with our water-molecules.  Like our ideal magnets, they approach each other for a time as wholes.  Previous to reaching the temperature 39 deg.  Fahr., the polar forces had doubtless begun to act, but it is at this temperature that their claim to more room exactly balances the contraction due to cold.  At lower temperatures, as regards change of volume, the polar forces predominate.  But they carry on a struggle with the force of contraction until the freezing temperature is attained.  The molecules then close up to form solid crystals, a considerable augmentation of volume being the immediate consequence.

Sec. 3. Ordinary Refraction of Light explained by the Wave Theory.

We have now to exhibit the bearings of this act of crystallization upon optical phenomena.  According to the undulatory theory, the velocity of light in water and glass is less than in air.  Consider, then, a small portion of a wave issuing from a point of light so distant that the minute area may be regarded as practically plane.  Moving vertically downwards, and impinging on a horizontal surface of glass or water, the wave would go through the medium without change of direction.  As, however, the velocity in glass or water is less than the velocity in air, the wave would be retarded on passing into the denser medium.

[Illustration:  Fig. 25.]

But suppose the wave, before reaching the glass, to be oblique to the surface; that end of the wave which first reaches the medium will be the first retarded by it, the other portions as they enter the glass being retarded in succession.  It is easy to see that this retardation of the one end of the wave must cause it to swing round and change its front, so that when the wave has fully entered the glass its course is oblique to its original direction.  According to the undulatory theory, light is thus refracted.

With these considerations to guide us, let us follow the course of a beam of monochromatic light through our glass prism.  The velocity in air is to its velocity in glass as 3:  2.  Let A B C (fig. 25) be the section of our prism, and a b the section of a plane wave approaching it in the direction of the arrow.  When it reaches c d, one end of the wave is on the point of entering the glass.  Following it still further, it is obvious that while the portion of the wave still in the air passes over the distance c e, the wave in the glass will have passed over only two-thirds of this distance, or d f.  The line e f now marks the front of the wave.  Immersed wholly in the glass it pursues its way to g h, where the end g of the wave is on the point of escaping into the air.  During the time required by the end h of the wave to pass over the distance h k to the surface of the prism, the other end g, moving more rapidly, will have reached the point i.