2 REPORT 1870. 



collision, or grapple in yet more fierce embrace, building up in secret the forms of 

 visible things. I have been guided by Prof. Sylvester to-wards those serene heights 



" Where never creeps a cloud, or moves a wind, 

 Nor ever falls the least white star of snow. 

 Nor ever lowest roll of thunder moans, 

 Nor sound of human sorrow mounts, to mar 

 Their sacred everlasting cahn." 



But who will lead me into that still more hidden and dimmer region where 

 Thought weds Fact, where the mental operation of the mathematician and the 

 physical action of the molecules are seen in their true relation ? Does not the way 

 to it pass through the very den of the metaphysician, strewed with the remains of 

 former explorers, and abhorred by every man of science ? It would indeed be a 

 foolhardy adventure for me to take up the valuable time of the Section by leading 

 you into those speculations which require, as we know, thousands of years even to 

 shape themselves intelligibly. 



But we are met as ctdtivators of mathematics and physics. In our daily work 

 we are led up to questions the same in kind with those of metaphysics ; and wo 

 approach them, not trusting to the native penetrating power of our own minds, but 

 trained by a long-continued adjustment of om- modes of thought to the facts of 

 external natiu'e. 



As mathematicians, we perform certain mental operations on the symbols of 

 nimiber or of quantity, and, by proceeding step by step from more simple to more 

 complex operations, we are enabled to express the same thing in many 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 mathema- 

 tician, who by long practice has acquired a familiarity with many of these forms, 

 and has become expert in the processes which lead fi-om 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 theii* relations. Every natural phenomenon is, to 

 cm" 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 featiires 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 demee 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 im- 

 portance, 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 formation of 

 language, and are going on still. No doubt the featm-o which strikes us first and 

 most forcibly in any phenomenon, is the pleasure or the pain which accompanies 

 it, and the agreeable or disagi'eeable results which follow after it. A theory of 

 nature from this point of view is embodied in many of our M'ords 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 un- 

 derstand the nature of things, the)' must begin by asking, not whether a thing is 

 good or bad, noxious or beneficial, but of what kind is it r 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 deAeloped, 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 thiis obtained. It is this scientific method of directing 

 our attention to those features of phenomena which may be regarded as quantities 

 which brings physical research imder the influence of mathematical reasoning. In 



