ON THE INTENSITY OF REFLECTED AND REFRACTED LIGHT. 41 7 



Again, by eliminating R, we obtain 



I sin <p' cos ^ + I sin <p' cos (p = T s,m(p cos ^ + T sin (p' cos (p' 



^^2 1 sin (f)' cos (f) 



' sin(p cos (p +sm(p' cos <p' 



, I sin </)' 



„^ COS<P \ ri 



= 21- X' 1 ■ ^cosrf) . ^, 



COS9 smd) ^+sm0' 



!. ,cos(p . \ 

 sm (p — zr, — sm 0' I 

 '^coscp ^ [ 



. jCosd) . ,,f 

 sin O) v. + sin O) 

 ^ COS ip "^ ) 



COS0 ( sin2(/) — sin2(^' 



~ 'cos<^'| sin20 + sin20' 



_ COS0 ( tan(0 — (/)') 

 ~ 'cos^'l tan </) + <^' 



These are precisely Fresnel's results ; in fact, the equation (2) con-esponds 

 with his empirical formula. 



In conclusion, I have only to observe, that some of the equations involve 

 what appears almost too accurate a substitution to be called an approximation, 

 but which may in some extreme cases give rise to considerable deviation from the 

 resulting formulae. It will not, however, repay us for the labour of entering into 

 the discussion of such points ; suffice it to say, that the more deviation a ray 

 suffers, the greater is the difference between the assumed and the real value of 

 some of the forces. Except, however, the deviation be very great indeed, they 

 cannot differ widely from each other. 



Edinbukoh, February 4. 1839. 



VOL. XIV. PART II. 3 O 



