xxxvi KANT'S UNIVERSAL NATURAL HISTORY 



of the time, were mainly those problems of Mathe- 

 matical Dynamics and Gravitational Astronomy 

 which had been- left uncompleted, or unsolved, by 

 the supreme genius of Newton ; and they one and 

 all applied themselves to their solution with the 

 greatest devotion, perseverance, and enthusiasm. 

 In particular, the problems arising out of the 

 applications of Newton's Law of Gravitation to the 

 motions of the Planets and their satellites in the 

 solar system, called forth and exercised all their 

 powers. Newton had mathematically established 

 the law of Gravitation as holding between any two 

 bodies, such as the Earth and the Moon, and the 

 Sun and each of the Planets, but it still remained 

 to verify and apply it to the disturbances or per- 

 turbations observed in the motions of the several 

 members of the Planetary System, arising from the 

 effect of their mutual attractions upon each other. 

 Newton's final problem was, therefore, this : 

 ' Given the eighteen bodies/ then known as 

 making up the solar system, ' and their positions 

 and motions at any time, to deduce from their 

 mutual gravitation, by a process of mathematical 

 calculation, their positions and motions at any 

 other time; and to show that these agree with 

 those actually observed/ 1 But the problem in this 

 universal form could not then be solved exactly 



A Short History of Astronomy, by Arthur Berry, p. 288, 1898. 

 Sir John Leslie gives a good account of this problem and its discus- 

 sion in his Dissertation* 



