22 A Synopsis of the principal 



sign. For, when the Earth is in its periheHon, the orbit of 

 the Moon is enlarged by the action of the Sun ; and the 

 Moon therefore requires more time to perform her revolu- 

 tion. But, as the Earth proceeds towards its aphelion, the 

 Moon's orbit contracts. Hence the period of this inequa- 

 lity is an anomalistic year: and, at its maximum, it 

 amounts to 1 1' 15",9. It is subject to a secular inequality. 



Th& figure of the Moon is that of an oblate spheroid, like 

 tlie Earth. Her mean diameter is in the proportion to that 

 of the Earth, as 5823 to 21332 ; or as I to 3-663. Whence 

 her mean diameter will be about 21 60 miles. 



Her volume, compared with that of the Earth, is ■^\: but 

 her mass is only -^-^ 



The apparent diameter of the Moon varies according to 

 her distance from the Earth. When nearest to us it is 

 33' 31'',! ; but at her greatest distance if is 2y' 2 [",9. Her 

 mean apparent diameter is 31' 26', 5. 



Her mean horizontal parallax is equal to 57' 34",2. 



The phases of the Moon are caused by the reflection of 

 the Sun's light ; and depend on the relative positions of 

 the Sun, the Earth, and the Moon. 



An eclipse of the Moon can take place only at the time 

 of her opposition to the Sun ; and is caused by her passing 

 through the shadow of the Earth. That shadow is 3i times 

 longer than the distance between the Moon and the Earth: 

 and its breadth, where it is traversed by the Moon, is about 

 2-j- times greater than the diameter of the Moon. The 

 breadth of the Earth's shadow, where it is traversed by the 

 Moon, is equal to the difference between the semidiameter 

 of the Sun, and the sum of the horizontal parallaxes of the 

 Sun and Moon. 



[The Moon cannot be eclipsed, however, if her distance 

 from the place of her node, at the time of her opposition, 

 exceeds 13° 21': but, if it is within 7° 47', there will cer- 

 tainly be an eclipse. The duration of the eclipse will de- 

 pend on the apparent diameter of the Moon, and on the 

 breadth of the shadow at the point where she traverses it.] 



The Sun cannot be eclipsed unless the Moon be in con- 

 junction : and then only when the centres of the Sun and 

 Moon are in the same straight line with the eye of the spec- 

 tator on the Earth, hi such case, if the apparent diameter 

 of the Moon be greater than that of the Sun, the eclipse 

 will be total: but, if it be less, it will be annular. Par- 

 tial eclipies, however, may arise ; as in the case of lunar 

 eclipse. 



[The Sun cannot be totally obscured for a longer period 



of 



