of Edinburgh, Session 1880-81. 
171 
connection with such an expression we have two kinds of 
quantitative symbols, 1st, those of the resultant ; 2d, those of the 
components. Thus in %{c m A.c f B) the compound representative 
term is first formed, and. then the sum taken; whereas in 
'^CnA.'ZcjB the sum of each component is taken separately, and 
then the sums are combined. The results must he identical ; hence 
%{c m A.c f B) = 'Zc m A.%c f B. The % of the resultant is conditioned by 
the S’s of the components in the following manner : — It cannot 
he greater than either of them ; it cannot be less than their sum 
minus the 2 of % U ; and it cannot be less than 0. 
§ 20. Let r denote any relationship, and p an individual in 
which such a relationship exists (§ 6), then 
U— + r + r + * . . + r } bJ ; 
where the degree-index 1 denotes that the genus relationship occurs 
once and once only in the person ; 2, that it occurs twice and twice 
only, and n that it occurs as often as is physically possible. For 
example, 
y ( e c ) 
that is, the brothers and sisters of any person are identical with the 
half-brothers and sisters, together with the full-brothers and sisters. 
Again, 
V^=sj-^‘ + -/\ u-, 
= 2?V, 
in all countries where the marriage of brother and sister is pro- 
hibited. 
This notation gives us the degree-index 0 as the proper symbol to 
express the negative particle non ; for it means that the kind of 
relationship in question is not found at all in the person. 
— ,0 
c 
A expresses all the non-brothers and non-sisters of A to be 
