Electromagnetic Theory of Light. 97 



glass for a red one, wo may revert to the original condition of 

 things, and observe the transition from perpendicularity to 

 obliquity over again. The change in the wave-length of the 

 light has the same effect as a change in the size of the par- 

 ticles; and the comparison gives curious information as to the 

 rate of growth. 



But even with homogeneous light it would be unreasonable 

 to expect an oblique direction of perfect polarization. So long 

 as the particles are all very small in comparison with the 

 wave-length, there is complete polarization in the perpendi- 

 cular direction ; but when the size is such that obliquity sets 

 in, the degree of obliquity will vary w T ith the size of the par- 

 ticles, and the polarization will be complete only on the very 

 unlikely condition that the size is the same for them all. It 

 must not be forgotten, too, that a very moderate increase in 

 dimensions may carry the particles beyond the reach of our 

 approximations. 



The fact that at this stage the polarization is a maximum 

 when the angle through which the light is turned exceeds a 

 right angle is the more worthy of note, as the opposite result 

 would probably have been expected. By Brewster's law this 

 angle in the case of a plate is less than a right angle; so that 

 not only is the law of polarization for a very small particle 

 different from that applicable to a plate, but the first effect of 

 an increase of size is to augment the difference. 



We must remember that our recent results are limited to 

 particles of a spherical form. It is not difficult to see that, 

 for elongated particles, the terms in ( AK) 2 may be of the same 

 order with respect to kc as the principal term ; so that if 

 (AK) 2 be sensible, mere smallness of the particle will not 

 secure complete evanescence of scattered light along z. The 

 general solution of the problem for an infinitesimal particle of 

 arbitrary shape must raise the same difficulties as beset the 

 general determination of the induced magnetism developed in 

 a piece of soft iron when placed in a uniform field of force. 

 In the case of an ellipsoidal particle the problem is soluble ; 

 but it is perhaps premature to enter upon it, until experiment 

 has indicated the existence of phenomena likely to be explained 

 thereby. 



For an infinitesimal particle in the form of a sphere, we may 

 readily obtain the complete solution without any approxima- 

 tion depending upon the smallness of AK. We know by the 

 analogous theory of magnetism, that a dielectric sphere situated 

 in a uniform field of electric force will undergo electric dis- 

 placement of uniform amount, and in a direction parallel to 

 that of the force. Thus the complete solution applicable to 



Phil. Mag. S. 5. Vol. 12. No. 73. Aug. 1881. II 



