230 
Proceedings of the Royal Society 
23. The notation I have framed is of great use in showing the 
ambiguities of the common terms of relationship. Thus uncle may 
may mean any one of eight things, or a combination of these. For 
example — 
Uncle and Nephew. 
1 1 
s-,— — 
S % 
1 1 
cr i — — 
°4 S 2 
1 1 
X <T 2 
l_ 1_ 
X -2 
Uncle and Niece. 
1 1 
s i s y 
*4 a 2 
J_ 1_ 
1 cr 4 
1_ 1_ 
X S 2 
1 I 
H S 2 
The relationships bracketed together generally coexist. 
24. To prove that 
s always = 1 
Let A = -sB, 
s ’ 
then sA = sB. 
But that is morally, if not physiologically, impossible unless A = B , 
- 5 = 1 . 
Similarly -<r = 1 . 
Observation . — Neither pernor can be equal to 1. 
25. To express that 
A is the brother of the brother of B. 
The expressions for brother are — 
1111 
half-brother s - , 
s 1 
s d’ 
( 1 1 
i / M 
\*s 1 
. J'sl 
\ 1 1 
j <T 
1 l 0- 8 J 
l o- ) 
and full brother 
Hence brother of brother is denoted by 
(i) 
i i i 
i i i 
S~ 8- = S- 
S S S 
( 2 ) 
5 - 85 = S-j 
s d d 
°v 
(Art. 24) 
