Again, if we take a natural crystal of calcareous spar, and paste upon one side of it a piece of black paper with a small hole in the middle, on holding the crystal to the light or over a piece of white paper, with the covered side next the light, two holes or two images of the hole will be seen; and if the crystal without the paper be placed over some print, the print will appear double. Hence the light passing through the hole is twice or doubly refracted, one ray following the ordinary law of refraction, while the other follows a different law, being retarded and pursuing a longer course; and so the two rays are called respectively the ordinary and extraordinary ray. And on viewing these through a tourmaline or a Nicol’s prism, as in the experiment with the two tourmalines, the images will become alternately visible and invisible, just as was then the case with the entire mass of light. The light which has undergone this singular change is said to be polarized, because the rays appear to have acquired poles or sides. In the above experiments the lower prism or tourmaline is called the polarizer, because it polarizes the light, and the upper is called the analyzer, because it analyzes or tests the light altered by the former. An idea of the cause of this change may be obtained by reference to the undulatory theory of light. Ordinary light consists of waves or undulations taking place in planes at right angles to each other, or in all planes; while in polarized light the undulations are all in one plane or in parallel planes. This may perhaps be understood by considering that books in a book-case are situated in parallel planes, the shelves being in planes at right angles to the former. And by imagining in polarizing substances the existence of some structure acting like a grating, a notion can be obtained how the rays in the different planes may be transmitted or intercepted. If the grating be so placed that the bars (representing the planes of polarization) are perpendicular, the books can pass between them; while if the grating be turned round a quarter of a circle, they will become transverse, and the books cannot pass, while the shelves could do so. Carrying on this analogy, the tourmaline or Nicol’s prism polarizes the light by transmitting only those rays whose undulations are in planes parallel to the bars; while the analyzer allows these undulations to pass through it when the direction of the planes coincides with that of the bars, but interrupts them when their direction is at right angles to the bars. And it is evident that the planes of polarization of the ordinary and extraordinary rays are opposite, from the opposite action of the analyzer upon them.