52 TRANSIT OF VENUS. SECT. VII 



nearly. Since the parallax is equal to the radius of the 

 earth divided by the distance of the moon, it varies with 

 the distance of the moon from the earth under the 

 same parallel of latitude, and proves the ellipticity of the 

 lunar orbit. When the moon is at her mean distance, 

 it varies with the terrestrial radii, thus showing that 

 the earth is not a sphere (N. 129). 



Although the method described is sufficiently accurate 

 for finding the parallax of an object as near as the moon, 

 it will not answer for the sun, which is so remote that 

 the smallest error in observation would lead to a false 

 result. But that difficulty is obviated by the transits of 

 Venus. When that planet is in her nodes (N. 130), or 

 within 1| of them, that is, in, or nearly in, the plane 

 of the ecliptic, she is occasionally seen to pass over the 

 sun like a black spot. If we could imagine that the sun 

 and Venus had no parallax, the line described by the 

 planet on his disc, and the duration of the transit, would 

 be the same to all the inhabitants of the earth. But as 

 the semi-diameter of the earth has a sensible magnitude 

 when viewed from the center of the sun. the line de- 

 scribed by the planet in its passage over his disc appears 

 to be nearer to his center, or farther from it, according 

 to the position of the observer ; so that the duration of 

 the transit varies with the different points of the earth's 

 surface at which it is observed (N. 131). This differ- 

 ence of time, being entirely the effect of parallax, fur- 

 nishes the means of computing it from the known 

 motions of the earth and Venus, by the same method as 

 for the eclipses of the sun. In fact, the ratio of the 

 distances of Venus and the sun from the earth at the 

 time of the transit are known from the theory of their 

 elliptical motion. Consequently the ratio of the paral- 

 laxes of these two bodies being inversely as their dis- 

 tances, is given ; and as the transit gives the difference of 

 the parallaxes, that of the sun is obtained. In 1769. the 

 parallax of the sun was determined by observations of a 

 transit of Venus made at Wardhus in Lapland, and at 

 Otaheite in the South Sea. The latter observation was 

 the object of Cook's first voyage. The transit lasted 

 about six hours at Otaheite, and the difference in dura- 

 tion at these two stations was eight minutes ; whence 



