382 THE PRINCIPLES OF SCIENCE. 



and thus consisting of the sum of the ratios between the 

 numbers of permutations and combinations of o, i, 2, 3, 4, 

 &c. things. 



Tables of prime numbers and of the factors of composite 

 numbers must not be forgotten. 



Another vast and in fact infinite series of numerical 

 constants contains those connected with the measure- 

 ment of angles, and embodied in trigonometrical tables, 

 whether as natural or logarithmic sines, cosines, and 

 tangents. It should never be forgotten that though 

 these numbers find their chief employment in connexion 

 with trigonometry, or the measurement of the sides of a 

 right-angled triangle, yet the numbers themselves arise 

 out of simple numerical relations bearing no special rela- 

 tion to space. 



Foremost among trigonometrical constants is the well 

 known number it, usually employed as expressing the 

 ratio of the circumference and the diameter of a circle ; 

 from TT follows the value of the arcual or natural unit 

 of angular value as expressed in ordinary degrees (see 



p. 358). 



Among other mathematical constants not uncommonly 

 used may be mentioned tables of factorials (p. 202), tables 

 of Bernouilli's numbers, tables of the error function 41 , 

 which latter are indispensable not only in the theory of 

 probability but also in several other branches of science. 



It should also be clearly understood that the mathe- 

 matical constants and tables of reference already in our 

 possession, although very extensive, are only an infinitely 

 small part of what might be formed. With the progress 

 of science the tabulation of new functions will be con- 

 tinually demanded, and it is worthy of consideration 

 whether public money should not be constantly available 



d See J. W. L. Glaisher, ' Philosophical Magazine,' 4th Series, vol. xlii. 

 p. 421. 



