44 DISPLACEMENT INTERFEROMETRY APPLIED TO 



e (6 cm. long) may be taken as 33 mg. of air. The forces registered by the pin- 

 hole valve in experiments with resonators did not exceed d/ = 3Xicr 4 . 

 Thus the increment of weight of e is but icr 2 dyne, which would lower the 

 index of the torsion balance only 0.3 mm. 



Finally, let the closed cylinder e be replaced by the cylinder r, open below 

 and capable of entering the pipe p. Let the length of r be such that the open 

 cylinder is in resonance with p. Then the conditions of the experiment are 

 obviously improved (though not as much so in the experiments I anticipated*) , 

 but the results will still be the same in character. The open end of r will tend 

 to enter the sounding-pipe p, which is the equivalent of the Mayer-Dvorak 

 experiment, and is here exhibited without any "neck" effect and without air- 

 currents. 



I may add a comparison of the compression observed in the given pipe (2.6 

 cm. diameter and 13 cm. long) when sounding loudly (i. e., when resistance in 

 the telephone circuit has been reduced as much as possible) and the com- 

 pression observed in Chapter V in the open organ-pipe of the standard form 

 on the interferometer. The embouchured organ-pipe tested on the interfer- 

 ometer ( 3 5 of Chapter V) showed for the maximum compression dp/p=io~ 3 X 

 14 in case of a moderately loud note. The telephone-closed pipe, tested with 

 the pin-hole valve at the end of a quill-tube thrust well within (as explained 

 above), gave a displacement of 20 fringes with 2,000 ohms in circuit. This is 

 equivalent to a pressure increment of 0.0120 cm. of mercury when but 100 

 ohms are in circuit, as was approximately the case in the experiments of this 

 paragraph. Thus in case of the probe dp/p=i.6Xio~*. Reservoirs R', figure 14, 

 of different volumes, gave the same quantitative result, which is curious, since 

 the reservoir vibrates. The increment (compression) does not quite vanish, 

 even in the plane of the mouth of p, but a little beyond. 



The ratio of the two compressions is thus 87; but while the interferometer 

 direct gives a fringe displacement rarely exceeding i, the pin-hole valve, under 

 like conditions, will give displacements easily several hundred times larger, 

 depending on the degree of approach to the critical diameter of the pin-hole. 



38. Conclusion. The main facts have been summarized, so far as possible, 

 in the graphs exhibited in the above paragraphs, but an attempt may be made 

 to obtain a working hypothesis as follows : Let the telephone be supplied with 

 a given non-symmetric current, and let an energy increment be thus imparted 

 to the region dominated by the telephone. In this case the mean static pres- 

 sure at a node would be p-\- &p. It will be recalled that Ap decreases some- 

 what within a few millimeters from the telephone plate, which must be moving. 

 Within the pin-hole valve Ap again vanishes to establish equilibrium with the 

 atmospheric pressure p without. Now let the telephone non-symmetric cur- 

 rent be reversed. In this case an energy quantity is withdrawn from the 

 region and the mean pressure at a node becomes p Ap. Within the pin-hole 



* On varnishing the paper resonator to stiffen it, forces over 2 dynes per cm. 3 were directly 

 measured. 



