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.
One must not suppose that these beautiful forms exist only in the laboratory. Every time we speak, spherical waves bounce off the floor, ceiling and walls of the room, while in any ordinary bowl or basin the curious crater-shaped echoes are formed. Glance once more at the wave surfaces produced within a hollow sphere, and try to imagine the complexity of the aerial vibrations caused by a fly buzzing around in an empty water-caraffe! The photographs enable us to realize what is going on around us all the time—this our perceptions are fortunately too dull to perceive. Life would be a nightmare if we were obliged to see the myriads of flying sound waves bounding and rebounding about us in every direction, and combining into grotesque and ever-changing forms. It is just as well, on the whole, that the light of the electric spark and the delicate optical device of Toepler are necessary to bring them into view.