THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



69 



For the root g i =0".6 166859, we get, 

 , 3.357579 



10 1 



^/"; ?/l =- 



1.360360 



Nr ; Zi = 



58981.24 



10 10 



W 



Whence /? 4 =67° 56' 38".9 ; log. N/ 

 N t =+0.000007695 ; 

 iV7 =+0.00001170; 

 N? =+0.000013569; 



A7"=+0.000021904 ; 



For the root <7 5 =2".727684, we get, 

 , 0.6476505 



10'° 



-W r ; 2/5 



10 1 ' 

 =95.8033000. 



N.r =+0.000063577; 

 N/ =+0.000071706; 

 N t " =+0.00155781; 

 iV=+0.01003935. 



0.1746351 Ar/r 345.2619 AT/r 



10 1 



Whence /3 6 =105° 5' 26".0 ; log. iV 5 ' 



iV 6 =+0.00056110 

 JV 5 ' =+0.00055299 

 iV 5 " =+0.00058126 

 JV 6 w =+0.00077406 



For the root <7 6 =3".716923, we get, 

 0.4583310 



10 



=97.2884328. 



N,' F =+0.00194282 

 NJ =+0.00176878 

 JV^' =+0.02973089 

 NJ"=— 0.00291023 



10 1 



N"- v -l - 8566739 ^- z _ i 22 " 5 L 056 N ™ 



Whence /3 =28° 8' 50".4 ; log. N 6 ir : 

 N a =+0.0238845; 

 N 6 ' =+0.0163985; 

 #/ =+0.0162413; 

 ^"=+0.0187424 ; 



For the root # 7 ,=22".460985, we get, 



10 io «■ > -o— i 10 , 



=98.6350898. 



N e ir =+0.04316083 

 N G r =+0.03410240 

 iV e r/ = — 0.04484797 

 JV 6 r "=+0.00141946, 



10" 



Whence /? 7 =307° 56' 52".2 

 JV 7 =—0.0001043 

 N 7 ' =+0.0004095 

 N 7 " =— 0.0024158 

 iV 7 '"=— 0.0152719 



1.009476 „„ . 0.7872105 Ar/r 



81.85731 



10 1 



10 1 

 log. iV/ r =98. 1941978. 



N/ v =+0.01563860; 

 N/ =—0.04835037 ; 

 iV 7 " =+0.00180575; 

 jV 7 m =+0.000136497 



N' y ' 



30. The assumed mass of the earth was obtained on the hypothesis that the 

 mean equatorial parallax of the sun is only 8".50. Recent investigations indicate 

 that the sun's parallax is greater by at least one-thirtieth part. Consequently the 

 assumed mass of the earth is too small by its one-ninth or one-tenth part ; and on 

 account of the importance of this element in most astronomical theories, we shall 

 here give another determination of the constants corresponding to an increment of 

 T V to the earth's mass. This new determination will be useful as an indication to 



