SECT. 2.] TO POSITION IN SPACE. 79 



As in the other method of article 67, we will determine the auxiliary angle 

 by the equation 



c. tan d 



tan , = -;. 



since 7 



and we shall have 



7 cos ( e) tana 



tan I = - 



cos f 



tan 5 = sin tan ( e) . 

 For proving the calculation, may be added, 



, _ cos d cos a __ cos ( ) cos d sin a 



COS - - j - - - ^ ; - i - , 



cos i cos f sin I 



For the determination of E, in the same way as in the preceding article, the fol 

 lowing equations will answer : 



j-, sin f cos a sin s cos I 



COS-E=- T = - 



COS COS O 



cos b cos $ sin .&quot; = cos sin b sin $ . 



The differentials of /, b, will be given by the formulas 



d, sin .E cos 5 , , cosl? -. , 

 ?=- = aa-\ --- rdo 



COS COS 



d ^ = cos E cos $ d a -(- sin .&quot; d d . 



/ 



69. 



We will compute, for an example, the longitude and latitude from the right 

 ascension 35543 45&quot;.30 = a, the declination 8 47 25&quot; == d, and the obliquity 

 of the ecliptic 23 27 59&quot;.26 = e. We have, therefore, 45 C + } a = 222 51 52&quot;.65, 

 45 . _ $ ( e _|_ s) = 37 39 42&quot;.87, 45 i (e d) = 28 52 17&quot;.87 ; hence also, 



log cos (45 + i a) . . 9.8650820M log sin (45 -f i a) . . 9.8326803n 

 logsin(45--i(e + d)) 9.7860418 log sin (45 * (e d)) 9.6838112 

 log cos (45 *( + &amp;lt;*)) 9.8985222 log cos (45 i (e &amp;lt;?)) 9.9423572 



log sin (45 ^)sini(^ /) . . 9.6511238 n 

 log sin (45 ii)cosi(J? /) . . 9.7750375 n 

 whence J (^E 1 /) = 21656 5&quot;.39 ; log sin (45 * J) = 9.8723171 



