41 



Dante's Infnno, where the poet describes himself, under the 

 guidance of Virgil, as reaching the exact centre where batan is 

 confined, then turning round, and climbing till he emerged at 

 the Antipodes. The investigations of Galileo had shown that 

 all bodies, apart from the resistance of the air, fall .at exactly 

 the same pace towards the centre of the earth, 16 feet in the farst 

 second. To generalise this fact beyond the earth was a guess 

 Newton's most wonderful guess; " anyone may make guesses at 

 scientific results, but to guess correctly and prove the correctness 

 is the work of genius only." Mr. Davey set out how Newton 

 calculated the orbit of the moon, and to his great disappoint- 

 ment found the fall towards the earth to amount to 13 feet 

 instead of 16. He laid aside the subject for years in conse- 

 quence, but accidentally heard at a meeting of the Eoyal bociety 

 that a fresh measurement of the earth had been made by 

 Picard, who found that a degree of arc measured 69 miles 

 instead of 60, as had been previously supposed. Then Newton 

 returned to his labour, proved the truth of his guess, and 

 showed that gravitation affected not only the earth, but was the 

 force that held together the entire solar system. Newton also 

 showed that the effect of gravitation would be to flatten the earth 

 at the poles, to occasion the precession of the equinoxes and the 

 phenomena of the tides; and that the masses of the heavenly 

 bodies might be computed by it. Yet, however, these results 

 might never have been published had it not been for Newton s 

 friend, Halley, who himself brought the matter before the Eoyal 

 Society, and paid the expense of printing the book. 



The title of the work, which finally came before the world in 

 1687 was FhilosophM Xatumlis Priucipia Jiat/icmfltiVrt,— Mathe- 

 matical Principles of Natural Philosophy. It is commonly called 

 the Priucii>ia. The very title of the work marked out its funda- 

 mental diflerence from all previous systems of the world. It was 

 a mathematical attempt to explain the constitution of the 



universe. ^^ , i xu 



In the first book of the Principia Newton showed mathe- 

 matically what laws would result if bodies attracted each other 

 by gravitation. The method is that of the ancient Synthetic 

 Geometry ; definitions and axioms are laid down, and succes- 

 sive theories and problems are solved. The most extraordinary 

 portion is the wonderful sixty-sixth proposition, with its twenty- 

 two corollaries. In the second book the method of fluxions (the 

 calculus) is laid down ; but Leibnitz had already published his 

 form of the calculus. Finally, the third book, by the aid of 

 the new mathematics, shows that all the known solar system 

 actually does follow the laws which had been shown in the first 

 book to rule if bodies attracted each other by gravitation. The 

 demonstration was as complete as it could be made by human 



