therefore every possible law which can exist concerning the relation of A and B must be marked by the exclusion of one or more of the above combinations. The number of possible laws then cannot exceed the number of selections which we can make from these four combinations. Since each combination may be present or absent, the number of cases to be considered is 2 × 2 × 2 × 2, or sixteen; and these cases are all shown in the following table, in which the sign 0 indicates absence or non-existence of the combination shown at the left-hand column in the same line, and the mark 1 its presence:-- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 * * * * * * * AB 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 A*b* 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 *a*B 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 *ab* 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 Thus in column sixteen we find that all the conceivable combinations are present, which means that there are no special laws in existence in such a case, and that the combinations are governed only by the universal Laws of Identity and Difference. The example of metals and conductors of electricity would be represented by the twelfth column; and every other mode in which two things or qualities might present themselves is shown in one or other of the columns. More than half the cases may indeed be at once rejected, because they involve the entire absence of a term or its negative. It has been shown to be a logical principle that every term must have its negative (p. 111), and when this is not the case, inconsistency between the conditions of combination must exist. Thus if we laid down the two following propositions, “Graphite conducts electricity,” and “Graphite does not conduct electricity,” it would amount to asserting the impossibility of graphite existing at all; or in general terms, A is B and A is not B result in destroying altogether the combinations containing A, a case shown in the fourth column of the above table. We therefore restrict our attention to those cases which may be represented in natural phenomena when at least two combinations are present, and which correspond to those columns of the table in which each of A, *a*, B, *b* appears. These cases are shown in the columns marked with an asterisk. We find that seven cases remain for examination, thus characterised-- Four cases exhibiting three combinations, Two cases exhibiting two combinations, One case exhibiting four combinations. It has already been pointed out that a proposition of the form A = AB destroys one combination, A*b*, so that this is the form of law applying to the twelfth column. But by changing one or more of the terms in A = AB into its negative, or by interchanging A and B, *a* and *b*, we obtain no less than eight different varieties of the one form; thus--