Kineinaiographic Demo list ration of Reflected Wave-fronts. 287 



well as the very beautiful instance of the formation of a train of waves, 

 or musical note, by the reflection of a single pulse from a steep flight 

 of steps (fig. 8). 



Fig. 8. 



lie turning now to the evolutions of plane and spherical waves after 

 reflection from spherical surfaces, I wish to bring to the attention of 

 the Society a method of demonstrating in a most graphic manner the 

 progressive changes in the wave-front reflected under these con- 

 ditions. 



Having been unable to so control the time interval between the two 

 sparks that a progressive series could be taken, I adopted the simpler 

 method of making a large niunber of geometrical constructions, and 

 then photographing them on a kinetoscope film. 



As a very large number of drawings (100 or so) must be made if the 

 result is to be at all satisfactory, a method is desirable that -will reduce 

 the labour to a minimum. I may be permitted to give, as an 

 instance, the method that 1 devised for building the series illustrating 

 the reflection of a plane wave in a spherical mirror. The construction 

 is shown in the figure. 



ABC is the mirror, AOC the plane wave. Around points on ABC 

 as centres describe circles tangent to the wave. These circles will be 

 enveloped by another surface, ADE, below the mirror (the orthogonal 

 siu-face). If we erect normals on this siu-face, we have the reflected 

 rays, and if we measm^e off" equal distances on the normals, we have the' 

 reflected wave-front. By drawing the orthogonal surface we avoid' 

 the complication of haAang to measure ofi" the distances around a 

 corner. The orthogonal surface is an epicycloid formed by the rolling- 

 of a circle of a diameter equal to the radius of ciu-vature of the mirror 

 on the mirror's surface, and normals can be erected by drawing the- 



