SECT. 2.] TO POSITION IN SPACE. 89 



Whence is obtained L = L 22&quot;.39. Finally we have 



log^i 1.88913* 



C. log 206265 .... 4.68557 



log 493 2.69285 



C. log cos 0.00165 



9.26920 R, 

 whence the reduction of time = B .186, and thus is of no importance. 



74. 



The other problem, to deduce the heliocentric place of a heavenly body in its orbit 

 from the geocentric place and the situation of the plane of the orbit, is thus far similar to 

 the preceding, that it also depends upon the intersection of a right line drawn 

 between the earth and the heavenly body with the plane given in position. The 

 solution is most conveniently obtained from the formulas of article 65, where the 

 meaning of the symbols was as follows : 



L the longitude of the earth, R the distance from the sun, the latitude B we 

 put =0, since the case in which it is not = 0, can easily be reduced to this by 

 article 72, whence R = R, I the geocentric longitude of the heavenly body, b 

 the latitude, A the distance from the earth, r the distance from the sun, u the 

 argument of the latitude, 8 the longitude of the ascending node, i the inclination 

 of the orbit. Thus we have the equations 



I. r cos u R cos (L 8 ) = d cos b cos (I 8 ) 

 II. r cos i sin u R sin (L &)=J cos b sin (I 8 ) 



III. r sin i sin u-=/l sin b . 



Multiplying equation I. by sin (L 8 ) sin b, H by cos (L 8 ) sin b, III. by 

 - sin (L 1} cos b, and adding together the products, we have 



cos u sin (L 8 ) sin b sin u cos i cos (L 8 ) sin b sin u sin i sin (L I) cos b 0, 

 whence 



IV. tan= sin(i-8)sin* 



cos i cos (L 2) s 



12 



