CELESTIAL MECHANICS: LEUSCHNER 5 



gaps, the question of stability and ultimate destiny, or in general 

 regarding their place in any hypothesis concerning the solar system, 

 final mean elements derived on the basis of accurate developments of 

 the perturbations are most essential. Fragments of fundamental 

 investigations of perturbations are available for a number of minor 

 planets. The value of some of these has been vitiated by corrections 

 made in connection with the accepted program of approximate pre- 

 diction, such as, for example, the correction of an accurate set of 

 osculating elements derived by special or general perturbations, to 

 represent later oppositions, either without perturbations or by taking 

 account only of approximate or incomplete perturbations. 



Fundamental investigations here are understood to include the 

 determination of osculating or mean elements from a limited number 

 of oppositions with complete regard of the perturbations, either special 

 or general, in so far as they may have been appreciable. In con- 

 nection with the study of the data existing for a limited number of 

 selected planets, it has been found that the failure of such elements 

 and perturbations to represent future oppositions in some cases can 

 be accounted for by the fact that the masses of the major planets 

 were known at the time with insufficient accuracy. The mere cor- 

 rection of the perturbations therefore, for the latest known values of 

 the masses may render such elements and perturbations far more 

 satisfactory than they appeared to be at the time when they were 

 discarded in favor of new determinations of elements with or without 

 perturbations. 



Freed from effects of changes which affect disadvantageously their 

 permanent value the fragments of fundamental investigations referred 

 to are of great importance as a basis for researches and their intel- 

 ligent application will involve a vast saving in computational and 

 theoretical work. 



At present it appears next to hopeless to the investigator to adopt 

 a profitable form of attack in connection with any of the older minor 

 planets without an enormous expenditure of time in searching astro- 

 nomical records. This accounts for the many duplications of effort 

 and for the disregard of previous valuable investigations. If 

 systematically undertaken, the task of bringing to light the important 

 data available for a final determination of the elements and general 

 perturbations of the minor planets, does not appear insurmountable. 

 Once available, such research surveys will be invaluable and 

 should prove an encouragement to research, particularly to young 

 investigators. 



The research surveys of the few planets which are given below are 



