SECT. 1.] THREE COMPLETE OBSERVATIONS. 219 



The right ascension of the point 2T is used in the calculation of article 138 

 instead of I . In this manner are found 



log T sin t 8.4868236 n 



log T cost 9.2848162 n 



Hence ^ = 189 2 48&quot;.83, log T = 9.2902527; moreover, #-f / = 2 79 3 52&quot;.02, 



log 8 9.0110566 n 



log Tsin (* + /). . . 9.2847950 n 

 whence J f o = 208 1 55&quot;.64, and = 4 50 53&quot;.32. 



In the formulas of article 140 sin 8, sin d , sin 8&quot; must be retained instead of 

 a, b and -, and also in the formulas of article 142. For these calculations we 

 have 



WD A&quot; = 171 50 8&quot;.18 log sin 9.1523306 log cos 9.9955759 n 



%jyJ =1741913.98 8.9954722 9.9978629 



WZ&amp;gt; A&quot; =172 54 13. .39 9.0917972 



2t Z&amp;gt; J +a = 175 52 56 .49 8.8561520 



W A 173 9 54 .05 9.0755844 



St ZX J + o- =174 18 11 .27 &quot; 8.9967978 



Hence we deduce 



log* =0.9211850, logJl = 0.0812057 n 



log x&quot; = 0.8112762, log X&quot; = 0.0319691 



log a = 0.1099088, a = -f- 1.2879790 



log b =0.1810404, 

 log* =0.0711314, 



whence we have log b = 0.1810402. We shall adopt log b = 0.1810403 the 

 mean between these two nearly equal values. Lastly we have 



log c = 1.0450295 

 d = -f 0.4489906 

 log e=9.2102894 



with which the preliminary calculations are completed. 



