62 OEIGIN AND SIGNIFICANCE OF 



would not seem to us very strange, comparatively 

 speaking; we should only at first be subject to illu- 

 sions in measuring by eye the size and distance of the 

 more remote objects. 



There would be illusions of an opposite description, 

 if, with eyes practised to measure in Euclid's space, we 

 entered a spherical space of three dimensions. We 

 should suppose the more distant objects to be more 

 remote and larger than they are, and should find on 

 approaching them that we reached them more quickly 

 than we expected from their appearance. But we 

 should also see before us objects that we can fixate 

 only with diverging lines of sight, namely, all those 

 at a greater distance from us than the quadrant of a 

 great circle. Such an aspect of things would hardly 

 strike us as very extraordinary, for we can have it even 

 as things are if we place before the eye a slightly pris- 

 matic glass with the thicker side towards the nose : the 

 eyes must then become divergent to take in distant 

 objects. This excites a certain feeling of unwonted 

 strain in the eyes, but does not perceptibly change the 

 appearance of the objects thus seen. The strangest 

 sight, however, in the spherical world would be the 

 back of our own head, in which all visual lines not 

 stopped by other objects would meet again, and which 

 must fill the extreme background of the whole per- 

 spective picture. 



