76 The Lije Story of the Fish 



just said that the angle X'FX" of the fish's window is un- 

 alterably fixed J therefore the affarent size of his window is 

 unalterably fixed, no matter what his depth. 



However, other things change as he changes his level. 

 Anything floating on the surface subtends a larger angle as 

 he approaches it and therefore appears to grow larger, even 

 as it would to us. A piece of wood two feet long and directly 

 overhead will be only about one-third the diameter of his 

 window when he is three feet down (Diagram H), but when 

 he rises to a one-foot depth, it will reach almost from one 

 side of the window to the other. Anything floating just in- 

 side the edge of his window — such as a boat with a man in it 

 — when he is, let us say, twelve feet down and his window is 

 about 26 feet in diameter, will be seen as one image:. the 

 bottom of the boat clear and undistofted under water, and 

 the side of the boat and the man somewhat distorted above 

 water, but all in one continuous piece. When the fish rises to 

 a depth of three feet, his window will be only six feet in 

 diameter. The boat will no longer be within the circle of the 

 window. Its bottom will be clearly visible oflF to one side, 

 protruding through the ceiling-mirror, but the man will 

 appear in an entirely different spot, as part of the border of 

 his window somewhat as in Diagram G. The bottom of the 

 boat and the man will be completely dissociated. 



Any object in the air directly overhead, such as a dragon- 

 fly hanging over the surface of the water, will appear to 

 grow larger as the fish rises, for the subtended angle will 

 increase, but a man standing on the bank will, so long as his 

 location is such that he is not included in the angle XTX", 

 appear to shrink. He forms part of the border of the window, 

 as in Diagram G. As the fish comes closer .to the surface, the 

 window will actually become smaller as we have seen, al- 

 though retaining the same apparent size to the fish. The 

 man will remain part of the border of the window, but the 

 angle subtended by his image will, because of the workings 



