or 



for Reflected and Refracted Light. 109 



theory. But it is easily seen that precisely the same remarks 

 apply if, instead of Maccullagh^s formulas, we adopt either of 

 the new forms of FresneFs, viz. — 



(B) which gives y^i), 



(C) which gives f ^=-j- j . 



The result of experiment would therefore seem equally decisive 

 against the hypothesis (A), and against (B) and (C) applied to 

 both N and k\ and would leave us to the sole adoption of FresneFs 

 original formulas (D). But before coming to this conclusion, 

 we must advert to another experimental case in which similar 

 considerations are involved. 



Dr. Lloyd's Interference Eocperiment. 



13. In an experiment long ago devised by Dr. Lloyd, a direct 

 ray interferes with one reflected at a very oblique incidence from 

 a plate of glass ; giving a set of stripes resembling generally one 

 half of those formed in the experiment of Fresnel when two 

 streams of direct light interfere (Mem. Roy. Irish Acad. vol. xvii. 

 ]834). 



In this experiment, it is first to be remarked that the first 

 dark band is intensely black, proving the equal intensity of the 

 interfering rays ; in agreement with theory, which at the extreme 

 incidence gives, on either hypothesis, reflected light of equal in- 

 tensity with the incident (see former paper (§58)). 



14. The stripes, however, present this peculiarity : on ordinary 

 suppositions, since the rays at the extreme limit must be in accord- 

 ance, there would first be half a blight band (reckoning from the 

 edge) followed by a whole dark, then a whole bright band, and 

 so on ; whereas, in fact, the first bright band is observed to be 

 of the entire breadth of an interval, as if the system commenced 

 from a point of discordance at the extreme limit, or as if the whole 

 were shifted from the edge through a distance equal to half the 

 interval of two bands. This was found to be equally the case 

 whether the light was previously polarized in a plane parallel or 

 perpendicular to the plane of incidence. In other words, the fact 

 indicates a diffei'ence in phase of 180° between the incident and 

 the reflected ray at the limit, and this equally in each case of the 

 direction of polarization. 



15. Now in FresneFs original formulas for vibrations perpen- 

 dicular to the plane of incidence, a difference of sign, indicative 

 of this difference o^ phase, occurs at all incidences in the formulas 

 for h', and for vibrations parallel to the plane of incidence at 



