284 Prof. E. W. Wood. Photography of Sound-vMces, and the 



volcanic cone with a bowl-shaped crater, the bowl eventually collapsing- 

 to a point, at the focus of the mirror, the sides of the cone running in 

 under it and crossing. From now on the wave diverges, and goes out 

 of the mirror in a form somewhat resembling the bell of a medusa, the 

 caustic form by twice-reflected rays being traced by a second cusp 

 (fig. 2). 



Fig. 2. 



These forms can, of course, be constructed geometrically, and we 

 have here a slide with a number of successive positions of the wave- 

 front, showing how the cusps follow the caustic surface (fig. 3). The 



Tig. 3. 



construction shows that there is a concentration of energy at the cusp ; 

 consequently we may define the cusp as a mo-^dng focus, and the caustic 

 as the surface traced by it. Though I hesitate in claiming that this rela- 

 tion, at once so apparent, is at all novel, I may say that, so far as I 

 have been able to find, it is not brought out in any of the text-books, 

 caustic surfaces being invariably treated by ra?/ rather than by ^mve- 

 fronf methods. 



If the wave starts at the principal focus of a hemispherical mirror, 

 the I'eflected front is nearly plane in the vicinity of the axis, curhng 

 up at the edges, however. As this flat-bottomed saucer moves up, the 



