TEEKESTKIAL PHENOMENA. 39 



rays, but what will, perhaps, cause most surprise is that 

 he made such a persistent attempt to explain so difficult a 

 series of phenomena. 



Aristotle also discusses the size of the rainbow, and 

 makes some very interesting statements about the conditions 

 under which it could be seen at Athens. In Meteorol. iii. 

 c. 2, s. 3, he says that the arch of the rainbow is never greater 

 than a semicircle, and in Meteorol. iii. c. 5, proceeds to give 

 a geometrical proof of this. Aristotle's statement is sub- 

 stantially correct for an observer on the earth's surface, for 

 the effect of refraction in the case of the rainbow is inappre- 

 ciable. That the arch is sometimes greater than a semicircle 

 is, however, well known, the arch being so when the 

 observer is at some high elevation. 



An error, however, occurs in Meteorol. iii. c. 2, s. 3, 

 where it is stated that, at sunset and sunrise, the circle of 

 the rainbow is least but the arch is greatest, and that, when 

 the Sun is high, the arch is less but the circle greater. The 

 external radius of the primary rainbow is constant, being 

 about 42°, and that of the secondary rainbow is also 

 constant, being about 54°. Still, it is clear that Aristotle 

 attempted to make observations in a thorough manner, and 

 it should be remembered that it was not possible to explain 

 the constancy of the angular dimensions of the rainbow 

 before Descartes proved that a concentration of the rays 

 occurs in certain directions. Aristotle also says, in a passage 

 which shows that he was a keen observer, that, after the 

 autumnal equinox and during the shorter days, a rainbow is 

 possible at all hours, but, in the summer, it is not possible 

 about midday.* He probably intended this statement to 

 refer to the appearances of rainbows at Athens. He 

 attempts to explain it in Meteorol. iii. c. 5, but his explana- 

 tion is defective, because he was not in possession of correct 

 data. 



A straight line from the centre of the Sun to the centre 

 of a rainbow passes through the observer's eye, and, there- 

 fore, if the Sun is more than 54° above the horizon, not 

 even the outer part of a secondary rainbow would be visible 

 to an observer at the sea-level at Athens. Referring to 

 Fig. 1, it will be seen that, at midday, June 21st, the alti- 

 tude of the Sun at Athens = 90°- (38°— 23" 28') - 75° 28', 

 the latitude of Athens being 38° and the inclination of the 



'■- Meteorol. iii. c. 2, s. 3. 



