208 



MR. JOSEPH JOHN MURPHY ON ADDITION 



street, X, Y, and Z houses on the south side, and no others 

 existing in the universe under consideration : — 



1. A is north of X; 



2. A is north of X ; 



3. A is north of X; 



4. A is north of X ; 



X is north of W ; There is no W. 



X is fellow-northern There is no W. 



ofW; 



X is fellow-southern A is north of Y. 



of Y; 



X is south of B ; A is fellow-northern 

 ofB. 



A is north of X. 



5. A is fellow-northern B is north of X ; 



ofB; 



6. A is fellow-northern B is fellow-northern A is fellow-northern 



ofB; ofC; of C. 



7. A is fellow-northern B is fellow-southern There is no W. 



ofB; ofW; 



8. A is fellow-northern B is south of W ; There is no W. 



ofB; 



9. X is fellow-southern Y is north of W ; There is no W. 



ofY; 



10. X is fellow-southern Y is fellow-northern There is no W. 



ofY; ofW; 



11. X is fellow- southern Y is fellow-southern X is fellow-southern 



of Y ; of Z ; of Z. 



12. X is fellow-southern Y is south of A; X is south of A. 



ofY: 



13. X is south of A ; 



14. X is south of A ; 



15. Xis south of A; 



16. X is south of A; 



A is north of Y ; X is fellow-southern 



ofY. 



A is fellow-northern X is south of B. 



ofB; 



A is fellow-southern There is no W. 



ofW; 



A is south of W ; There is no W. 



In the eight cases where the results are affirmative, they 

 are true of all relatives whatever; their truth is inde- 

 pendent of the meaning assigned to L ; and they are also 



for the Logic of Relatives " (Memoirs of the American Academy, vol. ix.), 

 but with a different notation. He calls these elementary relatives ; but I 

 have shown that there is a yet simpler case. 



