SECTION A ASTROMETRY 



(Hall 9, September 21, 10 a. m.) 



CHAIRMAN: PROFESSOR ORMUND STONE, University of Virginia. 



SPEAKERS: DR. OSKAR BACKLUND, Director of the Observatory, Pulkowa, 



Russia. 



PROFESSOR JOHN C. KAPTEYN. University of Groningen, Holland. 

 SECRETARY: PROFESSOR W. S. EICHELBERGER, U. S. Naval Observatory. 



THE DEVELOPMENT OF CELESTIAL MECHANICS DUR- 

 ING THE NINETEENTH CENTURY 



BY OSKAR BACKLUND 



[Oskar Backlund, Astronomer of the Imperial Academy of Science, St. Petersburg, 

 and Director of the Central Observatory Nicholas, Pulkowa, Russia, b. Len- 

 ghem, Sweden, April 22, 1846. Ph.D. University of Upsala, Sweden, 1875; 

 D.Sc. Cambridge; D.M. University of Christiania. Assistant Astronomer, Obser- 

 vatory at Stockholm, 1873-76; Astronomer, Observatory, Dorpat, Russia, 1876- 

 79; Astronomer, Pulkowa, Russia, 1879-87; Astronomer of the Imperial Acad- 

 emy of Science, 1883; Director, Observatory at Pulkowa, 1895; Member of the 

 Imperial Academy of Science of St. Petersburg; Mathematical Society, Moscow; 

 Royal Academy of Science, Stockholm; and numerous other scientific and learned 

 societies. Author of Calculs et recherches sur la Comete d' Encke ; Ueber die 

 Bewegungkkiner Planeten des Hecuba-Typus; and numerous other noted works 

 and memoirs on astronomy.] 



THE development of celestial mechanics during the nineteenth 

 century is such a comprehensive theme that a fundamental treat- 

 ment of it within the limits of an address of half an hour or so can- 

 not be thought of. I am therefore limited to the presentation of the 

 principal phases of the subject, and of course in doing so, by reason 

 of the necessary arbitrariness of choice, may not meet the approval 

 of this distinguished assembly. 



I will first consider the development of celestial mechanics in so 

 far as it concerns the motions of the planets. 



The nineteenth century received a great inheritance from the 

 eighteenth. With the five undying names of Euler, Clairaut, d'Alem- 

 bert, Lagrange, and Laplace are linked theoretical discoveries which 

 upon the basis of Newton's law explained all the motions of the 

 planets, satellites, and comets in so far as they were furnished by 

 the observations of that time. Was this inheritance so utilized 

 during the past century, that at the end of the same the results of 

 observation may be considered explained by theory? The following 

 discussion will give the answer. 



Laplace's Mecanique Celeste gives as it were a summing-up of the 



