398 THE SCIENTIFIC MONTHLY 



after his entry into Cambridge as an undergraduate. At this time his 

 chief subjects for lectures and investigation were optics and algebra, 

 the former of which involved him in much controversy. In fact all 

 through his active period of work in mathematics, he seems to have 

 suffered from the difficulties of having his great advances understood 

 and accepted, although there never seems to have been much question 

 amongst his contemporaries as to his wonderful powers. In 1679 he 

 discovered the law of areas and showed that a conic would be described 

 by a particle moving round a center of force under an attraction which 

 varied inversely as the square of the distance. But it was not until 

 1684 that he began to work seriously at gravitation problems, his first 

 step being to show that a uniform sphere exerts the same attraction as 

 a particle of the same mass placed at its center. From this time on 

 progress was rapid. Within two years the manuscript of the Principia 

 was finished and the following year printed. 



The Principia, like most of the works of the time consists partly of 

 results previously known, but by far the larger part of it is Newton's 

 own work. It begins with definitions, the formulation of the three 

 laws of motion and the principal properties which can be deduced from 

 them, with some examples, forming an introduction to the first book 

 which contains his main work on gravitation. The second book is 

 chiefly devoted to hydrodynamics and motion in a resisting medium 

 and the third to various applications of the first book to bodies and 

 motions in the solar system. As stated earlier, the proofs are cast into 

 a geometrical form and freed from all traces of the method of fluxions 

 which Newton had used to reach many of his results. 



This great effort seems to have nearly exhausted his great powers 

 for he produced little after its completion. In 1695 he accepted an 

 appointment at the Mint and six years later resigned his chair at Cam- 

 bridge. He was only forty-five when the Principia was published and 

 he lived for thirty-eight years afterwards. 



The half-century which followed the publication of the Principia 

 seems to have been mainly occupied in understanding and digesting 

 the advances made. On the continent, where Leibnitz' notation for the 

 calculus was mainly adopted, a firm foundation was laid for the prog- 

 ress which began in the middle of the eighteenth century. In England 

 the reverence for Newton was so great and separation from the con- 

 tinent so effective, that his methods dominated all the work for nearly 

 a century and a half. This was perhaps mainly due to the translation 

 of the Principia into geometry which ensured its early acceptance but 

 must have fostered a distrust of all results which could not be proved 

 in the same way. And further, Newton's notation for fluxions, which 

 did not bring out their essential properties, had great influence in pre- 

 venting advances as against that invented by Leibnitz. Nevertheless 



