PHOTOGEAPHY OF SOUND WAVES. 363 



it was usually possible to pick a series showing the wave in all stages 

 of its development, owing to the variations in the time interval 

 between the two sparks. 



In the Urst series the pictures were so small that it was necessary to 

 enlarge them several diameters. Those of the new series, owing to 

 the use of an 8-inch mirror in place of the 5-inch lens, and an objec- 

 tive of larger aperture and longer focus, required no enlarging. 



THE WAVE-FRONT PHOTOGRAPHS. 



In the study of optics we may treat the subject of regular reflection 

 in two ways, b}- ravs and by wave fronts. When spherical waves of 

 light are reflected from a plane surface, we know that the reflected 

 waves are also spherical in form, the center of curvature being a point 

 just as far beneath the reflecting surface as the source of light is above 

 it. In the first of the series of photographs we have the reflection of 

 a spherical wave of sound by a flat plate of glass, the wave appearing 

 as a circle of light and shade surrounding the image of the balls 

 between which the spark passed (fig. 3, PI. I). The reflected wave or 

 echo from the plate is seen to be spherical, with a curvature similar to 

 the incident wave. 



When we have a source of light in the focus of a parabolic mirror, 

 the rays leave the mirror's surface parallel to one another and move 

 out in an intense narrow beam. Treating this case from the wave- 

 front point of view, we ascertain b}" the usual geometrical construc- 

 tion that the spherical wave is changed by reflection into a plane or flat 

 wa^•e which moves out of the mirror without further divergence. In 

 the picture (fig. -i, PI. I) only a portion of the parabolic reflector is 

 shown near the bottom. The sound wave starts in the focus, and the 

 reflected portion appears quite flat.^ 



What happens now if we use a spherical mirror in the same way? 



Owing to the spherical aberration the reflected rays are not strictly 

 parallel, or the reflected wave is not a true plane. Let us start a sound 

 wave in the focus of such a mirror, and follow the reflected portion 

 out of the mirror (fig. 5, PL I). We notice that near the axis of the 

 mirror the effect is much the same as in the case of the parabola — that 

 is, the reflected front is plane. Thus we are accustomed to say that 

 if we confine ourselves to a small area around the axis, a mirror of 

 spherical form acts almost as well as a parabola. If, on the contrary, 

 we consider the reflection from the entire hemisphere, we see that the 

 reflected wave curls up at the edges, having a form not unlike a flat- 

 bottomed saucer. The flat bottom moves straight up, traveling every- 

 where normal to its surface; but the curled up edges converge inward, 

 coming to a focus in the form of a ring around the flat bottom. This 



^In thin series and some others left and right have been inadvertently interchanged 

 by tlie '.mgraver. The series should be followed by the numbers. 



