TRANSLATORS INTRODUCTION XXXV11 



by the available mathematics ; and so it took the 

 more particular form * of the so-called problem of 

 the three bodies, viz., given at any time the posi^ 

 tions and motions of three mutually attracting 

 bodies, to determine their positions and motions at 

 any other time/ Even this problem could not be 

 satisfactorily solved by the mathematical methods 

 of that time, and only approximate solutions by 

 the methods of the higher analysis could be 

 reached. 1 The whole of the elaborated detail of 

 these formal mathematical investigations of the 

 eighteenth century was completed and summed up 

 by Laplace in his immortal work, the Mecanique 

 Celeste, the first of the five volumes of which 

 appeared in 1799, and in which the stability of the 

 solar system and the permanent periodicity of its 

 perturbations were only too dogmatically demon- 

 strated. About 1750 these mathematical researches 

 were largely directed to the problems arising out of 

 the motions of the Moon, and the consequent con- 

 struction of Lunar Tables, which were desiderated 

 at the time as of the greatest practical importance 

 both for observational Astronomy and Navigation. 

 In 1713 the British Government had offered a 

 reward of 20,000 for the discovery of a method 

 of finding the longitude at sea to within half a 



1 See, e.g., Euler's Papers, Considerations sur le probteme des trots 

 corps, 1763, and his Nouvelle Mdhode de determiner les derangements 

 dans les mouvemens des corps celestes, causes par leur action mutuelh. 

 1763- 



