of Edinburgh, Session 1880-81. 
165 
with all the daughters of the sons, together with all the daughters 
of the daughters. The relationship can he expanded in other five 
ways by putting m or / after the last c. 
It is not impossible, biologically, for certain individuals who are 
present in the first group of equation (3), that is in % m c m cUy to be 
present also in the second group, that is, in % m CfC U ; and when we 
take the term great-grandchild and expand it in a similar manner 
there is no legal reason (according to the English Law) to prevent 
one and the same individual from appearing in two groups. The 
terms are mutually exclusive in respect of the relations , but not 
necessarily in respect of the individuals in which the relations exist. 
In the same man A there may be two great-grandsons of B. When 
it is necessary to denote the persons in which the relations exist, 
the Greek y may be used instead of the corresponding c. 
§ 7. To find the number of genus-relationships in the n th order. 
The first part of the Table of such relationships is as follows : — 
Order. 
Expression. 
Index Expression. 
Meaning. 
0 
1 
c° 
self 
I 
G 
c 1 
child 
1 
C 
c _1 
parent 
II 
cc 
c 2 
grandchild 
1 
c— 
c 
c 1 - 1 
child of parent 
1 
—c 
c 
C-l+1 
parent of child 
1 1 
c c 
c 2 
grandparent 
It will be observed that the terms for any order are derived from 
those of the preceding order by first prefixing c, and secondly by 
prefixing - before each term. Hence the number of genus terms 
for the ftth order is 2 n . 
§ 8. To find the number of the elementary relationships of the 
n th order. 
The nih. order has 2 W genus-relationships. Consider any one of 
these. A distinction of sex can be introduced before each c or 
