20 A Synopsis of the principal 



TTI. The square; of the fnnes of the revolutions of the sO' 

 teUitcs, round their respective primary planets, are to each 

 other us ike cubes of their mean distances from the primary, 



Jlloon. 



The motions of the Moon are exceedingly eccentric and 

 irregular. She performs her mean sidereal revolution in 

 27** 7'' 43' 1 1",5. But this period is variable: and a com- 

 parison of the modern observations with the ancient proves 

 incontestably an acceleration in her mean motion. Her 

 mean tropical revolution is 27'* 7'' 43' 4", 7 : and her mean 

 syiindical revolution is 29"' IS*' 44' 2", 8. 



Her mean distance from the Earth is 29*982175 times 

 the diameter of the terrestrial equator; or above 237 thou- 

 sand nnles. 



The eccentricity of her orbit is •0548')53 ; the mean dis- 

 tance from the Earth being taken e([ual to unity. But this 

 eccentricity is variable in each revolution. 



Her 7nean longitude, at the commencement of the pre- 

 sent century, was in 3^ 21° 36' 42", 1. 



Her velocity varies in different parts of her orbit. She 

 is swiftest in her perigee (or point nearest the Earth) ; and 

 slowest when in her apogee (or point furthest from the 

 Earth). Her mean diurnal velocity is equal to 13" 10'34"j9j 

 or about 13 times greater than that of the Sun. 



The greatest equation of her centre is 6^ 17' 34",5. 



The mean longitude of her perihelion was, at the com- 

 mencement of the present century, in 8' 26^ 6' 3",1 : but 

 the line of the apsides has a motion, according to the order 

 of the signs. The period of a sidereal revolution of the 

 apsides is 3232'' 13'' 56' 16',8, or nearly 9 years. The pe- 

 riod of a tropical revolution of the apsides is but 3231'' ll'^ 

 24' 8", 6. But these periods are not uniform : for thev have 

 a secular irregularity, and are retarded whilst the motion of 

 the Moon itself is accelerated. The period of an anomalistic 

 revolution of the Moon is 27'* 13'' 18' 37",4. 



Her orbit is inclined to the plane of the ecliptic in an 

 angle of 5^ 9' : but this inclination is variable. The greatest 

 inequality, which sometimes extends to 8' 4 7",1, is pro- 

 portional to the co-sine of the angle on which the inequality 

 in ihe motion of the nodes depends. 



Her orbit, at the commencement of the present century, 

 crossed the ecliptic in 0» 13=' 55' 26', 3: but the place of 

 her nodes is variable. They have a retrograde motion, and 



maka 



