BANDS SEEN IN THE SPECTRUM. 
233 
When the refractive indices of the plate and fluid are nearly equal, the last term in 
this equation may be considered insensible, so that it is not necessary to calculate /' 
at all. 
8. The formulae (2.), (4.), (5.), (6.) are of course applicable to the ordinary ray of 
a plate cut from a uniaxal crystal. If the plate be cut in a direction parallel to the 
axis, and if moreover the lower edge be parallel to the axis, so that the axis is parallel 
to the refracting edge of the prism, the formulae will apply to both rays. If (j,g, be 
the principal indices of refraction referring to the ordinary and extraordinary rays 
respectively, (jJ in the case last supposed must be replaced by for the bands polar- 
ized in a plane perpendicular to the plane of incidence, and by for the bands 
polarized in the plane of incidence. In the case of a plate cut from a biaxal crystal 
in such a direction that one of the principal axes, or axes of elasticity, is parallel to 
the refracting edge, the same formulae will apply to that system of bands which is 
polarized in the plane of ineidence. 
If the plate be cut from a biaxal crystal in a direction perpendicular to one of the 
principal axes, and be held in the vertical position, the formula (2.) will apply to both 
systems of bands, if the small effect of the obliquity be neglected. The formula would 
be exaet if the observations were taken by receiving each fixed line in succession at 
a perpendicular incidence. 
If the plate be cut from a uniaxal crystal in a direction perpendicular to the axis, 
and be held obliquely, we have for the extraordinary bands, which are polarized in a 
plane perpendicular to the plane of incidence, 
— i—fjj cos i), (7.) 
which is the same as the formula in Airy’s Tract, only modified so as to suit the case 
in which the plate is immersed in fluid, and expressed in terms of refractive indices 
instead of velocities. If we take a subsidiary angle j, determined by the equation 
sinj=— sin 
( 8 .) 
the formula (7.) becomes 
R=:T(|W/oCOSJ — /lACOSz), (9.) 
which is of the same form as (5.), and may be adapted to logarithmic calculation 
if required by assuming — = tan^>. The preceding formula will apply to the extra- 
ordinary bands formed by a plate cut from a biaxal crystal in the manner described 
in the last paragraph, and held obliquely, the extraordinary bands being understood 
to mean those which are polarized in a plane perpendicular to the plane of incidence. 
In this application we must take for /a,, those two of the three principal indices of 
refraction which are symmetrically related to the axis normal to the plate, and to 
the axis parallel to the plate, and lying in the plane of incidence, respectively; while 
