IN PLATES, TUBES, AND CYLINDERS OF GLASS. 35o 



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 d 2 

 t zz T---- r r|-, where D is the distance of either of the black 



fringes or lines of no polarisation from the centre of the plate. 



T d 2 

 The term -=-§- represents the influence of the principal axis, 



and would have given us the tint t 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 t must be equal to the differ- 



T d 2 

 ence of these tints, or to T ^-. 



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 2 D : B - 10 : 16.02, 

 and D zzz .312 B 2 . 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 



