It is also manifest that if the earth circles around S, as in fig. 14, the observed phenomena of apparent solar motion will be precisely the same as though the sun circled around the fixed earth. Let us follow the earth round from the position a, noting how the sun would appear to move on the ecliptic, and also how the length of day would be affected by the varying position of the earth's axis with respect to the sun. When the earth is at a, the beginning of Libra, about the 20th of March, the sun, as seen from the earth, appears at the beginning of Aries in the opposite part of the heavens, the north pole is just coming into light, and the sun is vertical to the equator, which, with all its parallels, is divided into two equal parts by the circle which forms the boundary between the dark and illuminated hemispheres, and therefore the days and nights are equal all over the earth. As the earth moves in the ecliptic, according to the order of the letters A, B, C, D, &c., the north pole P comes more and more into the light, and the days increase in length at all places north of the equator Æ. When the earth comes to the position between B and C, or the beginning of Capricorn, the sun, as seen from the earth, appears at the beginning of Cancer about the 21st of June; and the north pole of the earth inclines towards the sun, so as to bring into light all the north frigid zone, and more of each of the northern parallels of latitude in proportion as they are farther from the equator. As the earth advances from Capricorn towards Aries, and the sun appears to move from Cancer towards Libra, the north pole recedes from the light, which causes the days to decrease and the nights to increase in length till the earth comes to the beginning of Aries, and then they are equal as before, the boundary of light and darkness cutting the equator and all its parallels equally. The north pole then goes into the dark, and does not emerge till the earth has completed a semi-revolution of its orbit, or from the 22d of September till the 20th of March. Similar changes occur, mutatis mutandis, in the southern hemisphere.
It may be well to advise the reader not to allow his mind to be led astray by the proportions indicated in such pictures as fig. 14. It is absolutely impossible to illustrate the seasons, either by diagrams or by the use of a globe, without introducing incorrect relative dimensions; but by combining two sets of pictorial illustrations, the mental error apt to arise from the study of such pictures as fig. 14 may be got rid of. Thus, after carefully studying the relations illustrated in that figure, the reader should turn to Plate XXVII., and after noting that the figure of the earth there shown is the same as that in fig. 14 (held so as to have GgF uppermost), he should endeavour to picture to himself such a figure of the earth as is shown in the plate, travelling around the path EE′, but so reduced in dimensions that its whole disk would have a diameter less than the hundredth part of that of the small white disk, at the centre of the plate, which represents the sun. It will then be instructive to extend this method to Mars, as figured in Plate XXVII., carrying this planet (after first imagining his disk reduced 6000 times) round his path MM′, with constant axial pose. The planets pictured in Plate XXVIII. can be dealt with in like manner. From a careful study of the two plates, with special reference to the indicated scales, the general relations of the entire solar system can be inferred, and to some degree conceived. But for the purpose of actually picturing these relations to his mind, the reader may conveniently use Sir J. Herschel's illustration, as follows: Choose any well-levelled field. On it place a globe 2 feet in diameter to represent the sun; Mercury will be represented by a grain of mustard seed, on the circumference of a circle 164 feet in diameter for its orbit; Venus a pea, on a circle 284 feet in diameter; the earth a [somewhat larger] pea, on a circle of 430 feet; Mars a rather large pin's head, on a circle of 654 feet; the asteroids grains of sand, in orbits of from 1000 to 1200 feet; Jupiter a moderate-sized orange, on a circle of half a mile; Saturn a small orange, on a circle of 4/5ths of a mile; Uranus a full-sized cherry, on a circle more than 1½ miles; Neptune an extra-sized cherry, on a circle of 2½ miles in diameter.
Chapter V.—Apparent Motions of the Moon and Planets—Parallax.
We have seen that while the stars remain fixed, to all appearance, on the celestial concave, the sun circuits around a great circle of the star-sphere, moving always in one direction, and at a rate which, though variable in different parts of the circuit, does not vary largely, and is constant for each part of the ecliptic. Moreover, to ordinary observation, continued for periods of a few years, the sun's path in the heavens appears to remain always the same, and to bear the same relation to the poles and equator of the rotating star-sphere.
But we have now to consider bodies which neither remain fixed like the stars, nor move in a constant apparent path like the sun.
The moon is the most noteworthy of these bodies, because of her apparent size and brightness, and also because of the remarkable changes of appearance which she presents according to her varying position with reference to the sun. When she is seen near him in the heavens, she appears always like a fine sickle of light, with the horns turned away from him. When she is in the part of the heavens directly opposite to the sun, she appears with a full orb. When she is exactly midway between the point occupied by the sun and that opposite to him, she appears as a semicircle of light, with the convexity towards the sun; and in positions intermediate to these she appears with more or less of her circle illuminated, according as she is nearer to or further from the point directly opposite the sun. All this corresponds with what would happen if the moon were an opaque orb nearer to the earth than the sun, and illuminated by him.
Now, when the moon is watched, even for a few hours only, she is found to be travelling on the star-sphere in the same direction as the sun (and, like him, on a path inclined to the equator), but much more rapidly than the sun travels. It is impossible to watch the moon completely round the heavens, because she is found to pass close to the sun once in each circuit, and when very near to him cannot be seen. But while she is visible, she travels continuously in one direction, and when she reappears, after having been for a day or two lost in the sunlight, she is seen to have shifted her place as though, during that interval, she had travelled continuously onwards.
