of Vibration in the Air surrounding a Sounding Body. 325 



micrometer, founded on a beautiful suggestion of Dr. R. Radan, 

 who thus describes, in his excellent VAcoustique (Paris, 1867, 

 p. 272), a method of observing the flames of two similar sound- 

 ing organ-pipes : — " We attach to the two pipes two of Konig^s 

 flames arranged so that the point of one flame reaches above a 

 small fixed mirror which hides its base, but which shows by re- 

 flection the base of the other flame. This produces the illusion 

 of a single flame. If now we observe this hybrid image in the 

 revolving mirror while we sound the two pipes, the point sepa- 

 rates from the base, which proves that the two flames shine al- 

 ternately, and the one retracts while the other elongates ; if the 

 two tubes act on the same flame, the eff'ect is nil, and the flame 

 remains immoveable."" By placing the above '^ small fixed mirror^' 

 on a divided circle, or by silvering its back and determining its 

 angular displacements around a vertical axis by the method of 

 Poggendorff (that is, by observing through a telescope the re- 

 flections of a fixed scale from the mirror), we have devised a sim- 

 ple and precise micrometer for ascertaining the amount of dis- 

 placement of the resonator^s flame. For, having once deter- 

 mined for a given note the amount of angular motion of the 

 mirror required to move the bases of the flames over the distance 

 between the centres of two contiguous serrations, we have the 

 angular value of a displacement equal to that caused by moving 

 the resonator through a wave-length ; and a fraction of the 

 turn required to produce the above movement of the bases of 

 the flames will be equal to that produced by the remove of the 

 resonator over a corresponding fraction of a wave-length. In- 

 deed, even with the unaided eye and without the use of the 

 micrometric mirror, I have distinctly detected a displacement of 

 the flames on moving the resonator (UT3) over only 3 centi- 

 metres, or -^ of its wave-length ; and with the micrometer I 

 lelt assured that I could determine the wave-surface of a body 

 giving the note UTg, to within 1 centimetre of its true position. 

 Or course with higher notes we shall get a proportionally closer 

 determination. But the object of this paper is not to present 

 numerical results; I reserve these for a subsequent communi- 

 cation, in which I will also present diagrams of apparatus and 

 the appearances of the flames in various experiments. 



I will here remark that the success of the experiments depends 

 on the resonator with its attached tube being in perfect unison 

 with the organ-pipe ; also the relative heights and positions of 

 the flames should be so adjusted that the sharpest definitions 

 are obtained in the rotating mirror, and so we are able to detect 

 and measure the effects of small changes in the position of the re- 

 sonator; but these and other manipulative details will readily 

 occur to any physicist who repeats the experiments. 



