due to the Scattering of Light by Electrons. 727 



the same magnitude in both (i.) and (ii.), but it' it is plus for 

 one it will be minus tor the other. So that if (i.) rotates 

 the plane of polarization in one, (ii.) will rotate it in the 

 opposite direction. Thus a molecule represented graphically 

 by fig. 1 would rotate in the opposite direction to one 

 represented by fig. 2, or by fig. 8. 



Fig. 2. Fig. 3. 



B^r ^C A 



"0' 

 A 



C^ 78 



The geometrical meaning of Q is interesting. The term 

 tey'tex'z'-tez'tex'y' 



may be written 



■ e p e q\' V p x q)\ z p2/q -qUp) 



where x p , y p , z p ; x q , y 9 , z q are the coordinates of two points 

 P, Q at which the charges are e p} e q ; the expression may be 

 put in the form 



X^^PQ cos (j) . PQ sin <fi . p, 



where </> is the angle PQ makes with the axis of x, and p 

 the shortest distance between PQ and this axis. Since 

 PQ sin (f> . p is the moment of PQ about the axis of x, and 

 PQ cos (j> the component of PQ along the axis, the term is 

 equal to the product of the charges multiplied by the product 

 of the component of PQ along and its moment about the axis 

 of x. Thus it vanishes if PQ is parallel to the axis, or if it is 

 at right angles to it, or if it intersects it. The term is equal 

 to e p e q 6Y, where V is the volume of the tetrahedron whose 

 corners are P, Q and the projections of P and Q on the axis 

 of .r. The term is to be taken as positive or negative 

 according as the component of PQ along and its moment 

 about the axis of x are related like translation and rotation 

 in a right or left handed screw. 



The hypothesis we have made is that the whole molecule 

 rotates like a rigid body under the influence of the electric 

 forces in a light wave, so that there is no displacement of the 

 electrons relative to the atoms in a molecule. We shall now 

 consider whether on any reasonable supposition as to the 

 values of the quantities involved, the expressions we have 

 found would give values for the rotation of the same order 

 as those observed for optically active substances. 



