126 PROF. W. STANLEY JEVONS ON THE 



results of every form of law which I can find or invent. 

 If in the course of this work I obtain any series of com- 

 binations which had been previously marked off, I learn at 

 once that the law is logically equivalent to some law pre- 

 viously treated. It may be safely inferred that every 

 variety of the apparently new law will coincide in meaning 

 with some variety of the former expression of the same 

 law ; I have sufficiently verified this assumption in some 

 cases, and have never found it lead to error. Thus, just 

 as AB = ABC is equivalent to A.c=hbc, so we find that 

 ab = abC is equivalent to ac = «cB. 



Among the laws treated were the two A = AB and 

 A = B, which involve only two terms, because it may of 

 course happen that among three things two only are in 

 special logical relation, and the third independent ; and the 

 series of combinations representing such cases of relation 

 are sure to occur in the complete enumeration. All single 

 propositions which I could invent having been treated, 

 pairs of propositions were next investigated. Thus we 

 have the relations " all A's are B's, and all B's are C'&," 

 of which the old logical syllogism is the development. 

 We may also have c ' all A's are all B's, and all B's are C's," 

 or even " all A's are all B's, and all B's are all C's." All 

 such premises admit of variations, greater or less in num- 

 ber, the logical distinctness of which can only be deter- 

 mined by trial in detail. Disjunctive propositions, either 

 singly or in pairs, were also treated, but were often found 

 to be equivalent to other propositions of a simpler form ; 

 thus A=B-|-C (the sign •!• standing for the disjunctive 

 conjunction or in an unexclusive sense) is exactly the 

 same in meaning as a=bc. 



This mode of exhaustive trial bears some analogy to that 

 ancient mathematical process called the sieve of Eratos- 

 thenes. Having taken a long series of the natural num- 

 bers, Eratosthenes is said to have calculated out in succes- 



