SECT. XVIII. TERRESTRIAL REFRACTION. 155 



atmosphere is seen in its true place. But the deviation is so 

 small in ordinary cases that it causes no inconvenience, though 

 in astronomical and trigonometrical observations due allowance 

 must be made for the effects of refraction. Dr. Bradley'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. 191). 

 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 below the pole was noticed by Alhazen, 

 a Saracen astronomer of Spain, in the ninth century ; but its 

 existence was known to Ptolemy in the second, though he was 

 ignorant of its quantity. 



The refraction of a terrestrial object is estimated differently 

 from that of a celestial body. It is measured by the angle con- 

 tained between the tangent to the curvilineal path of the ray 

 where it meets the eye, and the straight line joining the eye and 

 the object (N. 192). Near the earth's surface the path of the 

 ray may be supposed to be circular ; and the angle at the centre 

 of the earth corresponding to this path is called the horizontal 

 angle. The quantity of terrestrial refraction is obtained by 

 measuring contemporaneously the elevation of the top of a moun- 

 tain above a point in the plain at its base, and the depression of 

 that point below the top of the mountain . The distance between 

 these two stations is the chord of the horizontal angle ; and it is 

 easy to prove that double the refraction is equal to the horizontal 

 angle, increased by the difference between the apparent elevation 

 and the apparent depression. Whence it appears that, in the 

 mean state of the atmosphere, the refraction is about the four- 

 teenth part of the horizontal angle. 



Some very singular appearances occur from the accidental 

 expansion or condensation of the strata of the atmosphere con- 

 tiguous to the surface of the earth, by which distant objects, 

 instead of being elevated, are depressed. Sometimes, being at 

 once both elevated and depressed, they appear double, one of the 

 images being direct, and the other inverted. In consequence of 



