28 



SECULAR VARIATIONS OF THE ELEMENTS OP 



Substituting these quantities in equations £52) we get, 



/ 1 =+0.00007643863iV log. 95.8833129 ; 



/,=-|-0.0005457711iV " 96.7370106; 



/,=— 0.001555269iV " 97.1918055%; 



/ 4 =+0.0005425501i\T " 96.7344399 ; 



/ 6 =-|-0.00007500820iV " 95.8751088 ; 



/ 6 =— 0.001555239^ " 97.1917972?*. 



With these values of f, f 2 , &c, and A lr A 2 , A 3 , D u D 2 , and D 3 , either of the 

 equations (93-95) will give 



N ir =— 0.00005102365iV log. 95.7077716%. • 



Therefore we shall easily find 

 ^ 1 ^ /r =+0.0001992746^V, AiV /r =+0.0009425372iV, J 3 ^ JF =+0.001545273iV. 



Then 



A^ Jr +/i=+0.0002757132i^; J a i^ /r +/ 2 =+0.0014883083i^; 



A a N ir +f s =— 0.000009996i\T; 

 ^i\r^_[_/. = _)_o.0002742828iV.; J 2 iV jr +/ 4 =+0.0014850873i^; 



J 3 ir r +/ 6 =— 0.000009966iV. 



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



Computation of N v and N TI . 

 constant log. 0.7159050 



Computation of N v and N YL 

 constant log. 0.8175689 



AN"+A 



' 96.4404576 



W+A 



' 97.1726929 



l-A 



' 98.5020596% 



l-^-A 



' 97.6681606% 



AN Ir +f 



' 94.9998262% 



W+A 



' 94.9985209% 



constant 



' 1.7982382 



constant 



' 0.8871514 



N r 



' 95.6584222% 



N r 



' 95.6584224% 



N ri 



' 95.3001240 



N vn 



< 93.5538329 



Computation of N YI and N TI 

 constant log. 99.2389545 



AN ir +f 



' 97.1717519 



l-s-A 



' 98.8894184 



A'N"+f 



' 96.4381985 



constant 



' 98.2262038 



N TI 



' 95.3001248 



N™ 



< 93.5538207 



The small differences in the different values of N YI and N vn , in this example, 

 are owing to the circumstance that A S N IT is nearly equal to f 3 and f 6 , and has a 

 contrary sign, which renders A s N IT -\-f z and A 3 N IT -\-f very small quantities. We 

 must therefore reject these values and use those depending on f and / 5 , 



