444 Dr. Macfarlane's Analysis of Relationships. 



Then the first line gives us the equation 



2cc- 1 A=2A; (1) 



and the second line gives the equation 



Hl c- 1 w X= m c m c~ 1 A (2) 



From (1) it follows that 



2c, n (r 1 A = A; 

 therefore substituting in (2), we get 



that is, A w T as the father of the man X. 



The Rule for transposing a relationship from one side of an 

 equation to the other is as follows : — Change the order of the 

 symbols, and change each symbol into its reciprocal, the reci- 

 procal of m being m, and of f being f. Applying this rule to 

 the above, we get 



that is, X was a son of the man A. 



(4) A lady, on being asked about a photograph in her 

 album, replied : — You know that I have no daughters ; well, 

 that person's daughter's son was the father of a grandchild of 

 mine. 



Let A denote the lady and X the person. Then 



V/ A=0 > (i) 



and 



m c f cX= m c' 1 cc f A (2) 



From (1), 



2c f A=Z m c f A; 



and from (2), by the above rule of transposition, 



X=c~ 1 /e -1 f»c~ 1 ccyA. . 

 therefore from (1), 



But m c~ l c m =l always (p. 440); therefore 



x=c-y i m c / A. 



Also f c~ x c f —\ always; therefore 



X=c- 1 / A; 



that is, X was either the father or the mother of the lady. 

 Thus the answer given to the question was perfectly determi- 

 nate. 



