THE ORBITS OF THE EIGHT PRINCIPAL 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 obliquity 

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

 given by the formulae [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 formulae corresponds to N", Nf, -iV 2 ", &c. in this work. If we denote the mean 

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

 by h, and also put 



f=l+g, fi=l+gi, / 2 =H-<fo /=*+# ft=t+gi=1, /6=Z+ft. &c., we shall have 

 the following formula) for determining the precession and obliquity : 



cot h -t 



n/t 1 sin 



-f GJ | cot h^tanh 1 sin 

 I /i i 



-J-Ca < cot 7t &* tan/t I sin 

 ( h 



Precession of the 

 Equinoxes on the 



(550) 

 Fixed Ecliptic. 



h 

 +c 3 1 cot h^-tanh 1 sin 



+c 4 { cot A ^-tan/t 1 sin 



I /4 



+c 5 1 cot h-totoah | sin (/ 6 <+/? 6 ) 

 +c 6 1 cot h^-tanh | sin (/ 8 +/3 6 ) 



( /6 



+c 7 { cot h^-tauh \ sin (/ T +/8 T ) 

 Ji 



l =A c cos (/<+/? ) c x cos (/iH-/?i) c 2 cos (/,<+iS 2 ) I Obliquity of the 

 -c 3 cos(/ 3 <+/3 3 )-c 4 cos(/ 4 <+/3 4 )-c 6 cos(/ 6 <+/3 5 ) } (551) 



)-c 7 cos (/ 7 <+A) g"* t? ; he 

 J Fixed Ecliptic. 



