32 CELESTIAL MECHANICS: LEUSCHNER 



from von der Groeben's Elements Bf brought forward by special 

 perturbations of Aa O s .42, AS +3".4 in 1894. 



The Elements Bg 20 to Bu given in the B. J. and in Kleine Planeten 

 from 1894 to 1919 are von der Groeben's elements probably brought 

 up to date in the same manner as before with the special perturbations 

 by Jupiter, Saturn and Mars and without any other correction. 



The following is a partial list of published corrections to the B. J. 

 ephemerides from von der Groeben's elements: 



1902, August 7 + 8 8 +0' Luther 21 



1903, October 26 +6 ra 38 +25' 2 Luther 22 



1905, March 1 + 2.77 - 8'3 Iwanowski 28 



1906, June 20 + 8.99 +11.3 Luther 24 



1907, September 7 + 21.68 +1' 23'l Luther 26 



1908, November 28 - 17.77 +0' 9'0 Luther 26 



1916, August 8 +0 m 3 +1' Luther 27 



1917, December 4 +l m 4 +7' Luther 28 

 1919, April 1 -I m 8 +6' Luther 29 



In a dissertation on the Jupiter perturbations of the group of small 

 planets whose mean daily motions are in the neighborhood of 750", 

 D. T. Wilson 30 gives an application of the Hansen-Bohlin method to 

 the Jupiter perturbations of this group. "The integration divisors for 

 certain values of the integers n, r and s become as small as 0.2. These 

 terms increase rapidly as the series advance. They were computed to 

 the third power of the eccentricities and to the fourth power of w. It 

 was found that all the terms of the third and fourth powers of w and 

 some of those of the third power of the eccentricities are negligible 

 when the eccentricity of the disturbed planet does not exceed 0.34 and 

 when the mean daily motion lies within the limits 720" to 780". There- 

 fore only those terms of the third power of the eccentricities which are 

 appreciable within the above limits have been retained. All the secular 

 terms have been computed to the fourth power of eccentricities." 



By means of these tables the Jupiter perturbations of Bellona were 

 computed and compared with the results previously obtained by 

 Hansen's method by Bohlin. 31 



The mass of Jupiter is taken as 1 : 1048 in the tables by Wilson. 



Of the three applications of these tables by D. T. Wilson that of 

 Bellona is by far the most interesting. This depends on the greater 

 proximity to the commensurability (748") and the cross position of 

 the line of apsides to that of Jupiter. The inequality 2g-5g' in rj8z 

 is the largest of all and amounts to 40'. But the difference between 

 the coefficients computed by Hansen's and Bohlin's methods is 

 large (2') and the comparison with the observations ought to decide 

 between the application of these methods to numerous planets in this 

 group. 



