CELESTIAL MECHANICS: LEUSCHNER 7 



also correcting the numerical coefficients in the general developments 

 by differential methods. 



After revision of independently determined elements and pertur- 

 bations for separate series of fairly consecutive oppositions, discon- 

 nected by a gap including a number of oppositions to which neither 

 series was extended either backward or forward, the separate funda- 

 mental investigations will, in some cases, probably be found to be 

 entirely consistent and thus become of permanent value, such as 

 Leveau's investigations on (4) Vesta, without involving extensive 

 theoretical and numerical work. In other similar cases the correction 

 of the elements and perturbations pertaining to fundamental investi- 

 gations for groups of oppositions separated by considerable gaps, so 

 as to represent the osculating data at a subsequent epoch, may establish 

 satisfactorily the connection between one or more groups of oppositions 

 for which elements and perturbations have been independently deter- 

 mined with accuracy. The mode of attack will vary with the avail- 

 able data for different planets, as indicated by the research surveys, 

 which this discussion advocates. The resurrection of the classical 

 contributions of the pioneer investigators of planetary perturbations 

 on a permanent basis, should produce material of great value 

 for the ultimate aims of astronomical science concerning planetary 

 investigations. 



The proposed program of fundamental investigations cannot 

 supersede the present astronomical practice in caring for the minor 

 planets in the immediate future, but as stated above it will be of 

 great assistance for the practical purposes of prediction, and should 

 gradually solve the now stupendous task of preserving planetary 

 discoveries, while furnishing at the same time the data for the more 

 fundamental aims of astronomical science. 



For the majority of the minor planets, probably the application 

 of four successive steps or processes will be necessary to preserve the 

 discoveries until final elements and perturbations can be made avail- 

 able. The first step or process represents the present practice 

 principally conducted by the Berlin Recheninstitut. The second step 

 is illustrated by Brendel's plan of supplying instantaneous elements 

 and approximate perturbations. The third step corresponds to the 

 determination of the elements and perturbations of the Watson 

 asteroids undertaken by Leuschner, which are intended to provide 

 fairly accurate but not final results. Hansen's and the Bohlin-v. 

 Zeipel methods have been found most practical and accurate in this 

 connection. The fourth and final step is demonstrated by the funda- 

 mental work of Leveau on (4) Vesta. It is the object of this discus- 



