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186 ON THE PASSAGE OF WA\7ES THROUGH FINE SLITS, ETC.
These are the numbers used in the plot of curve B, fig. 1. When much smaller than £, the modulus may be taken to be %kzb2. When large, the modulus approaches the same limiting form as in case (i).
This curve is applicable to electric, or luminous, vibrations incident a thin perfectly conducting screen with a linear perforation when the el vector is parallel to the direction of the slit.
It appears that if the incident light be unpolarised, .vibrations pe dicular to the slit preponderate in the transmitted light when the width < slit is very small, and the more the smaller this width. In the neighbou of kb = 1, or 26 = A./TT, the curves cross, signifying that the transmitted is unpolarised. When kb = 1^-, or 2b — 3X/27T, the polarisation is rev vibrations parallel to the slit having the advantage, but this advantage very great. When kb > 2, our calculations would hardly succeed, but seems no reason for supposing that anything distinctive would occu: follows that if the incident light were white and if the width of the slit about one-third of the wave-length of yellow-green, there would be dist: marked opposite polarisations at the ends of the spectrum.
These numbers are in good agreement with the estimates of Fi " Une ligne polarise'e perpendiculairement a sa direction a paru e'tre de de millimetre; une autre, beaucoup moins lumineuse, polarisee parallels a sa direction, a et6 estimee a j^^- de millimetre. Je dois aj outer qn valeurs ne sont qu'une approximation; elles peuvent etre en realite1 faibles encore, mais il est peu probable qu'elles soient plus fortes qu'il y a de certain, c'est que la polarisation parallele n'apparait que les fentes les plus fines, et alors que leur largeur est bien moindre q longueur d'une oiylulatioii qui est environ de ^^ de millimetre." I be remembered that the "plane of polarisation" is perpendicular t< electric vector.
It may be well to emphasize that the calculations of this paper : to an aperture in an .infinitely thin perfectly conducting screen. We scarcely be sure beforehand that the" conditions are sufficiently satisfied by a scratch upon a silver deposit. The case of an ordinary spectre slit is quite different. It seems that here the polarisation observed wit finest practicable slits corresponds to that from the less fine scratch silver deposits.n were the screen complete ; the second, the alteration required to take account of the aperture ; and let us distinguish by the suffixes TO and p the values applicable upon the negative. (minus), and upon the positive side of the screen. In the present case we have ...es*, to which it would 1