THE ORBITS OF THE EIGHT PKIKCIPAL PLANETS. 171 



CHAPTER IV. 



ON THE PRECESSION OF THE EQUINOXES AND THE OBLIQUITY OF THE 



ECLIPTIC. 



1. The analytical formulae for the precession of the equinoxes and the ohliquity 

 of the ecliptic to the equator, referred to a fixed and also to a movable plane, arc 

 given by the formula: [3100, 3101, 3107, and 3110], Mecanique Celeste. In order 

 to reduce them to numbers we shall observe that the letter c in the notation of 

 the formula? corresponds to N", N x ", NJ', &c. in this work. If we denote the mean 

 value of the precession in a Julian year by I, and the mean obliquity of the ecliptic 

 by h, and also put 



c= ih N "' c '-^/ v " c '=i+ a * ; ' &c * 



f=l+9> A=l+9i> fz=l-\-92i fs= l +9to A=1+9i=l, A= l +9<» &c, we shall bare 

 the following formulae for determining the precession and obliquity: 



cot h- 



4-c. < cot h — ^itan/t 



T I A ■ 



-k{ 



-|-c 2 < cot h — 

 c 3 < cot h — 

 +c 4 1 cot h-9± 



4-tan h 



"ftan/i 



-\-cA cot/t — i^tan/f 



T l A 



tan h 



-|-c 5 <^ cot/t — -^5-tan/t 



1 Jb 



-j-c c < cot /t — y-tan/t 

 I. /a 



+c 7 {cot/t_^ 

 1 Jl 



tan /i 



sin (/<+/?) 

 sin (/*+&) 

 sin (/ 2 *+/3 2 ) 

 sin(/ 8 <+&) 

 sin(/ 4 <+ft) 

 sin (.#+&) 

 sin (/,*+&) 

 sin (/ 7 «+/? 7 ) 



Precession of the 



Equinoxes on the 



(550) 



Fixed Ecliptic. 



1 



E{=h— c cos(/ t +/3)— c 1 cos(//+ j 5 1 )— c 2 cos (/„<+&) j Obliquity of the 

 — o 3 cos(/ 3 H-/? 3 )— c 4 cos(/ 4 <+/3 4 )— c 5 cos(/ 6 «-j-/3 6 ) }• (551) 



-c 6 cos(/^4-/3 6 )-c 7 cos(/ 7 <+^) I Equator to the 



J rixed Ecliptic. 



