78 THE PROBLEM OF THE GALLOPING HORSE 



we find that the celestial disc produces on the plate (as it 

 does on our eyes) a picture-disc of practically the same 

 size in both positions. In fact the high moon or sun pro- 

 duces a picture-disc of a little larger size than the low 

 moon or sun. I have here reproduced (PI. V) a photo- 

 graph, published by M. Flammarion, in which the moon 

 has been allowed to print itself on a photographic plate 

 exposed during the time the moon was rising, and it is 

 seen that the track of the moon has not diminished in 

 width as it rose higher and higher. No one will readily 

 believe this ; yet it is a demonstrable fact. Astronomers 

 have made accurate measurements which show that there 

 is no diminution of the disc under these circumstances, but 

 a slight increase since the moon is a very little nearer to 

 us when overhead than when we see it across the horizon. 

 If we put a piece of glass coated with a thin layer of 

 water-colour paint into a frame, and then make a peep- 

 hole in a board which we fix upright between us and the 

 upright piece of framed glass, we can keep the framed 

 glass steady (let us suppose it to be part of the window 

 of a room), and then we can move the peep-hole board 

 back from it into the room to measured distances. At a 

 distance of one and a half feet from the framed glass, which 

 is that at which an artist usually has his eye from his canvas 

 or paper, we can trace on the smeared or tinted piece of 

 glass the outlines of things seen through it exactly as they 

 fill up the area of the glass men, houses, trees, the moon. 

 The moon's disc (and the same is true of the sun) is found 

 always to occupy a space on the glass which is Tjg-th f 

 the distance of the eye from the framed glass plate. When 

 the eye-to-frame distance is eighteen inches, the diameter of 

 the disc of the moon on the smeared glass will occupy 

 exactly T |^th of eighteen inches, which is between one sixth 

 and one seventh of an inch. Similarly if the peep-hole is 

 at nine and a half feet or 1 1 4 inches from the framed glass 



