OPTICS AND MATHEMATICS 89 



with that faculty of scientific imagination, which 

 was possessed for example by Lord Kelvin in a 

 superlative degree, is for ever imagining models 

 which shall enable him by their working to represent 

 and depict the course of actual physical processes. 

 The possibility and consistency of such models 

 require Mathematical Analysis for their investiga- 

 tion. The mathematician may also, by tracing 

 the necessary consequences of the postulation of 

 a model of a particular type, formulate crucial 

 tests in accordance with which further experi- 

 ments will decide whether a particular type of 

 model can be retained, at least provisionally, or 

 whether it must be rejected as inadequate for the 

 representation of the known facts, and must give 

 place to some other model of a different type. 

 Perhaps the most striking example of the services 

 which have been rendered to Science by the con- 

 templation of various models, many or all of which 

 have ultimately been found to be inadequate for 

 complete representation, is to be found in the 

 history of Optics. The various forms of the 

 corpuscular theory, and of the wave theory, of 

 Light were all attempts to represent the phenomena 

 by models, the value of which had to be estimated 

 by developing their mathematical consequences, 

 and by comparing these consequences with the 

 results of experiments. The adynamical theory of 

 Fresnel, the elastic solid theory of the ether 

 developed by Navier, Cauchy, Poisson, and Green, 



