56 DISPLACEMENT INTERFEROMETRY APPLIED TO 



across the room. For the usual conversational intensity, the fringes are not 

 perceptibly crimped. The equivalent displacement of plate is thus below 

 4X io~ 6 cm. ; but there is no compelling evidence that the waves obtained are 

 due to parallel displacements of plate, as I shall show. 



50. Interpretation. Lines. Oscillation about a vertical axis. The key for 



the interpretation of these phenomena is to be found with the white lines s, 

 which are obviously slit-images arrested stroboscopically, for the ray hm'h', 

 figure 80, is periodically displaced in the field by the objective o only; whereas 

 the ray hmh' is displaced both by the latter and by any slight inclination or rota- 

 tion of the mirror m about an axis in its own plane. Hence the occurrence of 

 the lines 5 is proof positive that the plate can not vibrate simply in the type , 

 figure 83, with an even number of internal nodes, but must also vibrate in the 

 type, figure 84, with an odd number of internal nodes. Moreover, if 6 is the 

 effective angular amplitude of the telephone mirror m, r its period, T the 

 period of the objective, a its amplitude, f the length of the telescope eo from 

 objective to image, the displacement per second of the rays hm'h' in the center 

 of the field (equilibrium position) is a w = a2ir/T. The mean displacement 

 per second of the ray hmh 1 , due to m alone, is 2/co = 47r0//r. If these dis- 

 placements are equal and opposite, 



d = ar/2fT 



the slit-image from m would be momentarily stationary at the center and 

 visible in the glare of the image from m f . This is the largest amplitude a for 

 which a center line can occur. 



Since a, /, T are given and 6 is an exceedingly small quantity, T must also be 

 an exceedingly small quantity. In other words, T can only refer to the free 

 vibrations of the telephone plate, estimated as above io 3 per second. It is fur- 

 ther obvious that from the smallness of r there would be an infinite number of 

 repetitions of the static condition, but for the fact that T is highly damped. 

 Thus the lines 5 appear in finite number and soon vanish with the occurrence of 

 practically coincident slit-images, leaving room for the exhibition of wave 

 phenomena, figure 81, unless these also have died out, figure 82. 



The latter, however, have a two-fold character, consisting of those generated 

 by the parallel displacement of the mirror, figure 83, and ..^-^rir^TT^-s- p 

 those generated by the rotation of mirror, figure 84. In 83 



figure 8 1 these must be regarded as occurring consecu- -p'^.^.^^J^rr-^-^-p' 

 tively, whereas in figure 82 they occur together. Since 84 



the fringe displacement is an extremely sensitive measure of the angle 6, 

 such waves will much outlast the presence of slit-images s. Hence all the 

 waves observed must be regarded as superpositions* of the cases, figures 83 



*In relation to my note in Science (May 27, 1921), Prof. Paul F. Gaehr, of Wells College, 

 has been good enough to call my attention to certain experiments with which he was associated 

 and in which a variety of Chladni figures were nicely obtained by spreading carbon dust on 

 a specially designed open and horizontal telephone plate. The figures changed for definite 

 frequencies within the range examined (400 to 3,000). Much of the work was corroborated 

 with the inductometer bridge. 



