ON THE REFLEXION AND REFRACTION OF LIGHT. 257 



turbance of the particles to be wholly in the direction of the 

 axis of Zj which is the case with light polarized in the plane of 

 incidence, according to Fresnel. Then we have 



and supposing the disturbance the same for every point of the 

 same front of a wave, w and w t will be independent of z, and 

 thus the three general equations (4) will all be satisfied if 



d*w 



or by making = 



Similarly in the lower medium we have 



w t and 7, belonging to this medium. 



It now remains to satisfy the conditions (5) and (6). But 

 these are all satisfied by the preceding values provided 



w = w t , 



gdw = B dw, 



dx ' dx 



The formulae which we have obtained are quite general, and 

 will apply to the ordinary elastic fluids by making B = 0. But 

 for all the known gases, A is independent of the nature of the 

 gas, and consequently A = A t . If, therefore, we suppose B = B^ 

 at least when we consider those phenomena only which depend 

 merely on different states of the same medium, as is the case 

 with light, our conditions become* 

 w = w, | 



dw _ dw t \ (when x = 0) .................. (9). 



dx ~ dx] 



* Though for all known gases A is independent of the nature of the gas, 

 perhaps it is extending the analogy rather too far, to assume that in the lurnini- 



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