344 FOURTH REPORT— 1834. 



Young accordingly predicted that in this case the rings should 

 commence from a tvhite centre, instead of a black one, and the 

 prediction was soon after verified on trial*. 



The transmitted rings are accounted for, in the wave-theory, 

 by the interference of the direct light with that which has un- 

 dergone two reflexions within the plate; and it follows from the 

 preceding considerations that their colours must be comple- 

 mentary to those of the reflected system. This origin at once 

 shows the reason of the fact observed by M. Arago, that the 

 light of the transmitted rings is polarized in the jilane of re- 

 jiexion. M. Biot has laboured to reconcile this fact to the theory 

 of emission, with which it appears, at first view, at utter vari- 

 ance. The account which he has given of the phenomenon will, 

 I think, be hardly deemed satisfactory t- 



The theory of thin plates, as it came from the hands of Young, 

 was however incomplete. It is obvious that the intensity of the 

 two portions of light reflected from the upper and under sur- 

 faces of the plate can never be the same, the light incident on 

 the second surface being already weakened by partial reflexion 

 at the first. These two portions therefore cannot wholly destroy 

 one another b}^ interference; and the intensity of the light in the 

 dark rings^hould never entirely vanish, as it appears to do when 

 homogeneous light is employed. M. Poisson was the first to 

 point out and to remedy this defect of the theory. It is evident, 

 in fact, that there must be an infinite number of partial reflexions 

 within the plate, at each of which a portion is transmitted; and 

 that it is the sum of all these portions, and not the two first 

 terms of the series only, which is to be considered in the calcu- 

 lation of the eff"ect. Taking up the problem in this more gene- 

 ral form, and employing the formula obtained by himself and 

 Young for the intensity of the light reflected and transmitted at 

 a perpendicular incidence, M. Poisson has proved that — at this 

 incidence, and at points for which the thickness of the plate is 

 an exact multiple of the length of half a wave, — the intensity of 

 the reflected and transmitted lights will be the same as if the 

 plate were suppressed altogether, and the bounding media in ab- 

 solute contact ; so that when these media are of the same re- 

 fractive power, the reflected light must vanish altogether, and 

 the transmitted light be equal to the incident |. Fresnel after- 



• " Account of some Cases of the Production of Colours," Phil. Trans. 1802. 



t See Biot's " Traite de Physique" torn. iv. p. 308, et seq. 



% " Sur le Phenomene des Anneaux colores," Annales de Chimie, tom.xxii. 

 p. 337. M. Poisson has further shown that rings absolutely black will be formed 

 jit points corresponding to the bright rings in the ordinary case, when the velo- 



