249] ELECTROMAGNETIC WAVES. 521 



constant throughout space. But such a constant field is not 

 propagated at all, and we shall therefore disregard it, and put both 

 constants equal to zero. Both fields are consequently perpen- 

 dicular to the direction of propagation. It is for this reason that 

 Maxwell's theory is appropriate for an explanation of light, which, 

 as the phenomena of polarization show, is due to transverse undu- 

 lations. 



Although the forces of the two fields lie in the wave-plane, 

 and are constant over any particular wave-plane, it does not 

 follow that their directions are the same in all wave-planes, that 

 is for different values of s. We shall however assume that their 

 directions are the same in all wave-planes, and we will call the 

 direction cosines of F, a lf /3 it y lt and of H, a^, /3 2 , ry 2 . Such a 

 wave is said to be plane-polarized. Then we have 



(ii) Z = !<, F=&</>, = 7i& 1 = 0^, M 

 and our equations (7) and (8) take the form 



(12) - 



Multiplying the equations of the first set respectively by 

 2j &, 7a and adding, we get 



(H) 



or the electric and magnetic forces are mutually perpendicular, as 

 well as perpendicular to the direction of propagation. There are 

 accordingly two directions, either of which might be chosen to 

 define the plane of polarization, and it rests with experiment to 

 decide between them. 



Squaring and adding either equations (12) or equations (13) 

 gives 



e< /2 =/iip. 



Extracting the square root and integrating, 



