PROFESSOR STOKES, ON THE DYNAMICAL THEORY OF DIFFRACTION. 61 



Now with reference to the present investigation the question might naturally be asked, If such 



material changes in intensity are capable of being produced by such slight modifications in the 



diffracting edge, how is it possible to build any certain conclusions on an investigation in which 



the nature of the diffracting edge is not taken into account ? 



To facilitate the explanation of the apparent cause of the above-mentioned want of 



symmetry, suppose the diffraction produced by a wire grating in which the section of each 



wire is a right-angled triangle, with one side of the right angle parallel to the plane of the 



grating, and perpendicular to the incident light, and the equal acute angles all turned the same 



way. The triangles ABC, BEF in the figure represent sections of 



two consecutive wires, and GB, BB, IE represent incident rays, & H 



or normals to the incident waves, which are supposed plane. Let 



BE = e, and BD : BE :: n : 1 - w. Draw BK, BL, EM parallel 



to one another in the direction of the spectrum of the order v on 



the one side of the axis, so that v\ is the retardation of the ray 



v\ 

 EM relatively to BK, and therefore sin 9 = — ,9 being the angle 



€ 



of diffraction, or the inclination of BK to GB produced. Draw BN, FO, EP at an incli- 

 nation 9 on the other side of the axis, and let Z DBF = a. Then the retardation of BL 

 relatively to BK is equal to nu\, or we sin 9, and that of BN relatively to FO is equal to 

 we sin 9 + ne tana cos 9 -we tan a, so that if we denote these retardations by R^R^Ri — ne sin 9, 

 R 2 = we sin 9 —ne tan a versin 9. Let p lf p 2 be the greatest integers contained in the quotients 

 of i? 15 R-i divided by X, and let R , = p, X + r„ J?, = p 2 X + r 2 . Then the relative intensities 

 of the two spectra of the order + v and — v depend on r„ r 2 : in fact, we find for the ratio 



of intensities, on the theory of interference, sin 2 — : sin 2 . Now this ratio may have 



X X 



any value, and we may even have a bright spectrum on one side of the axis answering to an 



evanescent spectrum on the other side. It appears then in the highest degree probable that 



the want of symmetry of illumination in Fraunhofer's experiment was due to a different 



mode of interference on opposite sides of the axis. But this has nothing whatsoever to 



do with the nature of the polarization of the incident light, and consequently does not in 



the slightest degree affect the ratio of the intensities, or rather the ratio of the coefficients 



of vibration, of the two streams of light belonging to the same spectrum corresponding 



to the two streams of oppositely polarized light into which we may conceive the incident 



light decomposed, and consequently does not affect the law of the rotation of the plane of 



polarization of the diffracted light. 



G. G. STOKES 



P. S. Since the above was written, Professor Miller has determined for me the refractive 

 index of the glass plate by means of the polarizing angle. Four observations, made by 

 candle-light, of which the mean error was only l'A, gave for the double angle 113°20', whence 

 /x = tan56°40' = 1.52043, which agrees almost exactly with the value I had assumed. In two 



