38 NUTATION OF LUNAR ORBIT. SECT. V. 



velop these great inequalities, which at some most 

 distant period will amount to many circumferences 

 (N. 107). 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 lon- 

 gitude, and also that remarkable inequality in her lati- 

 tude, 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 propor- 

 tional to the effect, a comparison of these inequalities, 

 computed from theory, with the same given by obser- 

 vation, shows that the compression of the terrestrial 

 spheroid, or the ratio of the difference between the 

 polar and the equatorial diameters, to the diameter of 

 the equator, is ^37.7^ It is proved analytically, that if 

 a fluid mass of homogeneous matter, whose particles 

 attract each other inversely as the squares of the dis- 

 tance, were to revolve about an axis as the earth does, 

 it would assume the form of a spheroid whose compres- 

 sion is -^1^. Since that is not the case, the earth can- 

 not be Homogeneous, but must decrease in density from 

 its center to its circumference. Thus the moon's 

 eclipses show the earth to be round ; and her inequali- 

 ties not only determine the form, but even the internal 

 structure of our planet ; results of analysis which could 

 not have been anticipated. Similar inequalities in the 

 motions of Jupiter's satellites prove that his mass is not 

 homogeneous, and that his compression is T ^. ? . His 

 equatorial diameter exceeds his polar diameter by about 

 6000 miles. 



The phases (N. 108) of the moon, which vary from 

 a slender silvery crescent soon after conjunction to a 

 complete circular disc of light in opposition, decrease by 

 the same degrees till the moon is again enveloped in 

 the morning beams of the sun. These changes regulate 

 the returns of the eclipses. Those .of the sun can only 

 happen in conjunction, when the moon, coming between 

 the earth and the sun, intercepts his light. Those of 



