364 PHOTOGEAPHY OF SOUND WAVES. 



ring, of course, does not show in the photograph, which is a sectional 

 view, but it will be seen that in one of the views (No. 4) the curved 

 edge has disappeared entirely. In reality it is passing through a ring 

 focus, and presently it will appear again on th(^ other side of the focus, 

 curved the other way. of course, and trailing along after the flat bot- 

 tom. This curious evolution of the wav(» can b(^ shown I)}- geomet- 

 rical construction, and T shall show later how its development can be 

 shown with tlu^ cinematograph. 



When the spherical waves start in one focus of an elliptical mirror, 

 they are transformed by reflection into converging spheres, which 

 shrink to a point at the other focus, the surface being aplanatic for 

 raj's issuing from a point. An elliptical mirror was made ])y l)ending 

 a strip (tig. 6, PI. I) of metal into the required form, and a sound wave 

 started at one of the foci. The transformation of the diverging into a 

 converging sphere and the shrinkage of the lattei- to a point at the 

 other focus are well shown (tig. 0). 



We will consider next another case of spherical aberration. When 

 parallel rays of light enter a concave mirror those I'cflected from 

 ^points of the mirror near its axis converge approximateh' to a point 

 situated halfway between the surface of the mirror and its center of 

 curvature. The wave front in the case of parallel ra3's is, of course, 

 plane and is changed by reflection into a converging shell of approxi- 

 mately spherical curvature. If we investigate the case more carefull}', 

 we tind, however, thtit the reflected rays do not come accuratel}' to a 

 focus, but envelop a surface known as the caustic — in this case an 

 epicycloid. The connection between the wave front and the caustic is 

 perhaps not at once apparent. Let us examine the changes wrought 

 on a sound wave entering a concave hemispherical mirror (tig. 7, PI. II). 



If we follow the wave during its entrance into the mirror, we see 

 that the reflected portion trails along behind, being united to the unre- 

 flected part at the mirror's surface. After the reflection is complete 

 we tind the reflected wave of a form not unlike a volcanic cone with 

 a large bowl-shaped crater (No. 4). This l)owl-shaped portion we may 

 regard as a converging shell, which shrinks to a point at the focus of 

 the mirror. As it shrinks the steep sides of the cone run in under the 

 bowl, crossing :it about the moment when the converging portion is 

 passing through the focus (No. 6). The rim of the crater forms a cusp 

 on the wave front, and if we follow this cusp we shall see that it traces 

 the caustic surface. Hence we may detine the caustic as the surface 

 traced bj^ the cusp of the wave front. 



The portion of the wave which comes to a focus at once begins to 

 diverge again, luiiting with the sides of the crater, the whole moving- 

 out of the mirror in a form somewhat resembling a mushroom or the 

 bell of a Medusa jellytish. The turned-under edges of the beil are 



