SECT. 1.] 



THREE COMPLETE OBSERVATIONS. 



207 



so that 3&quot;.56 is to be added for the first observation, 5&quot;.28 for the second, 

 6&quot;. 74 for the third. 



Lastly the longitudes and latitudes of Juno are to be freed from the aberra 

 tion of the fixed stars ; thus it is found by well-known rules, that we must sub 

 tract from the longitudes respectively 19&quot;.12, 17&quot;.ll, 14&quot;.82, but add to the lati 

 tudes 0&quot;.53, 1&quot;.18, 1&quot;.75, by which addition the absolute values are diminished, 

 since south latitudes are considered as negative. 



151. 



All these reductions being properly applied, we have the correct data of the 

 problem as follows : 

 Times of the observations reduced 



to the meridian of Paris 

 Longitudes of Juno, a, a , a&quot; . 



Latitudes, p, p , p&quot; 



Longitudes of the earth, /, I , I&quot; 

 Logs, of the distances, R, R, R&quot; 



Oct. 5.458644 



35444 3r.60 



-4 59 31 .06 



12 28 27 .76 



9.9996826 



17.421885 



352 34 22&quot;.12 



-6 21 55 .07 



24 19 49 .05 



9.9980979 



27.393077 



35134 30&quot;.01 



-7 17 50 .95 



34 16 9 .65 



9.9969678 



Hence the calculations of articles 136, 137, produce the following numbers, 



, y&quot; 



logarithms of the sines 

 A D, AD , AD&quot; . . 

 A&quot;D, A&quot; I/. AD&quot; . . 



,* ,&quot;, 



logarithms of the sines 

 log sin $ e .... 

 loo; cos i e 



196 S&quot;.36 

 18 23 59 .20 

 9.4991995 

 232 6 26 .44 

 241 51 15 .22 

 2 19 34 .00 

 8.6083885 



32 19 24 .93 

 9.7281105 

 213 12 29 .82 

 234 27 .90 

 7 13 37 .70 

 9.0996915 

 8.7995259 

 9.9991357 



Moreover, according to article 138, we have 



log tan/? .... 8.9412494 n log tan p&quot; .... 9.1074080 n 

 log sin (&quot;? ) . 9.7332391 n log sin (a I } . . 9.6935181 n 

 log cos (a&quot; * ) . 9.9247904 log cos (a I } . . 9.9393180 



191 58 0&quot;.33 



19041 40&quot;.17 

 43 11 42 .05 

 9.8353631 

 209 43 7 .47 

 221 13 57 .87 

 4 55 46 .19 

 8.9341440 



