68 Mr. A. W. Ward. On the Magnetic Rotation [May 9, 



an equation which gives the true magnetic rotation, as of course it 

 should do. 



If a. = tt/4, so that a becomes infinite, the equation becomes 



= ?^ tan Jcz, 

 k 



except when kz = ?r/2. If kz = w/2, O takes an indeterminate form. 

 In this case the light is circularly polarised 



To examine this equation generally it is advisable to write it some- 

 what differently. Let us put 



_ 2mz logtan (^7r + -l^) + a 2 sinZ;^ 

 kz sec kz + a 2 cos kz 



where is the true magnetic rotation, and /3 is the total retardation 

 expressed as an angle. 



Hence fi = /C?M. 



e ft 



If then we trace the curve 



y = f(a 2 x), 



the ratio of y/x at any point gives us the ratio of the apparent to the 

 true rotation when ft = x. 

 With regard to the curve, 



y =/(»), 



it should be observed that y — whenever x is a multiple of Jtt, and 



that ^!=1 when x is an even multiple of -J77-, and = when x is an 



dx 



odd multiple of -J77-. Since all along the tangent at the origin y — x, 

 we may take the tangent to represent the true rotation, so that 



?/curve £2 



2/tangent © 



Tracings of the curve when a 2 = and 10 respectively are given 

 below. 



It appears from these curves that when a 2 = 10, the apparent 

 rotation is greater than the real rotation if /3 is less than 80°, while if 

 a 2 is equal to 0, Q/0 is always less than 1. When (3 is small it is easy 



