SECT. 2.] TO POSITION IN SPACE. 71 



with respect to the ecliptic ; hence, the geocentric longitude and latitude ; and 

 hence, finally, the right ascension and declination. Lest any thing should seeni 

 to be wanting, we will in addition briefly explain the two last operations. 



62. 



Let X be the heliocentric longitude of the heavenly body, /? the latitude ; / the 

 geocentric longitude, b the latitude, r the distance from the sun, A the distance 

 from the earth ; lastly, let L be the heliocentric longitude of the earth, B the Ia1&amp;gt; 

 itude, R its distance from the sun. When we cannot put B 0, our formulas 

 may also be applied to the case in which the heliocentric and geocentric places 

 are referred, not to the ecliptic, but to any other plane whatever ; it will only be 

 necessary to suppress the terms longitude and latitude : moreover, account can 

 be immediately taken of the parallax, if only, the heliocentric place of the earth 

 is referred, not to the centre, but to a point on the surface. Let us put, moreover, 



r cos /? = r, A cos b = A , R cos B = R . 



Now by referring the place of the heavenly body and of the earth in space to 

 three planes, of which one is the ecliptic, and the second and third have their 

 poles in longitude N and N-\- 90, the following equations immediately present 

 themselves: 



/ cos (I N) R cos (L N] = J cos (l N] 

 r sin (X N) R sin (L N}= A sin (I N} 

 /tan/? M tanB =/1 tanb, 



in which the angle N is wholly arbitrary. The first and second equations will 

 determine directly I N and A , whence b will follow from the third ; from b 

 and A you will have A. That the labor of calculation may be as convenient as 

 possible, we determine the arbitrary angle N in the three following ways: 

 I. By putting JVr= L, we shall make 



^sin(X L} = P, ^cos(X L} 1= Q, 

 and I L, -^, and b, will be found by the formulas 



