THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 95 



For the root r/ 5 =2".7706502, we get, 



0.15:382110 0.1345391 _318.2862 



10 ' io 10 ' "~io" ' 



Whence p 6 101 54' 14".5 ; log. # 5 /r =7.3115881. 



N, =+0.00061393; N b ' r =+0.00204922 ; 



JV 5 ' =+0.00059396 ;. N, r =+0.00185548 ; 



# 5 " =+0.00062031 ; N," = +0.0300096 ; 



N= +0.000821 54 ; # 5 r "= 0.00288234. 



For the root # =3". 722656, we get, 



_(U577640^ 0.8595159 r 2J2.63367 r2 



IO 10 ~1(P~~ 10' 

 Whence /3 6 =28 2' 20".5 ; log. # 6 ' r =8.6337215. 



# 8 = =+0.0245381 ; N 6 ' r =+0.0430251 ; 



N a ' =+0.0165876 ; N 6 r =+0.0339716 ; 



JV 6 " =+0.0163169; JV 6 "= 0.0466232; 



# 8 '"=+0.0187473 ; # 6 r/ '= 0.0015353. 



For the root # 7 =22".466817, we get, 



1.009767 0.7872124 r 81.89131 /r2 



x i InTo "! > y^ I iruo ""'l ' ^ H i Vuo ^7 



Whence /? 7 =307 56' 23".7 ; log. #/ r =8. 1940957. 



N 7 =0.0000974; JV/ F =+0.0156349; 



Nj' =+0.0003164 ; N, r =0.0483516 ; 



Nj'= -0.0023759 ; N 7 ri = +0.00 18091 ; 



#,'"=0.0150168 ; # 7 r// =+0.0001364. 



42. We have thus obtained the values of all the constants, corresponding to the 

 separate variations of the planetary masses. If we now subtract the values of the 

 constants which correspond to the assumed masses from the values which result 

 from the supposition that each planetary mass receives in succession a finite incre- 

 ment, and divide the difference of the constants by the supposed increment of 

 mass, and connect together the different results, we shall have the following system 

 of equations for the determination of the constants which correspond to any other 

 assumed finite variation of the masses. The unit of the coefficients of ^u, [i, fi", &c., 

 in the values of N, N', N", &c., N lt #/, #/', &c., are the seventh decimal place of 

 these coefficients. 



