IN PLATES, TUBES, AND CYLINDERS OF GLASS. 355 
being cooled rapidly from a red-heat, the axis perpendicular 
to the plane of the plate (which is always the principal axis), 
is positive ; but when the polarising structure is communicated 
by heating the plate in boiling oil, and then cooling it rapidly, 
the principal axis is negative. 
By measuring carefully the distances of the tints from the 
centre of the plate, I have found the following formula, dedu- 
ced from the supposition of two axes, perfectly correct, viz. 
t= Toa » where D is the distance of either of the black 
fringes or Jines of no polarisation from the centre of the plate. 
The term Se represents the influence of the principal axis, 
and would have given us the tint ¢ if that axis had existed 
alone. But as the axis in the plane of the plate produces an 
uniform tint T in every part of the plate, which acts in oppo- 
sition to the other tint; the tint ¢ must be equal to the differ- 
2 
ence of these tints, or to T— age 
In examining the relative intensities of the two axes in rec- 
tangular plates of considerable length, and in elliptical plates, 
in which the conjugate axis is very small when compared with 
the transverse axis, I have found that D, or half the distance 
between the black fringes, is a function of the breadth of the 
plate, that is, if B is the breadth of the plate 2D: B= 10: 16.02, 
and D=.312B*. As the excentricity of the elliptical plate 
diminishes, the value of D diminishes, or the polarising force 
of the axis in the plane of the plate diminishes ; and when the 
conjugate and transverse axes are equal, D is equal to 0, or the 
axis in the plane of the plate is destroyed. In elliptical plates, 
the black fringes which are seen when the transverse axis is 
inclined 45° to the plane of primitive polarisation, are convex 
towards the transverse axis, and their curvature is such, that 
they 
