A complete discussion of all of the cases that have been studied in this way would probably prove wearisome to the general reader. Prisms and lenses of collodion filled with carbonic acid and hydrogen gas have been made, and their action on the wave surface photographed. Diffraction, or the bending of the waves around obstacles, and the very complicated effects when the waves are reflected from corrugated surfaces, are also well shown. I shall, however, omit further mention of them and speak of but one other case, possibly the most beautiful of all. [Illustration: FIG. 8. A MUSICAL TONE.] In all the cases that we have considered, it must be remembered that we have been dealing with a single wave--a pulse, as it is called. Musical tones are caused by trains of waves, the pitch of the note corresponding to the distance between the waves, or to the rate at which the separate pulses beat upon the drum of the ear. For studying the changes produced by reflection, wave trains would have been useless, owing to the confusion which would have resulted from the superposition of the different waves. Moreover, it is doubtful whether an ordinary musical tone could be photographed in this way; for the distance between the waves, even in the shrillest tones, is four or five inches, and the abrupt change in density, necessary for the perception of the wave, is not present. It is possible, however, to create a wave train or musical tone which can be photographed. The reader may perhaps have noticed that on a very still night, when walking beside a picket fence or in front of a high flight of steps, the sounds of his footsteps are echoed from the palings as metallic squeaks. Each picket, as the single wave caused by the footfall sweeps along the fence, reflects a little wave; consequently a train of waves falls on the ear, the distance between the waves corresponding to the distance between the pickets. The closer together the pickets, the shriller the squeak. In point of fact, the distance between the waves in such a train is twice the distance between the palings, since they are not struck simultaneously by the footstep wave, but in succession. This phenomenon, of the creation of a musical tone by the reflection of a noise, was reproduced by reflecting the crack of the spark from a little flight of steps. In the first picture the wave is seen half way between its origin and the reflecting surface. In the second it has struck the top stair, which is giving off its echo, the first wave of our artificially constructed musical tone. In the third we find the original wave at the sixth step, with a well-developed train of five waves rising from the flight. The following three pictures show the further development of the wave train. The height of each step was about a quarter of an inch; consequently the distance between the waves was half an inch. This would correspond to a note about three octaves above the highest ever used in music.