Dr. Macfarlane's Analysis of Relationships, 441 



logical laws, in addition to the morphological law referred to 

 above. "Where polyandry prevails must becomes can in the 

 case of m. 



The expression mm between two relationship symbols is 

 equivalent to m 9 and ff to /; but mf or fm imply a contra- 

 diction. 



A compound relationship due to the coexistence of several 

 elementary relationships, may be denoted by writing the rela- 

 tionships after one another, the order being immaterial — for 

 example, a child of the man A, who is also a child of the 

 woman B, by c TO Ac/B. When B is the same as A, a dot may 

 be used to replace the first A ; for example, 



c m c~ 1 Ac/c~ 1 A 



(that is, a child of the father of A who is also a child of the 

 mother of A) may be denoted by 



c m c- 1 .c f c l A. 



It is convenient to have a special notation for a compound 

 relationship which consists of a number of specific forms of 

 one general relationship. This may be done by placing a 

 vinculum over the general relationship, and by means of an 

 index expressing the number of times the general relationship 



occurs. For example, c 1-1 denotes full brother or full sister; 



c 1-1 denotes half brother or half sister ; and c 1_1 is the ap- 

 propriate expression for a non-brother or non- sister. Accord- 

 ing to the laws of this country we may have c 2 ~ 2 , c 2-2 , c 2-2 ; 

 c 2-2 ? c 2-2 . that j s? g rs t cousin in four ways, first cousin in 

 three ways, first cousin in two ways, first cousin in one way, 

 and first cousin in no way. When distinctions of sex are in- 

 troduced, the relationship of first cousin may have any one of 

 192 significations. 



The notation for a compound term enables us to express 

 the universal law that a person cannot be his or her own 

 descendant. It is 



l.c»A=0 



whoever A be, and n being any number from 1 upwards. The 

 reciprocal aspect of the law is that 



c-».lA=0s 



that is, no person can be his or her own ancestor ; while the 

 most general statement of the law is 



Sc m .c-"A=0, 



provided m and n are not both 0. 



In a similar manner it enables us to express the consequences 



