26 



and the normal equations, 



= + 3.41 XX — 1.200 X y 



= — 1.20 + 12.250 



= —6.12 + 19.131 



= _ 4.83 — 4.929 



whence, 



X = — 0.902 267 

 y = — 0.251 045 

 z = —0.217 643 

 M = — 0.213 290 



and from these values, 



August 9, 1846, 

 April 6, 1847, 



— 6.117 X 2 — 4.825 X M + 0.415 



+ 19.131 — 4.929 +5.105 



+ 44.045 + 5.143 + 9-967 



+ 5.143 • + 16.651 —0.920 



A «„ = — 0.009 02267 S e£ 



= 0.75 



A «„ = — 0.251 0.674 7^^ 

 aJ(«— 1) 



= ± 0.25 



A ?■„ = — 0.002 176425 





A, >• = — 0.000 0042658 





= 30.003 3995 

 = 30.002 37.57 



^ = 326 42 1.328 

 J = 328 8 35.249 



These quantities, by Gauss' method, gave 7t and e. The further rectification 

 of the values of a j^ and a i gave the XIII conditional equations : 



Xd Q, + 0.307 X di 



-\- 0.303 



-j- 0.303 



+ 0.302 



+ 0.302 



+ 0.301 



-j- 0.300 



+ 0.300 



+ 0.298 



-j- 0.298 



+ 0.298 



-|- 0.298 



+ 0.309 



Their solution gave 



Ai= 2".49 +0.10XAS2 



In which the value of a S2 is arbitrary; and being made = 0, gives a ?' = 2".49. 



Elements V. were then formed from Elements IV, by applying the values of 

 A i and A Q, thus obtained, and by deducing the numerical values of rf, M, e, a, n, x, 

 by Gauss' method, from the two values of?- and «, for August 9, 1846, and April 

 6, 1846. 



I 



== 



— 



0.0311 



II 



= 



— 



0.0302 



III 



= 



— 



0.0300 



IV 



= 



— 



0.0299 



V 



= 



— 



0.0297 



VI 



= 



— 



0.0295 



VII 



= 



— 



0.0293 



VIII 



= 



— 



0.0292 



IX 



= 



— 



0.0289 



X 



= 



— 



0.0288 



XI 



= 



— 



0.0287 



XII 



= 



— 



0.0285 



XIII 



= 



— 



0.0288 





Residual A Dy 





Elements V. 



/; 



II 



1.48 



— 0.72 



0.38 



+ 0.37 



0.47 



4- 0.28 



0.66 



-j- 0.09 



0.04 



+ 0.71 



1.17 



— 0.42 



1.02 



— 0.27 



0.80 



— 0.05 



0.83 



— 0.08 



0.50 



+ 0.25 



0.42 



+ 0.33 



1.68 



— 0.93 



0.10 



+ 0.65 



