for Reflected and Refracted Light. 107 



account for FresneFs adoption of No. III. in one case {p) and 

 not in the other (x). That is, for vibrations parallel to the plane 

 of incidence this form is avowedly adopted by him, on the ground 

 that for that case the sign of the reflected vibration will be op- 

 posite to that of the incident at small incidences. But in the 

 case of vibrations perpendicular to the plane of incidence, he not 

 only makes no assumption of this form (Ilia.), but his result 

 being deduced directly from the analogy of impact — if this is to 

 be analysed up to the deduction of the same equation from the 

 principle of the vis viva — it -is evident (as shown in my former 

 paper (37)) that that analysis involves necessarily the assumption 

 of the law of equivalence No. II. Fresnel himself, however, 

 did not so deduce the equation, but appears to have simply 

 assumed it on the analogy of impact of elastic bodies. 



6. The assumption thus made by Fresnel (which he admits 

 to be somewhat empirical) in the one case, while no such assump- 

 tion is made in the other, may possibly be accounted for on the 

 consideration, that, in the case of vibrations parallel to the plane 

 of incidence alone, we can have any direct application of the 

 parallelogram of forces, from the construction of which he may 

 possibly have been led to this inference. In the other case, where 

 the vibrations are all perpendicular to the plane of incidence, 

 and parallel to the surface and to each other, no such construc- 

 tion can apply ; nor does he seem to have extended the idea of 

 mechanical equivalence by analogy to this case, as Maccullagh 

 has done. 



7. The crucial experiment of Professor Stokes obliges us to 

 set aside the supposition No. VI. (see former paper (62)), and 

 consequently (as the analysis shows) the supposition No. IV., 

 and thus the whole hypothesis (A) or MaccullagVs formulas. 

 Our choice then lies between the other hypotheses, or some new 

 combination. And it remains to decide whether the original form 

 of FresneFs formulas is of necessity required by any experimental 

 results, or whether the forms deduced on either of the hypotheses 

 :(B) or (C) will be equally applicable ; in other words, whether 

 the difference in the signs is of importance. 



Now in fact two well-known cases of experimental results are 

 adducible which appear to have a direct bearing on this question, 

 in which light we will proceed to examine them. 



Change in plane of Polarization, by Reflexion. 



8. It is a result long ago ascertained by the researches of 

 Fresnel, Arago, and Brewster (and, as far as the principal point 

 is concerned, easily capable of verification), that if a ray pre- 

 viously polarized in a plane inclined at a given angle to the plane 

 of incidence fall on a reflecting surface, then, after reflexion, in 



