506 
PROFESSOR JEVONS ON THE MECHANICAL 
the absence of A are unaffected by the statement that A’s are B’s ; they are thus ex- 
cluded from the sphere of meaning of the premise, and their consistency with truth 
cannot be affected by that premise. The middle group contains A-combinations, in- 
cluded within the meaning of the premise, but which also are B-combinations, and 
therefore comply with the condition expressed in the premise. The lowest group con- 
sists of A-combinations also, but such as are distinguished by the absence of B, and 
which are therefore inconsistent with the premise requiring that where A is, there B 
shall be likewise. This analysis would evidently be effected most simply by placing 
the eight combinations of the abecedarium in the middle rank, raising the a’s into a 
higher rank, and then lowering such V s as remain in the middle rank into a lower rank. 
But as we only require in the solution of a problem to eliminate the inconsistent com- 
binations, we must unite again the two upper ranks, and we then have 
Combinations consistent with 
the premise (1) . . . . 
Combinations inconsistent wit 
mise (1) 
24. Supposing we now introduce 1 
B is C, (2) 
;h the pre- 
A 
b 
C 
A 
b 
c 
a 
B 
C 
a 
B 
c 
a 
b 
C 
a 
b 
c 
:he second premise, 
the operations will be exactly similar, with the exception that certain combinations have 
already been eliminated from the abecedarium by the first premise. These contradicted 
combinations may or may not be consistent with the second premise, but in any case 
they cannot be readmitted. Whatever is inconsistent with any one condition, is to .be 
deemed inconsistent throughout the problem. Hence the analysis effected by the 
second premise may be thus represented: — 
f 
i a a 
Combinations excluded from (2) . . Ah 
Combinations included and 
A 
B 
consistent with (2) . . i ] J 
A 
Combinations 
consistent ■{ 
with (1). 
I 
rA a 
Combinations inconsistent with (1) lb b 
C c 
a 
B 
C 
Combinations inconsistent with (2)< B 
C c 
a 
B 
c 
To effect the above classification, we first move down to a lower rank the combinations 
inconsistent with (1) ; we then raise the b’s, and out of the remaining B’s lower the c’s. 
