144 



SECULAR VARIATIONS OP THE ELEMENTS OP 



For the root g 5 , we get, 



g & =— 0".6633671, 



N 5 =+1.231158iV/ r 

 N; =+1.130398iV/ r 

 iV 5 " =+1.107341iV 6 J7 

 Ni" =+1.049016iV 5 jr 

 JV/ =+0.9653980^/' 

 ^"=—0.9445346^/' 

 NJ"=— 9.899907iV 5 IF 



log. 0.0903139, 



" 0.0532315, 



" 0.0442814, 



" 0.0207820, 



" 9.9847064, 



" 9.975.2179w, 



" 0.9956311m. 



For the root g 6 , we get, 





# 6 =— 2".925086, 





jy 6 =+ 3.536719iV/ r 



log. Q.5486005, 



JV„' =+ 2.047060iV 6 rr 



" 0.3111304, 



JV 6 " =+ 1.83451 3iV 6 JF 



" 0.2635208, 



N B m =+ 1.310090iV 6 jr 



" 0.1173012, 



N 6 V =+ 0.8166500iV ' r 



" 9.9120360, 



N 6 yi =— 20.25015^ 



« 1.3064432w, 



iV 6 FJ/ =+ 2.169824^^ 



" 0.3364244. 



For the root # 7 , we get, 



<7 7 =— 26".117474, 



JV 7 =— 0.04211995iV 7 7r log. 8.6244879», 



N 7 > =_0.048514162V/ r " 8.6858685/*, 



iV 7 " =— 0.4329533iV 7 jr " 9.636441 On, 



N't" =— 1.477216iV 7 jr " 0.1694440//, 



N/ =— 2.515433iV 7 /F " 0.4006128m, 



iV 7 F '=+0.1096052iV/ F " 9.0398312, 



JV 7 F/J =+0.01229432iV/ F " 8.0897044. 



21. If we now substitute these values in equations (408) and (409), we shall 

 obtain the following quantities : — 



For the root g= — 5".153064, we get, 



, 0.616929 „ , 1.5676783 AT 13.836148 ,„ 



a= +-T(F"^ 2/=+-T(F— N ' g = 10" N - 

 Whence 0=21° 28' 52".l, and log. #=9.0855076. 



N =+0.121761, N IV =— 0.0000245922, 



N' =+0.014594, N r =—0.0000312577, 



N» =+0.0104106, N" =+0.0000272918, 



JV" =+0.0020644; ^"=+0.000000769538. 



