THE EXTERNAL WORLD 91 



a certain thickness. These two lines will meet in a certain 

 place in perspective space, i.e. in a certain perspective, 

 which may be defined as " the place (in perspective space) 

 where the penny is." It is true that, in order to prolong 

 our lines until they reach this place, we shall have to 

 make use of other things besides the penny, because, so 

 far as experience goes, the penny ceases to present any 

 appearance after we have come so near to it that it touches 

 the eye. But this raises no real difficulty, because the 

 spatial order of perspectives is found empirically to be 

 independent of the particular " things " chosen for defining 

 the order. We can, for example, remove our penny and 

 prolong each of our two straight lines up to their inter- 

 section by placing other pennies further off in such a way 

 that the aspects of the one are circular where those of our 

 original penny were circular, and the aspects of the other 

 are straight where those of our original penny were 

 straight. There will then be just one perspective in 

 which one of the new pennies looks circular and the other 

 straight. This will be, by definition, the place where the 

 original penny was in perspective space. 



The above is, of course, only a first rough sketch of the 

 way in which our definition is to be reached. It neglects 

 the size of the penny, and it assumes that we can remove 

 the penny without being disturbed by any simultaneous 

 changes in the positions of other things. But it is plain 

 that such niceties cannot affect the principle, and can only 

 introduce complications in its application. 



Having now defined the perspective which is the place 

 where a given thing is, we can understand what is meant 

 by saying that the perspectives in which a thing looks 

 large are nearer to the thing than those in which it looks 

 small : they are, in fact, nearer to the perspective which 

 is the place where the thing is. 



