plane inclined 45° to that of reflexion will again be plane 

 polarized in a plane inclined at a certain angle <f> (which is 

 17° for steel) to the plane of reflexion ; and we must have 



'2 



tan<A=-r. (13) 



a 



Also, at the maximum polarizing angle we must have 



8' -8= 90°. (14) 



And these two conditions will enable us to determine the 

 constants m and x for any metal, when we know its maximum 

 polarizing angle and the value of <p; both of which have been 

 found for a great number of metals by Sir David Brewster. 

 The following table is computed for steel, taking M — 3|, 

 x = 54°. 



i 



8 



S' 



a 2 



a 



$ {a -+-a j 



0° 



27° 



27° 



.526 



.526 



.526 



30 



23 



31 



.575 



.475 



.525 



45 



19 



38 



.638 



.407 



.522 



60 



13 



54 



.729 



.308 



.5 8 



75 



7 



98° 



.850 



.240 



.545 



85 



2 



152 



.947 



.491 



.719 



90 







180 



1. 



1. 



1. 



The most remarkable thing in this table is the last 

 column, which gives the intensity of the light reflected when 

 common light is incident. The intensity decreases very 

 slowly up to a large angle of incidence, (less than 75°,) and 

 then increases up to 90°, where there is total reflexion. This 

 singular fact, that the intensity decreases with the obliquity 

 of incidence, was discovered by Mr. Potter, whose experi- 

 ments extend as far as an incidence of 70°. Whether the 

 subsequent increase which appears from the table indicates a 

 real phenomenon, or arises from an error in the empirical for- 

 mulae, cannot be determined without more experiments. It 

 should be observed, however, that in these very oblique inci- 

 dences Fresnel's formulae for transparent media do not repre- 

 sent the actual phenomena for such media, a great quantity 



