INTENSITY OF REFLECTED AND REFRACTED LIGHT. 399 



Now ^'V=^^^+^^+-^^-l+-- 



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

 effect. We conclude that 



the S3rmbol 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 -p'^ oa 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 : 



+ 



^(*-4^^--)(S;^--0¥O <'> 



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

 common surface on the other. 



Also. ^^ = ^ (^..^..^) (g.a.,.0i|i.9i|^) 



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

 will be simplified, as we shall see presently. 



(<b' r \ 8 x^ 

 (pr + -—-dzn -Y- in equation (1) be designated by n^, it is clear that 



((f)' f \ 1/^ 

 0r+ ^— ^02\ _^ is also equal to n^. 



Denote 2 (^cpr, + ^ BzA -^ the expression in equation (2) by n/ 



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



2 (0/ + -^ dz'^ 8a/ = 2 (^cpr,+^8z,A 8 x, in equation (3) by P, 



