Dr. Macfarlane's Analysis of Relationships, 439 



When the expression for the relationship contains a change 

 of sign in the index, it may in certain cases be equivalent to 

 a relationship of a lower order ; but when the index does not 

 contain a change of sign, the relationship cannot be equivalent 

 to one of a lower order. The third column contains the 

 general meaning, and the fourth column the particular mean- 

 ing when the relationship is supposed irreducible. The first 

 reducible relationships are c 1-1 and c~ 1 + 1 , which may reduce 

 to 1. The relationship c 2_1 may reduce to c ; c 2 ~ 2 may reduce 

 to c 1_I , which we have seen may further reduce to 1. Con- 

 sider the relationship c m ~ n ; the reducible forms are c(" , -. 1 )-(«- , > J 

 c ( TO _ 2 )-(n-2) ? anc j so on ^ un til one of the numbers is reduced 

 to 0. Hence a relationship of an odd order can reduce only 

 to one of an odd order, and a relationship of an even order 

 only to one of an even order. 



It is not difficult to conceive how this table of relationships 

 (fully developed) may be useful to legislators in a case where 

 an exact and comprehensive view of relationships is required, 

 as, for example, in making a consistent and logical alteration 

 of the laws of marriage. How many are the ways in which 

 questions of comparative nearness of relationship arise, and 

 how important to have a simple and ready means of settling 

 them ! If this table does not classify relationships according 

 to their nearness, it at least provides the means for such a 

 classification. The principles which have to be settled are — 

 Supposing the distance of c to be measured as 1, what ought 

 to be the value assigned to c 1-1 , and what the value to c~ 1+1 ? 

 The former of these makes a relationship collateral, and the 

 latter makes a relationship one of affinity. According to the 

 method of reckoning degrees adopted by the Greek Church 

 (which is very elaborate) c 1-1 is reckoned 2, and c~ 1+1 is 

 reckoned 0. 



These general relationships are broken up into more specific 

 relationships by the introduction of symbols to denote sex. 

 Let a subscript m denote male, a subscript / denote female. 

 Then 



m C~ l denotes father. 



/C~ 1 ,, mother. 



c m " parent of man. 



Cj ,, parent of woman. 



mCm* " father of man. 



m Cf „ father of woman. 



j-C~ l „ mother of man. 



/Cf~ l >> mother of woman 



m C denotes 



son. 



fC „ 



daughter. 



C m » 



child of man. 



Cf „ 



child of woman. 



m C m " 



son of man. 



irfif » 



son of woman. 



/C m " 



daughter of man. 



/C f „ 



daughter of woman 



