Divisions of Time. 11 



can scarcely be at a loss to understand its opera- 

 tion. From this cause the sun appears, both at 

 rising and setting, above the horizon, when he is 

 actually below it. Let us suppose (fig. 4) T to 

 be the earth, t z the mass of the atmosphere, 

 S the sun just below the horizon, H h ; suppose 

 the ray S c then to be emitted from that lumi- 

 nary, and to arrive at the atmosphere , which 

 must be of greater density than the medium 

 through which the ray has hitherto been trans- 

 mitted. The ray is consequently refracted to- 

 wards the perpendicular p p 9 and reaches the 

 spectator at t, who then sees the sun in the di- 

 rection Is ; he sees him, therefore, in a situation 

 nearer the zenith than he really is. 



But since the atmosphere is not every where 

 of the same density, and since its density in- 

 creases as it approaches the surface of the earth, 

 the ray Da, for instance, must suffer many suc- 

 cessive refractions, and arrive at the spectator t 

 in a kind of curve a b c t ; and if the line t d is 

 the tangent to this curve, the observer will see 

 the luminous body D elevated to d. The effect 

 of refraction in our climate is to cause the sun, 

 when he is in the horizon, to appear about 32 or 

 33 minutes of a degree higher than he really is ; 

 whence it follows that he will appear above the 

 horizon when he is actually below it. 



I have said that the artificial day compre- 

 hends all that space of time during which the 

 sun is above the horizon ; but if we apply this 



