APPENDIX. 



315 



The longitudes of the sun were corrected for aberration by adding 20&quot;.06, 

 20&quot;.21, and 20&quot;.43, respectively, to the numbers given in the Nautical 

 Almanac. 



These reductions having been made, the correct data of the problem are as 

 follows : 



Times of observation. 



For Washington Meridian. 



Ceres slong. a, a , a&quot; 

 latitudes p, , 0&quot; 

 Earth s long. I, t, I&quot; 

 logs, of dist. R, R, R 



July 30. 372903. 



330 27 25&quot;.28 

 - 13 54 54 .49 

 307 39 43 .66 

 0.0064753 



Sept. 6. 248435. 



324 34 50.92 



14 45 28.28 



344 8 45.49 



0.0031709 



By the formulas of Arts. 136 and 137, we find 



7,7,7 



d,d ,S&quot; 



log d, d , d&quot; sines 

 A D,Aiy,AD&quot; 

 A D,A&quot;V,A D&quot;, 



f ff 

 , I , , 



log e, s , e&quot; sines, . . 

 log sin i K 

 log cos i e 



And by article 138, 



wherefore 



329 25 34&quot;.81 

 28 12 56 .84 



9.6746717 



199 45 41&quot;.00 



233 54 11 .72 



27 32 45 .72 



9.6650753 



log T sin t 

 log Tcost 



218 11 22&quot;.38 

 24 19 53 .34 



9.6149131 



204 8 25&quot;.14 



233 31 23 .54 



142 37 25 .44 



9.7832221 



9.9764767 



9.5057153 



6.2654993 n 

 9.2956278 n 



Whence 



*=180 3 12&quot;.63, log T . . . 9.2956280 



= 3814 / 35&quot;.01,logsin(&amp;lt;-f /) 9.7916898 



log S ...... 8.6990834 



logrsin^ + y) . . 9.0873178 

 log tan (&amp;lt;T a) . . . 9.6117656 

 6 a = 22 14 47&quot;.47 and a = 2 5 5&quot;.87. 



Oct. 14. 132915. 

 321 3 52.58 

 13 5 31.31 

 21 19 53.97 

 9.9985083 



194 59 35 .15 

 61 6 50.78 

 9.9422976 

 203 56 46&quot;.56 

 199 30 24 .04 

 115 4 41 .lu 

 9.956992 



