SECT. V. DISTANCES OF PLANETS, HOW FOUND. 43 



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 extending 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 

 phenomenon 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 meridian, when compared 

 with those computed for that- of Greenwich, and given in the 

 Nautical Almanac, furnish 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 399*7 or nearly 400 times greater than that of the 

 moon. The method of finding the absolute distances of the 

 celestial bodies, in miles, is in fact the same with that employed 

 in measuring the distances of terrestrial objects. From the ex- 

 tremities of a known base (N. 116), the angles which the visual 

 rays from the object form with it are measured ; their sum sub- 

 tracted from two right angles gives the angle opposite the base ; 

 therefore, by trigonometry, all the angles and sides of the triangle 

 may be computed consequently the distance of the object is 

 found. The angle under which the base of the triangle is seen 

 from the object is the parallax of that object. . It evidently in- 

 creases and decreases with the distance. Therefore the base must 

 be very great indeed to be visible from the celestial bodies. The 

 globe itself, whose dimensions are obtained by actual admeasure- 

 ment, furnishes a standard of measures with which we compare the 

 distances, masses, densities, and volumes of the sun and planets. 



