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will be seen that the empirical curve gives results somewhat too great for solar distances less than 60°, and too small for greater distances; but the deviation is so small, compared with the accidental errors, that we are justified in regarding the agreement as complete within the limits of errors of observation.

It will be noticed that no account is here taken of the points of no polarization or neutral points of the sky; but the polarization is very slight for some distance from them, and hence is not easily measured. They must be regarded as due to some secondary disturbing cause, as refracted light, which alters the general polarization of the sky but little.

When the polarimeter is directed towards a polished coloured plane surface, the two images assume different tints. One, which contains the light polarized in the plane of incidence, or A, is composed mainly of the light reflected specularly, and is therefore white like the source of light. The image B contains but little of the light reflected specularly, consisting principally of the rays emitted by the body, and hence partaking of its colour. The idea at once suggested itself, that testing the light of the sky in this way might give a clue to the cause of its colour. The experiment was tried several times with negative results, the two images appearing of precisely the same blue tint. But on the evening of July 15th, near sunset, when measuring the polarization of a point near the northern horizon where the blue colour was comparatively pale, a marked difference in the two images was observable. The image A was found to be of a yellowish brown, B of a greyish blue or violet tint. This observation has since been frequently repeated, and can, in fact, be made almost any clear evening near sunset. Evidently we may conclude from these colours that the true colour of the sky-particles is blue, a view quite in accordance with the observations of Professor Cooke with the spectroscope, and of Professor Tyndall on aqueous vapour in a state of formation.

Observations were next made to test the results found above for the light reflected and transmitted by several parallel surfaces of glass. To check the results which are given in figs. 6-10, two, and in some cases three independent methods were employed. To measure the polarization of the reflected ray, one or more sheets of glass were laid on a piece of black velvet and rendered horizontal with a spirit-level. The polarimeter was then mounted a short distance from them, carefully levelled, and then turned down so that the light should be reflected from their surfaces. Its angle of depression would then equal the complement of the angle of incidence. The line of junction of the two images was then rendered vertical, and the polarization measured in the usual way. The polarization of the sky, if

clear, would introduce a large error into the results; and care was therefore taken to make these observations only on cloudy days,

The second method was to replace the slit of a large Babinet's goniometer, or optical circle, by a Nicol's prism, which was free to turn round its axis, the angle of rotation being measured by a graduated circle and index. In the eyepiece of the observingtelescope a Nicol's prism was placed, and in front of it quartz wedges giving lines which were bright or dark-centred, according as the transmitted ray was polarized vertically or horizontally. On looking through the telescope, the field was seen to be traversed by lines, which disappeared only when the Nicol in the collimator was inclined 45° with the vertical. At any other angle, a, the vertical and horizontal components were cos2 a and sin2 a, and hence were equivalent to a beam polarized vertically by an amount cos 2a. If now any object was inserted between the two telescopes polarizing the light horizontally p, the bands would disappear only when p= cos 2a. Measuring the four positions of disappearance and taking their mean, gave an accurate measure of the polarization by a Table of natural cosines, as with the polarimeter described above. Another way of expressing the effect of this instrument is to say that the bands disappear when the Nicol is so turned that the plane of polarization shall be brought by the object under examination to an angle of 45°. The method of measuring the polarization of the reflected ray is now obvious. The pieces of glass are placed vertically on the centre plate between the two telescopes, the latter set at an angle of 2i, and the glass turned until the light is reflected from its surface, so as to render the field bright. The Nicol is then turned until the bands disappear, and its position recorded. The angle between the telescopes is then altered so as to make i successively 20°, 30°, 40°, &c., and the observation repeated. Various adjustments must be made to eliminate constant errors, but they need not be detailed here. One series was made with a glass prism having an index of 1·52, a second with a plate of coloured glass, a third with a sheet of plate glass, and others with four and ten microscope slides. The latter were used because the thickness of the plate glass was such that, when a number of plates were placed between the telescopes, a portion of the internal reflection would be lost.

To measure the polarization by refraction, two similar methods were employed. The plates were placed vertically over the centre of a graduated circle, and a piece of ground glass was viewed through them by the polarimeter. The plates were then set at various angles, and the polarization measured in each case. these observations were made in cloudy weather, to eliminate the

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effect of sky polarization. Several lines were made with the optical circle and Babinet's wedges, placing the telescopes opposite each other, and recording the angles of the Nicol for various positions of the plates. Still a third method was employed, already described in connexion with the Arago's polarimeter.

It will be noticed that no observations are given of the polarization of a beam transmitted by one surface of glass. There seemed to be no easy method of measuring this quantity. It might be done by making a series of prisms of such angles that when the light was incident on one face at 10°, 20°, 30°, &c., the refracted ray would strike normally on the second face. The effect of the latter would then be nothing; so that the polarization would in this case be entirely due to the first surface.

To determine the polarization of a single surface of glass, a plate was covered on one side with lampblack; but it was found to give the same results as when laid on velvet. A plate of coloured glass was therefore used instead.

Fig. 6 gives the results of the observations of the polarization effected by one surface of glass, fig. 7 that of two surfaces, fig. 8 of eight, fig. 9 the reflected beam for twenty surfaces, and fig. 10 the corresponding refracted beam. The smooth curves give the theoretical polarization, including the internal reflection, and the dotted lines omitting it. The observations of the reflected beam agree very well with theory, especially when the number of surfaces is small. The refracted beams, on the other hand, show a deviation from theory which becomes perceptible for one plate above 80°, for four plates above 65°, and for ten plates above 20°.

The errors most likely to occur, which would be common to all the observations on the refracted beams, are, first, stray light, or light entering the instrument without passing through the glass; secondly, light passing through the glass endwise, which might be recognized by its deep green colour; and thirdly, light reflected from the front surfaces of the plates. But all these errors would tend to diminish instead of increase the polarization; and hence, if eliminated, the divergence from theory would be still greater. Probably the true explanation is that internal reflection does not take place as completely as theory assumes, partly owing to the imperfect transparency of the medium, and partly to the dust and other impurities on the surface. It makes but little difference for the reflected rays, the polarization being the same for three values of i, namely, 0°, 57°, and 90°. For the refracted ray, on the other hand, the variations are very great, amounting in the case of twenty surfaces, at 90° incidence to over 50 per cent. From the dotted lines we see that a partial absence of the internal reflection would account

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