188 j\I. F. Eisenlohr on the Relation between the direction of 



aiTives at the bounding surface of two mediums, tlie motion of the 

 aether at this surface must be the same, and also must be conti- 

 nuous in both mediums, but taking into account therewith the 

 longitudinal vibrations, he found that the formidse previously 

 enunciated by Fresnel, which had not regarded these vibrations, 

 must be modified. These modifications were confirmed in the 

 most remarkable manner by the researches of Jamin. The 

 accuracy, indeed, with which the observed elliptic polarization, 

 and the intensity of reflected light, fulfil the hypotheses of 

 Cauchy is so great, that it hardly leaves a doubt of the sound- 

 ness of the theoretical basis of the latter ; and particularly the 

 hypothesis advanced by Cauchy, that the vibrations of the par- 

 ticles of fether in polarized light are perpendicular to the plane 

 of polarization, must be regarded as established. I have accord- 

 ingly felt no hesitation in applying to the theory of diffraction 

 the above-mentioned conditions, viz. that the motion of the par- 

 ticles of iether at the bounding surface of two mediums is the 

 same, and is continuous in both. In this way I have found that 

 the longitudinal vibrations, in this case at all events, exert a con- 

 siderable influence ; much greater, indeed, than in the experi- 

 ments of Jamin, since in these experiments a magnitude had to 

 be considered which depended on the very small difference of 

 the length of the waves, or, more correctly speaking, of the co- 

 efiicients of absorption of the longitudinal vibrations in the two 

 mediums, whereas the intensity of difi'racted light depends on 

 the product of these coefficients. For the present I shall con- 

 tent myself with announcing the results I have obtained, and 

 indicating generally the methods by which they were arrived at, 

 deferring the more detailed calculations to another occasion. 



We might expect to be not far out in determining the relative 

 intensity of rays of light that vibrate perpendicularly to the plane 

 of diffraction and those that vibrate in that plane, if we regarded 

 the ray diffracted out of glass into air as generated by the refrac- 

 tion of a ray whose direction is connected with that of the dif- 

 fracted ray by the law of Snellius, but whose vibrations are 

 parallel to the surface of the glass. In this way, with the assist- 

 ance of the above-mentioned conditions, we get a formula which 

 agrees tolerably well with the experiments of Holtzmann. But 

 the perpendicularly incident light is replaced in its effect on the 

 diffracted ray by an oblique pencil on the surface of the glass 

 itself, though not in the stratum lying infinitely close to that 

 surface, which it is necessary to consider according to the prin- 

 ciple of continuity. If this be so, we get the more accurate 

 equation now to be communicated. 



Let 7 and y' have the same meanings as before, let n be the 

 index of diflraction for glass, X, the length of a wave in glass, 



