170 Prof. Everett on the Optics of Mirage. 



The rate of decrease usually assumed as an average is g^ - of 

 a degree Fahrenheit, or -^\ 6 of a degree Cent, per foot. This 

 Mali give, at 0° C. and 760 millims., 



p 89000000 V 540 J' 

 whence p — 108000000 feet, or 5*2 radii of the earth. 



At 10° C, 760 millims., and the same rate of decrease as 

 above, p is equal to about 5 '6 radii of the earth, and the correc- 

 tion for refraction in levelling is therefore -1— of the correction 



T 5 6 



for the curvature of the earth. Rankine (Rules and Tables, 

 p. 131) says, "The correction for refraction to be added to the 

 reading is very variable and uncertain. On an average, it may 

 be taken at one sixth of the correction for curvature." 



In order that the curvature of a ray may be the same as that 



of the earth at 0° C. and 760 millims., the expression 1 + 96 — - 



must be equal to 89000000 feet divided by the earth's radius — - 

 that is, to about 4*26. We shall therefore have 



dt 3-26 1 



dy 96 ""29-4' 



that is, the temperature must increase at the rate of 1° C. for 

 29'4 feet of ascent, or 1° F. for 16'3 feet. Any portion of the 

 earth with such a state of things prevailing over it will appear 

 plane, distant, objects being no longer hidden by the intervening 

 convexity. A still more rapid increase will make the surface of 

 the earth appear concave. 



VIII. I shall now take up in detail the principal phenomena 

 of mirage, and indicate what I conceive to be their correct ex- 

 planations. 



1. An unusual extension of the range of vision, like that de- 

 scribed by Latham in the Philosophical Transactions for 1798, 

 when the coast of France from Calais to the neighbourhood of 

 Dieppe was clearly visible from Hastings. 



Explanation. — An increase of temperature with ascent, pro- 

 ducing an exaggeration of the ordinary downward curvature of 

 rays, as explained in the preceding section. 



2. Distant objects seen inverted above their true positions. 

 Some instances of this form of mirage are described by Vince in 

 the " Bakerian Lecture/'' Phil. Trans. 1799; many more are 

 described by Scoresby from his observations in the Arctic re- 

 gions; and the phenomenon is extremely common across exten- 

 sive sheets of calm water. Usually two images are seen, namely 

 an erect image in the true or w T hat appears to be the true posi- 

 tion, and an inverted image above it. Sometimes, however, the 



