[Illustration: FIG. 23.—Interfering ripples on a mercury surface, showing interference along hyperbolic lines (Vincent).] All along each hyperbola the disturbance due to the combined effect of the waves is either doubled or annulled when compared with that due to each wave-train separately. With the apparatus described, we can arrange to create and adjust two sets of similar water ripples from origins not far apart, and on looking at the complicated shadow-pattern due to the interference of the waves, we shall be able to trace out certain white lines along which the waves are annulled, these lines being hyperbolic curves (see Fig. 23). With the same appliances another characteristic of wave-motion, which is equally important, can be well shown. [Illustration: FIG. 24.] We make one half of the circular tank in which the ripples are generated much more shallow than the other half, by placing in it a thick semicircular plate of glass. It has already been explained that the speed with which long waves travel in a canal increases with the depth of the water in the canal. The same is true, with certain restrictions, of ripples produced in a confined space or tank, one part of which is much shallower than the rest. If waves are made by dropping water on to the water-surface in the deeper part of the tank, they will travel more quickly in this deeper part than in the shallower portion. We can then adjust the water-dropping jet in such a position that it creates circular ripples which originate in deep water, but at certain places pass over a boundary into a region of shallower water (see Fig. 24). The left-hand side of the circular tank represented in the diagram is more shallow than the right-hand side. When this is done, we notice two interesting facts, viz. that the wave-lines are bent, or _refracted_, where they pass over the boundary, and that the waves are shorter or nearer together in the shallower region. This bending, or refraction, of a wave-front in passing the boundary line between two districts in which the wave has different velocities is an exceedingly important characteristic of wave-motion, and we shall have brought before us the analogous facts in speaking of waves in air and waves in æther. [Illustration: FIG. 25.]