THE ORBITS OP THE EIGHT PRINCIPAL PLANETS. 151 



For the root g 6 =— 2".9514286, we get, 



0.3712512 _ _ 0.35 



10 10 



b 6 =+ 



//-, 



584.6008 



10 10 ' 0— 10 10 ' 

 Whence &=133° 48' 43".9 ; log. iV 6 ' r =96.9445043. 



N 6 =+0.0032017 ; N 6 ' r =+0.000880044 ; 



NJ =+0.0018341 ; N e T =+0.000718986 ; 



N a " =+0.0016409; iV 6 r/ =— 0.0177606 ; 



JV 6 " =+0.001 1616 ; iV 6 r "=+0.0018826. 



For the root ^=—26". 1183694, we get, 



0.2996395 _ , 0.2202 906 



^7 JqIo > 111 ~\ 



Whence ^ 7 =30Q o 19' 22".0 ; log. N, 

 JV 7 =—0.00002671 ; 

 Nj =— 0.00031380; 

 iV 7 "=— 0.0027363; • 

 iV 7 '"=— 0.0092366; 



57.99673 

 10 10 



10 io ~7 



=97.8070262. 



JV/ r =+0.00641248; 

 N 7 r =—0.0155812; 

 #/' = +0.00069663; 

 iV 7 r "=+0.000078059. 



24. For an increment of ^m 71 , to the assumed mass of Uranus, we shall obtain 

 the preliminary computations by merely making all the coefficients positive in 

 equations £326-331). We shall then obtain the following 



1 1 



Fundamental Equations for (i ri =-j-—; or for m r '= 



A =y 2 +38.068970.</ +181.871338; 

 A' =//"+23.1735927.j/+ 98.3308977 

 A"=<f+18J132214:.g-\- 72.8344734 

 ^1 1 = 7 2 +18.4995010.(/+ 61.4402060 

 ^ 3 = 7 2 +13.2095523.j/+ 9.147128 ; 

 ^3=^+26.3996602.^+ 10.055139. 



D =^+44.5054401.0+588.063848 ; 

 B =rf+51.9992925.(7+604.964956 ; 

 X>" =r/ 2 +32.1623093.r/+256.0208612; 

 £> 1 =f / 2 +43.98()9321.<7+175.644437; 

 Z) 2 =(7 2 +46.5212935. i /+ 33.556164 ; 

 D i= g 2 + 3.4429483.^+ 1.72374142. 



'23719' 



(503) 



£= | ^+32.45043 \ b; 



£' = {; 7+1 7.5804200 \b; ) 

 B H = | tf+ 13. 139086 j ft. j 



|2+22.255718| [9.4381189]ft'; 

 _ ^+17.6104269 j[9.1138076]//; 



C =• 



C" =+[0.3976676]ft'; 

 (7"'=+[0.4411620]ft'. 



(504) 



(505) 



(506) 



