SPACE AND GEOMETRY 49 



right is the compass, which in its simplest form 

 is a piece of string which is kept taut while one 

 end is fixed. The first instrument we may use in 

 all our flat geometries, but the second must be 

 modified in accordance with the rules of trans- 



FlGURE 4 



Non-Euclidean Compass 



formation which we decide to employ in place 

 of Euclidean rotation. 



Let me show you now an instrument which I 

 may call a non-Euclidean compass (Figure 4). 

 It consists of two rods, AB and BC, of which 

 the first is stationary and the second is allowed 

 to move about a hinge at B. A cord is attached 

 to the two rods at the points C and D, and now 

 if a piece of chalk is pressed against the string 

 so as to keep the upper part of the string coin- 

 cident with the rod BC and, maintaining this 



