54 



SECULAR VARIATIONS OF THE ELEMENTS OF 



For the root (/ 7 =22".460913, we get, 



1.009492 



N/ r , y, 



0.7872137 r _ 81.858 790 tT2 



10 1 



10 10 -7 , ^7— I 10 



Whence /3 7 =307° 56' 51".l ; log. iV/ r =98.1941950. 



iV 7 =—0.0001039; JV/ F =+0.0156385 



Nj' =+0.00036828 ; JV/ =—0.0483506 



N 7 "=— 0.00247996; iV/ J =+0.0018058 



iV/"=— 0.0150873 ; 2V 7 " =+0.0001365. 



28. We shall now suppose ^i"=-\-^ ; or, the mass of Earth to be »i"=(l+2V) 

 -368689=1-^-351132.4. Using this mass, we shall find, 



AroTo1=— 0".0430854 

 A|jn]=— .3315294 

 A[E3= 0. 

 AHTs]=— .0878224 



Whence we get, 



\^\=g— 5".6133412 

 |Trr|= 9 — 11 .6462976 

 (^=(7—13.0721730 

 fiT7]= |g — 17 .6406869 



AE3=— 0".0004406 

 A[?7^1=— 0.0000502 

 A[HI]=— .0000043 

 A[TT1=— 0.0000009, 



[77}=q— 7".5128160 

 \T^]=q— 18 .5962631 ; [ 

 R^1=<7— 2.7662565; 

 F3=<7— 0.6479578. 



These quantities give the following equations, 



[J7o][T7T]=/— 17.2596388.^+ 65.3746421455 

 [^[£3=^—18.6855142^+ 73.3785672744 

 [ o , o 1 1 3 , 3 1 = q*— 23.2540281.ff4- 99.0231945721 

 EH] [13=^— 24.7184706.^+152.2424170367 

 1 1 , 1 1 1 s , 3 1 — e^ 2 — 29.2869845.(y+205.4486895058 

 ED EZ]=9 2 — 30.7128599.^+230.6021109956 



\HH\nil=f— 26.1090791.^+139.7103029579 

 EH] [13=/— 10.2790725.^+ 20.7823760933 

 |4,4||7,7l=^— 8.1607738.^+ 4.8679877272 

 [7T^r^1 =,g 2 — 21.3625196.g4- 51.4420336761 

 |TT7| [7771=^—19.2442209.^+ 12.0495937275 

 [57J][777j=^_ 3.4142143.^+ 1.79241747598 



(232) 



(233) 



(234) 



(235) 



EH][IH][I3IIH]=/- 47.972498V + 826.06962154.^) r9qfi , 

 —5987.951367523.(7+15075.53048434 J K J 



EH][iH]EH][EH]=/— 29.5232934.<7 3 +230.64471166./ 

 —523.79928387.^+250.41918860 



} (237) 



We shall therefore obtain the following 



