THE 

 LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FOURTH SERIES.] 



JUNE 1851. 



LXI. On the Vibrations of Plane-Polarized Light. 

 By W. J. Macquorn Rankine, C.E.,F.R.S.E.,F.R.S.S.A. §r.* 



1. T^HE important question, whether the direction of \dbration 

 A in plane-polarized light is normal or parallel to the plane 

 of polarization, is equivalent to this : — whether the velocity of 

 propagation of a rectilinear transverse vibratory movement in the 

 medium which transmits light in ciystallized bodies is a function 

 of the direction of vibration only, or of the position of the plane 

 which includes the direction of vibration and the direction of trans- 

 mission. 



The former of these views was adopted by Fresnel, as being 

 necessary to explain the phfenomena of polarization by reflexion ; 

 and in Mr. Green's investigation of the laws of these phsenomena, 

 in which the conclusions of Fresnel are shown to agree either 

 exactly or approximately with the conseqviences of strictly mecha- 

 nical principles, the same supposition is adopted. 



But if we follow the generally received theory, that the differ- 

 ent velocities of differently polarized rays in crystalline bodies 

 are due solely to the different degrees of elasticity possessed by 

 the vibrating medium in different directions, Fresnel^s supposition 

 must be abandoned and the opposite one adopted. For if there 

 is any proposition more certain than others respecting the laws 

 of elasticity, it is this : — that the transverse elasticity of a medium, 

 or the elasticity which resists distortion of the particles, depends 

 upon the position of the plane of distortion, being the same for 

 all directions of distortion in a given plane. This law is impli- 

 citly involved in the researches of Foisson, of M. Cauchy, of 

 Mr. Green, and others on elasticity ; and in a memou- read to 

 the British Association at Edinbui-gh in 1850, and puljlished in 



* Communicated by tlie Author, having been read to the Royal Society 

 of Edinburgh, December 2, 1850. 



Phil. May. S. 4. Vol. 1. No. 6. June 1851. 2 H 



