4 CELESTIAL MECHANICS: LEUSCHNER 



the Newtonian law of gravitation may serve this purpose, provided 

 that the mathematical difficulties will not prove insurmountable. It 

 may be assumed that the rigid mathematical methods hitherto 

 developed are satisfactory for planets with moderate eccentricity and 

 inclination which are not in a very near commensurable ratio with 

 any of the major planets, but it has not been established so far 

 whether an accurate application of the Newtonian law would fully 

 account for the motion of the minor planets even in the ordinary cases 

 just referred to. 



Exhaustive researches are available only for a very limited number 

 of planets. Among these are (4) Vesta, (13) Egeria and (447) Valen- 

 tine. The researches on (4) Vesta are due to Leveau, whose extraordi- 

 nary investigations extend approximately over a complete century of 

 oppositions. In connection with his work on the motion of Vesta, 

 Leveau has aimed at a determination of the masses of Jupiter and 

 Mars. His final value is larger than the best available mass 

 of Jupiter by approximately one one-thousandth. On account 

 of the moderate perturbations, the motion of Vesta does not 

 lend itself as well to a determination of the mass of Jupiter 

 as the motion of other minor planets with very large perturba- 

 tions. Any slight departure from the true mass of Jupiter, 

 et cetera, can reveal itself through the motion of Vesta only in long 

 intervals of time, which accounts for Leveau's gradual improvement 

 of his adopted mass by successively including longer periods of 

 observation. For the present his results may be considered funda- 

 mental and final, so far as this planet is concerned. No other case has 

 been studied so exhaustively. Later predictions are well within the 

 errors of observation, and not the slightest departure from the New- 

 tonian law is noticeable. It remains, however, to establish the same 

 result for planets with large perturbations, particularly for such 

 planets as have a mean motion commensurable with that of Jupiter. 

 To avoid the necessity of gradually improving the Jupiter mass by 

 means of subsequent observations of Vesta, it appears advisable to 

 base further predictions on the best determined values of the masses 

 of the major planets. Vesta also furnishes an example of the weight 

 to be assigned to observations in the early part of the last century. 



Leveau's investigations furnish a striking example of the funda- 

 mental researches necessary for the promotion of astronomical science 

 as distinguished from the generally accepted program of observation 

 and prediction for the preservation of discoveries. 



For the study and interpretation of planetary statistics, particularly 

 with reference to the origin of minor planets, the explanation of the 



