SECT. XVIII. ASTRONOMICAL REFRACTION. 149 



bent ; and experience shows, that in the same surface, 

 though the sines of the angles of incidence and refrac- 

 tion 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 barometer 

 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 observa- 

 tions, within less than ten or twelve degrees of the 

 horizon, on account of irregular variations in the density 

 of the air near the surface of the earth, which are 

 sometimes the cause of very singular phenomena. The 

 humidity of the ah' produces no sensible effect on its 

 refractive power. 



Bodies, whether luminous or not, are only visible by 

 the rays which proceed from them. As the rays must 

 pass through strata of different densities in coming to us, 

 it follows that with the exception of stars in the zenith, 

 no object either in or beyond our atmosphere is seen in 

 its true place. But the deviation is so smalHp ordinary 

 cases that it causes no inconvenience, though in astro- 

 nomical and trigonometrical observations diie allowance 

 must be made for the effects of refraction. Dr. Brad- 

 ley's tables of refraction were formed by observing the 

 zenith distances of the sun at his greatest declinations, 

 and the zenith distances of the pole-star above and below 

 the pole. The sum of these four quantities is equal to 

 180, diminished by the sum of the four refractions, 

 whence the sum of the four, refractions was obtained ; 

 and from the law of the variation of refraction determined 

 by theory, he assigned the quantity due to each altitude 

 (N. 186). The mean horizontal refraction is about 

 35' 6", and at the height of forty-five degrees it is 58"-36. 

 The effect of refraction upon the same star above and 



