82 The Rev. S. Haughton on the Reflexion of Polarized Light 



In a memoir read before the Academy of Paris, Jan. 15, 1849, 

 M. Cauchy, after stating that Mr. Green had perceived the in- 

 fluence which the normal evanescent ray must have in changing 

 the phase of the real ray, adds, " et si, apres avoir fait cette 

 remarque, dans son memoire du 11 Decembre 1837, M. Green 

 n'a pas obtenu definitivement les veritables lois de ces pheno- 

 menes, cela nous parait tcnir principalement h ce qu'il a cru 

 pouvoir appliquer k Pettier consideVe isolement la formule gene- 

 rale du mouvement donne par Lagrange." (Comptes Rendus, 

 vol. xxviii.) * 



M. Cauchy proposes elsewhere to substitute the ' Principle of 

 continuity of Movement ' for the ' Principle of equality of Pres- 

 sures/ which latter is the principle obtained directly from the 

 method of Lagrange. 



M. Cauchy cannot have honoured Mr. Green's paper with an 

 attentive perusal, or he would have perceived that Mr. Green's 

 hypothesis as to the equality of coefficients in the two bodies in 

 contact reduces the principle of equality of pressures to that of 

 the continuity of movement. In fact, Mr. Green's conditions 

 at the limits (p. 17) are the same as those given by M. Cauchy's 

 Principle of Continuity of Movement. But although the prin- 

 ciples from which M. Cauchy and Mr. Green start are identical, 

 their results differ in two important particulars : — 1st, M. Cauchy 

 has introduced a constant distinct from the index of refraction, 

 and depending on the nature of the reflecting body ; 2nd, the 

 particular manner in which the condition of evanescent normal 

 waves is introduced is different, so that the results differ in form 

 as well as in the number of constants. 



The publication* of M. Jamin's beautiful experiments on the 

 reflexion of light at the surface of transparent bodies, affords an 

 opportunity of comparing Mr. Green's formulae with observation. 

 In this paper I propose to compare the form of Mr. Green's 

 results with M. Jamin's experiments on sulphuret of arsenic, as 

 there can be no doubt but that M. Cauchy is right in intro- 

 ducing a second constant proper to the reflecting surface : this 

 will appear in the course of the comparison. 



Let I and J denote the amplitudes of the reflected vibration 

 of the unit of light polarized in and perpendicular to the plane 

 of incidence respectively. 



Let e and e t denote the difference of phase between the inci- 

 dent and refracted, and reflected and refracted rays respectively. 



Let t and r denote the angles of incidence and refraction. 



And let Q be defined by the following equation, 



Q= (jf-i)* W 



where ju, denotes the refractive index. 



* Annales de Chimie et de Physique, vol. xxix. p. 263. 



