442 Mr. W. J. M. Rankine on the Vibrations of 



the Cambridge and Dublin Mathematical Journal for February 

 1851, I have showTi that it is true independently of all hypo- 

 theses respecting the constitution of matter, being a necessary 

 consequence of the conception of an elastic medium. Now a 

 wave of plane-polarized light is a wave of distortion : the plane 

 of distortion is the plane which includes the direction of trans- 

 mission and the direction of vibration : the elasticity called into 

 play depends on the position of this plane ; therefore, if the velo- 

 city of propagation depends upon elasticity alone, the plane of 

 distortion must be the plane of polarization ; and if a normal be 

 di-awn to that plane, the velocity of propagation will be a func- 

 tion of the position of that normal, and not, as supposed by 

 Fresnel, of the du'cction of vibration itself. 



2. Up to a vei'y recent period, no experimental data existed 

 adequate to determine which of these suppositions is supported 

 by facts ; for the phsenomena of double refraction are consistent 

 with either ; and the theory of polarization by reflexion is not 

 regarded as sufficiently certain to afford the means of deciding 

 this question. At length, however, the experimentum cruets has 

 been made by Professor Stokes, and the result is conclusive in 

 favour of the supposition of Fresnel. 



In his paper on Diffraction (Cambridge Transactions, vol. ix. 

 part 1), Professor Stokes has shown, that on any conceivable 

 theory of the propagation of undulations of light, vibrations 

 normal to the plane of diffraction must be transmitted round the 

 edge of an opake body with less diminution of intensity than 

 vibrations in that plane. Therefore, when light of which the 

 vibrations are oblique to the plane of diffraction is so transmitted, 

 the plane of vibration will be more nearly perpendicular to the 

 plane of diffraction in the diffracted ray than in the incident ray. 

 He has found by experiment, that when light of which the plane 

 of polarization is oblique to the plane of diffraction is transmitted 

 round the edge of an opake body, the plane of polarization is 

 more nearly parallel to the plane of diffraction in the diffracted 

 than in the incident ray. The necessary conclusion is, that the 

 dix'ection of vibration in plane-polarized light is normal to the 

 plane of polarization ; in other words, that the velocity of light 

 in crystallized media depends on the direction of vibration, as con- 

 jectured by Fresnel. 



This result of experiment is at variance with the necessary 

 consequences of the supposition, that the velocity of light depends 

 on elasticity alone ; therefore that supposition is inadequate to 

 explain the phsenomena of polarized light. 



3. Having considered what modifications must be introduced 

 into our hypothetical conceptions of the nature of the medium 

 which transmits light to make them adequate to explain the 



