8 REPORT — 1870. 



But the mind of man is not, like Foiirier'a heated body, continually settling 

 down into an ultimate state of quiet uniformity, the character of which we can 

 already predict ; it is rather like a tree, shooting out branches which adapt them- 

 selves to the new aspects of the sky towards which they climb, and roots which 

 contort themselves among the strange strata of the earth into which they delve. 

 To us who breathe only the spirit of our own age, and know only the characteristics 

 of contemporary thought, it is as impossible to predict the general tone of the science 

 of the future as it is to anticipate the particular discoveries which it will make. 



Physical research is continually revealing to us new features of natural processes, 

 and we are thus compelled to search for new forms of thought appropriate to these 

 features. Hence the importance of a careful study of those relations between 

 Mathematics and Physics which determine the conditions under which the ideas 

 derived from one department of physics may be safely used in forming ideas to be 

 employed in a new department. 



The figure of speech or of thought by which we transfer the language and ideas 

 of a famfliar science to one with which we are less acquainted maybe called Scien- 

 tific Metaphor. 



Thus the words Velocity, Momentum, Force, &c. have acquired certain precise 

 meanings in Elementary Dynamics, They are also employed in the DjTiamics of 

 R Connected System in a sense which, though perfectly analogous to the elementary 

 sense, is wider and more general. 



These generalized forms of elementary ideas may be called metaphorical terms in 

 the sense in which every abstract temi is metaphorical. The characteristic of a 

 truly scientific system of metaphors is that each term in its metaphorical use retains 

 all the formal relations to the other terms of the system which it had in its original 

 use. The method is then truly scientific — that is, not only a legitimate product of 

 science, but capable of generating science in its turn. 



There are certain electrical phenomena, again, which are connected together by 

 relations of the same form as those wliich connect dynamical phenomena. To apply 

 to these the phrases of dynamics with proper distinctions and provisional reserva- 

 tions is an example of a metaphor of a bolder kind ; but it is a legitimate metaphor 

 if it conveys a true idea of the electrical relations to those who have been abeady 

 trained in dynamics. 



Suppose, then, that we have successfully introduced certain ideas belonging to an 

 elementary science by applying them metaphorically to some new cla^s of pheno- 

 mena. It becomes an impoi'tant philosophical question to determine in what degree 

 the applicability of the old ideas to the new subject may be taken as evidence that 

 the new phenomena are physically similar to the old. 



The best instances for the determination of this question are those in which two 

 ditterent explanations have been given of the same thing. 



The most celebrated case of this kind is that of the corpuscular and the undulatory 

 theories of light. Up to a certain point the phenomena of light are equally well 

 explained by Doth ; beyond this point, one of them fails. 



To understand the true relation of these theories in that part of the field where 

 they seem equally applicable we must look at them in the light which Hamilton 

 has thrown upon them by his discovery that to every brachistochrone problem there 

 corresponds a problem of free motion, involving different velocities and times, but 

 resulting in the same geometrical path. Professor Tait has written a veiy interest- 

 ing paper on this subject. 



According to a theory of electricity which is making great progress in Germany, 

 two electrical particles act on one another directly at a distance, but with a force 

 which, according to Weber, depends on their relative velocity, and according to a 

 theory hinted at by Gauss, and developed by Riemann, Lorenz, and Neumann, acts 

 not instantaneously, but after a time depending on the distance. The power with 

 which this theory," in the hands of these eminent men, explains every kmd of elec- 

 trical phenomena must be studied in order to be appreciated. 



Another theory of electricity, which I prefer, denies action at a distance and attri- 

 butes electric action to tensions and pressures in an all-pervading medium, these 

 stresses being the same in kind with those familiar to engineers, and the medium 

 being identical with that in which light is supposed to be propagated. 



