28 SECULAR VARIATIONS OF THE ELEMENTS OF 



Substituting these quantities in equations (52) we get, 



^=-(-0.00007643863^ log. 95.8833129; 



/ 2 =4-0.0005457711JV " 96.7370106; 



/,= 0.001555269^" " 97.1918055n; 



/ 4 =+0.0005425501# " 96.7344399 ; 



^=4-0.00007500820^ " 95.8751088; 



/ 6 = 0.001555239^" " 97.1917972?*. 



With these values of / / 2 , &c., and A A 2 , A s , D u Z> 2 , and D 3 , either of the 

 equations (93-95) will give 



JV"=_0.00005102365JV log. 95.7077716. 



Therefore we shall easily find 

 ^#""=4-0.0001992746^, J 2 tf'"=4-0.0009425372iV, J 3 A r/r 



Then 



A z N' r +f z = 0.000009996^"; 



A 3 N' r +f 6 = 0.000009966M 



Equations (90-92) will now give the following : 



constant log. 



A^ ir +/. " 



1-s-A " 



A*N"+f z 



constant " 



N r " 



N n " 



Computation of N" and N v 

 constant log. 99.2389545 

 " 97.1717519 

 " 98.8894184 

 " 96.4381985 

 " 98.2262038 



constant 



N" 

 N r " 



" 95.3001248 

 " 93.5538207 



The small differences in the different values of N TI and N v ", in this example, 

 are owing to the circumstance that A 3 N' V is nearly equal to / 3 and / 6 , and has a 

 contrary sign, which renders A z N' r -\-f s and J 3 ^V /r -f-/ 6 very small quantities. We 

 must therefore reject these values and use those depending on / 4 and / s . 



