UNITS AND STANDARDS OF MEASUREMENT. 381 



rapidly grow in complexity, and the powers of scientific 

 prediction are correspondingly augmented. 



The late Mr. Babbage c proposed the formation of a 

 complete collection of all the constant numbers of nature ; 

 but such a collection would be almost coextensive with 

 the whole mass of scientific literature. Almost all numbers 

 occurring in works on Chemistry, Mineralogy, Physics, 

 Astronomy, &c. are natural constants, and it would be 

 impracticable to give in any one work more than a 

 selection of the more important numbers. 



Our present object will be to classify these constant 

 numbers roughly, according to their comparative gener- 

 ality 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 sig- 

 nificance of which has already been pointed out (p. 206.) 

 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, e, or e, being 



equal to the infinite series t + - H h 1- 1- . . 



i 1.2 1.2.3 1-2.3.4 



c British Association, Cambridge, 1833. Report, pp. 484-490. 



