TUTOR. Yes; and the reason is obvious: for, whilst the earth is revolving on its axis in twenty-four hours, the moon will be advancing in her orbit; therefore the earth must turn as much more than round its axis before the same place which was under her can come to the same place again with respect to her, as she has advanced in her orbit during that interval of time, which is 50 minutes. This being divided by 4, gives 12-1/2 minutes; so that it will be 6 hours 12-1/2 minutes from high to low-water, and the same time from low to high-water: or 12 hours 25 minutes from high-water to high-water again. PUPIL. This I understand perfectly well. TUTOR. I have now finished my description of the tides, and having a little time to spare, if you wish to know how to find the proportionate magnitude of the planets with that of the earth, and to calculate their distances from the sun, I will employ it that way. PUPIL. At our first conference I remember you shewed me the proportion that the other planets bear to the earth, with their periods and distances from the sun; but to have it in my power to make the calculations myself, will certainly give me great pleasure. TUTOR. To find what proportion any planet bears to the earth; or, that one globe bears to another, you must observe that, _all spheres or globes are in proportion to one another as the cubes of their diameters_. So that you have nothing more to do than to cube the diameter of each, and divide the greatest by the least number, and the quotient will shew you the proportion that one bears to the other. PUPIL. The operation appears very simple; but, as I do not know what a cube number is, I cannot perform it. TUTOR. You cannot forget what a square number is. PUPIL. The product of any number multiplied into itself is a square number, as 4 is the square of 2. TUTOR. Any square number multiplied by its root, or first power, will be a cube number. Thus 4 multiplied by 2 will be 8, which is the cube of 2; 9 is the square or second power, and 27 the cube or third power of 3, &c. This you will perhaps better understand by A TABLE OF Roots. 1. 2. 3. 4. 5. 6. 7. 8. 9. Squares. 1. 4. 9. 16. 25. 36. 49. 64. 81. Cubes. 1. 8. 27. 64. 125. 216. 343. 512. 729. PUPIL. I do, Sir; and am now prepared for an example. TUTOR. The diameter of the sun is 893552 miles, of the earth 7920 miles; how much does the sun exceed the earth in magnitude? PUPIL. The cube of 893522, the sun’s diameter, is 713371492260872648; and of 7920, the earth’s, 496793088000. And 713371492260872648 divided by 496793088000 is equal to 1435952, and so many times is the bulk of the sun greater than that of the earth. TUTOR. This one example may suffice, as I intend by and by to give you a table of diameters, &c.; you may then calculate the rest at your leisure. PUPIL. I shall now, Sir, be glad to have the other explained.