THE STABILITY OF THE SOLAR SYSTEM 295 



matical analysis had to grow to new powers. Newton had 

 lent a powerful aid with his invention of fluxions. The philo- 

 sopher Leibnitz had made very near the same discovery. To- 

 gether they had produced the new calculus. It was the new 

 weapon of analysis which, when the " Mathematical Principles/' 

 the Principia, finally had taken hold, gave such a tremendous 

 impetus to the mathematical treatment of scientific problems, 

 and especially those of astronomy. There seemed to spring up 

 a whole school of calculating geniuses to whom an unsolved 

 problem was as meat and drink. 



The foremost of the earlier ones was Euler, a Swiss. It is 

 related of him that when in middle life he lost one of his eyes, 

 he remarked that henceforth he would have less to distract him 

 from mathematics. Later on he lost the use of the other ; but 

 it seemed to make no difference in his astonishing activity. 

 Princes of the mind were then high in the favour of princes of 

 the land. Euler roamed about the courts of Europe, joining 

 first in the organisation of the newly created Academy of Sciences 

 in St. Petersburg, then in Frederick's reorganisation of the 

 Academy at Berlin, then back again. All the while he was turn- 

 ing out with an incredible rapidity papers upon new methods of 

 analysis, abstract dynamics, optics, the motion of fluids, the 

 movement of the planets ; every branch of physical investigation 

 seemed grist for his mill. Altogether he left some eight hundred 

 memoirs, besides several respectable volumes, and a charming 

 series of letters on the study of nature, addressed to a princess 

 friend. His versatility was amazing. It may be noted in passing 

 that this seems a characteristic of minds of the highest order. 

 It was particularly true in the first two centuries after Galileo, 

 before the sciences had become so intricate and highly special- 

 ised that mastery in more than one narrow field should make 

 a Helmholtz a marvel to his kind. 



Euler's association with the Bernouillis was so close that he 

 might almost be regarded as a member of that famous family 

 of mathematicians, two of whom were rivals of Newton, and 

 one of whom, Daniel Bernouilli, was the first important 

 Newtonian among mathematicians outside of Great Britain. 

 Euler and the latter found a keen competitor in the precocious 

 genius of Clairaut. He is remembered now, if he is remembered 

 at all, chiefly for his classical investigations into the figure of 

 the earth ; but in his own time his celebrity was considerable. 



