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equator changes during the course of a year. The orbit may be said in fact to have its summer and winter and its equinoxes, corresponding to the epochs when it is tilted with its northern. or southern side towards the Sun, or when its plane is turned directly towards him. The orbit opens out and closes up precisely as the ring-system of Saturn does, only in the course of rather less than a year instead of nearly thirty years, and also within much narrower limits of change.

There are reasons which render it unadvisable to attempt to illustrate the motion of the Moon's orbit around the Sun directly; the chief being that the distance of the Earth from the Sun so enormously exceeds the diameter of the Moon's orbit that a picture accurately drawn to scale and intended to show the Moon's orbit ought to be several yards in diameter. On the other hand, pictures not drawn to scale are most unsatisfactory illustrations of astronomical relations.*

Let us, however, picture the Moon's orbit, as supposed to be seen from the Sun's centre at different epochs of its passage around that orb.

First of all, let us consider the orbit when so placed as to appear like a straight line across the Earth's disc. It is then as shown at I. in fig. 98; in which E represents the Earth, mm' the Moon's orbit, м the Moon at a point on her orbit (this, merely to indicate her relative dimensions); and the dotted line a part of the Earth's path (that is, a part of the ecliptic). The arrow on this line shows the direction in which the Earth is moving while the small arrow on m m' shows the direction of the

* I am convinced that a large part of the perplexity which intelligent and thoughtful readers experience in the study of astronomical works is due to the incorrect proportions of the figured objects - orbits, globes, and so on. I believe, also, that but for these monstrous pictures the charlatans who pretend they think the Earth a plane or the like, would not find hearers, still less (as they do) believers. I know many worthy people, far from wanting in abilities, who only believe the theories of Copernicus, Kepler, and Newton, on the score of authority,-not because the evidence in astronomical treatises seems to them convincing or even intelligible.

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Moon's motion. It is to be noted that the arrow is supposed to lie on the nearer part of her orbit in all the presentations included in fig. 98.

Now, the Earth moving off towards the left, while the orbit m m' moves along with her and parallel to itself, it is perfectly obvious that we shall begin to see the orbit open out, its lower side (regarding it as a plane) becoming visible. In other

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Illustrating the apparent changes of the figure of the Moon's orbit as supposed to be viewed from the Sun.

words, it will begin to assume such an appearance as is shown at II. the nearer half uppermost and the slope diminished (the figures, letters, and arrows representing the same relations as before.)

But to simplify matters at this stage, let us consider the changes in another aspect. Since the Earth is going off towards

the left and round the observer, who is supposed to be at the Sun's centre, it is plain that the same changes will take place in the appearance of the Moon's orbit as though the latter remained fixed and the observer set off towards the right, and so went round the Earth. But we get the same changes of view in going round an object as though we remained still and the object simply turned round. For example, let fig. 99 represent

a plant in a flower-pot, and suppose that an observer, FIG. 99. keeping his eye on a level with the rim of the flowerpot, went round the pot, setting off towards the right : then it is perfectly obvious that he would see the same successive views of the plant as though he remained still and the flower-pot were slowly twirled (not shifted) by means of the suspending cords in the direction indicated by the arrow. Applying this consideration to the case in hand, we may conceive E in fig. 98 to be slowly rotated on the axis a a', carrying the orbit m m' with it, as if that orbit were rigidly attached to E; the rotation being such as to carry the nearer part of the orbit towards the left. Then all the changes of appearance will be precisely the same as occur in the actual case in which the Earth moves bodily off towards the left around the observer in the Sun.*

* This mode of considering the case is not only very convenient in this special instance, but also in many other cases. In such a way, a much clearer conception may be formed of the orderly succession of the seasons (see my Sun Views of the Earth) than by the ordinary way of conceiving the Earth on her progress around the Sun, a conception rendered difficult to the general reader, on account of the twofold orders of change--change of place and change of relative bearingwhich have to be attended to. In like manner, the changes in the appearance of the Saturnian ring-system, as supposed to be seen from the Sun, are far better understood in this way than in any other. The general principle on which this mode of considering such cases depends may be thus enunciated:-When a body or system shifts parallel to itself as it circles around a centre, the changes in the appearance of the body or system, as supposed to be seen from that centre, are precisely the same as though the body or system rotated on an axis at

The reader will at once see how the successive appearances represented in fig. 98, from I. to IX., would result from this simple rotation of the whole scheme upon a a'.* We see the orbit-ring opening out and becoming level, closing up and becoming inclined with the left extremity uppermost, opening out again and again becoming level, and lastly closing up and becoming inclined, as at first, with the right extremity uppermost. The whole rotation is supposed to take place in the course of a year, because the Earth takes one year in completing her circuit. Further on we shall have to consider a peculiarity which causes all these changes to take place in rather less than a year; but for the present we are not concerned with details of the sort.

Now, it only needs a glance at fig. 98, to see that when the orbit is presented as at I. there will be an eclipse of the Earth if the Moon is on the nearest part of her orbit, and an eclipse of the Moon if the Moon is on the farthest part of her orbit. For it is to be remembered that we are supposed to be stationed at the Sun; so that if м hides any part of E from us (i.e., from the Sun) that part of E must be in shadow; while if E hides any part of м, or the whole of M, from us, that part

right angles to the plane of its actual orbit, in a direction contrary to that of its real motion, and in the same period. In such a case as the illustration of the Earth's seasons, we must, after considering each change of bearing, consider the effect of a complete rotation of the Earth on her own axis; just as in the case dealt with in the text we consider the Moon's revolution in her orbit in addition to the successive changes in the aspect of the orbit. In my Sun Views of the Earth the twelve successive plates correspond to twelve changes in the Earth's general presentation towards the Sun during the course of the twelve months, while the four pictures in each plate correspond to the changes in the course of a day (at intervals, therefore, of six hours), owing to the Earth's rotation. So illustrated, this method of considering the subject of the seasons becomes singularly simple and truthful.

Of course the arrow on m m', and the globe of the Moon at м, are simply put in each figure at that part of the orbit which is most convenient, and are not supposed to be carried round with the rotation here specially dealt with.

or the whole of M is in shadow. But when the orbit is presented -a quarter of a year later-as at III., there can be no eclipse, wherever the Moon may be on her orbit. A quarter later, when the orbit is presented as at V., the same state of things results as at the beginning; and yet another quarter later, when the orbit is presented as at VII., no eclipse is possible.

The figure is drawn as nearly as possible to scale, and we see that the intermediate presentations of the orbit as at II., III., VI., and VII., are such that there can be no eclipses. We infer, therefore, that eclipses can only happen when the orbit is presented as shown at I., and for some relatively short time before and after that epoch. At such times, whenever the Moon (M) crosses the place of E, on the nearer or farther half of м's orbit, an eclipse must occur. But after that eclipse-season (if I may invent a word) has passed there can occur no eclipses of either sort until nearly half a year has passed and the presentation of the orbit has approached that shown at V. Then, for a while, eclipses are possible. Lastly, after this eclipse-season has passed, another period of nearly half a year passes during which eclipses cannot happen. And so on continually.

All this is perfectly simple and obvious. The recognition of the fact that these eclipse-seasons recur at intervals of about half-a-year tends also importantly to simplify the consideration of the whole matter. Let me note in passing that the term eclipse-season is not ill-chosen, inasmuch as one eclipse at least must needs takes place while the presentation of the orbit is changing through the critical aspects, such as I., V., IX. (fig. 98), and so on.

But let us now enter somewhat more into details. And first let us inquire how much the orbit m m' must be opened out in order that the Moon (M) may pass clear of E, whether on the nearer or farther side, in such sort that there may be no eclipse.

We have hitherto, for convenience, supposed the observer at the Sun's centre. But now we must give him liberty to traverse the whole of the Sun's globe; or rather we may suppose that millions of eyes placed all over the Sun's

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