CELESTIAL MECHANICS: LEUSCHNER 3 



In addition to the general pertubations of the thirty-six planets 

 which are being used by the Jahrbuch, the general pertubations of a 

 number of other planets have been .derived on the basis of what, at 

 the time, appeared to be reliable osculating elements. These pre- 

 sumably valuable data have been replaced by later elements derived 

 independently, more or less accurately, with or without general 

 perturbations, or upon the basis of arbitrary corrections. Bausch- 

 inger's Tabellen form a valuable key to some of these investigations, 

 but even in the Tabellen the elements and perturbations cited do not, 

 in all cases, represent the best elements and perturbations available, 

 although perhaps in every case they are the most reliable for subse- 

 quent oppositions. This arises from the fact that earlier investigations 

 were abandoned by Bauschinger in favor of later ones. Preliminary 

 calculations have shown, however, that some of the earlier elements 

 and perturbations represent distant oppositions at a later date more 

 satisfactorily than his adopted elements and perturbations represent 

 earlier oppositions equally remote. 



Of great importance for the program of the Recheninstitut are the 

 contributions of Brendel, who has developed methods for the approxi- 

 mate determination of the perturbations for certain groups of planets. 

 Perturbations greater than 3'.4 within fifty years are included, with 

 the object of reproducing geocentric places within 20' for 100 years. 

 So far the necessary data have been published by Brendel, Labitzke, 

 and Boda for 230 planets, approximately 25 per cent of the total 

 number of known minor planets. The advantage to be gained from 

 BrendeFs contributions for these planets is that for the practical 

 purpose of preserving these planets, by following their motion, it 

 should become unnecessary as a rule to compute special perturbations 

 for them, or even to apply corrections to the elements. Brendel plans 

 to continue the work of supplying instantaneous elements and 

 approximate perturbations for other groups of planets so that the 

 program of the Recheninstitut, of the Marseilles Observatory, and of 

 various investigators who, from time to time, publish improved 

 elements and perturbations for ephemeris purposes, will become 

 more and more simplified. 



The preservation of planetary discoveries by observation and pre- 

 diction with the aid of approximate perturbations is not the ultimate 

 aim of astronomical science, but a necessary and unavoidable means 

 to the end. The ultimate aim rests on the determination of mean 

 elements and general perturbations which hold for all time or at least 

 for very long periods within the limits of accuracy set by observation. 

 It is expected that the elements and perturbations determined under 



