150 Prof. R. W. Wood on Photography of Sound- Waves 



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 construction shows that there is a 



Fig. 3. 



concentration of energy at the cusp ; consequently we may 

 define the cusp as a moving focus, and the caustic as the 

 surface traced by it. Though I hesitate in claiming that this 

 relation, 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 ray rather than by wave-front methods. 



If the wave starts at the principal focus of a hemispherical 

 mirror, the reflected front is nearly plane in the vicinity of 

 the axis, curling up at the edges, however. As this flat- 

 bottomed saucer moves up, the curved sides come to a focus 

 along the circular edge of the flat bottom, so that in one 



Fig. 4. 



position the front appears as a true plane (fig. 4) ; but from 

 this point on the curved sides, having passed through a focus, 

 diverge again and follow the flat bottom. The cusp formed 

 by the union of these two portions traces the caustic surface, 



