58 OKIOIN AND SIGNIFICANCE OF 



parently solid and in fixed positions behind its surface. 

 But the images of the distant horizon and of the sun 

 in the sky lie behind the mirror at a limited distance, 

 equal to its focal length. Between these and the sur- 

 face of the mirror are found the images of all the other 

 objects before it, but the images are diminished and 

 flattened in proportion to the distance of their objects 

 from the mirror. The flattening, or decrease in the 

 third dimension, is relatively greater than the decrease 

 of the surface-dimensions. Yet every straight line or 

 every plane in the outer world is represented by a 

 straight line or a plane in the image. The image of a 

 man measuring with a rule a straight line from the 

 mirror would contract more and more the farther he 

 went, but with his shrunken rule the man in the 

 image would count out exactly the same number of 

 centimetres as the real man. And, in general, all 

 geometrical measurements of lines or angles made 

 with regularly varying images of real instruments 

 would yield exactly the same results as in the outer 

 world, all congruent bodies would coincide on being 

 applied to one another in the mirror as in the outer 

 world, all lines of sight in the outer world would be 

 represented by straight lines of sight in the mirror. 

 In short I do not see how men in the mirror are 

 to discover that their bodies are not rigid solids and 

 their experiences good examples of the correctness of 

 Euclid's axioms. But if they could look out upon our 



