228 Prof. A. McAulay on the Wave-Surface and Rotation 

 it will follow that a , = VB , D7iS(B - H , + B , E% 



because the expression on the right is an intensity. 



It can easily be verified directly that Mr. Heaviside's wave- 

 surface strains by means of the function /jl~% into a Fresnel 

 surface and similarly for the index-surface. 



In writing the above it has occurred to me that it is easy by 

 the methods of "M. T. E." to construct any number of mediums 

 which shall, according to equations (5) and (6), rotate the 

 plane of polarization of an electromagnetic plane polarized 

 wave. It should be carefully noticed that the special electrical 

 theory of " M. T. E." is not here involved. We deal with 

 Maxwell's theory pure and simple, as exemplified by equations 

 (5) and (6) above. It is only the mathematical methods of 

 " M. T. E." that are about to be used. 



In the mediums in question yJ and d vary in space but not 

 in time. I will first describe such a medium, and then 

 indicate how it is constructed. 



fju f and c' vary spirally, according to a certain law to be 

 mentioned directly, about a certain axis fixed in the medium. 

 For the sake of conciseness, suppose this axis is vertical. 

 Describe a circular cylinder of any radius R, having this axis 

 for its axis. On this cylinder describe a spiral making an 

 angle 6 (between 0° and +45°) with the horizon given by 

 the equation 



tan 26 = 2/i/R, (12) 



where h is a giveu constant length (positive, say, to fix the 

 ideas, though it must also be possibly negative). This spiral 

 will be referred to as the first spiral. A spiral on the same 

 cylinder cutting the first perpendicularly will be referred to 

 as the second spiral. Thus, through every point of the 

 medium we have a first spiral and a second spiral. 



The principal axes of permittivity and inductivity are the 

 tangents to these two spirals and the line at right angles to both 

 (i. e., the perpendicular from the point on the axis). 



The first axis will mean that along the tangent to the first 

 spiral, and the first permittivity will mean the corresponding 

 principal permittivity, and similarly for the first inductivity ; 

 similarly also for the second axis, permittivity, and inductivity. 

 The third axis is of course the remaining one, and similarly 

 for permittivity and conductivity. 



The third permittivity and third inductivity have constant 

 values c and fi Q throughout the medium: The first permittivity 

 and inductivity are c cot 2 6 and /ut, cot 2 6 respectively , and the 

 second are c tan 2 6 and /jl tan 2 6 respectively. 



In this medium a plane polarized wave with normal along 



