94 THE PRINCIPLES OF SCIENCE. [CHAP. 



earth within about one sixth part of the truth. The use 

 of wells in astronomical observation appears to have been 

 occasionally practised in comparatively recent times as 

 by Flamsteed in I6/9. 1 The Alexandrian astronomers 

 employed the moon as an instrument of measurement 

 in several sagacious modes. When the moon is exactly 

 half full, the moon, sun, and earth, are at the angles of a 

 right-angled triangle. Aristarchus measured at such a 

 time the moon's elongation from the sun, which gave him 

 the two other angles of the triangle, and enabled him to 

 judge of the comparative distances of the moon and sun 

 from the earth. His result, though very rude, was far 

 more accurate than any notions previously entertained, 

 and enabled him to form some estimate of. the comparative 

 magnitudes of the bodies. Eclipses of the moon were 

 very useful to Hipparchus in ascertaining the longtitude 

 of the stars, which are invisible when the sun is above 

 the horizon. For the moon when eclipsed must be 180 

 distant from the sun ; hence it is only requisite to measure 

 the distance of a fixed star in longitude from the eclipsed 

 moon to obtain with ease its angular distance from the 

 sun. 



In later times the eclipses of Jupiter have served to 

 measure an angle; for at the middle moment of the 

 eclipse the satellite must be in the same straight line with 

 the planet and sun, so that we can learn from the known 

 laws of movement of the satellite the longitude of Jupiter 

 as seen from the sun. If at the same time we measure 

 the elongation or apparent angular distance of Jupiter 

 from the sun, as seen from the earth, we have all the 

 angles of the triangle between Jupiter, the sun, and the 

 earth, and can calculate the comparative magnitudes of 

 the sides of the triangle by trigonometry. 



The transits of Venus over the sun's face are other 

 natural events which give most accurate measurements 

 of the sun's parallax, or apparent difference of position 

 as seen from distant points of the earth's surface. The 

 sun forms a kind of background on which the place of 

 the planet is marked, and serves as a measuring instru- 

 ment free from all the errors of construction which affect 



1 Baily's Account of Flamsteed, p. lix. 



