26 DISPLACEMENT INTERFEROMETRY APPLIED TO 



fringes. Hence the large volume R f is more favorable to a large displacement 

 than the smaller volume R. It will be observed at once that here these res- 

 ervoirs act merely like the outside air in the case of the original experiment, 

 figure 14. The acoustic pressure is produced in the volume which is in uninter- 

 rupted communication with the telephone and is larger in proportion as the 

 other volume (shut off nearly by the pin-hole) is larger. If the latter is as 

 high as 200 cm. 8 , it nearly replaces the atmosphere, seeing that the reduced 

 pressure here (R') acts in concert with the increased pressure on the other 

 side (R). Thus there is no true differential effect resulting from the size of 

 resonators, whether the region be closed, open, or partially open. 



25. Conical vents reversible. Periodicity. The conical vents c f , figure 34, 

 may be inserted into the branch tube t" in two ways; either in the salient 

 position a, with the convex surface around the pin-hole outward , or in the 

 re-entrant position b, with the convex surface at inward. The results ob- 

 tained are usually reversals of each other, so that a pressure excess is liable 

 to be on the concave side of the conical vent. Thus, for the high region R' 

 alone (R being in communication with the atmosphere), the position a gave 

 a pressure displacement of 28 fringes, while b gave dilatation equivalent to 

 70 fringes. In other experiments 37 and 14 fringes, 25 and i fringes, were 

 found, while the region R alone gave 45 and 1,36 and 10 fringes, etc. These 

 results were always consistent in character; but it was soon found that the 

 strength of the telephone current and the length / of the tube c' (fig. 34) , in the 

 re-entrant position, greatly modified them. When there is no resistance in 

 circuit, i. e-, when the telephone sounds harshly, reversal ceases, so that either 

 the case a or b produces a pressure within; but even here, on closing the 

 circuit, the fringes in case b are seen to move first toward a dilatation and then 

 turn in the direction of pressure. 



The position a being the normal case investigated above, the case b was 

 studied with 1,000 ohms in circuit, and for different lengths, I, of the quill- 

 tube c,' beyond 0, from / = 2 to over 40 cm. These results are given in figure 

 35, the abscissas showing the length / of tube taken and the ordinates the 

 fringe displacements s, both for the region R' alone (positive displacements 

 here denoting dilatation) and for the region R (positive displacements denoting 

 pressure). The graphs are periodic in marked degree, so that the quill-tube b 

 is a musical instrument with a pin-hole embouchure; and in fact, while the case 

 a is nearly silent, b audibly reproduces the sound of the telephone. The curve 

 for R' shows two resonance maxima and one minimum; but in all cases the 

 dilatation (positive displacement 5) within R' is sustained, merely changing 

 in degree. The curve for R, however (dilatations for negative 5), indicates the 

 occurence of both dilatations and pressures within this (smaller) region. Both 

 curves are quite consistent (although R' is nearly four times more capa- 

 cious than R) and one may infer the length of pipe ^ = 30 cm. (fig. 34), or the 

 wave-length 2/ = 6o cm., to be an harmonic of the telephone interrupter . 

 This was in fact close to the 4-foot c. 



