theorems and twelve problems. Book III. has fewer diagrams, less mathematics and more discussion. The principles of natural philosophy are applied to the explanation of the solar system, and such topics as comets and tides are carefully treated. There are forty-two propositions, twenty-two problems and twenty theorems. The whole work covers 507 printed pages, and has a total of 192 propositions, 113 problems and 79 theorems, besides lemmas and scholiums in abundance.
Oliver Lodge in an outline of the "Principia" selects seventeen points for special emphasis. Of these a few may be reviewed.
1. Newton shows from Kepler's laws the following: (a) From the first law, that the law of gravity is inversely as the square of the distance, (b) From the second law, that this force is directed toward the sun as center, (c) From the third law, that all the planets are acted on by the same law of gravity; i. e., that the law of gravity extends to the uttermost confines of the solar system.
2. From the length of the year and the distance of any planet from the sun Newton calculates the planet's mass, using the earth's mass as a unit.
3. He recognized the comets as members of the solar family and showed how to calculate their orbits.
4. He showed that the earth, as a result of its rotation, must be flattened at the poles, and calculated the amount (28 miles).
5. He laid the foundation for a complete theory of the tides.
We have but noted the high lights, as it were, of Newton's work. No wonder that he became lost to external events as his mind grappled with problem after problem, and one by one lay bare the secrets of the universe. As an example of the style in which the "Principia" is written, we may quote from the beginning of the third book where he lays down rules for reasoning in philosophy:
The "Principia" was finished in the spring of 1686. It was published by order of the Royal Society, being issued from the press in July, 1687. Newton, from being a little-known member of the faculty of Cambridge, was at once recognized as the foremost scientist of the world. Honors were showered upon him. He was sent to parliament. He was elected president of the Royal Society. The queen made him a knight of the realm. He was given a lucrative position under government and moved to London. His work for science was finished, and for forty years he reaped the reward of his labors.
- The first cometary orbit to be calculated was done by Halley upon the comet bearing his name, which last year made its third return since Newton's day.