THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



77 



For the root </ )i =2".736961, we get, 



. 0.6488003 ._ jr 0.1681608 . rir 346.3853 „_ 



«%=+ ip ^ ;2/5= 10^ *• ' *= 10" ^ • 



Whence /i 6 =104° 31 50" 1 ; log. iV 5 "=97.2866700. 



iV 5 =+0.00056493; N & ir =+0.00193495; 



NJ =+0.00055366 ; JV 6 " =+0.00175748 ; 



iV 5 " =+0.00057992; iV 5 " =+0.0296571 ; 



iV d '"= +0.00077274 : N™=— 0.00289263. 



For the root </ =3".723307, we get, 



0.4594222 



" 10 10 



AT; 2/ u =+ 



0.8649404 

 10 10 



M 



22.67899_ 

 - i 2.0 10 



Whence /3 6 =27° 58' 31". 7 ; log. 2V 6 ir =8.6353288 



JV 5 =+0.0243002; 

 N e ' =+0.0165168; 

 JV " =+0.0 162693; 

 JV '"=+0.0187715; 



N a JT =+0.0431846 



iV c r =+0.0340618 

 iV c "=— 0.0451079 

 JV "=+0.0014293 



For the root # 7 =22".636578, we get, 



1.021673 „„ . 0.7951379 . Tir . 83.56643 .__ 

 *i= Jo 15 " N *>yi=+- io^r -W T ; 2 7 =H 1( p -^V/ 2 . 



Whence /? 7 =307° 53' 32".2; log. iV/ r =8J901156. 



JV 7 =—0.0000952; iV/ r =+0.0154923 



Nj' =+0.0002967 ; 

 N/—— 0.0023449; 

 iV 7 '"=— 0.0149630 ; 



N/ =—0.0484622 

 N/ 1 =+0.0017952 

 iV 7 m = +0.000 1359. 



36. We shall now suppose that ^ r =+ ; and the mass of Saturn will become, 



40 



1+tV 

 3501.6 



1 

 3416.195"' 



Using this value of Saturn's mass, we shall find, 



AF^1 = — 0".00 19316, 

 A[J7T] = — .0049722, 

 AQr7J] = — .0081629, 

 AF^1 = — 0.0157850, 



A[[7JJ = — 0".1849094, 

 A[«3=-0. 

 A[J7JJ=— .0348880, 

 A[T7?1 =— 0.0051937. 



(307) 



Whence we get, 



nr^1=q— 5".5721874 

 [Tm= g — 11 .3197404 

 |T7T|=jy — 13 .0803359 

 \TJ] =q— 17.5686495 



RTq=<7— 7". 6972848; 1 

 [777] =<y—18.5962129; ' 

 [7771 =<y— 2.8011402; 

 |7771=(y— 0.6531506. 



(308) 



