THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



71 



For the root # 6 =2".727818, we get, 

 , 0.6479474 . TIT 



.1763111 r _346.4665 



1A10 ^'5 > Z 5 "" 11)0 6 



Whence /? 5 =105° 13 19".4; log. iV 6 /r =97.2873891. 



JV 5 =+0.000562809 

 JV 5 ' =+0.000554059 

 JV 5 " =+0.000581368 

 iV 5 "=+0.000774334 



JV 6 ' F =+0.00193816; 

 W 5 r =+0.00176509; 

 ^" =+0.0297147; 

 K rn = —0.00290829. 



For the root # =3".718622, we get, 



»6= + 



0.4583136 

 ~F0 10 



iVa /r , 2/a=+- 



0.8566921 



10 1 



NJ 



_ 22.50708 2 



Whence &=28° 8' 45".3 ; log. N 6 ,T =98.6351607. 



N 6 =+0.0240344 

 N£ =+0.0164295 

 JV 6 " =+0.0162055 



JV 6 "=+0.0187844 



iV/" =+0.0431679 

 NJ =+0.0341122 

 JV 6 r/ =— 0.0447780 

 jV 6 m =+0.0014139. 



-Nr\ I/:'- 



For the root # 7 =22".461946, we get, 

 1.009108 

 Xr ~ 10 



Whence /3 7 =307° 56' 52".8 ; 

 JV 7 =—0.0000878; 

 Nj' =+0.0002258 ; 

 JV 7 "=— 0.0020272; 

 iV 7 "'=— 0.0151238; 



0.7869276 



H~ JQ10 ^7 



_ 81.83667 



2 7 j^qio ^*7 • 



log. iV/ r =98.1941499. 



JV/" =+0.0156369 

 N 7 V =—0.0483362 

 N 7 ri =+0.0018051 

 iV 7 "=+0.0001364. 



34. We shall now suppose ^ r =+ T -i- jJ ; and the mass of Jupiter will become, 

 l+ f / r 1.01 1 



— 1047.879 

 shall find, 



1047.879 1037.504 



Using this value of Jupiter's mass, we 



A[TT]=— 0".0160284 

 AQTT] =— .0420284 

 AdH] =— .0706826 

 A[TT1=— Q .1465990 



Whence we get, 



ro7o1=qr— 5".5862842; 

 [77T|— g— 11 .3567966; 

 [172]=//— 13.1428556; 

 prnq =g— 17.6994635; 



A[7J7]= 0". 

 A[I3=— 0.1824735 

 AFT^ =— 0.0093732 

 AQ7t]=— .0017907, 



|T7]=#— 7". 5 123754 



[TI]=//— 18 .7786864 

 [«Z\=g— 2.7756254 

 [77?]=^— 0.6497476 



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