54 PROFESSOR STOKES, ON THE DYNAMICAL THEORY OF DIFFRACTION. 



First, that the diffraction takes place in air, before the light reaches the glass : 



Second, that the diffraction takes place in glass, after the light has entered the first surface 

 perpendicularly : 



Third, that the diffraction takes place in air, after the light has passed perpendicularly 

 through the plate. 



On the first supposition let a„ a.,, a be the azimuths of the plane of polarization of the light 

 after diffraction, after the first refraction, and after the second refraction respectively, and 9' 

 the angle of refraction corresponding to the angle of incidence 9, so that sin 9 = p. sin 9',/u being 

 the refractive index of the plate : and first, let us suppose the vibrations of plane-polarized 

 light to be perpendicular to the plane of polarization. Then by the theory of this paper we 

 have tan cti = sec 9 tan w, and by the known formula applying to refraction we have tan ct 2 = cos 

 {9 - 9') tan oti, tan a = cos (9 — ff) tan a 2 » whence tan a = m tan zzr, where 



m = sec 9 cos 51 (9 - 9'). 



On the second supposition, if a t be the azimuth after diffraction at an angle 9' within 

 the glass, we have tan a, = sec 9' tan -ar, tan a = cos {9 — 9') tan a„ whence tan a = m tan sr, 

 where 



m = sec 9' cos (9 - 9 1 ). 

 On the third supposition we have tan a = m tan tst, where 



m = sec 9. 



If we suppose the vibrations parallel to the plane of polarization, we shall obtain the same 

 formulas except that cos 9, cos 9' will come in place of sec 9, sec 9', the factor cos (9 — 9') 

 being unaltered. 



Theory would lead us to expect to find the value of log m deduced from observations 

 in which the grooved face was turned from the polarizer lying between the values obtained on 

 the second and third of the suppositions respecting the place of diffraction, or at most not much 

 differing from one of these limits. Similarly, we should expect from theory to find the value 

 of logm deduced from observations in which the grooved face was turned towards the polarizer 

 lying between the values obtained on the first and second suppositions, or at most not lying far 

 beyond one of these values. 



The following table contains the values of log m calculated from theory on each of the 

 hypotheses respecting the direction of vibration, and on each of the three suppositions respect- 

 ing the place of diffraction. The numerals refer to these suppositions. The table extends 

 from 9 = to 9 = 90°, at intervals of 5°. When 9 = 0, m = l, and logm = 0, in all cases. 

 In calculating the table, I have supposed /x — 1. 52, or rather equal to the number, (1.5206,) 

 whose common logarithm is .182. This table is followed by another containing the values of 

 logrra deduced from experiment. 



