SECT. V LUNAR THEORY 33 



Jar phenomenon of being retrograde, or from east to 

 west ; while all the planets and the other satellites re- 

 volve in the contrary direction. Sir John Herschel could 

 not perceive the smallest indication of a ring. 



SECTION V. 



Lunar Theory Periodic Perturbations of the Moon Equation of Center- 

 Evection Variation Annual Equation Direct and Indirect Action of 

 Planets The Moon's Action on the Earth disturbs her own Motion- 

 Eccentricity and Inclination of Lunar Orbit Invariable Acceleration 

 Secular Variation in Nodes and Perigee Motion of Nodes and Perigee 

 inseparably connected with the Acceleration Nutation of Lunar Orbit 

 Form and Internal Structure of the Earth determined from it Lunar, 

 Solar, and Planetary Eclipses Occultations and Lunar Distances Mean 

 Distance of the Sun from the Earth obtained from Lunar Theory Abso- 

 lute Distances of the Planets, how Found. 



OUR constant companion, the moon, next claims our 

 attention. Several circumstances concur to render her 

 motions the most interesting, and at the same time the 

 most difficult to investigate, of all the bodies of our sys- 

 tem. In the solar system, planet troubles planet ; but in 

 the lunar theory, the sun is the great disturbing cause ; 

 his vast distance being compensated by his enormous 

 magnitude, so that the motions of the moon are more 

 irregular than those of the planets ; and, on account of 

 the great ellipticity of her orbit, and the size of the sun, 

 the approximations to her motions are tedious and diffi- 

 cult, beyond what those unaccustomed to such investiga- 

 tions could imagine. The average distance of the moon 

 from the center of the earth is only 237,360 miles, so 

 that her motion among the stars is perceptible in a few 

 hours. She completes a circuit of the heavens in 

 27 d 7 h 43 m 4 8 -7, moving in an orbit whose eccentricity is 

 about 12,985 miles. The moon is about four hundred 

 times nearer to the earth than the sun. The proximity 

 of the moon to the earth keeps them together. For so 

 great is the attraction of the sun, that if the moon were 

 farther from the earth, she would leave it altogether, and 

 would revolve as an independent planet about the sun. 



The disturbing action (N. 101) of the sun on the moon 

 is equivalent to three forces. The first, acting in the 

 direction of the line joining the moon and earth, in- 

 3 



