438 Dr. Macfarlane's Analysis of Relationships, 



pressions c 1_1 and c~ 1 * 1 may or may not reduce to c°, which 

 means self. 



Relationships expressed in terms of c and c~ l take no account 

 of distinctions due to difference of sex ; they may therefore be 

 called general relationships, in contrast to the specific relation- 

 ships into which they are broken up by the introduction of 

 distinctions of sex. Let the order of any general relationship 

 be defined as the number of times c enters into its expression, 

 whether directly or inversely. The relationships of the 

 (n + l)th order are derived from those of the nth order by 

 prefixing c and c~ l before each of the latter. In the case of 

 the first order c and c~ l are applied to 1. Hence, in order to 

 obtain all the relationships of the nth order, we have merely 

 to expand (c + c -1 ) n , but in such a manner that the order of 

 the factors in each term is preserved. It is evident from the 

 mode of development, that the number of general relationships 

 in the nth order is 2". Appended is the first portion of the 

 development. 



General Relationships, 



Order 



Expression. 



Meaning, if reducible. 



Meaning, if irreducible. 





 I. 



II. 



0». 



ci-i. 





Self. 



Child. 



Parent. 



Grandchild. 



Brother or sister. 









Child of parent. 





0-1+1. 



Parent of child. 



Consort. 





0-2. 





Grandparent. 



III. 



03. 





Greatgrandchild. 

 Nephew or niece. 





02—1. 



Grandchild of parent. 





01-1+1. 



Child of parent of child. 



Step-child. 





0l— 2. 



Child of grandparent. 



Uncle or aunt. 





0-1+2. 



Parent of grandchild. 



Child-in-law. 





0— 1 + 1-1. 



Parent of child of parent. 



Step-parent. 





0-8+1. 



Grandparent of child. 



Parent-in-law. 





0-3. 





Greatgrandparent. 



IV. 



0*. 





Greatgr eatgr andchild . 

 Grandnephew or grandniece. 





03-1. 



Greatgrandchild of parent. 





02-1+1. 



Grandchild of parent of child. 



Child of step-child. 





02-2. 



Grandchild of grandparent. 



First cousin. 





01-1+2. 



Child of parent of grandchild. 



Child of child-in-law. 





01-1+1-1. 



Child of parent of child of parent. 



Step-brother or step-sister. 





01-2 + 1. 



Child of grandparent of child. 



Brother-in-law or sister-in-law. 





01-3. 



Child of greatgrandparent. 



Granduncle or grandaunt. 





C-l+3. 



Parent of greatgrandchild. 



Consort of grandchild. 





C- 1+2-1. 



Parent of grandchild of parent. 



Consort of brother or sister. 





0-1 + 1-1+1 



Parent of child of parent of child. 



Consort of consort. 





e-1+1-2. 



Parent of child of grandparent. 



Step-grandparent. 





C-2 + 2. 



Grandparent of grandchild. 



Parent of child-in-law. 





0—2+1-1. 



Grandparent of child of parent. 



Parent-in-law of parent. 





0-3+1. 



Greatgrandparent of child. 



Grandparent of consort. 





0-4. 





Greatgreatgranclparent. 



