[Illustration: FIG 9. THE REFLECTION INSIDE THE HOLLOW SPHERE.] While experimenting with the complete circular mirror, which, it will be remembered, gave the most complicated forms, it occurred to me that a very vivid idea of how these curious wave surfaces are produced could be obtained by preparing a complete series in proper order on a kinetoscope film, and then projecting them in succession on the screen. The experimental difficulties were, however, too great to make it seem worth while to attempt to obtain a series of pictures of the actual waves, it being very difficult to accurately regulate the time interval between the two sparks. The easier method of making a large number of geometrical constructions, and then photographing them in succession on the film, was accordingly adopted. Three complete sets of drawings, to the number of about one hundred each, were prepared for three separate cases of reflection;--viz.: the entrance of a plane wave into a hemispherical mirror, the passage of a spherical wave out from the focus of a hemispherical mirror, and the multiple reflection of a spherical wave inside of a complete spherical mirror. Special methods were devised for simplifying the constructions, and much less labor was required in the preparation of the diagrams than one would suppose. The results fully justified the labor, the evolutions of the waves being shown in a most striking manner. These films I exhibited before the Royal Society in February last, and a more complete description of the manner of preparing them may be found in the Proceedings of the Society. A portion of one of these series is reproduced, about one in four or five of the separate diagrams being given. The series runs from left to right in horizontal rows. When projected on the screen, the spherical wave is seen gradually to expand from the focus point, like a swelling soap bubble; it strikes the surface, and the bowl-shaped echo bounces off and follows the unreflected portion across the field; these two portions are then reflected in turn, and the curiously looped wave flies back and forth across the mirror, changing continuously all the time, and becoming more complicated at each reflection. These diagrams should be compared with the photographs shown in the fourth series.