42 DISTANCES, HOW FOUND. SECT. V. 



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 ob- 

 served distance of the moon from the sun, or from a 

 particular star or planet, at any instant. The lunar the- 

 ory is brought to such perfection, that the times of these 

 phenomena, observed under any meridian when com- 

 pared with those computed for Greenwich in the Nauti- 

 cal 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 pro- 

 portional 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 

 finding the absolute distances of the celestial bodies in 

 miles, is in fact the same with that employed in meas- 

 uring the distances of terrestrial objects. From the 

 extremities of a known base (N. 115), the angles which 

 the visual rays from the object form with it, are meas- 

 ured ; their sum subtracted 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 admeasurement, furnishes a standard 

 of measures, with which we compare the distances, 

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



