816 APPENDIX. 



By articles 140-143, we find 



A&quot; D 8&quot; = 172 24 32&quot;.76 log sin 9.1208995 log cos 9.9961773 n 

 AD 8 =175 55 28.30 8.8516890 9.9989004 n 



A D S&quot; =172 47 20.94 9.0987168 



AD d + o =177 30 53.53 8.6370904 



AD&quot; d =175 43 49.72 8.8718546 



AD&quot; $ + a=lll 15 36.57 8.6794373 



log a ..... 0.0095516, a =1.0222370 



log 4 ..... 0.1389045. 



Formula 13, which serves as a check, would give log b = 0.1389059. We 

 prefer the latter value, because sin ( A D $ -j- o) is less than sin (A D&quot; 

 -tf + a). 



The interval of the time (not corrected) between the second and third obser 

 vations is 37.884480 days, and between the first and second 37.875532 days. 

 The logarithms of these numbers are 1.5784613 and 1.5783587 ; the logarithm 

 of k is 8.2355814 ; whence log 6 = 9.8140427, log d&quot; = 9.8139401. 



We shall put, therefore, for the first hypothesis 



x = log P = ? = 9.9998974 



y log Q = 6 6&quot; = 9.6269828 

 and we find 



01 = 5 43 56&quot;.13 



&amp;lt;o + = 7 49 2 .00 

 log Qc sin w = 0.9112987 



It is found, by a few trials, that the equation 



Q c sin w sin 4 z = sin (z -j- 7 49 2&quot;.00) 

 is satisfied by the value 



= 7 59 30&quot;.30, 

 whence log sin z = 9.1431101, and 



/= = 0.474939. 



sin z 



