CELESTIAL MECHANICS: LEUSCHNER 



factory results obtained for the planets (10) Hygiea, and (175) 

 Andromache, by the application of Leuschner's revision of von 

 ZeipePs tables for the Hecuba group. Further reference to the great 

 importance of "Gruppenweise Berechnung der Stoerungen," inaug- 

 urated by Bohlin, may therefore be omitted here. The methods of 

 Bohlin and his followers serve admirably in connection with the third 

 of the four stages outlined above for the determination of funda- 

 mental results. In certain cases of limited eccentricity and inclination, 

 they will, no doubt, lead to final results. 



No claim is made that the planets for which research surveys are 

 given below are the ones most in need of immediate attention. 

 Further study of available data will be necessary to classify the 

 planets with reference to the requirements of observation and com- 

 putation, as outlined in the report of the American Committee on 

 Comets and Asteroids, presented at the Brussels meeting of the 

 International Astronomical Union in 1919; nor are the planets con- 

 sidered below the most important for fundamental scientific purposes. 

 The list, however, may be considered as fairly representative of the 

 immediate research requirements. To some extent the selection has 

 been accidental. Thus the computing section of the British Astro- 

 nomical Society has undertaken the computation of the ephemerides 

 of the first four planets. In this connection it sought advice regarding 

 the best available data and methods of procedure. The research sur- 

 veys of the first four planets were undertaken to aid the computing 

 section in its undertaking. The importance of the Trojan group is 

 too well known to be emphasized. For further investigations con- 

 cerning the theories of the six planets belonging to this group the 

 research surveys given will be of considerable value. It is of interest 

 to note that Leuschner's orbit methods as applied by Einarsson, 

 appear to be the most promising for the determination of preliminary 

 osculating elements, while Wilkens' method deserves careful trial 

 in deriving the perturbations. E. W. Brown's unpublished theory 

 promises to be thoroughly fundamental. For the two planets of the 

 Trojan group last discovered, more accurate preliminary osculating 

 elements are immediately needed. For other planets, the list of 

 research surveys themselves will reveal the most necessary work to 

 be done. In general, reference to theoretical investigations is included 

 only in connection with a simultaneous new determination of elements. 

 Thus the numerous and important investigations on the theory of 

 the Trojan group are not considered here, the chief object of the 

 surveys of these planets being to furnish numerical data and encourage 

 their improvement as a basis for such theories. 



