and the Evolutions of Reflected Wave-Fronts. 353 



Returning now to the evolutions of plane and spherical 

 waves after reflexion 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 conditions. 



Fig. 8. 



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 number 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 I devised 

 for building the series illustrating the reflexion of a plane 

 wave in a spherical mirror. The construction is shown in 

 the figure (p. 154). 



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 surface). If we erect 

 normals on this surface, we have the reflected rays, and if we 

 measure off equal distances on the normals, we have the 

 reflected wave-front. By drawing the orthogonal surface 

 we avoid the complication of having to measure off 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 curvature of the mirror on the mirror's 



