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.