for Reflected and Refracted Light. 



19 



60. The question whether the plane of vibration is parallel or 

 perpendicular to the plane of polarization, has been lately dis- 

 cussed at large by M. Haidinger, who, after an extended com- 

 parative view of the experimental consequences involved in con- 

 nexion with various optical phsenomena on either supposition, 

 decides in favour of the superior simplicity and consistency of 

 FresneVs view, that the plane of vibration is perpendicular to the 

 plane of polarization. (See Phil. Mag. March 1856, vol. xi. 

 p. 242, No. 71. The original is in Poggendorff's Annalen, Oct. 

 1855. See also Silliman^s Journal, Jan. 1856.) 



61. A very refined and ingenious suggestion for a direct 

 " experimentum crucis" was made by Mr. J. A. Dale to the 

 British Association in 1846, but practical difiiculties appear to 

 stand in the way of its application. (See ' Report,' 1846, Sec- 

 tion A.) 



62. But a more recent result of Prof. Stokes is perfectly con- 

 clusive on the question of the direction of the plane of vibration. 

 In his paper " On the Dynamical Theory of Diffraction ^' (Cam- 

 bridge Transactions, vol. ix. part 1, 1849), he has estabhshed 

 theoretically the conclusion, that the plane of vibration of a dif- 

 fracted ray previously polarized, is in general different from that of 

 the incident, except when perpendicular, and when parallel, to the 

 plane of diffraction. For intermediate positions their directions 

 are connected by a simple law, which may be expressed by saying, 

 that if the arcs of inclination of the vibrations to the perpen- 

 dicular to the plane of diffraction be measured on two semicircles 

 intersecting in a common diameter coinciding with that perpen- 

 dicular, and inclined to each other at the angle of diffraction, 

 then the arc of inclination of the incident vibration, measured from 

 the point of intersection, being taken as longitude, that of the 

 diffracted vibration will be the corresponding right ascension. 



If the two semicircles, whose planes are 

 respectivelyperpendicular to the directions 

 of the incident and the difiracted rays, be 

 inclined at an angle 6, equal to the angle 

 of diffractive deviation, and if a^ and a^ be 

 the inclinations of the diffracted and inci- 

 dent vibrations measured from the inter- 

 section (f, by Mr. Stokes's theory they 

 are connected by the equation 



tan oLd= cos 6 tan ui, 



which leads to the construction here re- 

 presented by the arc of a great circle pass- 

 ing through the extremities of u^ and «£ perpendicular to the 

 plane of a^. Whence it follows, that near the intersection {(f), 



C2 



