INTENSITY OF RKFLECTED AND REFRACTED LIGHT. 399 



Now ^'y=^^-+^^+-#T-+-- 



8 X being supposed small for those limits to which the force produces a sensible 

 eflFect. We conclude that 



the symbol 2 being supposed to extend to the sensible limits of the force ; but the 

 particle in each case not near the confines of the medium. - 



It is clear that the term involving -f-^ ^ vanishes, and the equations are 



thereby simplified. 



By the same process, we may obtain the equation of motion of a particle in 

 the upper medium, near the confines, to be the following : 



the symbol now extending indefinitely on one side, but being bounded by the 

 common sm-face on the other. 



Also. ^^^.{f..*^^,) (g;^,,.0?|i.9i|^) 



If the particles last considered coincide in the bounding surface, the results 

 will be simplified, as we shaU see presently. 



^'• + ~ osM -2" in equation (1) be designated by w, it is clear that 

 2 (^»- + J— Ss^j -^ is also equal to ii. 

 Denote 2 \A>r,-v^-^ ^zj\ —^ the expression in equation (2) by n/ 

 2 (^cf>r + ^8z^^ 5a;in(3)byP 

 2(^<p/+^Bz'\ 8a/=i (0r,+-^'5sA 8x, in equation (3) by F, 



