THE ORBITS OF THE EIGHT PRINCIPAL PLAN E T S 



131 



For the root g a — — 2".916080, we get, 



. 0.3678561 __ /r 0.3544989 xr „ 581.0130 „ IY 



«V=H iQio — N* ; VtF= iqTo — W r ; z»=~^w—W v . 



Whence /3 6 =133° 56' 26".3; and log. iVy r =6.9441240. 



N 9 =+0.003086, N," ==+0.000879273, 



NJ =+0.001797, N r =+0.000717874, 



N e " =+0.001615, iV " = — 0.0176858, 



JV e '"=+0.001157, ^"=+0.00190082. 



For the root 7 = — 25".934782, we get, 



0.2996357 



0.22 03002 _59.02984 



10 io "I . vi— 1 1() 



Whence /? T =306° 19' 27".6 ; and log. iV/ r =7. 7993611. 



JV 7 =—0.0002690, iV/ r =+0.00630030, 



JV/ =—0.0002227, iV/ =—0.01569181, 



iV 7 " = - 



-0.0027550, 



-0.0093164, 



N™= +0.000688861, 



N/' =+0.000077 1929. 



(455) 



16. For an increment of t l, to the mass of the earth, we have the preliminary 

 computations by merely making all the coefficients positive in equations (251-256). 

 We shall then obtain the following 



Fundamental Equations for /t"=-| ; or for m"==l-r-335172. 



A =0 S +4O.O92595.0 +195.673045; 

 A =(/ 2 +23.4348156.<7+100.8391921 ; 

 ^"=^+19.4622137.^+ 77.7179078 ; 

 ^=^+18.4089042.0+ 60.3313475 ; 

 J L2 =0 2 +13.1935918.0+ 8.982096; 

 4,=0 2 +26.3829396.0+ 9.895893. 



D =c/ 2 +46.O863772.0+633.1 39825; 

 Z/ =^+52.8372995.^+622.776921 ; 

 Z>"=0 2 +32.49O3462.0+261.2498776 ; 

 A=0 2 +43.89879O2.0+172.463686 ; 

 Z> 2 =(/ 2 +46.4944263.</+ 32.948508 ; 

 D 3 =g 2 + 3.4291886.0+ 1.69252948. 



J3=J0+34.38795^; 



J B' = |0+17.7555387}5) 

 £"= ^+13.801975 } h J 



C =— J0+27.173766 } [9.4381 149]i'; 

 C" =—{0+17. 7855450 J [9.1138076]J'; 



6"'=+[0.3976676]6'; 

 6'"'=+[0.4411620]6'. 



(456) 



(457) 

 (458) 



