Divisions of Time. 13 



coming in an oblique direction, they are refracted 

 towards the perpendicular, and inclined to tt t t. 

 As the sun descends, fewer rays reach the sur- 

 face of the atmosphere, so as to take this direc- 

 tion. The twilight, therefore, gradually dimi- 

 nishes, and at last totally disappears in the 

 manner already stated. 



The duration of twilio-ht is not the same at 



t? 



all places, nor even at the same place in all sea- 

 sons; since, at certain places, and at certain 

 times, the sun rises and descends perpendicularly 

 from the horizon, while at others his motion 

 both at rising and setting is more oblique, and 

 the most so when his declination is the greatest, 

 at which period it is plain that he must occupy 

 more time in rising or descending a space which 

 shall measure 18 degrees in the vertical direc- 

 tion. 



The sun appears to traverse 15 degrees of the 

 equator, or of some circle parallel to it, every 

 hour ; twilight therefore must endure for one 

 hour and twelve minutes in those places where 

 the sun rises or sets perpendicularly to the horizon, 

 which is at the time of the equinoxes to those 

 who live under the equator, or who have a right 

 sphere. The length of twilight increases in pro- 

 portion as the sun is further from the equator, or 

 has more declination. 



We must therefore conclude, that to those 

 who live between the equator and one of the 

 poles, or who have an oblique sphere, the length 



