140 



of 3.°43 between the anniuil Tariatioi: for both, however, makes the 

 variation of the two arguments differ 180° in 52 years and so the 

 two terms cannot be combined into one. 



The complete formulae for the corrections, which must still be 

 added after Brown's inequalities have been taken into account, are 

 therefore 



_/i=-0".60 4-0".0034|«- -1900.01 + 0" 66cos[244°.4 + 40°.35(«- 1900.0)1 

 — yb=—0".52— 0".0090 1^—190'). 0| + 0".6r5s{?^{244°.4 + 40°.35(i— 1900.0) 



The two periodic terms can also be combined, as was done above. 

 Let us now consider the meaning of the corrections found, first 

 as regards the non-periodic parts. We have : 



— he — + 2(fe 



— kc ^= — 2eöjt 



in which tfe and d-r represent the corrections to the eccentricity and 

 the longitude of the perigee adopted by Hansen for his tables. 



We find thus 



de=-~ 0".30 + 0".0017 {t — 1900.0) 

 é.r = + 4".7 + 0".082 {t — 1900.0). 



The correction found for the annual variation of the eccentricity 

 is certainly too small to be considered as real. If we assume it to 

 be zero, we find 



öe = — 0".32. 



The correction found for Hansen's annual motion of the perigee 

 may be compared with what was found by others. 



The correction -|- 0".08 must be applied to Hansen's tabular value 

 of the sidereal motion in a Julian year for 1850.0, 146435". 23, 

 which was deduced by him from the observations. 



We get thus for 1850.0. 



Annual motion of .t =: 146435". 31. 



CowELL found from his discussion of the observations at Greenwich 

 (Monthly Notices Jan. 1905) 146435". 38, in near agreement with 

 the result obtained here. 



Brown (Monthly Notices April 1904) gives as the result of his 

 theoretical calculation of the motion of the perigee two values, 

 holding for two different values of the ellipticity of the earth, viz. 

 1 : 292.9 and 1 : 296.3. Extrapolating from these for the value which 

 is at present considered the most accurate 1:297.5, we find for 

 1850.0 



Annual motion of jt = 146435".05 

 for which Brown gives as "extreme possible error" =t 0".10. 



