188 PEOGEESS IN ASTEONOMY. 



subsequent discovery of the external body not far from the place at 

 which their mathematical analysis had h'd them to believe it would be 

 seen will forever be regarded as a line triumph of the human intellect. 



But the results of the inquiries which now concern us are generally 

 of not so sensational a character, although they lie at the root of our 

 knowledge of celestial motions. They more often take the shape of 

 tables and discussions relating to the movements of the bodies which 

 make up our j-olar system. 



Gauss ma}" be said to have led the way during the present century 

 b\' his Theorla nwhis cc/rjxjrurii c<X'le><ttuiii nolem airibientium. This was 

 a worthy sequel to the Mechanique Celeste, in which work, toward 

 the end of the preceding century, Laplace had enshrined all that was 

 known on the planetary results of gravitation. 



In later years Le Verrier and Newcomb have been among the chief 

 workers on whom the mantle of such distinguished predecessors has 

 fallen. From them the planet and satellite tables now in use have 

 been derived. 



But the motion of our own satellite, the moon, has had fascinations 

 for other analysts besides those we have named. 



The problem, indeed, of the moon\s motion is one of the most difS- 

 cult, and has taxed the ingenuity of astronomers from an early date. 

 Even at the present day it is impossible to predict the exact position 

 of the moon at any one moment, owing to inequalities and perturba- 

 tions the exact varying values of which are not known. 



The two most important theories of the motion of the moon, com- 

 pleted toward the middle of the century, were due to Hansen and 

 Delaunay. The former's appeared in 1838, the lunar tables being 

 published later (1857), while the latter's was published in I860. 



Hansen's theory had for its chief object the formation of tables. To 

 avoid the inconvenience of using in his calculations series which slowly 

 converge he inserted numerical values throughout. In Hansen's solu- 

 tion the problem is one actually presented by nature, allowance being 

 made for everv known cause of disturbance. There is one disadvan- 

 tage, namely, thateshould observations demand a change in an}" of the 

 constants used there is no means of making any correction in the 

 results. 



Delaunay's theory surmounted this difficulty, but at the expense of 

 still greater inconvenience for making an ephemeris. The slow con- 

 vergence of certain series involved an immense amount of labor to give 

 sufficiently approximate results. 



More recently, as the century is closing. Dr. Brown has taken up the 

 subject and made a fresh attempt to calculate the motion of our satellite. 

 It may l)e stated that he adopts all Delaunay's modifications of the 

 problem and works them out algebraically; but there are many tech- 

 nical differences which it would be out of place to mention here. 



