4 REPORT 1870. 



mathematical class. "When this condition is fulfilled, the illustration is not only 

 convenient for teaching science in a pleasant and easy manner, but the recognition 

 of the formal analogy between the two systems of ideas leads to a knowledge of 

 both, more profound than could be obtained by studying each system separately. 



There are men who, when any relation or law, however complex, is put before 

 til em in a symbolical foriii, can grasp its full meaning as a relation among abstract 

 quantities. Such men sometimes treat with iudiiference the further statement 

 that quantities actually exist in nature which fulfil this relation. The mental 

 image of the concrete; reality seems rather to disturb than to assist their contem- 

 plations. 



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

 retain in their minds the unembodied symbols of the pure mathematician, so that, 

 if science is ever to become popular, and yet remain scientific, it must be by a pro- 

 found study and a copious application of those principles of the mathematical clas- 

 sification of quantities which, as we have seen, lie at the root of every truly scien- 

 tific 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 ener- 

 gies into the scene which they conjure up. TJiey learn at what a rate the planets 

 rush through space, and they experience a delightful feeling of exhilaration. They 

 calculate the forces with which the heavenly bodies pull at one another, and they 

 feel their o\vn 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 pre- 

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

 appears in tlie 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. 1 shall only mention the name of that im- 

 portant 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, Aviien it shall have been tlioroughly vuiderstood by 

 men of the illusti'ative 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 of 

 still further encroaching on the valuable time of the Section, I shall say a few words 

 on a branch of physics which not very long ago would have been considered rather 

 a branch of metapliysics. I mean the atomic theory, or, as it is now called, the 

 molecular theory of the constitution of bodies. 



Not many years ago if we had been asked in what regions of physical science the 

 advance of discovery was least apparent, we should have ponited to the hope- 

 lessly distant fixed stars on the one hand, and to the inscrutable delicacy of the 

 texture of material bodies on tlie other. 



Indeed, if we are to regard Comte as in any degree representing the scientific 

 opinion of his time, the research into what takes place beyond our own solar system 

 seemed then to be exceedingly unpromising, if not altogether illusory. 



The opinion that the bodies which we see and handle, which we can set in 

 motion or leave at rest, which we can break in pieces and destroy, are composed of 

 smaller bodies which we cannot see or handle, which are always in motion, and 

 which can neither be stopped nor broken in pieces, nor in any way destroj-ed or 

 deprived of the least of their properties, was known by the name of the Atomic 

 Theory. It was associated with the names of Democritus, Epicurus, and Lucretius, 



