Light by Unsymmetrical Atoms and Molecules. 399 



the scattered light reaching P from one atom need not 

 be the same as that reaching it from another atom. For 

 this phase depends to some extent on the orientation of 

 the atom. Hence if the orientation of these atoms is 

 quite irregular, the phase of part of the light scattered 

 by different atoms will also be quite irregular, and in 

 calculating the intensity of this part of the light we have 

 to add the intensities of the light scattered by the different 

 atoms, and not, as in the case of the symmetrical atom, 

 add the magnetic forces and take the square of this sum 

 as proportional to the energy. Thus the energy in this 

 part of the light will be proportional to the number of 

 atoms and not to the square of the number. It must be 

 remembered, however, that even with unsymmetrical atoms 

 the phase of every part of the scattered light cannot be 

 made to change sign by altering the orientation of the atom. 



If we refer to the equations on p. 3%, we see that the 

 part of the light arising from the accelerations along 

 x and y can be made to do so, but that depending on 

 the acceleration along z cannot : hence part of the light 

 scattered by N unsymmetrical atoms will be proportional 

 to N 2 and another part to N. The light due to the 

 acceleration parallel to z vanishes along the axis of Z — that 

 is, along the direction of the electric force in the incident 

 light ; so that in this direction the scattered light would be 

 proportional to N. In other directions there would be a 

 part proportional to the square of the number of atoms, 

 provided the linear dimensions of the space occupied by 

 these atoms were not large compared with the wave-length 

 of the light. For large volumes we see, by Huyghens' 

 principle, that the intensity of this part of the scattered 

 light would be comparable with that scattered by the atoms 

 contained in a layer whose thickness was of the order of the 

 wave-length. 



To see the conditions necessary for this statement to 

 be true, we notice that the magnetic force in the scattered 

 light at a point whose distance r from any of the atoms is a 

 large multiple of the wave-length is given by an expression 

 of the form 



- - ( a cos — ( vt — ( Ix i + miji 4- nz l ) ) 



2tt 

 a cos — — 



A. 



( vt — (lx. 2 + my 2 + nz 2 ) ) + ... i 



where .r r , ?/ r , z r are the co-ordinates of one of the atoms, 

 and /, m, n are constant. 



