338 Dr. J. Kerr on Rotation of the Plane of Polarization 



To apply this result to the first half of the second experi- 

 ment. By trial we give to a such a value that sensibly a' = p' , 

 and then apply successively the three sets of operations 



(R,N), (R), (R,S). 



The corresponding intensities in the polariscope are 



{-a'-df, (-«% {-a' + a'y, 



which are as the numbers 4, 1, 0. The actual results, as 

 already specified, were bright, faint, black (10). * 



24. Returning to the sixth experiment. In discussing the 

 expression 



e 2 + p' 2 — 2e//cosc/>, 



found in art. 22, I shall suppose the rotation of the second 

 jSTicol always righthanded, or the angle € always positive. 

 The amplitude p' is positive for S, negative for 1ST. The angle 

 <f> varies continuously with the angle of incidence, from zero 



rrr 



at normal incidence, through ^ at principal incidence (75° or 



76°), up to 7r at grazing incidence. It will be observed that 



the -r- at principal incidence in the present case is the §7r of 



equation (2) of art. 15, diminished by the it of reversal due 

 to reflection. 



(1) When the value of the angle of incidence is consider- 

 ably less than 75°, cos (j> has some positive value c, and the 

 additions made to the primitive intensity e 2 by the operations 

 N and S are 



p f2 + 2ep / c and p /2 -2ep'c. 



In this case, therefore, the effect of N in the polariscope is 

 always an increase, and always more pronounced than the 

 effect of S. 



Let e f be the value of e which is determined by the equation 



p'-2ec=0. 



When e = e', the effect of S in the polariscope is reduced to 

 zero ; when e < e', the effect of S is a small increase ; when 

 e>e / , the effect of S is a decrease. 



(2) When the value of the angle of incidence is consider- 

 ably greater than 75°, cos <£ has some negative value — e, and 

 the additions made to the primitive intensity e 2 by !N" and $ are 



p r2 -2ep / e and p' 2 + 2ep'e. 



Here, therefore, contrary to what holds in the first case, the 

 effect of S is always an increase, and always more pronounced 

 than the effect of 1ST. Here also, as e increases from zero, the 



