ment seems to need less explanation than that just made about the way which the Sun turns. In fact, however, it is hard to get a really distinct notion of what a complete rotation is. When a wheel rolls along a track, we say that it has turned round once in the time which has been needed for every part of its rim to come once into contact with the track; and this notion is clear enough. But in forming it, we consider the track as stationary. When we remember that the track itself is turning along with the rest of the Earth, we see that there is a sense in which the wheel has not turned round exactly once in the time during which every part of its rim has once touched the track. In counting the rotations of any thing, then, we need something to reckon from, which we can consider fixed and motionless. But we know that the celestial objects are all in motion. If we assumed that the Earth had no motion except that of rotation, we should have to say that one rotation of the Sun occupied about 27 days instead of 25. This difficulty cannot be entirely removed except by acquaintance with practical astronomy; but the principle according to which the rotations of any celestial object must be counted may perhaps be partially explained by examples of its application to terrestrial movements.

44. Suppose a model to be made of a flock of birds in flight, showing the exact places of all the birds in the flock at some particular moment with respect to each other; and suppose another model to be made, showing in the same manner the places of these birds with respect to each other a few seconds later. We could then, by comparing the models, examine the changes which had taken place during those few seconds in the arrangement of the birds. To get a more definite notion of this comparison, let us suppose that we calculate separately for each model what would be called the centre of gravity (34) of the flock in the arrangement which that model represented, and put into each model a little mark of some kind, such as a small shot, to show whereabouts this centre of gravity is. We could then consider how any bird in either model was placed with regard to a line drawn from

that bird to the centre of gravity of the flock. To be accurate, we should have to draw the line from the same part of the bird in the two models. In one model, the bird might be facing towards the centre of gravity, and in the other facing away from it. We might then consider, if we pleased, that he had turned half round, or made half a rotation, while the birds were passing from one to the other of the arrangements represented by the two models; and if, instead of two models only, we could have one for any instant that we could name, we could then trace the gradual progress of the bird's rotation.

45. If the movements of celestial objects were apparently as irregular as those of a flock of birds, there would be little satisfaction in investigating them in any manner like that described in the preceding illustration, which is, of course, not intended to exhibit the actual method by which the Sun's period of rotation is determined. But it is a general principle that, when we have nothing that can be considered motionless from which to measure the movements of other objects, we must supply the want by using the positions of those objects with respect to each other at a given time as a fixed model, so to speak, with which their positions at other times may be compared. This principle is that on which we supposed ourselves to proceed in examining the movements of birds; and it is that on which astronomers must proceed in examining the movements of celestial objects. The laws which regulate the course of many of these objects are so well known that their effect can be calculated for any moment within many centuries, past and future. We might actually construct a model showing the directions of all these objects with respect to some among them at any such moment; but, in practice, the results of calculation are sufficient for our purposes, and no actual model is needed. Thus we can determine the appearance of the stars as seen not only from places we have never reached, but also at times before astronomy was studied.

46. It appears, from what has been said, that as we learn

more about astronomy we constantly have to correct our former conclusions about the movements of certain objects by means of the new knowledge which we acquire with regard to the relations of these objects with others. Thus, if we learn more hereafter than we now know about the Sun's movement among the other stars, we shall have to alter the figures which now express its period of rotation. But this alteration will be very slight indeed; and before it can be perceptible at all, we must have learned to observe the Sun and to determine its period of rotation with regard to the Earth much more accurately than we can at present.

47. The comparative thickness of the Earth and Sun has already been stated (21). From this it appears by geometry that the bulk of the Sun is over one million and a quarter times that of the Earth. The Sun, however, has been found not to exceed the Earth in mass as much as in bulk. Still, as the Sun would outweigh three hundred and twenty thousand bodies each as heavy as the Earth, its actual mass is as much beyond our distinct comprehension as if it were heavy in proportion to its bulk. The small comparative density of the Sun is obviously one of the reasons for supposing it to be a gaseous, or at least not a solid, body.

48. In speaking of the bulk of the Sun, we take into account only the globe lying within the outer limits of the photosphere, since this is all which can be readily seen. But our knowledge of the Sun's mass is derived from our observation of the influence it exerts upon the movements of other bodies, and this mass is accordingly that of the Sun and its atmosphere taken together. The mass of this atmosphere, however, must apparently form only an insignificant part of what we call the mass of the Sun.

49. Although it has long been known that the Sun is a globe, this fact is not immediately evident to any one who sees the Sun, but was originally learned only by putting together the results of many observations of other objects as well as of the Sun itself. It seems, when we look at it, like a round flat object, one side of which is turned towards

us.

In fact, however, the various movements of the Earth and Sun are constantly changing our view of it, so that all the outer portions of the photosphere are brought in sight of the Earth at one time or another. The disk of the Sun is the name given to that part of the photosphere which we can see at any one time; so that in speaking of the disk we are speaking of the Sun as it appears and not as it is. The edge of the disk is called the limb of the Sun. That part of the limb which rises and sets first is called the preceding limb, and that which rises and sets last is called the following limb. The words preceding and following are much more convenient than western and eastern for use in astronomy, because it is sometimes hard to tell what is meant by west and east. The northern limb of the Sun is of course that part of its limb between its preceding and following limbs on that side of the disk which is nearest the northern sky; and the southern limb is opposite to the northern. We need not lay down any exact boundaries between these different limbs; when we have to speak precisely, we use other terms. To a terrestrial observer stationed north of the Tropic of Cancer the northern limb of the Sun always seems uppermost at

noon.

50. The Sun's disk is too bright to allow us ordinarily to look directly at it; and when it is studied with telescopes, it is necessary to take care to protect the eyes properly against the light and heat which would otherwise seriously injure them. The safest way of doing this is to form an image of the Sun by means of a telescope upon a screen, and not to look through the telescope at all. When the disk is closely examined in this or any other suitable way, it is usually found not to be equally bright in all parts, although the darkest parts of it are undoubtedly very bright, and only appear dark by contrast with the brighter parts.

51. In the first place, the disk is on the whole brightest in the middle, and gradually grows darker towards the limb. On this account, a good photograph of the Sun generally makes it look somewhat solid, or like a globe, such as it

really is, instead of making it seem like a mere flat disk. This, however, is only an effect of light and shade, and the photograph of a round piece of pasteboard properly shaded would have the same solid appearance. In order to understand why the Sun's disk is brightest in the middle, let us first consider why the whole Sun usually seems brighter the higher it seems to be in the sky. When the Sun has just risen or is about to set, we look at it along the ground, so that between us and it there is a great deal of that denser and heavier part of the air which hes close to the Earth. But when we look at the Sun in the middle of the day, we are looking almost directly away from the Earth, so that the Sun's light reaches us after traversing only so much of the air as lies nearly above the place from which we look. The air grows thinner very fast as we go farther from the Earth, so that wherever its limits are, the great mass of it, at all events, lies within a few miles of the land and sea. Hence it appears that the higher the Sun stands in the sky the smaller is the mass of air between us and it. The air is not so transparent as we are apt to think it, so that a great deal of any light which enters it is stopped on its way, or, according to the usual expression, is absorbed; and the greater the mass of the air through which the light has to come, the greater is this absorption. This explains the comparative dimness of the Sun when seen near the horizon.

52. The Sun's atmosphere, like the Earth's, absorbs much light; and any part of it has undoubtedly more density and more absorbent power the nearer it lies to the photosphere. Now, when we look at the limb of the Sun, we are, in fact, looking about half-way round the photosphere from that part of it which seems to be in the middle of the disk to the part directly opposite, on the other side of the Sun. The light which reaches us from the limb must accordingly have passed along a considerable part of the photosphere through the denser portion of the Sun's atmosphere; while the light from the middle of the disk has come to us directly away from the Sun, and therefore through as little as might be of its atmos