I do not think it needful to publish at present the complete table of 193 series of combinations and the premises corresponding to each. Such a table enables us by mere inspection to learn the laws obeyed by any set of combinations of three things, and is to logic what a table of factors and prime numbers is to the theory of numbers, or a table of integrals to the higher mathematics. The table already given (p. 140) would enable a person with but little labour to discover the law of any combinations. If there be seven combinations (one contradicted) the law must be of the eighth type, and the proper variety will be apparent. If there be six combinations (two contradicted), either the second, eleventh, or twelfth type applies, and a certain number of trials will disclose the proper type and variety. If there be but two combinations the law must be of the third type, and so on. The above investigations are complete as regards the possible logical relations of two or three terms. But when we attempt to apply the same kind of method to the relations of four or more terms, the labour becomes impracticably great. Four terms give sixteen combinations compatible with the laws of thought, and the number of possible selections of combinations is no less than 2^{16} or 65,536. The following table shows the extraordinary manner in which the number of possible logical relations increases with the number of terms involved. +---------+-------------+---------------------------------------+ |Number of| Number of |Number of possible selections of combi-| | terms. | possible | nations corresponding to consistent | | |combinations.| or inconsistent logical relations. | +-----------------------+---------------------------------------+ | 2 | 4 | 16 | | 3 | 8 | 256 | | 4 | 16 | 65,536 | | 5 | 32 | 4,294,967,296 | | 6 | 64 | 18,446,744,073,709,551,616 | +---------+-------------+---------------------------------------+ Some years of continuous labour would be required to ascertain the types of laws which may govern the combinations of only four things, and but a small part of such laws would be exemplified or capable of practical application in science. The purely logical inverse problem, whereby we pass from combinations to their laws, is solved in the preceding pages, as far as it is likely to be for a long time to come; and it is almost impossible that it should ever be carried more than a single step further.