PART II. 



EXPERIMENTS ON THE ROTATION OF THE PLANE OF POLARIZATION OF 



DIFFRACTED LIGHT. 



Section I. 



DESCRIPTION OF THE EXPERIMENTS. 



If a plane passing through a ray of plane-polarized light, and containing the direction 

 of vibration, be called the plane of vibration, the law obtained in the preceding section for the 

 nature of the polarization of diffracted light, when the incident light is plane-polarized, may 

 be expressed by saying, that any diffracted ray is plane-polarized, and the plane of vibration 

 of the diffracted ray is parallel to the direction of vibration of the incident ray. Let the 

 angle between the incident ray produced and the diffracted ray be called the angle of diffrac- 

 tion, and the plane containing these two rays the plane of diffraction ; let a { , a d be the angles 

 which the planes of vibration of the incident and diffracted rays respectively make with planes 

 drawn through those rays perpendicular to the plane of diffraction, and 9 the angle of diffrac- 

 tion. Then we easily get by a spherical triangle 



tan a d ■ cos 9 tan a { . 



If then the plane of vibration of the incident ray be made to turn round with a uniform 

 velocity, the plane of vibration of the diffracted ray will turn round with a variable velocity, 

 the law connecting these velocities being the same as that which connects the sun's motions in 

 right ascension and longitude, or the motions of the two axes of a Hook's joint. The angle of 

 diffraction answers to the obliquity of the ecliptic in the one case, or the supplement of the 

 angle between the axes in the other. If we suppose a series of equidifferent values given 

 to a,., such as 0°, 5°, 10°,... 355°, the planes of vibration of the diffracted ray will not be dis- 

 tributed uniformly, but will be crowded towards the plane perpendicular to the plane of 

 diffraction, according to the law expressed by the above equation. 



Now the angles which the planes of polarization of the incident and diffracted rays, (if 

 the diffracted ray prove to be really plane-polarized,) make with planes perpendicular to the 

 plane of diffraction can be measured by means of a pair of graduated instruments furnished 

 with Nicol's prisms. Suppose the plane of polarization of the incident light to be inclined at 

 the angles 0°, 5°, 10°..., successively to the perpendicular to the plane of diffraction; then the 

 readings of the instrument which is used as the analyzer will shew whether the planes of 

 polarization of the diffracted ray are crowded towards the plane of diffraction or towards the 

 plane perpendicular to the plane of diffraction. If sr> a be the azimuths of the planes of 

 polarization of the incident and diffracted rays, both measured from planes perpendicular to 

 the plane of diffraction, we should expect to find these angles connected by the equation 

 tan a = sec0 tan-ar in the former event, and tana = cosfl tan-zsr in the latter. If the law and 



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