164 
Proceedings of the Boycd Society 
§ 5. We evidently have 
2cU=2 m cU+ S/jCT, 
that is, all the children of any person are identical with all the sons 
of that person, together with all the daughters of that person. 
This equation may be written — 
^cU=^ m+f cU . . . ( 1 ), 
similarly 
%cTJ='%c m+f U . . . ( 2 ), 
and 
’2 t cU='% m+ fC m+ fU . . , ( 3 ). 
We also have 
Sc 
that is, all the parents of a person are identical with all the fathers 
of the person, together with all the mothers.. Here 2 on the left- 
hand side has the value 2, and in each case on the right-hand side 
the value 1. 
The equation may be written 
Sc'V=S„ +/ c' 1 ^ . 
• • (4). 
Also 
2c" 1 t/' = Sc" 1 „ +/ ?7 . 
• • (5), 
and 
s c- 1 u=s m+jC -\ +f u 
• • (6). 
§ 6. Let 
us consider a genus-relationship of 
the second order, 
such as grandchild. We have 
• 
%ccU = %( m cc + f cc) U . 
• • (i), 
= + CfC)U 
• • (2), 
= t{ m C m C + m CfC +fC m C +jCfC) U 
• • (3). 
Equation (1) expresses that all the grandchildren of a person 
are identical with all the grandsons of the person, together with all 
the granddaughters of the person. Equation (2) expresses that the 
same are identical with all the children of the sons of the person 
together with all the children of the daughters of that person ; 
and equation (3) expresses that they are identical with all the sons 
of the sons, together with all the sons of the daughters, together 
