You will now observe that such logic as connects our experiments is simply a transcript of the logic of Nature.  On the screen before you are two disks of light produced by the double refraction of Iceland spar.  They are, as you know, two images of the aperture through which the light issues from the camera.  Placing the tourmaline in front of the aperture, two images of the crystal will also be obtained; but now let us reason out beforehand what is to be expected from this experiment.  The light emergent from the tourmaline is polarized.  Placing the crystal with its axis horizontal, the vibrations of its transmitted light will be horizontal.  Now the spar, as already stated, has two directions of vibration, one of which at the present moment is vertical, the other horizontal.  What are we to conclude?  That the green light will be transmitted along the latter, which is parallel to the axis of the tourmaline, and not along the former, which is perpendicular to that axis.  Hence we may infer that one image of the tourmaline will show the ordinary green light of the crystal, while the other image will be black.  Tested by experiment, our reasoning is verified to the letter (fig. 29).

[Illustration:  Fig. 29.]

[Illustration; Fig. 30.]

Let us push our test still further.  By means of an endless screw, the crystal can be turned ninety degrees round.  The black image, as I turn, becomes gradually brighter, and the bright one gradually darker; at an angle of forty-five degrees both images are equally bright (fig. 30); while, when ninety degrees have been obtained, the axis of the crystal being then vertical, the bright and black images have changed places, exactly as reasoning would have led us to suppose (fig. 31).

[Illustration:  Fig. 31.]

[Illustration:  Fig. 32.]

Considering what has been already said (p. 114) regarding the reflection of light polarized by transmission through tourmaline, you will readily foresee what must occur when we receive upon a plate of glass, held at the polarizing angle, the two beams emergent from our prism of Iceland spar.  I cause both beams to pass side by side through the air, catch them on a glass plate, and seek to reflect them upwards.  At the polarizing angle one beam only is capable of being thus reflected.  Which?  Your prompt answer will be, The beam whose vibrations are horizontal (fig. 32).  I now turn the glass plate and try to reflect both beams laterally.  One of them only is reflected; that, namely, the vibrations of which are vertical (fig. 33).  It is plain that, by means either of the tourmaline or the reflecting glass, we can determine in a moment the direction of vibration in any polarized beam.

[Illustration:  Fig. 33.]