ADDRESS TO THE MATHEMATICAL AND PHYSICAL SECTIONS 



relation. The mental image of the concrete reality seems rather to disturb 

 thnn to assist their contemplations. 



But the great majority of mankind are utterly unable, without long 

 training, to retain in their minds the unembodied symbols of the pure mathe- 

 matician, so that, if science is ever to become popular, and yet remain scientific, 

 it must be by a profound study and a copious application of those principles 

 of the mathematical classification of quantities which, as we have seen, lie at 

 the root of every truly scientific illustration. 



There are, as I have said, some minds which can go on contemplating with 

 satisfaction pure quantities presented to the eye by symbols, and to the mind 

 in a form which none but mathematicians can conceive. 



There are others who feel more enjoyment in following geometrical forms, 

 which they draw on paper, or build up in the empty space before them. 



Others, again, are not content unless they can project their whole physical 

 energies into the scene which they conjure up. They learn at what a rate the 

 planets rush through space, and they experience a delightful feeling of exhila- 

 ration. They calculate the forces with which the heavenly bodies pull at one 

 another, and they feel their own muscles straining with the effort. 



To such men momentum, energy, mass are not mere abstract expressions 

 of the results of scientific inquiry. They are words of power, which stir their 

 souls like the memories of childhood. 



For the sake of persons of these different types, scientific truth should be 

 presented in different forms, and should be regarded as equally scientific, whether 

 it appears in the robust form and the vivid colouring of a physical illustration, 

 or in the tenuity and paleness of a symbolical expression. 



Time would fail me if I were to attempt to illustrate by examples the 

 scientific value of the classification of quantities. I shall only mention the name 

 of that important class of magnitudes having direction in space which Hamilton 

 has called vectors, and which form the subject-matter of the Calculus of Qua- 

 ternions, a branch of mathematics which, when it shall have been thoroughly 

 understood by men of the illustrative type, and clothed by them with physical 

 imagery, will become, perhaps under some new name, a most powerful method 

 of communicating truly scientific knowledge to persons apparently devoid of the 

 calculating spirit. 



The mutual action and reaction between the different departments of human 

 thought is so interesting to the student of scientific progress, that, at the risk 





