Prof. Bessel on the Occultations of Stars by the Moon. 411 



As a first approximation we assume the value of t in the 

 quantities p\ 5', «', "J = 0, and obtain 



p' = +0'5'240 q' = -0-16'79 



u' = +0-1013 t/ = —0-0091 



n sin N = +0-4227; n cos N = —0-1588 



N = 110° 35' 26"; log n = 9-65470 

 t = +0-2402 hF 0-1690 

 or, Immersion 7'"0712; Emersion 7''*4092. 



We next obtain for the second approximation by the for- 

 mulae of section 6. 



Immersion. Emersion. 



j^ +0-52402 +0-52404 



q' —0-16790 -0-16791 



and by the Table at the end of this paper, 



X +32' 7"-7 + 3° 4' 38"-6 



log A 9-41915 9-41895 



by which we shall find next 



ti' = +0-10250 +0-10780 



7)' = —0-00907 -0-00873 



« sin N = +0-42152 +0*41624 



7i cos N = -0-15883 —0-15918 



N = 110° 38' 47" 110° 55' 41" 



log n = 9-65365 9*64898 



•24026 +0*23997 



16857 +0*16621 



= +0-07169 +0-40618 



The third approximation gives again the values of jp' and j' 

 obtained in the second approximation ; and besides 



X +32' 20"-9 +3° 3' 16"-9 



log X. .. 9-41915 9-41895 



u' = +0-10251 +0-10774 



1/ = —0*00907 —0-00873 



« sin N = +0-42151 +0-41630 



w cos N = -0-15883 —0-15918 



N = 1 10° 38' 49" 1 10° 55' 30" 



log n = 9-65364 9-64904 



•24026 +0-23996 



16857 —0-16625 



= +0-07169 +0-40621 



and as these results differ very little from the preceding ones, 

 we may here conclude the calculation. We have therefore the 

 times of the two phu;nomena = 7" 4' 18"*1, and 7" 24' 22"-4, 

 and the angle denoted by Q = 36 ^ 49'-6, and 5° 9'*2. 



3 G 2 9. Such 



_ f +0*2'^ 



_ r +0-2^ 

 ~ \— 0-l( 



