338 THE POPULAR SCIENCE MONTHLY 



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 proposi- 

 tions, twenty-two problems and twenty theorems. The whole work 

 covers 507 printed pages, and has a total of 192 propositions, 113 prob- 

 lems 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. (&) 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. 2 



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 : 



Rule I. We are to admit no more causes of natural things than such as 



are both true and sufficient to explain their appearances. To this purpose the 



philosophers say that nature is pleased with simplicity and affects not the 

 pomp of superfluous causes. 



The " Principia " was finished in the spring of 1686. It was pub- 

 lished by order of the Eoyal 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 Eoyal Society. The queen made him 

 a knight of the realm. He was given a lucrative position under gov- 

 ernment and moved to London. His work for science was finished, 

 and for forty years he reaped the reward of his labors. 



2 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. 



