August 9, 1 900] 



NATURE 



347 



arranged on a cylindrical surface, the wave starting at 

 the centre of curvature. In No. 2 of the series the union 

 of the secondary disturbances coming from the openings 



into a new wave-front is beautifully shown. In No. 3 



the reflected wavelets have converged to the centre, but 



as each one is a complete hemicylinder, we see them 



radiating from the centre. This form 



can be constructed by describing 



semicircles around points on a circle 



of such radius that they all pass 



through the circle's centre. These 



semicircles represent secondary 



wavelets starting simultaneously 



from the various grating elements. 



In the last three pictures of the 



series the wave passes dAwn, strikes 



the table, and is reflected up again, 



and it is interesting to see how the 



medium is broken up into meshes 



by the crossing and recrossing of 



the secondary waves. 



Fig. 17 shows the form of the 

 secondary wavelets formed by the 

 reflection of a wave from a corrugated 

 surface, and is interesting in con- 

 nection with reflection gratings. 



The formation of a musical note 

 by the reflection of a single pulse 

 from a flight of steps is shown photo- 

 graphed in Fig. 18. This pheno- 

 menon is often noticed on a still 

 night when walking on a stone pave- 

 ment alongside a picket-fence, the 

 sound of each footstep being reflected 

 from the pailings as a metallic squeak, 

 which Young has pointed out to be analogous to the 

 power of a diff'raclion grating to construct light of a 

 definite wave-length. 



It occurred to me,, while making some geometrical 



NO. 1606, VOL. 62] 



constructions to aid in unravelling some of the com- 

 plicated forms reflected from surfaces of circular curva- 

 ture, that a very vivid idea of how these curious wave- 

 fronts are derived one from another 

 could be obtained if a complete series 

 could be prepared on the film of a. 

 cinematograph, and projected ir> 

 motion on a screen. 



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 cine- 

 matograph film. 



As a very large number of draw- 

 ings (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 build- 

 ing the series illustrating the reflec- 

 tion of a plane wave in a spherical 

 mirror. The construction is shown, 

 in Fig. 19. 



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 oflf 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 



vcvOOO 



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 surface, and normals can be 

 erected by drawing the arc FG (the path of the centre of 



