172 ASTEONOMTCAL EEFEACTION. [SECT. xvnr. 



uniform, the refractive power of the air is greatest at the 

 earth's surface, and diminishes upwards. 



A ray of light from a celestial object falling obliquely on 

 this variable atmosphere, instead of being refracted at once 

 from its course, is gradually more and more bent during its 

 passage through it so as to move in a vertical curved line, 

 in the same manner as if the atmosphere consisted of an 

 infinite number of strata of 'different densities. The object 

 is seen in the direction of a tangent to that part of the curve 

 which meets the eye ; consequently the apparent altitude 

 (N. 185) of the heavenly bodies is always greater than their 

 true altitude. Owing to this circumstance, the stars are 

 seen above the horizon after they are set, and the day is 

 lengthened from a part of the sun being visible, though he 

 really is behind the rotundity of the earth. It would be 

 easy to determine the direction of a ray of light through the 

 atmosphere if the law of the density were known ; but, as this 

 law is perpetually varying with the temperature, the case is 

 very complicated. When rays pass perpendicularly from 

 one medium into another, they are not bent ; and experience 

 shows, that in the same surface, though the sines of the 

 angles of incidence and refraction retain the same ratio, the 

 refraction increases with the obliquity of incidence (N. 184). 

 Hence it appears that the refraction is greatest at the 

 horizon, and at the zenith there is none. But it is proved 

 that, at all heights above ten degrees, refraction varies nearly 

 as the tangent of the angular distance of the object from the 

 zenith, and wholly depends upon the heights of the baro- 

 meter and thermometer. For the quantity of refraction 

 at the same distance from the zenith varies nearly as the 

 height of the barometer, the temperature being constant ; 

 and the effect of the variation of temperature is to diminish 

 the quantity of refraction by about its 480th part for every 

 degree in the rise of Fahrenheit's thermometer. Not much 

 reliance can be placed on celestial observations, within less 

 than ten or twelve degrees of the horizon, on account of 



