OF LOGICAL CLASS-FREQXTENCIES, ETC. 
107 
Table T.— Number of Conditions of Consistence for a Congruence of the mih deg-ree 
O O 
and {m — l)th order; specifying separately the number involving 3, 5, 7, or 9 
(m — l)tli order terms. 
Degree of congruence = 
m. 
Terms involved (= c). 
3. 
4. 
5. 
G. 
7. 
8. 
9 
Inferior congruence, 1 
12 
32 
80 
192 
448 
1024 
2304 
3 
4 
32 
160 
640 
2240 
7168 
21504 
5 
— 
— 
16 
192 
1344 
7168 
32256 
7 
— 
— 
— 
— 
64 
1024 
9216 
9 
— 
— 
— 
— 
— 
— 
256 
Total superior congruence only . 
4 
32 
176 
832 
3648 
15360 
63232 
Grand total. 
16 
64 
256 
1024 
4096 
16384 
65536 
The whole number of conditions for a congruence of the nth order and ndh 
degree is 
22 « _ 
?»(■/« — l)(/n. — 2) . . . {m — n) 
(n + 1)! 
viz., the number of conditions for a congruence of order n, degree (n +1), multiplied 
by the numljer of (n + l)th degree cozigruences into which the znth-degree con¬ 
gruence can be resolved. The actual figures are— 
Table II.—Whole Number of Conditions of Consistence for a Congruence of degree 
O G 
m order n. 
Degree of congruence = 
m. 
Order of congruence = n. 
i 
i 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
1 
2 
16 
64 
160 
320 
560 
896 
1344 
1 3 
64 
320 
960 
2240 
4480 
8064 
4 
256 
1536 
5376 
14336 
32256 
5 
1024 
7168 
28672 
86016 
i 
4096 
32768 
147456 
i 7 
16384 
147456 
8 
65536 
