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Proceedings of the Royal Society 
found within the community of persons considered. Hence we 
have the following identity : — 
3 £ 7 = 3 1 f + r + r 4 - . . . + r \^‘ 
For example, 
t £7=3 \ 1 1 1 U 
“ l - c c + + - c « J 
that is, all the men are identical with all the non-brothers of A, 
together with all the half-brothers of A, together with all the full- 
brothers of A. The equation can also be written in the form 
o o i o — o i 
11 11 1 1 
mPm, ~ m C / g d" m C m ^ m C f ^ + m C m ^ m Cy ^ 
~ t \ r 1 } 
+ m C m c ' ™ C f c J 
which agrees with the Boolian form of development. 
§ 21. The biological law that a person cannot be his or her 
own descendant is expressed by the equation 1 ‘c n A = 0, where n 
denotes any integer from 1 upwards, and A denotes any person. 
The reciprocal aspect of this truth is that l'c~*A = 0, that is, a 
person cannot be his or her own ancestor. The most general state- 
ment of the law is 3 c m .c~ n A = 0, provided m and n are not both 0. 
This equation denies the possibility of the transmigration of souls, 
if A be considered to denote the identity of soul without necessary 
continuity of body. 
§ 22. The effect of the laws of marriage of a nation is to annul 
within that nation certain compound relationships of the second 
degree. For example, = 0, whoever A is. This means 
that the children of any man A who are also children of any 
daughter of the man A are none. Since A may be any man, sub- 
stitute instead m - f B; the equation then becomes 
c 
% C M = 0 
2 ,17 
= S { 
