88 Vibrations of a Film in reference to the PJioneidoscope, 



or six sets meeting in pairs whose directions do not make equal 

 angles with one another. 



In the phoneidoscope we have a soap -film thrown into a 

 state of vibration by a musical note. The effect is to send the 

 matter of the film towards the ventral segments, and to make 

 them the thickest part of the film. The consequence is that 

 the colours of thin plates are seen less at the ventral segments 

 than at other parts of the film; and we can recognize the ven- 

 tral segments in this manner. This effect on the film may be 

 illustrated by M. Decharme's experiments on Chladni's plates*, 

 in which he shows that if a thin layer of water instead of sand 

 be spread over the plate, the water covers the ventral segments 

 and the nodes are left bare. 



The two following experiments may, I think, be explained 

 by what has been said. 



(1) A square film, ^ of an inch in side, was thrown into 

 vibration by a note having 92 vibrations in a second. The 

 position of the ventral segments was that shown in figs. 5 

 and 7. Hence the vibration of the film was the result of four 

 sets of waves starting simultaneously from the four sides of 

 the film ; and the wave-length was approximately ^ of the side; 

 and the wave-velocity was approximately -J x \^ x 92 inches 

 per second — that is, about 28 inches per second. 



(2) An equilateral triangle, one inch in height, was thrown 

 into vibration by a note having 152 vibrations in a second. 

 The position of the ventral segments was that shown in figs. 

 4 and 6. Hence the vibration of the film may be the result 

 of three sets of waves starting simultaneously from the three 

 sides of the A, and giving by reflection three other sets moving 

 in the opposite directions. And the wave-length would then 

 be approximately -£- of the height ; and the wave-velocity was 

 approximately \ - x 1 x 152 inches per second, or about 30^ 

 inches per second. Or the figure may be the result of one set 

 of waves starting perpendicular to one of the sides of the tri- 

 angle (see fig. 8). In this case the wave-length would be ^ 

 of the side of the triangle ; and the wave-velocity would be 



3 2 



zrx x —-K x 152 inches per second, or about 52J inches per 



second. As this wave-velocity differs very much from the 

 wave -velocity derived from the experiment with the square 

 film, we must reject this latter explanation. 



The two experiments may be made to give the same wave- 

 velocity by supposing a change of phase equal to half a period 

 to take place at each reflection. In the first experiment the 



* Ann. de Chim. et de Phys. s6r. 5. vol, xvi. pp. 338-376. 



