56 Britain's Heritage of Science 



alone would give him a high place among discoverers. He 

 first constructed a spirit level, but others had anticipated 

 him in the use of the Vernier. He was the first to use light 

 powders to study the vibration of sounding bodies, and 

 invented an instrument to measure the depth of the sea. His 

 more theoretical speculations always showed acuteness, 

 and might have led to great things if he had been more 

 persevering. In 1674 he published views on a universal 

 gravitation which was to explain the planetary motions ; 

 with the exception of the law of the inverse square, these 

 contained the main principles of the theory which Newton 

 had then already worked out, though not published. In 

 optics, Hooke favoured the undulatory theory, and even 

 expressed the idea that the motion of the particles of the 

 medium which transmitted light was transverse to the direc- 

 tion of propagation, differing in this respect from the waves 

 of sound. Newton, who disliked controversies, is said to 

 have delayed the publication of his book on optics until after 

 Hooke's death for fear of rousing an acrimonious discussion. 



The second edition of Newton's " Principia " was pub- 

 lished in 1713 by Cotes (1682-1716), a distinguished and 

 promising mathematician, who died at the early age of thirty- 

 four, having held during the last ten years of his life the 

 newly-founded Plumian Professorship at Cambridge. 



Among the professional representatives of mathematics 

 during the eighteenth century, it must suffice to name 

 Maclaurin (1698-1746), Professor of Mathematics at Aberdeen ; 

 Matthew Stewart (1717-1785), who succeeded him in the 

 Professorship, and Thomas Simpson, the son of a grocer, 

 who ultimately became Professor of Mathematics at the 

 Royal Woolwich Academy. 



After Newton had placed astronomy on a sound 

 dynamical foundation, a vast field was opened out to further 

 research. It had still to be proved that the law of gravita- 

 tion was sufficient to account for every detail of the motions 

 of celestial bodies, and was not only a first approximation 

 to be supplemented by other effects. Hence it became 

 necessary to increase the accuracy of astronomical observa- 

 tions, and to extend the theoretical investigations, based 

 on the laws of gravity, so as to include the mutual action 



