SUMMER TWILIGHT 141 



after sunset will it be before the sun sinks so low, and 

 how will the season of the year affect the time ? 



Draw a circle to represent the apparent path of the 

 sun in the heavens, and draw chords in the circle to 

 represent the horizon on particular days. In summer 

 the chord will be low down, and the diurnal path 

 will be greater than the nocturnal. In winter the 

 chord will be high up, and the nocturnal path greater 

 than the diurnal. 



Parallel to each chord, and beneath it, draw a line, 

 to represent the limit of twilight. The arc inter- 

 cepted between the two lines will measure the duration 

 of twilight. It will be seen that the arc intercepted 

 will be shorter, the nearer the two lines approach the 

 equator of the circle, shortest of all when one is as 

 much above the equator as the other is below it. 

 That position will occur twice in the year, a little 

 before the vernal equinox, and a little after the 

 autumnal equinox. At the equinox itself the horizon 

 will coincide with the equator of the circle, and the 

 limit of twilight will be i8 3 below it. As we approach 

 the solstices the intercepted arc will increase in length, 

 but as the limit of twilight is always below the horizon, 

 it will come nearer to the equator at the winter than 

 at the summer solstice. The maximum for the year 

 will be at midsummer. In London twilight never 

 ends between May 22 and July 21. There is a second 

 maximum in midwinter, when twilight lasts about 2 

 hrs. 10 min. The minima fall about February 28 and 

 October 12, when twilight lasts only about I hr. 50 



