Page:Scientific Memoirs, Vol. 1 (1837).djvu/94

then will

$m-m_{\prime }=(o-e)\left({\frac {1}{\lambda }}-{\frac {1}{\lambda _{\prime }}}\right).$

As ${\frac {1}{\lambda }}-{\frac {1}{\lambda _{\prime }}}$ is a constant quantity for a definite substance, the difference $m-m_{\prime }$ will be proportional to the quantity $o-e$. Hence it follows, That when for one definite colour the light is circularly polarized by an interposed crystallized lamina, it may for the other colours be linearly and oppositely circularly polarized, and that the difference between the single colours increases with the thickness of the lamina and with the intensity of the double refraction.

If the incident light is circular for the centre of the spectrum, when the diiference of path is ¼ for ths centre, the light is not yet linear for the extreme limits of the spectrum. If it is here linear in the red, with a ½ undulation difference of path, in the blue it is circular. With ¾ difference of path in the red, it will, if it is circular to the right, be linear in the blue, and circular to the left in the extreme violet. Linear light in the red, with difference of path 1 , gives on the left in the green a circular light, in the indigo a linear light perpendicular thereto and approaching the circular on the right in the extreme violet; finally, on the left, circular in the red, with difference of path ⁵⁄₄, will give linear in the yellow, circular on the right where the blue passes into the indigo, and perpendicular to it linear at the commencement of the violet, and so forth. In order to prove this by experiment an equilateral prism of Guinand's flint glass was placed upright, so that after the removal of the condensing-lens $p$ the red end of the spectrum fell exactly upon the aperture e of the Nicol's polarizing prism. The cube had by gradual heating exhibited the phænomena which corresponded to a difference of path of ¼,½ ¾, undulation, and the other coloured rays were brought into the axis of the polarizing-apparatus, and the alteration of the Iceland spar figure examined. This might easily be accomplished without revolving the prism, as the height of the instrument may be altered at pleasure by means of the sliding-tube, as may its inclination by means of the motion of the prismatic rod. Mica plates of various thicknesses were examined in the same manner as the heated cube. The changes may be seen most beautifully when, beginning with the violet, the instrument is slowly lowered in the sliding-tube through the single colours of the spectrum. The gradual transitions are, in respect to the difference of colours from one end of it to the other, exactly the same as those which are obtained by the heating and cooling of the cube.

In the same manner the phænomena, when the incident light is circularly analysed by a mica plate inserted before the Iceland spar, are throughout similar to those before described. Instead of the homogeneous rays of the spectrum, we can of course also employ in these experiments a monochromatic lamp or absorption by coloured glasses. It is only when the light has been circularly polarized in one colour