48 OCCULTATIONS. [SECT. v. 



millions of years separate the epochs of the contemporaneous 

 conjunctions of the six great planets. 



The motions of the moon have now become of more im- 

 portance to the navigator and geographer than those of any 

 other heavenly body, from the precision with which terres- 

 trial longitude is determined by occultations of stars, and by 

 lunar distances. In consequence of the retrograde motion 

 of the nodes of the lunar orbit, at the rate of 3' 10"'64 daily, 

 these points make a tour of the heavens in a little more than 

 eighteen years and a half. This causes the moon to move 

 round the earth in a kind of spiral, so that her disc at different 

 times passes over every point in a zone of the heavens ex- 

 tending rather more than 5 9' on each side of the ecliptic. 

 It is therefore evident, that at one time or other she must 

 eclipse every star and planet she meets with in this space. 

 Therefore the occultation of a star by the moon is a pheno- 

 menon of frequent occurrence. The moon seems to pass over 

 the star, which almost instantaneously vanishes at one side 

 of her disc, and after a short time as suddenly reappears on 

 the other. A lunar distance is the observed distance of the 

 moon from the sun, or from a particular star or planet, at 

 any instant. The lunar theory is brought to such perfection, 

 that the times of these phenomena, observed under any me- 

 ridian, when compared with those computed for Greenwich 

 in the Nautical Almanac, give the longitude of the observer 

 within a few miles (N. 95). 



From the lunar theory, the mean distance of the sun from 

 the earth, and thence the whole dimensions of the solar 

 system, are known ; for the forces which retain the earth 

 and moon in their orbits are respectively proportional to the 

 radii vectores of the earth and moon, each being divided by 

 the square of its periodic time. And, as the lunar theory 

 gives the ratio of the forces, the ratio of the distances of the 

 sun and moon from the earth is obtained. Hence it appears 

 that the sun's mean distance from the earth is 396 or nearly 

 400 times greater than that of the moon. The method of 



