128 
ME. Ct. UDNY yule on THE THEORY OF CONSISTENCE 
positively associated. Either inference would be quite incorrect. Let us proceed to 
discuss the conditions of consistence. 
§ 34. We have shown (§ 8) that a congruence of the fourth degree and second 
order is self-consistent when the conditions of consistence hold for each of the four 
congruences of the third degree into which it may he resolved. These conditions 
are as follows in the present instance ; writing for brevity 
Xy — (AB)/('?t) x., = (AC)/(i() = (AD)/(w) 
X, = ('BC)/(!0 X, = (BD)/(») a:, = (CD)/(rO. 
Congruence. 
ABC 
ABI) 
1. Boys. 
x^ = 0 
aj = 
0 
o 
11 
A 
a^ = 0*0878 
ao = 
0*0285 
x^ z= 0*0285 
(^1 “h ^3 ~h ^4 
= — 
0*7752) 
/v* 1 ryt _ /v* 
*-^4, 
z= 
0 0878 
a'l — a^ A -A 
= 
0*1085 
a‘2 ~p A ^4 
z= 
0*0285 
a^ = 0 
a’g = 
0 
ag = 0 
x^ = 0*0878 
0*0789 
ag = 0*0789 
(a + •'*3 + ^0 
=i — 
0*7248) 
x^ —p ay — a^ 
= 
0*0878 
" ^3 + ^0 
0*1085 
+ a’s + 
= 
0*0789 
AC I ) x,2 =0 u’g = 0 ;rg =0 
aq = 0'0285 x^ = 0'0789 x^ = 0’0285 
(aq x^ Xq = 0'8051) 
cco -f- aq — X(^ = 0*0875 
x^ — Xg -p a,. = 0*0285 
— Xo -p ^3 + Xg == 0*0789 
BCl) a I =0 ~ 
aq = 0*0285 an = 0*0789 a^ = 0*0285 
(ai, + X- + ag = — 0*7841) 
(a.^ + ag — ag = 0-1085) 
a^. — ay + ay = 0*0285 
— x^ -p X- -p ag — 0*0/ 89. 
Congruence. II. Girls. 
ABC = 0 a^ = 0 .a^ = 0 
x■^ = 0*0682 .To = 0*0325 a^^, = 0*0325 
(a^ + ao -P a^, = — 0*8142) 
A >ro — ' A = 0*068*2 
a, — .Bo A ^^4 = 0*0850 
— aj A d“ ^4 “ 0 0325 
