256 Mr R. T. Glazehrook, On the theory [April -20, 



as they depend on the motion at 0, lie in the planes OZR , OZR 

 and are perpendicular to OR and OR respectively. 



Ro 



Join ZR Q , ZR by great circles and take Q R . QR each equal 

 to ^tt, the directions of vibration meet the sphere in Q and Q. 



Let P , P be the poles of the great circles Q R , QR respec- 

 tively. Then QP, Q P , meeting in B suppose, are the traces of 

 the wave fronts, and PBP = S, the angle of diffraction. Also B is 

 the pole of the plane of diffraction RR , and on Fresnel's hypo- 

 thesis the azimuths of the planes of polarization of the two waves 

 are BQ and BQ respectively, while on the other hypothesis the 

 azimuths are BP and BP. Now let ZR = p so that p is the 

 angle between the direction of motion over the surface and the 

 direction of the ray directly reflected. Then 



ZQ = p Q - 90° = ZP Q , 



and since Zis the pole of PP o , ZP P= 90° and PP Q = Po . 



Hence the triangle PBP gives 



sin BP cot BP = sin PBP cot PP B + cos PBP cos BP . 



Or on Fresnel's hypothesis 



tan cp = cos S tan <f> + sin 8 sec (p cot p . 



While if we take the other hypothesis we have to put ^ — (f> and 

 — — <p Q for <p and cp Q and get 



Li 



cot </> = cos S cot <f> + sin S cosec <£ cot p . 



If we are considering diffraction by transmission, the incidence 

 being direct, this gives Prof. Stokes' well-known law, for then, 

 taking as the ray corresponding to p , (p Q , the ray transmitted 

 directly, it is clear that the disturbance over the diffracting sur- 



