of Edinburgh, Session 1880 - 81 . 
7 
The relationship cc may be denoted without ambiguity by c 2 , 
and - by c _1 ; and generally an index may be used to denote the 
number of times c or y is repeated, whether directly or inversely. 
The meaning of each of the permutations of the four symbals c, y, 
c -1 , y _1 two together, with one another, and with themselves, is given 
in Table II. (p. 12.) In the first row we have the different species of 
grandchildren. In the second row we have c Y ~ l A and y 1-1 A, which 
denote respectively the children of the father of A, and the children 
of the mother of A ; hence the two species of brothers and sisters, 
the origin being included as a special case. We have also cy~ l A and 
y c~ 1 A, which denote the children by male descent of the mother of 
A, and the children by female descent of the father of A ; each of 
which must always have the value 0, on account of the monoecious 
nature of mankind. Any term in which either cy -1 or yc' 1 occurs 
whether singly or in combination has the value 0, on account of the 
morphological law referred to. In the third row we have c~ 1+1 A 
and y“ 1+1 Z?, which denote respectively the father of the children of 
the man A, and the mother of the children of the woman B ; they 
are therefore equivalent to A and to B. Of the other two terms c~ l yB 
denotes the fathers of the children of the woman B, and y~ l cA denotes 
the mothers of the children of the man A. Thus the terms of this 
row break up into two groups denoted respectively by consorts and 
self The terms belonging to the latter group are enclosed. In the 
fourth row we have the expressions for the grandparents. 
In Table III. I have written out all the terms which are expressed 
by three symbols, omitting those which are null from containing 
cy -1 or yc -1 . The terms in the first row are the terms of the ex- 
pansion of (c + y) 3 ; those in the second row of (c + y ) 2 ^ ^ ; those 
in the third of (c + y) ^- + (c + y), and so on. The method of 
deriving the terms is evidently exhaustive, and it supplies us not 
only with a means of denoting all possible relationships, but also of 
classifying them in a scientific manner. It will be convenient to 
have words to denote the different classes and sub-classes, and for 
this purpose I propose to employ the classificatory terms — Order, 
Genus, Species, Variety. By the order of a relationship I mean 
the number of symbols required to express it ; for example, those of 
