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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 familiar science to one with which we are less acquainted may be 

 called Scientific Metaphor. 



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

 meanings in Elementary Dynamics. They are also employed in the Dynamics 

 of a 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 term is metaphorical. The charac- 

 teristic 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 which connect dynamical phenomena. 

 To apply to these the phrases of dynamics with proper distinctions and pro- 

 visional reservations 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 already trained in dynamics. 



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

 to an elementary science by applying them metaphorically to some new class 

 of phenomena. It becomes an important 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 different explanations have been given of the same thing. 



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