Every new natural constant which is recorded brings many fresh inferences within our power. For if *n* be the number of such constants known, then 1/2 (*n*^{2}--*n*) is the number of ratios which are within our powers of calculation, and this increases with the square of *n*. We thus gradually piece together a map of nature, in which the lines of inference from one phenomenon to another rapidly grow in complexity, and the powers of scientific prediction are correspondingly augmented. Babbage[230] proposed the formation of a collection of the constant numbers of nature, a work which has at last been taken in hand by the Smithsonian Institution.[231] It is true that a complete collection of such numbers would be almost co-extensive with scientific literature, since almost all the numbers occurring in works on chemistry, mineralogy, physics, astronomy, &c., would have to be included. Still a handy volume giving all the more important numbers and their logarithms, referred when requisite to the different units in common use, would be very useful. A small collection of constant numbers will be found at the end of Babbage’s, Hutton’s, and many other tables of logarithms, and a somewhat larger collection is given in Templeton’s *Millwright and Engineer’s Pocket Companion*. [230] British Association, Cambridge, 1833. Report, pp. 484–490. [231] *Smithsonian Miscellaneous Collections*, vol. xii., the Constants of Nature, part. i. Specific gravities compiled by F. W. Clarke, 8vo. Washington, 1873. Our present object will be to classify these constant numbers roughly, according to their comparative generality and importance, under the following heads:-- (1) Mathematical constants. (2) Physical constants. (3) Astronomical constants. (4) Terrestrial numbers. (5) Organic numbers. (6) Social numbers. *Mathematical Constants.* At the head of the list of natural constants must come those which express the necessary relations of numbers to each other. The ordinary Multiplication Table is the most familiar and the most important of such series of constants, and is, theoretically speaking, infinite in extent. Next we must place the Arithmetical Triangle, the significance of which has already been pointed out (p. 182). Tables of logarithms also contain vast series of natural constants, arising out of the relations of pure numbers. At the base of all logarithmic theory is the mysterious natural constant commonly denoted by *e*, or ε, being equal to the infinite series 1 + 1/1 + 1/1.2 + 1/1.2.3 + 1/1.2.3.4 +...., and thus consisting of the sum of the ratios between the numbers of permutations and combinations of 0, 1, 2, 3, 4, &c. things. Tables of prime numbers and of the factors of composite numbers must not be forgotten.