18 Prof. Powell on the Demonstration of FresnePs Formulas • 



This was Dr. Young's formula, deduced in an early stage of these 

 inquiries. 



If we suppose /ia = 1*5, this will give 



I,= l_r=-96. 



Also ^^^,co8 (i-r)^^ 



cos (i + r) 

 whence J = k!^ = h'^ ='04>, J^=-96. 



(2.) For the angle of complete polarization 2 + r=90°, 

 sin (t — r) = cos 2r, sin (i + r) = 1, tan i = /^ = 1 -5 = tan 56*^ 1 9', 

 I=A'2= cos«2r, J=l-A'«= sin22r, 

 j^^a^ tanM«-r) ^ j=l«;t«=l. • 



CO ' 



(3.) In the limit of oblique incidence, 



t = 90°, sin (i — r) = cos r, sin (i + r) = cos r, 

 I = A'2=1, J = l-r=0, 

 tan(90-r) = tan(904-r), 

 I^=jt'«=l, J^=l-A'2=0. 

 (4.) For these and other incidences generally, the following 

 table will show the approximate intensities. 



Intensities at different Incidences. 



59. The necessary imperfections of photometry preclude any 

 accurate verification of these numerical results ; but by throwing 

 the two images of a round hole in an opake plate covering one 

 end of a rhomboid of iceland spar on a surface of glass, at dif- 

 ferent incidences, the eye can readily compare the intensities 

 in some of the more marked cases, both of the reflected and 

 the transmitted rays, of the two beams polarized in planes at 

 right angles to each other; which show a general agreement with 

 theory. 



