114 



Mr GREEN'S SUPPLEMENT TO A MEMOIR ON 



merely noticed, but not insisted upon, these inferences, feeling persuaded 

 that in researches like the present, little confidence is due to such con- 

 sequences as are not supported by a rigorous analysis. 



The principal object of this supplement has been to put the equations 

 due to the surface of junction of two media, and belonging to light 

 polarized perpendicular to the plane of incidence, under a more simple 

 form. The resulting expressions have here been made to depend on 

 those before given in our paper on Sound, and thus the determination 

 of the intensities of the reflected and refracted waves becomes in every 

 case a matter of extreme facility. As an example of the use of the 

 new formulae, the intensities of the refracted waves have been de- 

 termined for both kinds of light : the consideration of which waves had 

 inadvertently been omitted in a former communication. 



Perhaps I may be permitted on the present occasion to state, that 

 though I feel great confidence in the truth of the fundamental principle 

 on which our reasonings concerning the vibrations of elastic media have 

 been based, the same degree of confidence is by no means extended to 

 those adventitious suppositions which have been introduced for the sake 

 of simplifying the analysis. 



Let us here resume the equations of the paper before mentioned, 

 namely, 



dcp d\j/ _ d<p t d^f, " 

 dx dy dx dy 



(17) 



d(j> 

 dy 



djf_ 

 dx 



dy 



dx 



i (when x = 0). 



d*(j> d'cp, 

 g*dt* g ;d? 



y*dt* yfdt 2 



where u and v, the disturbances in the upper medium parallel to the 

 axes x and y, are given by 



