224 ADDITION ETC. OF LOGICAL RELATIVES. 



A is north of B ; 

 B is north, of C ; 

 A is north of C. 



But if A is north of B, B is not north of A. Distance^ on 

 the contrary, is invertible but not transitive : if A is a 

 mile from B, B is a mile from A ; but from the premises 



A is a mile from B, 

 B is a mile from C, 



we can only infer that A and C are equidistant by a mile 

 from B, Perhaps these relations may hereaftei lead to 

 the establishment of some connexion between logic and 

 geometry analogous to that which Boole and his continu- 

 ators have shown to exist between logic and arithmetical 

 algebra. 



Note added while correcting proof. — On seeing the abs- 

 tract of this paper, Prof. Pierce wrote to me that my 

 addition of relative terms is, in all but notation, the- same 

 as his internal multiplication of the same. This is quite 

 true. See his paper in the ' Algebra and Logic/ reprinted 

 from the ' American Journal of Mathematics/ vol. iii. 



