Fig. 51. 



423 



angle. But the true elevation is equal to the apparent elevation dimin- 

 ished by the refraction; and the true depression is equal to the ap- 

 parent depression increased by refraction. Hence twice the refraction 

 is equal to the horizontal angle augmented by the difference between the 

 apparent elevation and the apparent depression. 



NOTE 188, p. 151. Fig. 52 represents the phenomenon in question. SP 

 is the real ship, with its inverted and direct images seen in the air. 



Were there no refraction, the rays would come from the ship S P to the 

 eye E in the direction of the straight lines ; but, on account of the variable 

 density of the inferior strata of the atmosphere, the rays are bent in the 

 curved lines PcE, PdE, SmE, SnE. Since an object is seen in the 

 direction of the tangent to that point of the ray which meets the eye, 

 the point P of the real ship is seen at p and p\ and the point S seems to 

 be in s and s' ; and as all the other points are transferred in the same 

 manner, direct and inverted images of the ship are formed hi the air 

 above it. 



