due to the Scattering of Light by Electrons. 721 



If the dimensions of the molecule are small compared with 

 the wave-length of the light, we have, very approximately, 



/, = / + (hi Vs, 



where Z is the value of Z at the origin a point inside 

 the molecule. Thus the moment of the forces about the 

 axis of x is 



Z 2,ey s -f , zexsi/s. 

 ax 



Similarly there is a couple around the axis of y equal to 



Zv dL§ v 2 

 2<ex s j—zexs 1 . 



These couples acting on the system of electrical charges 

 considered as a rigid body will cause it to rotate, and 

 thus move the individual charges. If the system is not 

 symmetrical the average velocity of the charges parallel to y 

 may be finite, and hence, by equation (1), give rise to an 

 electric wave in which the electrical force has a component 

 parallel to Y. The phase of this force is the same as that of 



^e-j-. The amount of rotation of the plane of rotation will 

 at L 



depend entirely on that part of the force Y which is in the 



same phase as Z. There may be other parts differing in phase 



from Z by a quarter of a period ; these will affect the 



eilipticity of the polarization, but not the rotation. 



Though the values of dy/dt for the different electrical 



charges may be all in the same phase, yet, since the charges 



are not all in the wave-front, the secondary waves from them 



will not, when they arrive at a point, be all in the same 



phase. Thus, if x s be the x coordinate of one of the particles, 



the phase of a vibration due to this particle relative to one 



27T 



starting from the origin will be accelerated by x s —- , so that, 



A, 



if the velocity of this particle were represented by 



2tt 



cos-— (y— # ), 



the electric force due to it would have the phase corresponding 

 to 



27T. 



cos (vt—x + x s ), 



A 



and would be represented, since .r,/\ is small, by 



27r 2ir . 2tt 



cos ( rt— x,,) — x % sin (rt — x () ). 



A A, A. 



