PROFESSOR STOKES, ON THE DYNAMICAL THEORY OF DIFFRACTION. 59 



Let i', p be the angles of refraction corresponding to the angles of incidence, i, i + 9. 

 Then in the case of the first image the tangent of the azimuth of the plane of polarization 

 is multiplied by cos (i + 9 - p) sec (i + 9 + p) in consequence of reflection, and by cos (i + 9 - p) 

 in consequence of refraction; and in the case of the second image by cos (i - i') in consequence 

 of refraction, and by cos (i - i) sec (i + i') in consequence of reflection. Hence if rri be the 

 factor corresponding to diffraction and the accompanying refraction, m the factor got from 

 observation, and regarded as correct, we have 



for 1st image, log rri = log m + log cos (i + 9 + p) - 2 log cos (i + 9 - p), 



for 2nd image, log rri = log m + log cos (i + »') - 2 log cos (i — i'). 



In the case of the first image, rri relates to diffraction at refraction from air into glass, 

 where i is the angle of incidence in air, and p - i' the angle of diffraction in glass. In the 

 case of the second image, m relates to diffraction from glass into air, where i' is the angle of 

 incidence in glass, and 9 the angle of diffraction in air. 



In experiment No. 11, 1st image, we have from Table II, log m = +.289; for the 

 2nd image log to = + .061. In this experiment i= 14°50', 9 = 22°30', whence i = 9°4l', 

 p = 23°30'. We thus get 



for 1st image, log rri = + .289 - -286 = + .003, 

 for 2nd image, log rri = + .061 - .037 = + .024. 



The positive values of log rri which result from these experiments, notwithstanding the 

 refraction which accompanied the diffraction, bear out the results of the experiments already 

 discussed, and confirm the hypothesis of Fresnel. It may be remarked that log rri comes 

 out larger for the second image, in which diffraction accompanied refraction from air into glass, 

 than for the first image, in which diffraction accompanied refraction from glass into air. This 

 also agrees with the experiments just referred to. 



In experiment No. 12, the light which entered the eye came in a direction not much 

 different from that in which light regularly reflected would have been perfectly polarized. 

 Since in regularly reflected light the amount of crowding of the planes of polarization changes 

 rapidly about the polarizing angle, it is probable that small errors in /u, i, and 9 would produce 

 large errors in to. Hence little can be made of this experiment beyond confirming the 

 formula (49). 



I will here mention an experiment of Fraunhofer's, which, when the whole theory is made 

 out, will doubtless be found to have a most intimate connexion with those here described. 

 In this experiment the light observed was reflected from the grooved face of a glass-grating ; 

 the reflection from the second surface was stopped by black varnish. In Fraunhofer's notation 

 e is the interval from one groove to the corresponding point of its consecutive, and is measured 

 in parts of a French inch, a is the angle of incidence, t the inclination of the light observed 

 to the plane of the grating, (Et) the value of t for the fixed line E, and the numerals mark 

 the order of the spectrum, reckoned from the axis, or central colourless image, the order being 

 reckoned positive on the side of the acute angle made by the regularly reflected light with 

 the plane of the grating. The following is a translation of Fraunhofer's description of the 

 experiment. 



8—2 



