PHOTOGRAPHY OF SOUND WAVES. 369 



The center of the mirror and the point where its axis meets the 

 surface are also indicated in the same manner. The sheets are now 

 separated, and t-orrespondino- pin holes are united on each sheet by a 

 broad black line, which represents the wave front. After a time it 

 becomes necessary to consider double reflections, and to do this we are 

 compelled to construct twnce-reflected rays (indicated by dotted lines), 

 and measui-e around a corner each time. 



About a hundred pictures are prepared for each series, and the 

 pictures then photoo-raphed separately on the tilm, which, when mm 

 through the animatog'raph, giye a very \'iyid representation of the 

 motion of the wave front. 



Three films have been prepared thus far — reflection of a wave enter- 

 ing a concave hemispherical mirror (flg. iJO, PI. V); reflection of a 

 spherical wave starting in the principal focus of a concaye hemi- 

 spherical mirror (fig. ^1, PI. V), and the reflection of a similar wave 

 within a complete spherical mirror (fig. 22, PI. VI). A number of these 

 constructions, taken at intervals along the film, are reproduced, and 

 comparison of them with the actual photographs shows the close agree- 

 ment between the calculated forms and those actually obtained. 



I have alread}" mentioned the fact that the cusps on the wave fronts 

 trace out the caustic surfaces. This is beautifully shown in figs. 23 

 and 2-i, PI. VI, where the successiye fronts are seen superposed. The 

 former is for the reflection of a plane wave in a spherical mirror, the 

 latter for the reflection of a spherical wave starting at the focus of a 

 similar mirror. The caustic curve is shown by a dotted line in fig. 23, 

 and is seen to be traced by the cusps on the wave fronts. The con- 

 struction shows that there is a concentration of energy at the cusp; 

 consequently w^e 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 l)een 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. 



The cinematograph series illustrating reflection inside a comph^te 

 sphere was the most diflicult to prepare, as several reflections had to 

 be considered. It has been completed for three reflections, and ^Ir. 

 Max Mason, of Madison, to whom I am greatly indebted for his patient 

 work in assistino- me, is ffoing on with the series. As will be seen, the 

 wave has already become quite complicated, and it will be mteresting 

 to see what further changes result after three or four more reflections. 

 I am also under obligations to Prof. A. B. Porter, of Chicago, who 

 prepared the set of drawings illustrating the passage of a wave out 

 from the principal focus of a hemispherical mirror. 



