THE EXACT MEASUREMENT OF PHENOMENA. 343 



modes. When the moon is exactly half full, the moon, 

 sun, and earth, are at the angles of a right-angled triangle. 

 He proposed therefore at such a time to measure the 

 moon's elongation from the sun, which would give him 

 the two other angles of the triangle, and enable 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 also 

 very useful in ascertaining the longitudes of the stars, 

 which were invisible when the sun w r as above the horizon. 

 For the moon when eclipsed must be 180 distant from 

 the sun ; hence it was 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 usefully 

 served to give a measure of an angle ; for at the middle 

 moment of the eclipse the satellite must be exactly 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 ap- 

 parent 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 cal- 

 culate the comparative magnitudes of the sides of the 

 triangle by simple trigonometry. 



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

 natural events which seem to give most accurate measure- 

 ments 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- 



