OCTOBKE 25, 1912] 



SCIENCE 



559 



THE SYMBOLIC STATEMENT OF RELATIONSHIPS 



The simplest way in whicli to state the re- 

 lationship of two persons symbolically is to 

 denote each by a number indicating the 

 number of generations since the nearest com.- 

 mon ancestor (counting that ancestor as one) 

 and to write the numbers with a sign of re- 

 lationship between them, that one being 

 placed first whose relationship is to be ex- 

 pressed. A convenient and appropriate sym- 

 bol of relationship is the ratio sign [:]. 

 Thus the relationship of parent would be 1:2, 

 of child 2 : 1. Here and elsewhere in this 

 paper a person is regarded as his own ances- 

 tor, bearing to himseK a relationship of 

 identity [1:1]. The relationship of grand- 

 parent would be 1:3, of grandchild, 3:1, of 

 great-grandparent, 1 : 4, and so on. That of 

 brother or sister would be 2:2, of own-cousin 

 3:3, of second cousin 4 : 4, etc., the degree of 

 cousinship being found by subtracting two 

 from the symbol. The relationship of uncle 

 or aunt would be 2 : 3, of niece or nephew 3 : 2, 

 of great-uncle or aunt 2 : 4, and so on. This 

 method also discriminates between relation- 

 ships for which we have no separate names; 

 thus we speak of a " first cousin once re- 

 moved," whether we mean the older or 

 younger of the two. The former would be 

 symbolically, 3 : 4 and the latter 4 : 3. Like- 

 wise a third cousin four times removed would 

 be 5:9 or 9:5. These are evidently as dif- 

 ferent relationships as parent and child or 

 uncle and niece. 



Suppose now we desire to take sex into ac- 

 count, as we do in our names when we dis- 

 tinguish between sister and brother or uncle 

 and aunt. When we do thus distinguish we 

 take account only of the sex of the person 

 whose relationship is being stated. A male 

 person is a brother alike to a male or female 

 child of the same parents. A man is an uncle 

 and a woman an aunt, no matter whether 

 nephews or nieces are in question. In cousin- 

 ships we do not consider sex at all in naming 

 the relationships. We can do as much as this 

 by attaching a sex initial (M for male and F 

 for female) to the first number in the symbol, 



thus: 2(M):3 (uncle); 2(F): 3 (aunt); 

 3(M):2 (nephew); 3(F): 2 (niece). 



But we may go further than our ordinary 

 nomenclature and say 2(M):3(M) (the rela- 

 tion of uncle to nephew), 1(M):3(F) (rela- 

 tion of grandfather to granddaughter), etc. 



Furthermore, we may, if desired, substitute 

 for each number a series of sex-initials giving 

 the line of descent in each case, and thus ex- 

 pressing facts that would require many sen- 

 tences if we were to attempt to put them 

 into words. Thus the following all express 

 the relation of an elder to a younger second 

 cousin once removed, the lines of descent by 

 sex being different in the various cases 



MMMM : MMMMM 



MFMF : MMFFF 



FFFM : FMMMF 



etc. etc. 



The first letters, since they denote the com- 

 mon ancestor, will in all cases be the same. 



Hitherto no distinction has been made be- 

 tween relationship of the whole or of the haK 

 blood. Thus, in the first formula just above 

 the common ancestor is a man, and there is 

 no effort to tell whether or not the descent 

 is through the same or different mothers. If 

 it is desired to emphasize the fact that the 

 relationship is of the whole blood the two 

 letters (MF) may be used together when 

 necessary. Thus, (MF)M: (MF)F is the re- 

 lationship of own brother and sister, while 

 FM : FF would be that of half brother and 

 sister on the mother's side. Generally it will 

 be necessary to make this distinction only in 

 the case of the common ancestor. Intermar- 

 riages in the line, causing double relation- 

 ships, introduce complexity. The only way to 

 denote these is to make a symbol for each re- 

 lationship separately and join them by a plus 

 sign. In very complicated cases the symbol 

 ceases to be an abbreviation and the dia- 

 gram is clearer. 



Suppose that a brother and sister marry a 

 brother and sister, so that their children are 

 double cousins. The relationship, if those 

 children are boys, is: 



[(mf)Mm:: (mf)fm] -f [(mf)fm: (mf)mm:]. 



