THE ORBITS OP THE EIGHT PRINCIPAL PLANETS. 133 



Equations (455-466) will now give the following values: 

 For the root g, we get, 



g= 5".2136546 ; 



2V' =+0.12006842V log. 9.0794288; 



2V" =+0.08711802V " 8.9401080; 



2V'" =+0.018442172V " 8.2658120; 



2V'"= 0.00021192252V 96.3261770rc; 



2V r = 0.0002712742V " 96.4334082n; 



2V"=+0.0002285892V " 96.3590546; 



2V "'=+0.0000069 104722V " 94.8395077. 



For the root g lt we get, 



9l = 6".6692717; 

 2VJ = 0.26830562V, 

 2V/' = 0.21891682V1 

 2VT =0.04878432^ 

 2V,' r =+0.00034441462^ 

 2V/ =4-0.0004893l02T, 

 N," = 0.000247679 2Vj 

 #,"'= 0.00001526832^ 



For the root g^ we get, 



^ 2 = 17".6265859; 

 Nj =: 5.55453^ 2 



NJ =+ 



N 2 ir = 0.00179671^, 

 N, T = 0.0172969^ 2 

 N 2 "=+ 0.00164470JV2 

 N z v "=+ 0.000189469JV 2 



For the root g s , we get, 



/ 3 = 18".9364959; 

 N 3 ' = 6.27941 JV 3 

 N 3 " =+6.067662^ 

 2V 3 '" =7.198122^ 

 2V 3 jr = 0.00004612212^3 

 N 3 r =0.00129815^ 

 2V^ 3 r/ =+0.0001076252Vr 3 

 2V7'=:+0.0()001241762V3 



log. 



9.4286296n; 



9.3402791n; 



8.6882800?*; 

 96.5370815; 

 96.6895841; 

 96.3938898n; 

 95.1837912n. 



log. 



log. 



0.7446477n; 



0.5654561; 



1.6342060; 

 97.2544790; 

 98.2379690n; 

 97.2160878; 

 96.2775388. 



0.7979189n; 



0.7830214; 



0.8572192; 

 95.6639090n; 

 97.1133248?i; 

 96.0319138; 

 95.0940376. 



For the root g^ we get, 



