170 
Proceedings of the Eoyal Society 
The rule for transforming such an equation is : — Any symbol may 
be taken from the front of one side provided its reciprocal be placed 
in front of the other side ; the reciprocal of the qualification m 
being m, and of f being f. For instance, this rule applied to the 
first form of the above equation gives us 
c m A = i (3 c f B + 2cy(7) 
D 
each of three children of B and two children of 0 was a child 
of A. 
m A = c~ 1 ^ (3c f B + 2cfi) 
the man A was the parent of each of, &e., 
4 = „c-ii(3c / B + 2 C/ 0). 
A was the father of each of, &c. 
§ 18. If the sex symbols preceding and succeeding the ex- 
pression c — are the same, the expression may reduce to 1 ; but if 
G 
the sex symbols are different, the expression cannot reduce to 1. 
If the sex symbols preceding and succeeding the expression 
- c are the same, the expression must reduce to 1 ; and if these 
c 
symbols are different the expression cannot reduce to 1. These 
laws apply to all states of society, with the exception that w -c TO does 
not necessarily reduce to 1 in communities where polyandry pre- 
vails. 
Should the transformation of an equation result in bringing mm 
or ff between two relationship elements, as in c mm c, such an expres- 
sion is consistent, and mm is equivalent to m and ff to f • but 
should the transformation result in bringing mf or fm between two 
elements, the expression is contradictory. 
§ 19. Compound terms. — The factors in a compound relation- 
ship are commutative with one another. For example, the rela- 
tionship c m A.c f B is equivalent to the relationship c f B.c m A. In 
