SCIENCE ABSOLUTE OF SPACE. 61 



around a track in opposite directions, and 

 also on page 87 of Richardson s Euclid, 1891, 

 read, &quot;The sides of the figure must be pro 

 duced in the same direction of rotation ; . . . 

 going round the figure always in the same 

 direction,&quot; we do not wonder that when Mr. 

 Ziwet had written: &quot;he therefore bases the 

 definition of the straight line on these two 

 ideas,&quot; he stops, modifies, and rubs that out 

 as follows, &quot;or rather recommends to eluci 

 date the intuitive idea of the straight line 

 possessed by any well-balanced mind by means 

 of the still simpler ideas of direction&quot; [in a 

 circle] &quot;and distance&quot; [on a curve]. 



But when we come to geometry as a science, 

 as foundation for work like that of Cayley and 

 Ball, I think with Professor Chrystal: &quot; It is 

 essential to be careful with our definition of a 

 straight line, for it will be found that vir 

 tually the properties of the straight line de 

 termine the nature of space. 



&quot;Our definition shall be that two points in 

 general determine a straight line.&quot; 



We presume that Mr. Ziwet glories in that 

 unfortunate expression &quot;a straight line is the 

 shortest distance between two points,&quot; still 

 occurring in Wentworth (New Plane Geom 

 etry, page 33), even after he has said, page 5, 



