“Good!” I replied. “And now, perhaps, you will have the patience to listen to an explanation of a very important relation which exists between the moon and the earth. We are led to it by what I have just said concerning tides. You know, of course that the tides in the oceans are due principally to the attraction of the moon. The sun also raises tides in the seas, but the moon, being so much nearer than the sun, is the chief agent in producing them. Sometimes the moon and the sun act together; at other times they pull in different directions. At Full Moon and at New Moon they pull together, because then they are either on opposite sides of the earth, or both on the same side. At such times we have the highest tides in all our seaports. That occurs about once every fortnight. But when the moon is at either First or Last Quarter, as you will perceive by looking at the diagram, her position, as seen from the earth, is at a right angle with a line drawn to the sun. Then the sun raises tides in one direction and the moon in another direction. The result is that at such periods the tides are lowest. An exact knowledge of these things is very important for mariners because there are harbors whose channels can be navigated by large ships only when the tides are high. Tables predicting the times and heights of the tides have been prepared for all the principal seaports of the world. In truth, the moon renders important services to the inhabitants of the earth, not merely in supplying them with a certain amount of light in the absence of the sun, but also in enabling them to navigate waters which are too shallow for ships except when deepened by the tide. The tides also, in many cases, serve to scour out channels and keep them open.” “Really, I am quite interested, and the more so because I find the moon, like a dutiful daughter, trying to be of some use to her mother. But have I not heard that the tides occur on both sides of the earth at once, and not simply on the side where the moon happens to be at the time? Please tell me how that can be so?” “A complete reply to your question would carry us into the realm of mathematical physics, but perhaps I can throw a little light upon the matter with the aid of this second diagram. [Illustration: The Moon and the Tides. ]