380 THE PRINCIPLES OF SCIENCE. 



Natural Constants and Numbers. 



Having acquired accurate measuring instruments, and 

 decided upon the units in which the results shall be 

 estimated and expressed, there remains the question, 

 What use shall be made of our powers of measurement ? 

 Our principal object must be to discover general quanti- 

 tative laws of nature ; but a very large amount of pre- 

 liminary labour is employed in the accurate determination 

 of the dimensions of existing objects, and the numerical 

 relations between diverse forces and phenomena. Step 

 by step every part of the material universe is surveyed 

 and brought into known relations with other parts. Each 

 manifestation of energy is correlated with each other kind 

 of manifestation. Professor Tyndall has described the care 

 with which such operations are conducted b . 



* Those who are unacquainted with the details of 

 scientific investigation, have no idea of the amount of 

 labour expended on the determination of those numbers 

 on which important calculations or inferences depend. 

 They have no idea of the patience shown by a Berzelius 

 in determining atomic weights ; by a Eegnault in deter- 

 mining coefficients of expansion ; or by a Joule in deter- 

 mining the mechanical equivalent of heat. There is a 

 morality brought to bear upon such matters which, in 

 point of severity, is probably without a parallel in any 

 other domain of intellectual action.' 



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 ^ (n 2 n) is the 

 number of ratios which are within our powers of cal- 

 culation, 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 



b Tyndall's 'Sound/ isted. p. 26. 



