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The experiments of the present volume are either direct applications of displacement interferometry or they embody the correlative work which has grown out of such applications, often at widely different times. In the arrangement of the chapters it has therefore been expedient to depart from chronological order in favor of an arrangement of subjects which belong together.In a former report I had already used a U-tube in connection with the interferometer, but the design of the apparatus was limited in scope. In the present paper (Chapter I) the open mercury manometer is made directly available for pressure measurement, and as the attainable sensitiveness is easily a few hundred thousandths of a centimeter of mercury per fringe displacement, it is well worth while to see what can be gained by using it. The applications to air thermometry on a micrometric scale and an attempt to revive the old absolute electrometer in Chapter II are merely incidental, though in each case much more may be done than I have here attempted, as I hope to show at some other opportunity. The manometer also admits of further improvement in ways which can not be included in the present report.A more suitable field for testing the immediate capabilities of the mercury U-tube is detailed in Chapters III and IV, where the endeavor is made to give an account of the pressures and dilatations observable in a region vibrating acoustically. If this is quite closed or quite open to the atmosphere, the record of the U-tube within is without interest; but if the region is all but closed up-open, for instance, through a pin-hole less than 0.5 mm. in diameter-the gage shows pronounced fringe displacements as a rule and particularly at the frequency of the harmonics. If the sound generator is a telephone, the displacements are proportional to the effective currents actuating it and at the harmonics much more than 10,000 ohms may be put in circuit before the fringes cease to move appreciably. Similarly under low resistance, very small fractions of a semi-tone are registered and the ear becomes a poor apparatus for discrimination. The investigations are made along two lines, in the first of which the sound generator and the U-tube lie within the boundary carrying the pin-hole; in the second the sound generator lies without and is independent, so that the pin-hole valve carried on a long tube becomes an appropriate probe, or sonde, for the pressures within sounding pipes and cavities. As all the harmonics are thus saliently registered, there should be no serious difficulty in exploring the acoustics of the mouth cavity uttering word sounds, for instance. A curious result of the survey of the distribution of pressure increments in relation to pitch is the replacement of pressures by dilatations in different orders of frequency....

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