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expected net polarization, while at high inclination, the polarization is reduced by occultation Their analysis was also applied to the variation of polarization from binary systems in which the scattering material consists of a rotating onedimensional plume etween the stars, superposed on an axisymmetric disc They showed that the inclination of the system and the radial structure of the plume can be deduced for suf ciently high inclinations (i > 60 ) The extent to which the method can be generalized to an arbitrarily distributed two-dimensional scattering region was considered via Fourier analysis It was found that the inclination of the system is largely insensitive to the density distribution when the distribution function is of a simple power-law form The question was also raised that for some stars, the polar mass loss will have a greater ionization fraction than the equatorial region, such that the pole might be the dominant source for free electrons In the third paper of this series, Fox (1991) considered the effects of occultation and nite sized-source depolarization, concluding that the net polarization has a complicated inclination dependence, and that the simple result of it being p / sin2 i, obtained by Brown & McLean (1977), does not hold For Be stars with high intrinsic polarizations, the circumstellar envelope must be concentrated either towards equatorial or polar regions, and that a substantial optical depth is required with > 005 The possible variability of the observed polarization from an obliquely rotating envelope has been investigated by Fox (1992), such a scenario having been mooted by others as being an alternative interpretation to diagnoses involving binary motion, but with lack of spectroscopic evidence to add weight to such duplicity The results of the exercise were not too sanguine as it was evident that effects due to rotation about a body axis and binary orbital motion are indistinguishable It was also found that the physical geometry of the obliquely rotating envelope could not be inferred When the light source is considered to have nite extent, discrimination between envelope geometries emerges to some degree as a result of the occultation of parts of the envelope by the extended source Further modelling by Fox (1993a) has emphasized the effect that an extended light source has on the resulting polarization by scattering in circumstellar envelopes If the underlying star is non-spherical, as a result of its large rotational velocity say, its photosphere will also generate a net polarization, adding to that which is produced by scattering within the extended atmosphere This situation has been modelled by Fox (1993a) who found that, in general, the predicted polarization was a factor of 2 3 times larger than what is observed for Be star systems It was also noted that the theoretical models for Be star envelopes had not yet reached a level of sophistication to estimate by polarimetry the number density of free electrons throughout the circumstellar envelope The origin of stellar winds in Be stars may be in uenced by magnetic elds and Fox (1993b) has considered this additional parameter in polarimetric models From his analysis, the range of observed values of p can be explained if the stars possess small magnetic elds of B0 < 100 G Observed increases in p during the onset of a shell phase is indicative of an increased magnetic eld.



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of a polarizer in a rotatable mount calibrated in angular measure by suspending it in a beam of polarized light The exercise requires that the extinction is obtained, and the angular setting noted; after rotating the mount by 180 about the suspension axis, extinction is obtained again, and the setting noted on the mount The mid-point between the two noted angular measurements corresponds to the axis of the polarizer According to Aspnes (1970), however, small systematic errors can occur with this technique when determining the axis of prism polarizers such as the Glan Taylor air-gap calcite device It has also been noted by Serkowski (1974a) that some Polaroids are not perfect in that they may rotate the direction of vibration by as much as 0 2 To secure the reference axis of a Polaroid with respect to equatorial coordinates, Serkowski (1965) directed the telescope to the daylight cloudy sky with the telescope exactly in the meridian By placing a glass plate in a perfectly horizontal position, the telescope was adjusted in Declination so that the sky was viewed through it and the Polaroid after re ection at Brewster s angle Extinction was achieved by rotation of the Polaroid to an angular setting with uncertainty not exceeding 0 3 In the exercise to establish a set of polarization standard stars for the Hubble Space Telescope, Schmidt, Elston & Lupie (1992) measured lunar light scattered by the Earth s atmosphere in the Sun Moon Earth plane, the polarization azimuth being normal to this The direction of vibration of the polarization of light from planets or asteroids is either perpendicular or parallel to the scattering plane, according to the phase angle Calibration of the instrumental axis relative to equatorial coordinates can be obtained by observing these objects at suitable phase angles as suggested by Serkowski (1974a), following an earlier description of the process by Gehrels & Teska (1960) In the scheme devised by Dolan & Tapia (1986), a Glan Thompson prism was insertable in a slide so that its principal axis was aligned with cross-hairs of the eyepiece used to view the eld around any target star The polarimeter was then rotated on its mounting plate so that the cross-hairs were parallel to the N/S and E/W directions, this being checked by moving the telescope in these directions via the guidance controls When inserted, the polarizing prism converts any targeted star to act as a reference source with p D 100%, and with the position angle parallel to the N/S axis of equatorial coordinates For this arrangement the reference axis was determined with an uncertainty < 0 1 Another possibility might involve the use of an insertable Savart plate so that a pair of stars produces four images By rotating the plate these images may be adjusted so that they are co-linear Each of the four pencils will comprise light with p D 100%, with directions of vibration set at 45 to the line joining the images; one pair of images will carry a direction of vibration orthogonal to that of the other pair Measurement of the polarizations allows the directions of vibration to be referred to the line joining the images which in turn can be related to equatorial coordinates via the catalogued coordinates of the pair of stars Most new polarimetric studies do not undertake fundamental observational procedures as outlined above, but determine the instrumental axis by reference to.

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