Elements of Astronomy. g-l 



make a sidereal revolution in 6793'^ lO'' 6' 30''^0; or in 

 about 1 8*6 Julian ytars. This variation, however, is subject 

 to many inequalities : of which, the greatest is proportional 

 to the sine of douijle the distance ot the Moon from the 

 Sun; and extends to l" 37' 43", () at its maxinmm. A sv- 

 nodica! revohition oi" the nodes is performed in 346'' 14'' 

 52'43",f). The moiion of the nodes is subject also to a 

 secular inequality, dependent on the acceleration of the 

 Moon's mean nintion. 



The rttnthn of the Moon on her axis is equal and uni- 

 form : and it is performed in the same time as the tropical 

 revolution in her orliit ; whence she always presents nearly 

 the same face to the Earth. But, as the motion of the 

 Moon, in her orbit, is periodically variable, we sometimes 

 see more of her eastern edce, and sometimes more of her 

 western edge. This appearance is called the libration of 

 the Moon in longilwle. 



The axis of the Moon is inclined to the plane of the 

 ecliptic in an angle of 8S^ 29' 49''. In consequence of this 

 position of the Moon, her poles alternately become visible 

 to, and obscured from us : and this phienomenon is called 

 lier libration in latitude. 



There is also another optical deception arising from the 

 Moon being seen from the surface of the Earth, instead of 

 the centre. This appearance is called her diurnal libration. 



There are other inequalities in the Moon's motion, aris- 

 ing from the action and influence of the Sun. The prin- 

 cipal of these are, 



1. The £t'ec/io«; whose constant effect is to diminish the 

 equation of the centre in the syzigies, and to augment it in 

 the quadratures. If this diminution and increase were al- 

 ways the same, the evection would depend only on the an- 

 gular distance of the Moon from the Sun : but its absolute 

 value varies also with the distance of the Moon from the 

 perigee of its orbit. After a long series of observations, 

 we are enabled to represent this inequality by supposino- it 

 equal to the sine of double the distance of the Moon from 

 the Sun, minus the distance of the Moon from its perif^ee. 

 At its maximum, it amounts to 1° 18' 2'',4. 



2. The {Variation; which disappears in the syzigies and 

 quadratures, and is greatest in the octants. It is then equal 

 to 31' 44", 1: whence it is proportional to the sine of double 

 the distance of the Moon from the Sun. Its duration is 

 half a synodical revolution of the Moon. 



3. The Annual Equation ; which follows exactly the same 

 law as the equation of the centre of the Sun^ with a contrary 



B 3 sign. 



