“Very well, I’ll spare your attention as much as possible. To begin with the eclipses of the moon: The reason why they are not of regular monthly occurrence is simply because the orbit of the moon is a little inclined, about 5¼°, to the orbit of the earth. Even then there would be an eclipse once every month if the orbit of the moon were fixed in space, and if the point where that orbit crosses the plane of the earth’s orbit were always directly opposite to the sun. But instead of being fixed in position the orbit of the moon has a curious motion of revolution of its own. This causes the two opposite points, where it crosses the plane of the earth’s orbit, and which are called the moon’s ‘nodes,’ to move continually onward in a direction opposite to that in which the moon revolves, but much more slowly. A period of about nineteen years is required for the moon’s nodes to complete a revolution. The consequence is that the nodes are not always in line with the earth and the sun, and except when they _are_ nearly in line no eclipse can occur. To enter into a complete explanation of this would require more ‘mathematics’ than you would like, but what I have said may at least serve to give you an idea of the reason why eclipses are comparatively of rare occurrence.” “I think I understand the reason sufficiently. But what a complicated affair you astronomers make of what, it seems to me, should really be a very simple thing.” “It is like a sewing machine,” I replied, “which seems very simple when you see it running smoothly, and do not trouble yourself about all the various parts of its mechanism. But if you undertake to explain to yourself, or to make clear to another person, exactly how the machine works, you find that your attention is rather severely taxed, and that the apparent simplicity is based upon no little complexity of construction and interaction of parts. You will have understood from what I have said, that the reason why the moon does not eclipse the sun once every month is based upon the same fact, namely, the inclination of the moon’s orbit to the plane of the orbit of the earth; and that when she does eclipse the sun her nodes must be somewhere near a line drawn from the earth to the sun. There is one broad difference between an eclipse of the moon and an eclipse of the sun which I have not yet mentioned. This arises from the fact that the moon being so much smaller than the earth, her shadow, when she hides the sun, does not cover the entire earth, as the earth’s shadow covers the whole moon, but comes almost to a point before reaching the earth. The average length of the moon’s shadow is only 232,150 miles, 6,690 miles less than the average distance between the moon and the earth. But since, in consequence of the eccentricity of her orbit, the moon’s distance is continually varying, the length of her shadow also varies to the extent of about 4,000 miles each way. Thus it may be as short as 228,300 miles, or as