38 NUTATION OF LUNAR ORBIT. SECT. V. 



perigee accomplishes a revolution, called of the moon's apsides, 

 in 3232* 13 h 48 m 29 8 *6, or a little more than nine years, notwith- 

 standing its motion is sometimes retrograde and sometimes 

 direct : but such is the difference between the disturbing energy 

 of the sun and that of all the planets put together, that it 

 requires no less than 109,830 years for the greater axis of the 

 terrestrial orbit to do the same, moving at the rate of 11" - 8 

 annually. The form of the earth has no sensible etfect either on 

 the lunar nodes or apsides. It is evident that the same secular 

 variation which changes the sun's distance from the earth, and 

 occasions the acceleration in the moon's mean motion, must affect 

 the nodes and perigee. It consequently appears, from theory as 

 well as observation, that both these elements are subject to a 

 secular inequality, arising from the variation in the excentricity 

 of the earth's orbit, which connects them with the Acceleration, 

 so that both are retarded when the mean motion is anticipated. 

 The secular variations in these three elements are in the ratio of 

 the numbers 3, 0*735, and 1 ; whence the three motions of the 

 moon, with regard to the sun, to her perigee, and to her nodes, 

 are continually accelerated, and their secular equations are as the 

 numbers 1, 4*702, and 0*612. A comparison of ancient eclipses 

 observed by the Arabs, Greeks, and Chaldeans, imperfect as they 

 are, with modern observations, confirms these results of analysis. 

 Future ages will develop these great inequalities, which at some 

 most distant period will amount to many circumferences (N. .108). 

 They are, indeed, periodic ; but who shall tell their period? Millions 

 of years must elapse before that great cycle is accomplished. 



The moon is so near, that the excess of matter at the earth's 

 equator occasions periodic variations in her longitude, and also 

 that remarkable inequality in her latitude, already mentioned as 

 a nutation in the lunar orbit, which diminishes its inclination to 

 the ecliptic when the moon's ascending node coincides with the 

 equinox of spring, and augments it when that node coincides 

 with the equinox of autumn. As the cause must be proportional 

 to the effect, a comparison of these inequalities, computed from 

 theory, with the same given by observation, shows that the com- 

 pression of the terrestrial spheroid, or the ratio of the difference 

 between the polar and the equatorial diameters, to the diameter 

 of the equator, is 553.55. It is proved analytically, that, if a fluid 

 mass of homogeneous matter, whose particles attract each other 



