Very elaborate observations have been made during several Arctic expeditions of the azimuths of the summits of auroral arcs.
As to the azimuths in individual cases, 130 differed from the mean by less than 10°, 118 by from 10° to 20°, 82 by from 20° to 30°, 21 by from 30° to 40°, 14 by from 40° to 50°; in six cases the departure exceeded 50°, and in one case it exceeded 70°.
Also, whilst the mean azimuths deduced from the observations between 6 A.M.
As to individual azimuths, 113 lay within 10° of the mean, 37 differed by from 10° to 20°, 18 by from 20° to 30°, 6 by from 30° to 40°, whilst 6 differed by over 40°.
Azimuths were also measured at Jan Mayen for 338 auroral bands, the mean being 22.0° W., or 7.9° to the east of the magnetic meridian.
The instrument is thus a theodolite, although, compared with its other dimensions, feeble as an apparatus for the measurement of absolute altitudes and azimuths, although capable of determining these co-ordinates with considerable precision.
The almucantar was therefore used only to observe the vertical transits of stars in different azimuths over fixed horizontal webs, without touching the telescope.
If the incident light be polarized in a plane, making an angle a with the plane of incidence, the stream may be resolved into two that are polarized in the principal azimuths, and these will be reflected in accordance with the above laws.
Franz Neumann and James MacCullagh, starting from the opposite assumption of constant density and different elasticities, arrived at the same formulae for the intensities of the reflected light polarized in the principal azimuths, but in this case the vibrations must be regarded as parallel to the plane of polarization.
Applying this interpretation to the formulae given above, it follows that when the incident light is polarized at an azimuth a to the plane of incidence and the second medium is the less refracting, the reflected light at angles of incidence exceeding the critical angle is elliptically polarized with a difference of phase A between the components polarized in the principal azimuths that is given by tan (A/2) =cot i l l (1 - µ 2 cosec 2 i).
Wernicke and others have established that in general light polarized in any but the principal azimuths becomes elliptically polarized by reflection, the relative retardation of phase of the components polarized in these azimuths becoming 42 at a certain angle of incidence, called the principal incidence.