THE REFLEXION AND REFRACTION OP LIGHT. 119 



In order, therefore, to form an estimate of the effect which would 

 be produced by a continuous though rapid change of state of the 

 ethereal medium in the immediate vicinity of the surface of junction, 

 we will resume the conditions (29), which belong to light polarized in 

 a plane perpendicular to that of Reflexion, viz. 



and instead of supposing the index of refraction to change suddenly 

 from to /a, we will conceive it to pass through the regular series of 

 gradations, 



MO. Ml! l"2j M3 fi„; 



t being the common thickness of each of these successive media. 



Then it is clear we should have to replace the last system by 

 m to = to, and $ - % - £^ £ C . T ), 



to = to, <*%-%- J^fj Sf c* = •* 



*->*-«--**• "* "3F" ■ "3* " m!-, « + rf-0 6 ^ {•-(■-i.-OI. 



But it is evident from the form of the equations on the right 

 side of system (33), that the total effect due to the last terms of 

 their second members will be far less when n is great, than that due 



