from the point; the same is true in the case of the echo, the rays radiating from the image point below the reflecting surface. In all subsequent cases the reader can, if interested in tracing the analogy between sound and light, draw lines perpendicular to the reflected wave surfaces representing the system of reflected waves.
We will now consider a second case of reflection. We know that if a lamp is placed in the focus of a concave mirror, the rays, instead of diverging in all directions, issue from the mirror in a narrow beam. The headlight of a locomotive and the naval searchlight are examples of the practical use made of this property. If the curvature of the mirror is parabolical, the rays leaving it are parallel; consequently mirrors of this form are employed rather than spherical ones. But what has the mirror done to the wave surface which is obviously spherical when it leaves the lamp, and what is its form after reflection? The wave surface, I have said, is always perpendicular to the rays: consequently in cases where we have parallel rays we should expect the wave to be flat or plane.
Examine the second photograph, which shows a spherical sound wave
starting at the focus of a parabolic mirror. The echo appears as a straight line, instead of a circle as in the previous case, which shows us that the wave surface is flat.
If now our mirror is a portion of a sphere instead of a paraboloid, our reflected wave is not flat, and the reflected rays are not all parallel, the departure from parallelism increasing as we consider rays reflected from points farther and farther away from the center of the mirror. A photograph illustrating the reflection of sound under these conditions is next shown, the echo wave being shaped like a flat-bottomed saucer. As the saucer moves upward the curved sides converge to a focus at the edge of the flat bottom, disappearing for the moment (as is shown in the fourth picture of the series), and then reappearing on the under side after passing through the focus, the saucer turning inside out.
If, instead of having a hemisphere, as in the last case, we have a complete spherical mirror, shutting the wave up inside a hollow ball, we get exceedingly curious forms; for the wave can not get out, and is bounced back and forth, becoming more and more complicated at each reflection. This is illustrated in our next photograph, the mirror being