THE ORBITS OF THE EIGHT PRINCIPAL PLANETS 161 



For the root g 6 — — 2".9612185, we get, 



_ 0.3722380 _ O3654807 _600.4976 



x 6 H jo 10 ' ^ 6 — 10 10 ' 2 ° — lo 1 " 



Whence #,=134° 28' 30".7; log. iV "=96.9388828. 



JV 6 =+0.0031860; iV /r =+0.000868726 ; 



JV 6 ' =+0.0018190 ; N 6 T =+0.00070661 ; 



N 6 " =+0.0016265; #„" = — 0.0177657 ; 



#,"=+0.001 1488 ; N™ =+0.00187456. 



For the root g 7 =— 25".9401904, we get, 



_ 0.2997138 0.2203005 _59.04657 



x i ~ jqIo > ill— I JQ10 — J 2 7 — — jqio 



Whence /i 7 =306° 19' 2".l ; log. iV/ r =97. 79931 16. 



N 7 =—0.00026499 ; N/ r =+0.00629958 ; 



Nj =—0.00029362 ; iV/ =—0.0156932 ; 



iV 7 " = — 0.00272577; N™ =+0.00068996 ; 



N 7 '"=— 0.00924274 ; N/' =+0.000077181. 



28. Having thus obtained the values of all the constants, corresponding to the 

 separate variation of the planetary masses, it now remains to find the coefficients 

 of these variations. This we shall do by taking the difference between the con- 

 stants corresponding to the assumed masses and those depending on the assumed 

 variation of mass for each planet, and dividing by the assumed variation. By this 

 means we shall obtain the following table — observing that the coefficients of ft, j?, u", 

 Sec, in the values of N, N', N", &c, are given in units of the seventh decimal place 

 of these coefficients. 



g=— 5".126112+0".207l90 /[ f— 1".49906/— 0".88154/— 0". 060606/'— 2".6952/ r 



— 0". 129080/— 0".00318/'— O".O0121/"; 

 (3=21° 6' 26".8+6752".6,u— 35940>'— 71170"/+1984".7/+134530"/ r 



+ 31452> r — 1 2596> "— 1 070"/"; 

 JV=+0.121076+276274u— 5680(%'— 140640/+34384/'+68S000,/ r 



+95880 lW r +29840 r/ +1630« r "; 

 iV'=+0.014867+127798«+276820/— 52360/— 6929/"— 273100/"— 4800/ 



+2840/'— 70/"; 

 #"=+0.010650+88422^+230840/- 23860/— 6601/'— 239000/ r — 5360^ 



+ 1960/'+ 20/"; 

 #'"=+0.002128+17510 / «+51480 i u'+7640/— 1066/'— 63400/ r — 1680/ 



+;320/'+0„ r "; 



N ir =— 0.0000252— 255.4^—480^'— 14/+7.2/'+580/ r +84/— 32« r/ — 2 ( « F "; 

 N r =— 0.0000320— 313.4^— 648/— 42/+7.6/+740/ r +104.8/— 24/'— 2/"; 

 iv" v =+0.0000280+350.4 i u+364«'— 74/— 14.0/'— 750/ r +252/+36« r ' 



+54u m ; 

 #"=+0.000000775+4.28 J u+24 / /+5.2/+0.1/—5/ r — 7.6/^—31. 2«" 



-2.9^™'. 



21 March, 1872. 



