NIPHER — ON CERTAIN PROBLEMS IN REFRACTION. 329 



V //2 _ r 

 the value of which for water is i 5^2- 

 The axes of this hyperbola would be 



a = d= nd' , o z=i ziz —, 



If ;2=v/2, the equilateral hyperbola would be the limiting 

 case, the eye being in the water surface. 



3°. The eye being in the more refracting mediii-n, it is reqidred to Jitid 

 the surface in the other medium which shall appear plane. 



Let d' z= the depth of the eye below the surface ; 

 d" z=i distance of the plane from the surface ; 

 D and Z = coordinates of any point in the curved 

 surface, the origin being in the water surface above 

 the eve. 



EXI'LANATION OF CUT. 

 a f d ^ critical angle cone. 



h" b" = apparent pnsitinn of h> b' as seep from /. 

 b' b' = apparent position of <>(? as seen from /, but referring only to the part 



within the critical angle cone, 

 .c.t ^: water surface. 



The angle / being within the more refracting medium, we have 



^ tan / , , d" cos r 



D = d' — . . . . . (10) 



tan r n cos t 



