times as great as in the former case. And this is merely equivalent to the statement that the precession-producing capacity of a body varies inversely as the cube of the distance.
It is this consideration which gives to the moon animportance as a precession-producing agent to which its mere attractive capacity would not have entitled it. Even though the mass of the sun be 26,000,000 times as great as the mass of the moon, yet when this number is divided by the cube of the relative value of the distances of the bodies (386), it is seen that the efficiency of the moon is more than twice as great as that of the sun. In other words, we may say that one-third of the movement of precession is due to the sun, and two-thirds to the moon.
For the study of the joint precessional effect due to the sun and the moon acting simultaneously, it will be advantageous to consider the effect produced by the two bodies separately; and as the case of the sun is the simpler of the two, we shall take it first. As the earth travels in its annual path around the sun, the axis of the earth is directed to a point in the heavens which is 23-1â„2° from the pole of the ecliptic. The precessional effect of the sun is to cause this point—the pole of the earth—to revolve, always preserving the same angular distance from the pole of the ecliptic; and thus we have a motion of the type represented in the diagram. As the ecliptic occupies a position which for our present purpose we may regard as fixed in space, it follows that the pole of the ecliptic is a fixed point on the surface of the heavens; so that the path of the pole of the earth must be a small circle in the heavens, fixed in its position relatively to the surrounding stars. In this we find a motion strictly analogous to that of the peg-top. It is the gravitation of the earth acting upon the peg-top which forces it into the conical motion. The immediate effect of the gravitation is so modified by the rapid rotation of the top, that, in obedience to a profound dynamical principle, the axis of the top revolves in a cone rather than fall down, as it would do were the top not spinning. In a similar manner the immediate effect of the sun's attraction on the protuberance at the equator would be to bring the pole of the earth's axis towards the pole of the ecliptic, but the rapid rotation of the earth modifies this into the conical movement of precession.
The circumstances with regard to the moon are much morecomplicated. The moon describes a certain orbit around the earth; that orbit lies in a certain plane, and that plane has, of course, a certain pole on the celestial sphere. The precessional effect of the moon would accordingly tend to make the pole of the earth's axis describe a circle around that point in the heavens which is the pole of the moon's orbit. This point is about 5° from the pole of the ecliptic. The pole of the earth is therefore solicited by two different movements—one a revolution around the pole of the ecliptic, the other a revolution about another point 5° distant, which is the pole of the moon's orbit. It would thus seem that the earth's pole should make a certain composite movement due to the two separate movements. This is really the case, but there is a point to be very carefully attended to, which at first seems almost paradoxical. We have shown how the potency of the moon as a precessional agent exceeds that of the sun, and therefore it might be thought that the composite movement of the earth's pole would conform more nearly to a rotation around the pole of the plane of the moon's orbit than to a rotation around the pole of the ecliptic; but this is not the case. The precessional movement is represented by a revolution around the pole of the ecliptic, as is shown in the figure. Here lies the germ of one of those exquisite astronomical discoveries which delight us by illustrating some of the most subtle phenomena of nature.
The plane in which the moon revolves does not occupy a constant position. We are not here specially concerned with the causes of this change in the plane of the moon's orbit, but the character of the movement must be enunciated. The inclination of this plane to the ecliptic is about 5°, and this inclination does not vary (except within very narrow limits); but the line of intersection of the two planes does vary, and, in fact, varies so quickly that it completes a revolution in about 18-2â„3years. This movement of the plane of the moon's orbit necessitates a corresponding change in the position of its pole. We thus see that the pole of the moon's orbit must be actually revolving around the pole of the ecliptic, always remaining at the same distance of 5°, and completing its revolution in 18-2â„3years. It will, therefore, be obvious that there is a profound difference between the precessional effect of the sun and of the moon in their action on the earth. The sun invites the earth's pole to describe a circle around a fixed centre; the moon invites the earth's pole to describe a circle around a centre which is itself in constant motion. It fortunately happens that the circumstances of the case are such as to reduce considerably the complexity of the problem. The movement of the moon's plane, only occupying about 18-2â„3years, is a very rapid motion compared with the whole precessional movement, which occupies about 26,000 years. It follows that by the time the earth's axis has completed one circuit of its majestic cone, the pole of the moon's plane will have gone round about 1,400 times. Now, as this pole really only describes a comparatively small cone of 5° in radius, we may for a first approximation take the average position which it occupies; but this average position is, of course, the centre of the circle which it describes—that is, the pole of the ecliptic.
We thus see that the average precessional effect of the moon simply conspires with that of the sun to produce a revolution around the pole of the ecliptic. The grosser phenomena of the movements of the earth's axis are to be explained by the uniform revolution of the pole in a circular path; but if we make a minute examination of the track of the earth's axis, we shall find that though it, on the whole, conforms with the circle, yet that it really traces out a sinuous line, sometimes on the inside and sometimes on the outside of the circle. This delicate movement arises from the continuous change in the place of the pole of the moon's orbit. The period of these undulations is 18-2â„3years, agreeing exactly with the period of the revolution of the moon's nodes. The amount by which the pole departs from the circle on either side is only about 9·2 seconds—a quantity rather less than the twenty-thousandth part of the radius of the sphere. This phenomenon, known as "nutation," was discovered by the beautiful telescopic researches of Bradley, in 1747. Whether we look at the theoretical interest of the subject or at the refinement of the observations involved, this achievement of the "Vir incomparabilis," as Bradley hasbeen called by Bessel, is one of the masterpieces of astronomical genius.
The phenomena of precession and nutation depend on movements of the earth itself, and not on movements of the axis of rotation within the earth. Therefore the distance of any particular spot on the earth from the north or south pole is not disturbed by either of these phenomena. The latitude of a place is the distance of the place from the earth's equator, and this quantity remains unaltered in the course of the long precession cycle of 26,000 years. But it has been discovered within the last few years that latitudes are subject to a small periodic change of a few tenths of a second of arc. This was first pointed out about 1880 by Dr. Küstner, of Berlin, and by a masterly analysis of all available observations, made in the course of many years past at various observatories, Dr. Chandler, of Boston, has shown that the latitude of every point on the earth is subject to a double oscillation, the period of one being 427 days and the other about a year, the mean amplitude of each being O´´·14. In other words, the spot in the arctic regions, directly in the prolongation of the earth's axis of rotation, is not absolutely fixed; the end of the imaginary axis moves about in a complicated manner, but always keeping within a few yards of its average position. This remarkable discovery is not only of value as introducing a new refinement in many astronomical researches depending on an accurate knowledge of the latitude, but theoretical investigations show that the periods of this variation are incompatible with the assumption that the earth is an absolutely rigid body. Though this assumption has in other ways been found to be untenable, the confirmation of this view by the discovery of Dr. Chandler is of great importance.
The Real and Apparent Movements of the Stars—How they can be Discriminated—Aberration produces Effects dependent on the Position of the Stars—The Pole of the Ecliptic—Aberration makes Stars seem to Move in a Circle, an Ellipse, or a Straight Line according to Position—All the Ellipses have Equal Major Axes—How is this Movement to be Explained?—How to be Distinguished from Annual Parallax—The Apex of the Earth's Way—How this is to be Explained by the Velocity of Light—How the Scale of the Solar System can be Measured by the Aberration of Light.
The Real and Apparent Movements of the Stars—How they can be Discriminated—Aberration produces Effects dependent on the Position of the Stars—The Pole of the Ecliptic—Aberration makes Stars seem to Move in a Circle, an Ellipse, or a Straight Line according to Position—All the Ellipses have Equal Major Axes—How is this Movement to be Explained?—How to be Distinguished from Annual Parallax—The Apex of the Earth's Way—How this is to be Explained by the Velocity of Light—How the Scale of the Solar System can be Measured by the Aberration of Light.
Wehave in this chapter to narrate a discovery of a recondite character, which illustrates in a forcible manner some of the fundamental truths of Astronomy. Our discussion of it will naturally be divided into two parts. In the first part we must describe the nature of the phenomenon, and then we must give the extremely elegant explanation afforded by the properties of light. The telescopic discovery of aberration, as well as its explanation, are both due to the illustrious Bradley.
The expressionfixedstar, so often used in astronomy, is to be received in a very qualified sense. The stars are, no doubt, well fixed in their places, so far as coarse observation is concerned. The lineaments of the constellations remain unchanged for centuries, and, in contrast with the ceaseless movements of the planets, the stars are not inappropriately called fixed. We have, however, had more than one occasion to show throughout the course of this work that the expression "fixed star" is not an accurate one when minute quantities are held in estimation. With the exact measures of modern instruments, many of these quantities are so perceptible that they have to be always reckoned with in astronomical enquiry. We can divide themovements of the stars into two great classes: the real movements and the apparent movements. The proper motion of the stars and the movements of revolution of the binary stars constitute the real movements of these bodies. These movements are special to each star, so that two stars, although close together in the heavens, may differ in the widest degree as to the real movements which they possess. It may, indeed, sometimes happen that stars in a certain region are animated with a common movement. In this phenomenon we have traces of a real movement shared by a number of stars in a certain group. With this exception, however, the real movements of the stars seem to be governed by no systematic law, and the rapidly moving stars are scattered here and there indiscriminately over the heavens.
The apparent movements of the stars have a different character, inasmuch as we find the movement of each star determined by the place which it occupies in the heavens. It is by this means that we discriminate the real movements of the star from its apparent movements, and examine the character of both.
In the present chapter we are concerned with the apparent movements only, and of these there are three, due respectively to precession, to nutation, and to aberration. Each of these apparent movements obeys laws peculiar to itself, and thus it becomes possible to analyse the total apparent motion, and to discriminate the proportions in which the precession, the nutation, and the aberration have severally contributed. We are thus enabled to isolate the effect of aberration as completely as if it were the sole agent of apparent displacement, so that, by an alliance between mathematical calculation and astronomical observation, we can study the effects of aberration as clearly as if the stars were affected by no other motions.
Concentrating our attention solely on the phenomena of aberration we shall describe its particular effect upon stars in different regions of the sky, and thus ascertain the laws according to which the effects of aberration are exhibited. When this step has been taken, we shall be in a position togive the beautiful explanation of those laws dependent upon the velocity of light.
At one particular region of the heavens the effect of aberration has a degree of simplicity which is not manifested anywhere else. This region lies in the constellation Draco, at the pole of the ecliptic. At this pole, or in its immediate neighbourhood, each star, in virtue of aberration, describes a circle in the heavens. This circle is very minute; it would take something like 2,000 of these circles together to form an area equal to the area of the moon. Expressed in the usual astronomical language, we should say that the diameter of this small circle is about 40·9 seconds of arc. This is a quantity which, though small to the unaided eye, is really of great relative magnitude in the present state of telescopic research. It is not only large enough to be perceived, but it can be measured, with an accuracy which actually does not admit of a doubt, to the hundredth part of the whole. It is also observed that each star describes its little circle in precisely the same period of time; and that period is one year, or, in other words, the time of the revolution of the earth around the sun. It is found that for all stars in this region, be they large stars or small, single or double, white or coloured, the circles appropriate to each have all the same size, and are all described in the same time. Even from this alone it would be manifest that the cause of the phenomenon cannot lie in the star itself. This unanimity in stars of every magnitude and distance requires some simpler explanation.
Further examination of stars in different regions sheds new light on the subject. As we proceed from the pole of the ecliptic, we still find that each star exhibits an annual movement of the same character as the stars just considered. In one respect, however, there is a difference. The apparent path of the star is no longer a circle; it has become an ellipse. It is, however, soon perceived that the shape and the position of this ellipse are governed by the simple law that the further the star is from the pole of the ecliptic the greater is the eccentricity of the ellipse. The apparent path of the starsat the same distance from the pole have equal eccentricity, and of the axes of the ellipse the shorter is always directed to the pole, the longer being, of course, perpendicular to it. It is, however, found that no matter how great the eccentricity may become, the major axis always retains its original length. It is always equal to about 40·9 seconds—that is, to the diameter of the circle of aberration at the pole itself. As we proceed further and further from the pole of the ecliptic, we find that each star describes a path more and more eccentric, until at length, when we examine a star on the ecliptic, the ellipse has become so attenuated that it has flattened into a line. Each star which happens to lie on the ecliptic oscillates to and fro along the ecliptic through an amplitude of 40·9 seconds. Half a year accomplishes the journey one way, and the other half of the year restores the star to its original position. When we pass to stars on the southern side of the ecliptic, we see the same series of changes proceed in an inverse order. The ellipse, from being actually linear, gradually grows in width, though still preserving the same length of major axis, until at length the stars near the southern pole of the ecliptic are each found to describe a circle equal to the paths pursued by the stars at the north pole of the ecliptic.
The circumstance that the major axes of all those ellipses are of equal length suggests a still further simplification. Let us suppose that every star, either at the pole of the ecliptic or elsewhere, pursues an absolutely circular path, and that all these circles agree not only in magnitude, but also in being all parallel to the plane of the ecliptic: it is easy to see that this simple supposition will account for the observed facts. The stars at the pole of the ecliptic will, of course, show their circles turned fairly towards us, and we shall see that they pursue circular paths. The circular paths of the stars remote from the pole of the ecliptic will, however, be only seen somewhat edgewise, and thus the apparent paths will be elliptical, as we actually find them. We can even calculate the degree of ellipticity which this surmise would require, and we find that it coincides withthe observed ellipticity. Finally, when we observe stars actually moving in the ecliptic, the circles they follow would be seen edgewise, and thus the stars would have merely the linear movement which they are seen to possess. All the observed phenomena are thus found to be completely consistent with the supposition that every star of all the millions in the heavens describes once each year a circular path; and that, whether the star be far or near, this circle has always the same apparent diameter, and lies in a plane always parallel to the plane of the ecliptic.
We have now wrought the facts of observation into a form which enables us to examine into the cause of a movement so systematic. Why is it that each star should seem to describe a small circular path? Why should that path be parallel to the ecliptic? Why should it be completed exactly in a twelvemonth? We are at once referred to the motion of the earth around the sun. That movement takes place in the ecliptic. It is completed in a year. The coincidences are so obvious that we feel almost necessarily compelled to connect in some way this apparent movement of the stars with the annual movement of the earth around the sun. If there were no such connection, it would be in the highest degree improbable that the planes of the circles should be all parallel to the ecliptic, or that the time of revolution of each star in its circle should equal that of the revolution of the earth around the sun. As both these conditions are fulfilled, the probability of the connection rises to a value almost infinite.
The important question has then arisen as to why the movement of the earth around the sun should be associated in so remarkable a manner with this universal star movement. There is here one obvious point to be noticed and to be dismissed. We have in a previous chapter discussed the important question of the annual parallax of stars, and we have shown how, in virtue of annual parallax, each star describes an ellipse. It can further be demonstrated that these ellipses are really circles parallel to the ecliptic; so that we might hastily assume that annual parallax was the cause of the phenomenon discovered by Bradley. A single circumstance will, however, dispose of thissuggestion. The circle described by a star in virtue of annual parallax has a magnitude dependent on the distance of the star, so that the circles described by various stars are of various dimensions, corresponding to the varied distances of different stars. The phenomena of aberration, however, distinctly assert that the circular path of each star is of the same size, quite independently of what its distance may be, and hence annual parallax will not afford an adequate explanation. It should also be noticed that the movements of a star produced by annual parallax are much smaller than those due to aberration. There is not any known star whose circular path due to annual parallax has a diameter one-twentieth part of that of the circle due to aberration; indeed, in the great majority of cases the parallax of the star is an absolutely insensible quantity.
There is, however, a still graver and quite insuperable distinction between the parallactic path and the aberrational path. Let us, for simplicity, think of a star situated near the pole of the ecliptic, and thus appearing to revolve annually in a circle, whether we regard either the phenomenon of parallax or of aberration. As the earth revolves, so does the star appear to revolve; and thus to each place of the earth in its orbit corresponds a certain place of the star in its circle. If the movement arise from annual parallax, it is easy to see where the place of the star will be for any position of the earth. It is, however, found that in the movement discovered by Bradley the star never has the position which parallax assigns to it, but is, in fact, a quarter of the circumference of its little circle distant therefrom.
A simple rule will find the position of the star due to aberration. Draw from the centre of the ellipse a radius parallel to the direction in which the earth is moving at the moment in question, then the extremity of this radius gives the point on its ellipse where the star is to be found. Tested at all seasons, and with all stars, this law is found to be always verified, and by its means we are conducted to the true explanation of the phenomenon.
We can enunciate the effects of aberration in a somewhat different manner, which will show even more forcibly how thephenomenon is connected with the motion of the earth in its orbit. As the earth pursues its annual course around the sun, its movement at any moment may be regarded as directed towards a certain point of the ecliptic. From day to day, and even from hour to hour, the point gradually moves along the ecliptic, so as to complete the circuit in a year. At each moment, however, there is always a certain point in the heavens towards which the earth's motion is directed. It is, in fact, the point on the celestial sphere towards which the earth would travel continuously if, at the moment, the attraction of the sun could be annihilated. It is found that this point is intimately connected with the phenomenon of aberration. In fact, the aberration is really equivalent to drawing each star from its mean place towards the Apex of the Earth's Way, as the point is sometimes termed. It can also be shown by observation that the amount of aberration depends upon the distance from the apex. A star which happened to lie on the ecliptic will not be at all deranged by aberration from its mean place when it happens that the apex coincides with the star. All the stars 10° from the apex will be displaced each by the same amount, and all directly in towards the apex. A star 20° from the apex will undergo a larger degree of displacement, though still in the same direction, exactly towards the apex; and all stars at the same distance will be displaced by the same amount. Proceeding thus from the apex, we come to stars at a distance of 90° therefrom. Here the amount of displacement will be a maximum. Each one will be about twenty seconds from its average place; but in every case the imperative law will be obeyed, that the displacement of the star from its mean place lies towards the apex of the earth's way. We have thus given two distinct descriptions of the phenomenon of aberration. In the first we find it convenient to speak of a star as describing a minute circular path; in the other we have regarded aberration as merely amounting to a derangement of the star from its mean place in accordance with specified laws. These descriptions are not inconsistent: they are, in fact, geometrically equivalent; but the latter is rather the more perfect, inasmuch as it assigns completely the direction and extent of thederangement caused by aberration in any particular star at any particular moment.
The question has now been narrowed to a very definite form. What is it which makes each star seem to close in towards the point towards which the earth is travelling? The answer will be found when we make a minute enquiry into the circumstances in which we view a star in the telescope.
The beam of rays from a star falls on the object-glass of a telescope; those rays are parallel, and after they pass through the object-glass they converge to a focus near the eye end of the instrument. Let us first suppose that the telescope is at rest; then if the telescope be pointed directly towards the star, the rays will converge to a point at the centre of the field of view where a pair of cross wires are placed, whose intersection defines the axis of the telescope. The case will, however, be altered if the telescope be moved after the light has passed through the objective; the rays of light in the interior of the tube will pursue a direct path, as before, and will proceed to a focus at the same precise point as before. As, however, the telescope has moved, it will, of course, have carried with it the pair of cross wires; they will no longer be at the same point as at first, and consequently the image of the star will not now coincide with their intersection.
The movement of the telescope arises from its connection with the earth: for as the earth hurries along at a speed of eighteen miles a second, the telescope is necessarily displaced with this velocity. It might at first be thought, that in the incredibly small fraction of time necessary for light to pass from the object-glass to the eye-piece, the change in the position of the telescope must be too minute to be appreciable. Let us suppose, for instance, that the star is situated near the pole of the ecliptic, then the telescope will be conveyed by the earth's motion in a direction perpendicular to its length. If the tube of the instrument be about twenty feet long, it can be readily demonstrated that during the time the light travels down the tube the movement of the earth will convey the telescope through a distance of about one-fortieth of an inch.[42]This is a quantity very distinctly measurable with the magnifying power of the eye-piece, and hence this derangement of the star's place is very appreciable. It therefore follows that if we wish the star to be shown at the centre of the instrument, the telescope is not to be pointed directly at the star, as it would have to be were the earth at rest, but the telescope must be pointed a little in advance of the star's true position; and as we determine the apparent place of the star by the direction in which the telescope is pointed, it follows that the apparent place of the star is altered by the motion of the earth.
Every circumstance of the change in the star's place admits of complete explanation in this manner. Take, for instance, the small circular path which each star appears to describe. We shall, for simplicity, refer only to a star at the pole of the ecliptic. Suppose that the telescope is pointed truly to the place of the star, then, as we have shown, the image of the star will be at a distance of one-fortieth of an inch from the cross wires. This distance will remain constant, but each night the direction of the star from the cross wires will change, so that in the course of the year it completes a circle, and returns to its original position. We shall not pursue the calculations relative to other stars; suffice it here to say that the movement of the earth has been found adequate to account for the phenomena, and thus the doctrine of the aberration of light is demonstrated.
It remains to allude to one point of the utmost interest and importance. We have seen that the magnitude of the aberration can be measured by astronomical observation. The amount of this aberration depends upon the velocity of light, and on the velocity with which the earth's motion is performed. We can measure the velocity of light by independent measurements, in the manner already explained inChapter XII. We are thus enabled to calculate what the velocity of the earthmust be, for there is only one particular velocity for the earth which, when combined with the measured velocity of light, will give the measured value of aberration. The velocity of the earth being thus ascertained, and the length of the year being known, it is easy to find the circumference of the earth's path, and therefore its radius; that is, the distance from the earth to the sun.
Here is indeed a singular result, and one which shows how profoundly the various phenomena of science are interwoven. We make experiments in our laboratory, and find the velocity of light. We observe the fixed stars, and measure the aberration. We combine these results, and deduce therefrom the distance from the earth to the sun! Although this method of finding the sun's distance is one of very great elegance, and admits of a certain amount of precision, yet it cannot be relied upon as a perfectly unimpeachable method of deducing the great constant. A perfect method must be based on the operations of mere surveying, and ought not to involve recondite physical considerations. We cannot, however, fail to regard the discovery of aberration by Bradley as a most pleasing and beautiful achievement, for it not only greatly improves the calculations of practical astronomy, but links together several physical phenomena of the greatest interest.
Heat and Astronomy—Distribution of Heat—The Presence of Heat in the Earth—Heat in other Celestial Bodies—Varieties of Temperature—The Law of Cooling—The Heat of the Sun—Can its Temperature be Measured?—Radiation connected with the Sun's Bulk—Can the Sun be Exhausting his Resources?—No marked Change has occurred—Geological Evidence as to the Changes of the Sun's Heat Doubtful—The Cooling of the Sun—The Sun cannot be merely an Incandescent Solid Cooling—Combustion will not Explain the Matter—Some Heat is obtained from Meteoric Matter, but this is not Adequate to the Maintenance of the Sun's Heat—The Contraction of a Heated Globe of Gas—An Apparent Paradox—The Doctrine of Energy—The Nebular Theory—Evidence in Support of this Theory—Sidereal Evidence of the Nebular Theory—Herschel's View of Sidereal Aggregation—The Nebulæ do not Exhibit Changes within the Limits of our Observation.
Heat and Astronomy—Distribution of Heat—The Presence of Heat in the Earth—Heat in other Celestial Bodies—Varieties of Temperature—The Law of Cooling—The Heat of the Sun—Can its Temperature be Measured?—Radiation connected with the Sun's Bulk—Can the Sun be Exhausting his Resources?—No marked Change has occurred—Geological Evidence as to the Changes of the Sun's Heat Doubtful—The Cooling of the Sun—The Sun cannot be merely an Incandescent Solid Cooling—Combustion will not Explain the Matter—Some Heat is obtained from Meteoric Matter, but this is not Adequate to the Maintenance of the Sun's Heat—The Contraction of a Heated Globe of Gas—An Apparent Paradox—The Doctrine of Energy—The Nebular Theory—Evidence in Support of this Theory—Sidereal Evidence of the Nebular Theory—Herschel's View of Sidereal Aggregation—The Nebulæ do not Exhibit Changes within the Limits of our Observation.
Thata portion of a work on astronomy should bear the title placed at the head of this chapter will perhaps strike some of our readers as unusual, if not actually inappropriate. Is not heat, it may be said, a question merely of experimental physics? and how can it be legitimately introduced into a treatise upon the heavenly bodies and their movements? Whatever weight such objections might have once had need not now be considered. The recent researches on heat have shown not only that heat has important bearings on astronomy, but that it has really been one of the chief agents by which the universe has been moulded into its actual form. At the present time no work on astronomy could be complete without some account of the remarkable connection between the laws of heat and the astronomical consequences which follow from those laws.
In discussing the planetary motions and the laws of Kepler, or in discussing the movements of the moon, the proper motions of the stars, or the revolutions of the binary stars, we proceedon the supposition that the bodies we are dealing with are rigid particles, and the question as to whether these particles are hot or cold does not seem to have any especial bearing. No doubt the ordinary periodic phenomena of our system, such as the revolution of the planets in conformity with Kepler's laws, will be observed for countless ages, whether the planets be hot or cold, or whatever may be the heat of the sun. It must, however, be admitted that the laws of heat introduce certain modifications into the statement of these laws. The effects of heat may not be immediately perceptible, but they exist—they are constantly acting; and in the progress of time they are adequate to effecting the mightiest changes throughout the universe.
Let us briefly recapitulate the circumstances of our system which give to heat its potency. Look first at our earth, which at present seems—on its surface, at all events—to be a body devoid of internal heat; a closer examination will dispel this idea. Have we not the phenomena of volcanoes, of geysers, and of hot springs, which show that in the interior of the earth heat must exist in far greater intensity than we find on the surface? These phenomena are found in widely different regions of the earth. Their origin is, no doubt, involved in a good deal of obscurity, but yet no one can deny that they indicate vast reservoirs of heat. It would indeed seem that heat is to be found everywhere in the deep inner regions of the earth. If we take a thermometer down a deep mine, we find it records a temperature higher than at the surface. The deeper we descend the higher is the temperature; and if the same rate of progress should be maintained through those depths of the earth which we are not able to penetrate, it can be demonstrated that at twenty or thirty miles below the surface the temperature must be as great as that of red-hot iron.
We find in the other celestial bodies abundant evidence of the present or the past existence of heat. Our moon, as we have already mentioned, affords a very striking instance of a body which must once have been very highly heated. The extraordinary volcanoes on its surface place this beyond anydoubt. It is equally true that those volcanoes have been silent for ages, so that, whatever may be the interior condition of the moon, the surface has now cooled down. Extending our view further, we see in the great planets Jupiter and Saturn evidence that they are still endowed with a temperature far in excess of that which the earth has retained; while, when we look at our sun, we see a body in a state of brilliant incandescence, and glowing with a fervour to which we cannot approximate in our mightiest furnaces. The various fixed stars are bodies which glow with heat, like our sun; while we have in the nebulæ objects the existence of which is hardly intelligible to us, unless we admit that they are possessed of heat.
From this rapid survey of the different bodies in our universe one conclusion is obvious. We may have great doubts as to the actual temperature of any individual body of the system; but it cannot be doubted that there is a wide range of temperature among the different bodies. Some are hotter than others. The stars and suns are perhaps the hottest of all; but it is not improbable that they may be immeasurably outnumbered by the cold and dark bodies of the universe, which are to us invisible, and only manifest their existence in an indirect and casual manner.
The law of cooling tells us that every body radiates heat, and that the quantity of heat which it radiates increases when the temperature of the body increases relatively to the surrounding medium. This law appears to be universal. It is obeyed on the earth, and it would seem that it must be equally obeyed by every other body in space. We thus see that each of the planets and each of the stars is continuously pouring forth in all directions a never-ceasing stream of heat. This radiation of heat is productive of very momentous consequences. Let us study them, for instance, in the case of the sun.
Our great luminary emits an incessant flood of radiant heat in all directions. A minute fraction of that heat is intercepted by our earth, and is, directly or indirectly, the source of all life, and of nearly all movement, on our earth. To pour forth heat as the sun does, it is necessary that his temperaturebe enormously high. And there are some facts which permit us to form an estimate of what that temperature must actually be.
It is difficult to form any numerical statement of the actual temperature of the sun. The intensity of that temperature vastly transcends the greatest artificial heat, and any attempt to clothe such estimates in figures is necessarily very precarious. But assuming the greatest artificial temperature to be about 4,000° Fahr., we shall probably be well within the truth if we state the effective temperature of the sun to be about 14,000° Fahr. This is the result of a recent investigation by Messrs. Wilson and Gray, which seems to be entitled to considerable weight.
The copious outflow of heat from the sun corresponds with its enormous temperature. We can express the amount of heat in various ways, but it must be remembered that considerable uncertainty still attaches to such measurements. The old method of measuring heat by the quantity of ice melted may be used as an illustration. It is computed that a shell of ice 43-1â„2feet thick surrounding the whole sun would in one minute be melted by the sun's heat underneath. A somewhat more elegant illustration was also given by Sir John Herschel, who showed that if a cylindrical glacier 45 miles in diameter were to be continually flowing into the sun with the velocity of light, the end of that glacier would be melted as quickly as it advanced. From each square foot in the surface of the sun emerges a quantity of heat as great as could be produced by the daily combustion of sixteen tons of coal. This is, indeed, an amount of heat which, properly transformed into work, would keep an engine of many hundreds of horse-power running from one year's end to the other. The heat radiated from a few acres on the sun would be adequate to drive all the steam engines in the world. When we reflect on the vast intensity of the radiation from each square foot of the sun's surface, and when we combine with this the stupendous dimensions of the sun, imagination fails to realise how vast must be the actual expenditure of heat.
In presence of the prodigal expenditure of the sun's heat,we are tempted to ask a question which has the most vital interest for the earth and its inhabitants. We live from hour to hour by the sun's splendid generosity; and, therefore, it is important for us to know what security we possess for the continuance of his favours. When we witness the terrific disbursement of the sun's heat each hour, we are compelled to ask whether our great luminary may not be exhausting its resources; and if so, what are the prospects of the future? This question we can partly answer. The whole subject is indeed of surpassing interest, and redolent with the spirit of modern scientific thought.
Our first attempt to examine this question must lie in an appeal to the facts which are attainable. We want to know whether the sun is showing any symptoms of decay. Are the days as warm and as bright now as they were last year, ten years ago, one hundred years ago? We can find no evidence of any change since the beginning of authentic records. If the sun's heat had perceptibly changed within the last two thousand years, we should expect to find corresponding changes in the distribution of plants and of animals; but no such changes have been detected. There is no reason to think that the climate of ancient Greece or of ancient Rome was appreciably different from the climates of the Greece and the Rome that we know at this day. The vine and the olive grow now where they grew two thousand years ago.
We must not, however, lay too much stress on this argument; for the effects of slight changes in the sun's heat may have been neutralised by corresponding adaptations in the pliable organisms of cultivated plants. All we can certainly conclude is that no marked change has taken place in the heat of the sun during historical time. But when we come to look back into much earlier ages, we find copious evidence that the earth has undergone great changes in climate. Geological records can on this question hardly be misinterpreted. Yet it is curious to note that these changes are hardly such as could arise from the gradual exhaustion of the sun's radiation. No doubt, in very early times wehave evidence that the earth's climate must have been much warmer than at present. We had the great carboniferous period, when the temperature must almost have been tropical in Arctic latitudes. Yet it is hardly possible to cite this as evidence that the sun was then much more powerful; for we are immediately reminded of the glacial period, when our temperate zones were overlaid by sheets of solid ice, as Northern Greenland is at present. If we suppose the sun to have been hotter than it is at present to account for the vegetation which produced coal, then we ought to assume the sun to be colder than it is now to account for the glacial period. It is not reasonable to attribute such phenomena to fluctuations in the radiation from the sun. The glacial periods prove that we cannot appeal to geology in aid of the doctrine that a secular cooling of the sun is now in progress. The geological variations of climate may have been caused by changes in the earth itself, or by changes in its actual orbit; but however they have been caused, they hardly tell us much with regard to the past history of our sun.
The heat of the sun has lasted countless ages; yet we cannot credit the sun with the power of actually creating heat. We must apply to the tremendous mass of the sun the same laws which we have found by our experiments on the earth. We must ask, whence comes the heat sufficient to supply this lavish outgoing? Let us briefly recount the various suppositions that have been made.
Place two red-hot spheres of iron side by side, a large one and a small one. They have been taken from the same fire; they were both equally hot; they are both cooling, but the small sphere cools more rapidly. It speedily becomes dark, while the large sphere is still glowing, and would continue to do so for some minutes. The larger the sphere, the longer it will take to cool; and hence it has been supposed that a mighty sphere of the prodigious dimensions of our sun would, if once heated, cool gradually, but the duration of the cooling would be so long that for thousands and for millions of years it could continue to be a source of lightand heat to the revolving system of planets. This suggestion will not bear the test of arithmetic. If the sun had no source of heat beyond that indicated by its high temperature, we can show that radiation would cool the sun a few degrees every year. Two thousand years would then witness a very great decrease in the sun's heat. We are certain that no such decrease can have taken place. The source of the sun's radiation cannot be found in the mere cooling of an incandescent mass.
Can the fires in the sun be maintained by combustion, analogous to that which goes on in our furnaces? Here we would seem to have a source of gigantic heat; but arithmetic also disposes of this supposition. We know that if the sun were made of even solid coal itself, and if that coal were burning in pure oxygen, the heat that could be produced would only suffice for 6,000 years. If the sun which shone upon the builders of the great Pyramid had been solid coal from surface to centre, it must by this time have been in great part burned away in the attempt to maintain its present rate of expenditure. We are thus forced to look to other sources for the supply of the sun's heat, since neither the heat of incandescence nor the heat of combustion will suffice.
There is probably—indeed, we may say certainly—one external source from which the heat of the sun is recruited. It will be necessary for us to consider this source with some care, though I think we shall find it to be merely an auxiliary of comparatively trifling moment. According to this view, the solar heat receives occasional accessions from the fall upon the sun's surface of masses of meteoric matter. There can be hardly a doubt that such masses do fall upon the sun; there is certainly no doubt that if they do, the sun must gain some heat thereby. We have experience on the earth of a very interesting kind, which illustrates the development of heat by meteoric matter. There lies a world of philosophy in a shooting star. Some of these myriad objects rush into our atmosphere and are lost; others, no doubt, rush into the sun with the same result. We also admit that the descent of a shooting star into the atmosphere of the sunmust be attended with a flash of light and of heat. The heat acquired by the earth from the flashing of the shooting stars through our air is quite insensible. It has been supposed, however, that the heat accruing to the sun from the same cause may be quite sensible—nay, it has been even supposed that the sun may be re-invigorated from this source.
Here, again, we must apply the cold principles of weights and measures to estimate the plausibility of this suggestion. We first calculate the actual weight of meteoric indraught to the sun which would be adequate to sustain the fires of the sun at their present vigour. The mass of matter that would be required is so enormous that we cannot usefully express it by imperial weights; we must deal with masses of imposing magnitude. It fortunately happens that the weight of our moon is a convenient unit. Conceive that our moon—a huge globe, 2,000 miles in diameter—were crushed into a myriad of fragments, and that these fragments were allowed to rain in on the sun; there can be no doubt that this tremendous meteoric shower would contribute to the sun rather more heat than would be required to supply his radiation for a whole year. If we take our earth itself, conceive it comminuted into dust, and allow that dust to fall on the sun as a mighty shower, each fragment would instantly give out a quantity of heat, and the whole would add to the sun a supply of heat adequate to sustain the present rate of radiation for nearly one hundred years. The mighty mass of Jupiter treated in the same way would generate a meteoric display greater in the ratio in which the mass of Jupiter exceeds the mass of earth. Were Jupiter to fall into the sun, enough heat would be thereby produced to scorch the whole solar system; while all the planets together would be capable of producing heat which, if properly economised, would supply the radiation of the sun for 45,000 years.
It must be remembered that though the moon could supply one year's heat, and Jupiter 30,000 years' heat, yet the practical question is not whether the solar system could supply the sun's heat, but whether it does. Is it likely that meteors equal in mass to the moon fall into the sunevery year? This is the real question, and I think we are bound to reply to it in the negative. It can be shown that the quantity of meteors which could be caught by the sun in any one year can be only an excessively minute fraction of the total amount. If, therefore, a moon-weight of meteors were caught every year, there must be an incredible mass of meteoric matter roaming at large through the system. There must be so many meteors that the earth would be incessantly pelted with them, and heated to such a degree as to be rendered uninhabitable. There are also other reasons which preclude the supposition that a stupendous quantity of meteoric matter exists in the vicinity of the sun. Such matter would produce an appreciable effect on the movement of the planet Mercury. There are, no doubt, some irregularities in the movements of Mercury not yet fully explained, but these irregularities are very much less than would be the case if meteoric matter existed in quantity adequate to the sustentation of the sun. Astronomers, then, believe that though meteors may provide a rate in aid of the sun's current expenditure, yet that the greater portion of that expenditure must be defrayed from other resources.
It is one of the achievements of modern science to have effected the solution of the problem—to have shown how it is that, notwithstanding the stupendous radiation, the sun still maintains its temperature. The question is not free from difficulty in its exposition, but the matter is one of such very great importance that we are compelled to make the attempt.
Let us imagine a vast globe of heated gas in space. This is not an entirely gratuitous supposition, inasmuch as there are globes apparently of this character; they have been already alluded to as planetary nebulæ. This globe will radiate heat, and we shall suppose that it emits more heat than it receives from the radiation of other bodies. The globe will accordingly lose heat, or what is equivalent thereto, but it will be incorrect to assume that the globe will necessarily fall in temperature. That the contrary is, indeed, the case is a result almost paradoxical at the first glance; but yet it can be shown to be a necessary consequence of the laws of heat and of gases.
Let us fix our attention on a portion of the gas lying on the surface of the globe. This is, of course, attracted by all the rest of the globe, and thus tends in towards the centre of the globe. If equilibrium subsists, this tendency must be neutralised by the pressure of the gas beneath; so that the greater the gravitation, the greater is the pressure. When the globe of gas loses heat by radiation, let us suppose that it grows colder—that its temperature accordingly falls; then, since the pressure of a gas decreases when the temperature falls, the pressure beneath the superficial layer of the gas will decrease, while the gravitation is unaltered. The consequence will inevitably be that the gravitation will now conquer the pressure, and the globe of gas will accordingly contract. There is, however, another way in which we can look at the matter. We know that heat is equivalent to energy, so that when the globe radiates forth heat, it must expend energy. A part of the energy of the globe will be due to its temperature; but another, and in some respects a more important, part is that due to the separation of its particles. If we allow the particles to come closer together we shall diminish the energy due to separation, and the energy thus set free can take the form of heat. But this drawing in of the particles necessarily involves a shrinking of the globe.
And now for the remarkable consequence, which seems to have a very important application in astronomy. As the globe contracts, a part of its energy of separation is changed into heat; that heat is partly radiated away, but not so rapidly as it is produced by the contraction. The consequence is, that although the globe is really losing heat and really contracting, yet that its temperature is actually rising.[43]A simple case will suffice to demonstrate this result, paradoxical as it may at first seem. Let us suppose that by contraction of the sphere it had diminished to one-half its diameter; and let us fix our attention on a cubic inch of the gaseous matter in any point of the mass. After the contraction has taken place each edgeof the cube would be reduced to half an inch, and the volume would therefore be reduced to one-eighth part of its original amount. The law of gases tells us that if the temperature be unaltered the pressure varies inversely as the volume, and consequently the internal pressure in the cube would in that case be increased eightfold. As, however, in the case before us, the distance between every two particles is reduced to one-half, it will follow that the gravitation between every two particles is increased fourfold, and as the area is also reduced to one-fourth, it will follow that the pressure inside the reduced cube is increased sixteenfold; but we have already seen that with a constant temperature it only increases eightfold, and hence the temperature cannot be constant, but must rise with the contraction.
We thus have the somewhat astonishing result that a gaseous globe in space radiating heat, and thereby growing smaller, is all the time actually increasing in temperature. But, it may be said, surely this cannot go on for ever. Are we to suppose that the gaseous mass will go on contracting and contracting with a temperature ever fiercer and fiercer, and actually radiating out more and more heat the more it loses? Where lies the limit to such a prospect? As the body contracts, its density must increase, until it either becomes a liquid, or a solid, or, at any rate, until it ceases to obey the laws of a purely gaseous body which we have supposed. Once these laws cease to be observed the argument disappears; the loss of heat may then really be attended with a loss of temperature, until in the course of time the body has sunk to the temperature of space itself.
It is not assumed that this reasoning can be applied in all its completeness to the present state of the sun. The sun's density is now so great that the laws of gases cannot be there strictly followed. There is, however, good reason to believe that the sun was once more gaseous than at present; possibly at one time he may have been quite gaseous enough to admit of this reasoning in all its fulness. At present the sun appears to be in some intermediate stage of its progress from the gaseous condition to the solid condition. We cannot,therefore, say that the temperature of the sun is now increasing in correspondence with the process of contraction. This may be true or it may not be true; we have no means of deciding the point. We may, however, feel certain that the sun is still sufficiently gaseous to experience in some degree the rise of temperature associated with the contraction. That rise in temperature may be partly or wholly obscured by the fall in temperature which would be the more obvious consequence of the radiation of heat from the partially solid body. It will, however, be manifest that the cooling of the sun may be enormously protracted if the fall of temperature from the one cause be nearly compensated by the rise of temperature from the other. It can hardly be doubted that in this we find the real explanation of the fact that we have no historical evidence of any appreciable alteration in the radiation of heat from the sun.
This question is one of such interest that it may be worth while to look at it from a slightly different point of view. The sun contains a certain store of energy, part of which is continually disappearing in the form of radiant heat. The energy remaining in the sun is partly transformed in character; some of it is transformed into heat, which goes wholly or partly to supply the loss by radiation. The total energy of the sun must, however, be decreasing; and hence it would seem the sun must at some time or other have its energy exhausted, and cease to be a source of light and of heat. It is true that the rate at which the sun contracts is very slow. We are, indeed, not able to measure with certainty the decrease in the sun's bulk. It is a quantity so minute, that the contraction since the birth of accurate astronomy is not large enough to be perceptible in our telescopes. It is, however, possible to compute what the contraction of the sun's bulk must be, on the supposition that the energy lost by that contraction just suffices to supply the daily radiation of heat. The change is very small when we consider the present size of the sun. At the present time the sun's diameter is about 860,000 miles. If each year this diameter decreases by about 300 feet, sufficient energy will be yielded to accountfor the entire radiation. This gradual decrease is always in progress.
These considerations are of considerable interest when we apply them retrospectively. If it be true that the sun is at this moment shrinking, then in past times his globe must have been greater than it is at present. Assuming the figures already given, it follows that one hundred years ago the diameter of the sun must have been nearly six miles greater than it is now; one thousand years ago the diameter was fifty-seven miles greater; ten thousand years ago the diameter of the sun was five hundred and seventy miles greater than it is to-day. When man first trod this earth it would seem that the sun must have been many hundreds, perhaps many thousands, of miles greater than it is at this time.
We must not, however, over-estimate the significance of this statement. The diameter of the sun is so great, that a diminution of 10,000 miles would be but little more than the hundredth part of its diameter. If it were suddenly to shrink to the extent of 10,000 miles, the change would not be appreciable to ordinary observation, though a much smaller change would not elude delicate astronomical measurement. It does not necessarily follow that the climates on our earth in these early times must have been very different from those which we find at this day, for the question of climate depends upon other matters besides sunbeams.
Yet we need not abruptly stop our retrospect at any epoch, however remote. We may go back earlier and earlier, through the long ages which geologists claim for the deposition of the stratified rocks; and back again still further, to those very earliest epochs when life began to dawn on the earth. Still we can find no reason to suppose that the law of the sun's decreasing heat is not maintained; and thus we would seem bound by our present knowledge to suppose that the sun grows larger and larger the further our retrospect extends. We cannot assume that the rate of that growth is always the same. No such assumption is required; it is sufficient for our purpose that we find the sun growinglarger and larger the further we peer back into the remote abyss of time past. If the present order of things in our universe has lasted long enough, then it would seem that there was a time when the sun must have been twice as large as it is at present; it must once have been ten times as large. How long ago that was no one can venture to say. But we cannot stop at the stage when the sun was even ten times as large as it is at present; the arguments will still apply in earlier ages. We see the sun swelling and swelling, with a corresponding decrease in its density, until at length we find, instead of our sun as we know it, a mighty nebula filling a gigantic region of space.
Such is, in fact, the doctrine of the origin of our system which has been advanced in that celebrated speculation known as the nebular theory of Laplace. Nor can it be ever more than a speculation; it cannot be established by observation, nor can it be proved by calculation. It is merely a conjecture, more or less plausible, but perhaps in some degree necessarily true, if our present laws of heat, as we understand them, admit of the extreme application here required, and if also the present order of things has reigned for sufficient time without the intervention of any influence at present unknown to us. This nebular theory is not confined to the history of our sun. Precisely similar reasoning may be extended to the individual planets: the farther we look back, the hotter and the hotter does the whole system become. It has been thought that if we could look far enough back, we should see the earth too hot for life; back further still, we should find the earth and all the planets red-hot; and back further still, to an exceedingly remote epoch, when the planets would be heated just as much as our sun is now. In a still earlier stage the whole solar system is thought to have been one vast mass of glowing gas, from which the present forms of the sun, with the planets and their satellites, have been gradually evolved. We cannot be sure that the course of events has been what is here indicated; but there are sufficient grounds for thinking that this doctrine substantially represents what has actually occurred.
Many of the features in the solar system harmonise with the supposition that the origin of the system has been that suggested by the nebular theory. We have already had occasion in an earlier chapter to allude to the fact that all the planets perform their revolutions around the sun in the same direction. It is also to be observed that the rotation of the planets on their axes, as well as the movements of the satellites around their primaries, all follow the same law, with two slight exceptions in the case of the Uranian and Neptunian systems. A coincidence so remarkable naturally suggests the necessity for some physical explanation. Such an explanation is offered by the nebular theory. Suppose that countless ages ago a mighty nebula was slowly rotating and slowly contracting. In the process of contraction, portions of the condensed matter of the nebula would be left behind. These portions would still revolve around the central mass, and each portion would rotate on its axis in the same direction. As the process of contraction proceeded, it would follow from dynamical principles that the velocity of rotation would increase; and thus at length these portions would consolidate into planets, while the central mass would gradually contract to form the sun. By a similar process on a smaller scale the systems of satellites were evolved from the contracting primary. These satellites would also revolve in the same direction, and thus the characteristic features of the solar system could be accounted for.
The nebular origin of the solar system receives considerable countenance from the study of the sidereal heavens. We have already dwelt upon the resemblance between the sun and the stars. If, then, our sun has passed through such changes as the nebular theory requires, may we not anticipate that similar phenomena should be met with in other stars? If this be so, it is reasonable to suppose that the evolution of some of the stars may not have progressed so far as has that of the sun, and thus we may be able actually to witness stars in the earlier phases of their development. Let us see how far the telescope responds to these anticipations.
The field of view of a large telescope usually discloses a number of stars scattered over a black background of sky;but the blackness of the background is not uniform: the practised eye of the skilled observer will detect in some parts of the heavens a faint luminosity. This will sometimes be visible over the whole extent of the field, or it may even occupy several fields. Years may pass on, and still there is no perceptible change. There can be no illusion, and the conclusion is irresistible that the object is a stupendous mass of faintly luminous glowing gas or vapour. This is the simplest type of nebula; it is characterised by extreme faintness, and seems composed of matter of the utmost tenuity. On the other hand we are occasionally presented with the beautiful and striking phenomenon of a definite and brilliant star surrounded by a luminous atmosphere. Between these two extreme types of a faint diffused mass on the one hand, and a bright star with a nebula surrounding it on the other, a graduated series of various other nebulæ can be arranged. We thus have a series of links passing by imperceptible gradations from the most faintly diffused nebulæ on the one side, into stars on the other.
The nebulæ seemed to Herschel to be vast masses of phosphorescent vapour. This vapour gradually cools down, and ultimately condenses into a star, or a cluster of stars. When the varied forms of nebulæ were classified, it almost seemed as if the different links in the process could be actually witnessed. In the vast faint nebulæ the process of condensation had just begun; in the smaller and brighter nebulæ the condensation had advanced farther; while in others, the star, or stars, arising from the condensation had already become visible.
But, it may be asked, how did Herschel know this? what is his evidence? Let us answer this question by an illustration. Go into a forest, and look at a noble old oak which has weathered the storm for centuries; have we any doubt that the oak-tree was once a young small plant, and that it grew stage by stage until it reached maturity? Yet no one has ever followed an oak-tree through its various stages; the brief span of human life has not been long enough to do so. The reason why we believe the oak-tree to have passed through all these stages is, because we are familiar with oak-treesof every gradation in size, from the seedling up to the noble veteran. Having seen this gradation in a vast multitude of trees, we are convinced that each individual passes through all these stages.
It was by a similar train of reasoning that Herschel was led to adopt the view of the origin of the stars which we have endeavoured to describe. The astronomer's life is not long enough, the life of the human race might not be long enough, to watch the process by which a nebula condenses down so as to form a solid body. But by looking at one nebula after another, the astronomer thinks he is able to detect the various stages which connect the nebula in its original form with the final form. He is thus led to believe that each of the nebulæ passes, in the course of ages, through these stages. And thus Herschel adopted the opinion that stars—some, many, or all—have each originated from what was once a glowing nebula.
Such a speculation may captivate the imagination, but it must be carefully distinguished from the truths of astronomy, properly so called. Remote posterity may perhaps obtain evidence on the subject which to us is inaccessible: our knowledge of nebulæ is too recent. There has not yet been time enough to detect any appreciable changes: for the study of nebulæ can only be said to date from Messier's Catalogue in 1771.
Since Herschel's time, no doubt, many careful drawings and observations of the nebulæ have been obtained; but still the interval has been much too short, and the earlier observations are too imperfect, to enable any changes in the nebulæ to be investigated with sufficient accuracy. If the human race lasts for very many centuries, and if our present observations are preserved during that time for comparison, then Herschel's theory may perhaps be satisfactorily tested.