76 RELATIONS PERTAINING SIMPLY [BOOK I. 



When B = 0, then 1? = R, Z= 0. According to these formulas our example is 

 solved as follows : 



L 8 = 21312 0&quot;.32. 



logr ...... 0.3259877 log 11 ..... 9.9980979 



log cos u ..... 9.9824141 n log cos (L Q) . . 9.9226027re 



log sin u ..... 9.4454714 n log sin ( L Q, ) . . 9.7384353 n 



0.3084018w logJC ..... 9.9207006w 



logr sin M .... 9.7714591 n 

 log cos * f ..... 9.9885266 

 log sin? ..... 9.3557570 



logy ...... 9.7599857w logF ...... 9.7365332 



logz ...... 9.1272161w Z= 



Hence follows 



log(z X) . . . 0.0795906 



log(y-Y) . . . 8.4807165w 



whence (/ Q) = 18126 33&quot;.49 J = 35234 22&quot;.22 



logJ ...... 0.0797283 



log tan* ..... 9.0474878 n b= 62155.06 



66. 



The right ascension and declination of any point whatever in the celestial 

 sphere are derived from its longitude and latitude by the solution of the spherical 

 triangle which is formed by that point and by the north poles of the ecliptic and 

 equator. Let be the obliquity of the ecliptic, I the longitude, b the latitude, a 

 the right ascension, 8 the declination, and the sides of the triangle will be e, 

 90 - - b, 90 - - 6 ; it will be proper to take for the angles opposite the second 

 and third sides, 90 -f- &amp;lt;*, 90 - - 1, (if we conceive the idea of the spherical triangle 

 in its utmost generality) ; the third angle, opposite e, we will put = 90 JS. We 

 shall have, therefore, by the- formulas, article 54, 



