494 



NOTES. 



the angle E A B, above its real place. Again, the real depression of A, when 

 viewed from B, is F B A, whereas its apparent depression is F B E, so E B A is 

 due to refraction. The angle F B A is equal to the sum of the angles BAH 

 and A C B ; that is, the true elevation is equal to the true depression and the 

 horizontal angle. But the true elevation is equal to the apparent elevation 

 diminished by the refraction; and the true depression is equal to the apparent 

 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. 175. Fig. 52 represents the phenomenon in question. S P is 

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



Fig. 52. 



no refraction, the rays would come from the ship S P to the eye E in the direc- 

 tion 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 P c E, P d E, 

 S m E, S n E. 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 atp 

 an,d p 1 , 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 in the air above it. 



Fig. 53. 



NOTE 189, p. 175. Fig. 53 represents the / 

 section of a poker, with the refraction pro- 

 duced by the hot air surrounding it. 



