52 CELESTIAL MECHANICS: LEVSCHNER 



Aa cos 6 A5 



1. 1894 +8!76t +7!22 



2. 1899a 2.81 2.36 



3. 1899b +1.57 +4.86 



4. 1901 2.51 +0.73 



5. 1902 +1.86 +2.00 



6. 1904 0.68 0.31 



7. 1906 +1.97 1.05 



The approximate perturbations due to Mars were found to be in- 

 effective since they remained less than 0".01. 



For the purpose of improving Elements G by means of additional 

 observations, Osten 6 first computes special perturbations due to Jupiter 

 and Saturn by the method of variation of elements, and determines 

 new Mean Elements H from the corrections which the observations 

 successively indicate. For the other six major planets the general 

 perturbations are computed after the method in Tisserand, Vol. 1, 

 Chap. 22. All the masses are taken from Bauschinger, "Tafeln z. 

 Theor. Astr." From this combination of special and general pertur- 

 bations a set of osculating elements for the ten oppositions 1899-1912 

 results, forming the basis for the formation of normal places. A de- 

 tailed investigation of the comparison stars and the observations leads 

 to normal places with relative weights and corrections for magnitude 

 equation in a. The equations of conditions are solved under four 

 different assumptions, thus Elements I without and Elements J with 

 magnitude equation. No definite solution is accepted, but the impor- 

 tance of using a observations free from magnitude equation is em- 

 phasized. 



In the next work Osten 7 proceeds to determine the perturbations 

 of the second order starting with Elements I. Hansen's method is 

 followed throughout (correcting an error in "Auseinandersetzung II, 

 page 98," which acts nearly as a change of the perturbing mass). A 

 capital difficulty is encountered in the near commensurabilities (+2e 

 5e' +le") with a period of 8650 years. 



Osten proposes to treat such inequalities by expansion into power 

 series in the time and then eliminate one of the anomalies. For (447) 

 the term 3e 7e' is thereby much enlarged. A comparison is made 

 between the special and general perturbations by Jupiter and Saturn. 

 Some deviations of the order of V are attributed to the perturbations 

 of the third order. Eight tables contain the perturbations. 



In the hope of obtaining as accurate results for (447) as for the 

 major planets Osten 8 completes his former theory and gives the last 



t Uncertain. 



j Normal places from Kreutz. 



