504 
PROFESSOR JEVONS ON THE MECHANICAL 
All the classes of things which can possibly exist will be represented by an appropriate 
selection from this list ; B will consist of (a), (j3), (s) and (Q ; C will consist of (a), 
(y), (g) and (y) ; B C will consist of the combinations common to these classes, as (a) 
and (g ) ; and so on. If we wish, then, to effect a complete solution of a logical problem, 
it will save much labour to make out in the first place the complete development of 
combinations, to examine each of these in connexion with the premises, to eliminate the 
inconsistent combinations, and afterwards to select from the remaining consistent com- 
binations such as may form any class of which we desire the description. Performing 
these processes in the case of the premises (1) and (2), we find that of the eight con- 
ceivable combinations only four remain consistent with the premises, viz. : — 
ABC (a) 
a B C (g ) 
a b C (O 
ale (6) 
In this list of combinations the conditions (1) and (2) are, as it were, embodied and 
expressed, so that we at once learn that A according to those conditions consists of 
ABC only ; 
B consists of (a) or (a) 
0 » » 00 or ( 6 ) 
c „ „ 00 
« „ „ («)> 00 or ( 6 )- 
20. It is easily seen that the solution of every problem which involves three terms 
A, B, C will consist in making a similar selection of consistent combinations from the 
same series of eight conceivable combinations. Problems involving four distinct terms 
would similarly require a series of sixteen conceivable combinations, and if five or six 
terms enter, there will be thirty-two or sixty-four of such combinations. These series of 
combinations appear to hold a position in logical science at least as important as that of 
the multiplication table in arithmetic or the coefficients of the binomial theorem in the 
higher parts of mathematics. I propose to call any such complete series of combinations 
a Logical Abecedarium , but the number of combinations increases so rapidly with the 
number of separate terms that I have not found it convenient to go beyond the sixty- 
four combinations of the six terms A, B, C, D, E, F and their negatives. 
21. To a person who has once comprehended the extreme significance and utility of 
the Logical Abecedarium, the whole indirect process of inference becomes reduced to the 
repetition of a few uniform operations of classification, selection, and elimination of con- 
tradictories. Logical deduction becomes, in short, a matter of routine, and the amount 
of labour required the only impediment to the solution of any question. I have directed 
much attention, therefore, to reduce the labour required, and have in previous publi- 
cations described devices which partially accomplish this purpose. The Logical Slate 
consists of the complete Abecedarium engraved upon a common writing slate, and merely 
