ADDRESS TO THE MATHEMATICAL AND PHYSICAL SECTIONS 



method of directing our attention to those features of phenomena which may 

 be regarded as quantities which brings physical research under the influence of 

 mathematical reasoning. In the work of the Section we shall have abundant 

 examples of the successful application of this method to the most recent con- 

 queets of science; but I wish at present to direct your attention to some of 

 tin- reciprocal effects of the progress of science on those elementary conceptions 

 which are sometimes thought to be beyond the reach of change. 



If the skill of the mathematician has enabled the experimentalist to see 

 that the quantities which he has measured are connected by necessary n Li: 

 the discoveries of physics have revealed to the mathematician new I'mi: 

 quantities which he could never have imagined for himself. 



Of the methods by which the mathematician may make his labours 

 useful to the student of nature, that which I think is at present most im- 

 portant is the systematic classification of quantities. 



The quantities which we study in mathematics and physics may be clas> 

 in two different ways. 



The student who wishes to master any particular science must make hii 

 familiar with the various kinds of quantities which belong to that science. When 

 lie understands all the relations between these quantities, he regards tin: 

 forming a connected system, and he classes the whole system of quantities I 

 as belonging to that particular science. This classification is the most natural 

 from a physical point of view, and it is generally the first in order of time. 



But when the student has become acquainted with several different seic- 

 he finds that the mathematical processes and trains of reasoning in one sc' 

 resemble those in another so much that his knowledge of the one science may 

 be made a most useful help in the study of the other. 



When he examines into the reason of this, he finds that in the t\v<. 

 sciences he has been dealing with systems of quantities, in which the mathe- 

 matical forms of the relations of the quantities are the same in both - 

 though the physical nature of the quantities may be utterly different. 



He is thus led to recognize a classification of quantities on a new principle, 

 according to which the physical nature of the quantity is subordinated t 

 mathematical form. This is the point of view which is characteristic of the 

 mathematician ; but it stands second to the physical aspect in order of time. 

 because the human mind, in order to conceive of different kinds of quant 

 must have them presented to it by nature. 



