OF THE BRITISH ASSOCIATION. 217 



different forms. The equivalence of these different forms, though a necessary 

 consequence of self-evident axioms, is not always, to our minds, self-evident; 

 but the mathematician, who by long practice has acquired a familiarity with 

 many of these forms, and has become expert in the processes which lead from 

 one to another, can often transform a perplexing expression into another which 

 explains its meaning in more intelligible language. 



As students of Physics we observe phenomena under varied circumstances, 

 and endeavour to deduce the laws of their relations. Every natural phenomenon 

 is, to our minds, the result of an infinitely complex system of conditions. 

 What we set ourselves to do is to unravel these conditions, and by viewing 

 the phenomenon in a way which is in itself partial and imperfect, to piece 

 out its features one by one, beginning with that which strikes us first, and 

 thus gradually learning how to look at the whole phenomenon so as to obtain 

 a continually greater degree of clearness and distinctness. In this process, the 

 feature which presents itself most forcibly to the untrained inquirer may not be 

 that which is considered most fundamental by the experienced man of science ; 

 for the success of any physical investigation depends on the judicious selection 

 of what is to be observed as of primary importance, combined with a voluntary 

 abstraction of the mind from those features which, however attractive they 

 appear, we are not yet sufficiently advanced in science to investigate with profit. 



Intellectual processes of this kind have been going on since the first for- 

 mation of language, and are going on still. No doubt the feature which strikes 

 us first and most forcibly in any phenomenon, is the pleasure or the pain 

 which accompanies it, and the agreeable or disagreeable results which follow 

 after it. A theory of nature from this point of view is embodied in many of 

 our words and phrases, and is by no means extinct even in our deliberate 

 opinions. 



It was a great step in science when men became convinced that, in order 

 to understand the nature of things, they must begin by asking, not whether 

 a thing is good or bad, noxious or beneficial, but of what kind is it ? and 

 how much is there of it ? Quality and Quantity were then first recognized as 

 the primary features to be observed in scientific inquiry. 



As science has been developed, the domain of quantity has everywhere 

 encroached on that of quality, till the process of scientific inquiry seems to have 

 become simply the measurement and registration of quantities, combined with 

 a mathematical discussion of the numbers thus obtained. It is this scientific 



VOL. II. 28 



