216 ADDRESS TO THE MATHEMATICAL AND PHYSICAL SECTIONS 



cm three other* in contact) to build up the Ideal Pyramid is a discourse on 

 the Relation of the two branches (Mathematics and Physics) to, their act inn 

 and reaction upon, one another, a magnificent theme, with which it is to be 

 hoped that some future President of Section A will crown the edifice and make 

 the Tetralogy (symbolizable by A + A', A, A', AA') complete." 



The theme thus distinctly kid down for his successor by our late Presi 

 IB indeed a magnificent one, far too magnificent for any efforts of mine to 

 realize. I have endeavoured to follow Mr Spottiswoode, as with far-reaching 

 vision he distinguishes the systems of science into which phenomena, our k: 

 ledge of which is still in the nebulous stage, are growing. I have been carried 

 by the penetrating insight and forcible expression of Dr Tyndall into that 

 sanctuary of minuteness and of power where molecules obey the laws of their 

 \istence, clash together in fierce collision, or grapple in yet more fierce embrace, 

 building up in secret the forms of visible things. I have been guided by Prof. 

 Sylvester towards 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 calm." 



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 cultivators of mathematics and physics. In our daily 

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

 and we approach them, not trusting to the native penetrating power of our 

 own minds, but trained by a long- continued adjustment of our modes of thought 

 to the facts of external nature. 



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

 number 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 



