How Eclipses Occur

I have Raid that the sun pursue8 a certain definite path among the stars, about half a degree wide, whioh you could see if be left any trace there ; so, also, if you couM mark the position of the moon tonigt among the stars, and mark its position at every hour during her whole courae, you would find that she ulso has pursued a definite path among the stars, but you would not find this path to be the same as the sun's path. If it were the same, we should have an eclipse of the sun every time the moon crossed the sun, and an eclipse of the moon every time that the moon passed on the other siche of the earth from the sun. But the two paths are inclined to each other about 5 degrees. They cross each other at a point which, in the month of October, 1874, is very near the sun. The moon's path is south of the sun's in nearly all that part of the heavens which we can seen in the evenings of that month; but it approaches the sun's path, and crosses it near the eastern horizon, and in most of the invisible half of the sphere, or that part below the horizon, the moon's path is farther north. All this will be clear on examiniug the star maps, where the dotted line 6hows the path of ;he moon during 1874, crossing the sun's path in tbe constellations Aries and Libra. These two opposing points in which ;he moon's path crosses the path of the sun are called the nodes. It is very clear that unless the sun is near one of the moon's nodes when the moon herself passes by, the moou will pass above or aelow the sun, according as her path is above or below that of the sun at this point, and consequently there will be no íclipse. But if the sun happens to be near the node, then the moon will neces sarily pass over his face and eclipse some portion of him. Now, as I have just explained, there are two opposite nodes ; the one set a few hours ago, and the other has just Since the sun makes the whole cirauit of the heavens iu the course of a year, he crosses the moon's nodes ' twice in that time. In 1874 he crossed the node in May, and will cross the other node in November ; consequently it is ouly about these two times that any eclipse can take place during this year. If the moon always followed tbe same path in the heavens, we could never have any eclipses but at those two seasons. But if we watch the motions of the moon for several years in suceession, we shall fiad that her patb is continually chaning. At the present time she passes seven degrees north of Aldebaran ; a month henee she will seem to pass the star at almost exactly the same distance ; but if you coutiue your observations for four or five months, you will find that she passes it perceptibly farther north, and in three years you will find that she crosses it at the distance of about ten degrees. After that she would begin to cross farther south, passing near Aldebaran at every revolution for eight years, until in 1885 and 1886 she will pass right over it. If the moon's path were painted on the heavens, you would see that every time the moon carne round to the same point in her path, which takes place about every twenty-seven days, she would cross the suu's path about three of her own diameters sooner than the month before. In the course of a year, therefore, she will have crossed about thirty-six diameters sooner, or farther to the west. In the course of twenty years you will find that this motion has been kept up until she crosses at the same point she does now, and thus the nodes have made a complete circuit of the heavens. The seasons of eclipses vary, therefore. in the same manner. This year they are in May and October ; in five years from now they will occur three months earlier, and we shall have them in Pebruary and August ; five years more, and they will be in October and May five years more, in August and February ; five years more, and they will correspond once