MATHEMATICS AND PHYSICAL SCIENCE 87 



opinion as to the precise scope and conditions of 

 validity of the processes adopted by Biometricians, 

 it is practically certain that their methods will, 

 in some degree, form a permanent part of the stock 

 of implements employed by biological investigators. 

 In Economic Science also mathematical methods 

 have recently attained to a considerable and in- 

 creasing prominence. 



It is a very common misconception to suppose 

 that the sole function of Mathematics in relation 

 to various departments of Physical Science is that 

 of providing the means of carrying out whatever 

 calculations may be necessary; and thus that 

 Mathematics plays in these sciences a comparatively 

 humble part analogous to that of a mechanical 

 tool. As a matter of fact mathematical thinking 

 has done very much more than merely to provide 

 methods of calculating; it has often played a 

 dominant part in the formation of the concepts 

 with which the Physical Sciences work; it has 

 decided in many cases for them not only how to 

 calculate but what the things are that they ought 

 to calculate; it has reduced the originally vague 

 conceptions which arise in connection with physical 

 observation to precise forms in which they can be 

 exhibited as measurable quantities. Some of these 

 concepts could only have been definitely formulated 

 as the result of a long train of previous mathe- 

 matical development. For example, the conception 

 of Energy as a measurable quantity, and the exact 



