THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



For the root </ 6 =2". 736961, we get, 



0.6488003_ . 0.1681608 _346.3853_ 



io 10 io 10 6 ' Zf> ~ "To 15 6 



Whence &=1()4 31 50" 1 ; log. ^"=97.2866700. 



N b =+0.00056493; N" =+0.00193495 ; 



AV =+0.00055366 ; - N t r =+0.00175748; 



Ay =+0.00057992 ; N s " =+0.0296571 ; 



Ay"= +0.00077274 : A 7 /'^ 0.00289263. 



For the root r/ 6 =3".723307, we get, 



_0.4594222 , 0.8649404 r i ??1 67899 _ AT^Z 



^o jmu " > y^ "I JQIO ** ' Z 6 ~T JQIO -*^ 



Whence &=27 58' 31".7 ; log. AV r =8.6353288. 



A; =+0.0243002 ; N e ' r =+0.0431846 ; 



N a ' =+0.0165168 ; N 6 r =+0.0340618 ; 



^"=+0.0162693; N 6 ri = 0.0451079; 



A r 6 '"=+0.0187715 ; A r 6 F "=+0.0014293. 



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



1.021673 ,. 0.7951379 , 83.56643 Ar/ ,. 2 



^7 T?no "' ' 2/7 T f?uo "T ' Z 7 H T7\io *M 



Whence /3 7 =307 53' 32".2; log. JV/ r =8J901156. 



N 7 =0.0000952; N 7 !T =+0.0154923; 



N 7 ' =+0.0002967 ; N/ =0.0484622 ; 



iV 7 "= 0.0023449 ; N, VI =+0.0017952 ; 



N 7 '"= 0.0149630 ; A7"=+0.0001359. 



36. We shall now suppose that /u r =-| ; and the mass of Saturn will become, 



14- L 1 



v =: - n ^-=-oTfcTKc" Using this value of Saturn's mass, we shall find, 

 oOUl.b 



AU7o]= 0".0019316, 

 ^QZ1= -0049722, 

 A[|72] = .0081629, 

 A[Ts]= .0157850, 



Whence we get, 



I^o]=j7 5".5721874; 

 03=^11 .3197404; 

 Q3=flr 13.0803359; 

 pTTI =/717.5686495; 



rTl = 0". 1849094, 



[erg =0.0348880, 

 |T771= 0.0051937. 



[TT4]= 7 - 7".6972848; 

 [771]=, ff 18.5962129; 

 [^]=g 2.8011402; 

 [777]=^ 0.6531506. 



(307) 



(308) 



