PROFESSOR STOKES, ON THE DYNAMICAL THEORY OF DIFFRACTION. 47 



Section II. 



DISCUSSION OF THE NUMERICAL RESULTS OF THE EXPERIMENTS, WITH REFERENCE 



TO THEORY. 



According to the known formulae which express the laws of the rotation of the plane of 

 polarization of plane-polarized light which has undergone reflection or refraction at the surface 

 of a transparent uncrystallized medium, if sr, a be the azimuths of the planes of polarization 

 of the incident and reflected or refracted light, both measured from planes perpendicular to the 

 plane of incidence, they are connected by the equation 



tan a = m tan •&, (48) 



where m is constant, if the position of the surface and the directions of the rays be given, 

 but is a different constant in the two cases of reflection and refraction. According to the 

 theory developed in this paper, the same law obtains in the case of diffraction in air, or even 

 within an uncrystallized medium, but m has a value distinct from the two former. It seems 

 then extremely likely that the same law should hold good in the case of that combination of 

 diffraction with reflection or refraction which exists when the diffraction takes place at the 

 common surface of two transparent uncrystallized media, such as air and glass. If this be 

 true, it is evident that by combining all the observations belonging to one experiment in such 

 a manner as to get the value of m which best suits that experiment, we shall obtain the 

 crowding of the planes of polarization better than we could from the direct observations, and 

 we shall moreover be able in this way easily to compare the results of different experiments. 

 It seems reasonable then to try in the first instance whether the formula (48) will represent 

 the observations with sufficient accuracy. 



In applying this formula to any experiment, there are two unknown quantities to be 

 determined, namely, m, and the index error of the analyzer. Let e be this index error, so 

 that o = a + e. The regular way to determine e and m would no doubt be to assume an 

 approximate value e x of e, put e = e, + A e 19 where A e L is the small error of ei, form a series of 

 equations of which the type is 



tan (a - ei) - sec s (a — e,) Aei = m tan sr, 



and then combine the equations so as to get the most probable values of Ae { and m. But 

 such a refinement would be wholly unnecessary in the case of the present experiments, which 

 are confessedly but rough. Moreover e can be determined with accuracy, except so far as 

 relates to errors produced by changes in the direction of the light, by means of the observations 

 taken at the standard points, the light being in such cases perfectly polarized. By accuracy 

 is here meant such accuracy as experiments of this sort admit of, where a set of observations 

 giving a mean error of a quarter of a degree would be considered accurate. Besides, when- 

 ever the values of w selected for observation are symmetrically taken with respect to one of the 

 standard points, a small error in e would introduce no sensible error into the value of m which 

 would result from the experiment, although it might make the formula appear in fault when 

 the only fault lay in the index error. 



