163 
of Edinburgh, Session 1880-81. 
of A, two children of A, three children of A, and so on. These 
may he called partial or indefinite numbers, as the first corresponds 
to the indefinite article. 
Second. A dot placed over a number may he used to express that 
it is the complete number ; as \cA the only child of A, 2cA the 
two children of A. These may he called complete or definite 
numbers as they involve the definite article in their meaning. 
Third. The proper mathematical expression for the eldest child 
of A will he c Y A, for the second c 2 A, and so on. 
When there is no quantitative symbol attached to c , the particle 
any is to be understood. 
§ 3. There are in all four kinds of fundamental relationships. 
Of these I have already discussed the set of four s, cr, d , 8, 
denoting respectively the relationship of a man to his father, of a 
man to his mother, of a woman to her father, and of a woman to 
her mother; and also the set of two c, y, denoting respectively the 
relationship of a person to his or her father, and of a person to his 
or her mother. There is another set of two, namely, the relation- 
ship of a man to his parent, and of a woman to her parent ; and 
there is finally the relationship of greatest generality, child of a 
person , which is the relationship obtained by considering c and y 
as equivalent (Part II. p. 8). Each of these relationships has its 
appropriate reciprocal. 
§ 4. Let c be used to denote the relationship of child , , then 
c~ l denotes parent. These symbols, together with m and / to 
express male and female , suffice to express the other fundamental 
relationships, and consequently (with the aid of auxiliary symbols) 
any relationship whatever. Thus 
m c denotes son of a person 
c- 1 
m 
denotes 
father of a person 
/ 
PP 
daughter of a person 
r -l 
/ 
P 1 
mother of a person 
P P 
child of a man 
c- 1 
m 
PP 
parent of a man 
c / 
P P 
child of a woman 
c -i 
f 
P9 
parent of a woman 
r* 
mm 
99 
son of a man 
C - 1 
in m 
PP 
father of a man 
m C f 
P P 
son of a woman 
cfi 
in f 
PP 
father of a woman 
f C m 
pp 
daughter of a man 
/- 1 
/ m 
P P 
mother of a man 
S c f 
pp 
daughter of a woman 
c - 1 
ff 
P 9 
mother of a woman 
