Kinematographic Demonstration of Reflected Wave-fronts. ^S'S 



curved sides come to a focus along the circular edge of the flat bottom, 

 so that in one position the front appears as a true plane (fig. 4) ; hut 



Fig. 4. 



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

 diverge again and follow the flat bottom. The cusp formed b}^ the 

 union of these two portions traces the caustic siu*face, which is in this 

 case a very tapering funnel, as is shown well by the geometrical con- 

 struction (fig. 5). 



Fig. 5. 



If now we substitute for the hemisphere a complete sphere, we 

 obtain very complex forms which cannot be followed except by 

 geometrical constructions, for the wave is shut up in the mirror and 

 reflected back and forth, becoming more complicated at each reflection 

 (fig. 6). That all of these very intricate forms can be constructed by 



z 2 



