160 Lord Rayleigh's Acoustical Observations. 



are liable to be puzzled in attempting to analyze compound 

 sounds of such complication and irregularity. The following 

 results, however, are believed to be trustworthy. 



The principal tone corresponds to mode (1) ; the tone cor- 

 responding to (2) is about a fifth higher; that of mode (3) 

 is about a major seventh above the principal tone ; the tone of 

 mode (4) is a little higher again, forming an imperfect oc- 

 tave with the principal tone. For the corresponding modes 

 of a uniform membrane vibrating in vacuo, the theoretical in- 

 tervals are those represented by the ratios 1*34, 1'66, 1*83, or 

 about a fourth, a major sixth, and an interval nearly midway 

 between a major and a minor seventh, respectively. 



In experimenting on this subject it is important to bear in 

 mind that the system of tones is really double, and that its 

 components coincide only on the supposition of perfect sym- 

 metry. In practice the requirement of symmetry is difficult 

 to attain even approximately ; and thus it is that beats are . 

 generally heard, arising from the superposition of vibrations 

 of nearly equal frequency. For the purpose of identifying 

 the various modes, the want of symmetry is rather advan- 

 tageous than otherwise. In the case of the gravest mode, I 

 fastened with cement a small load (a halfpenny) to a point 

 of the membrane situated about halfway between its centre 

 and edge. In this way the two gravest tones fell asunder to 

 about a semitone, one of them (the graver) being excited 

 alone by a blow anywhere along the diameter through the 

 load, the other alone by a blow anywhere along the perpen- 

 dicular diameter. With the aid of a resonator tuned to the 

 pitch of the subordinate tone, the nodal diameters of the two 

 modes (1) maybe fixed with great precision by the absence of 

 beats. With a resonator turned to a pitch midway between 

 those of the two tones, the beats are most distinct when the 

 blow is delivered at a point near the middle of one of the 

 four quadrants formed by the two nodal diameters ; but the 

 position for the most distinct beats necessary varies with the 

 pitch of the resonator, and also with the situation of the ob- 

 server. It may be remarked that, provided the deviation from 

 symmetry be moderate, the same vibrations (except as to phase) 

 are excited, whether a blow be delivered at any point, or at 

 the other point on the same diameter equally distant from the 

 centre ; and vibrations excited by striking one point are 

 damped by touching the other. The other modes with nodal 

 diameters only were identified in a similar way. The mode 

 (4) with a nodal circle is known by the cessation of sound at 

 a particular point when various places along a radius are tried ; 

 on either side of this point the sound revives. 



The drum that I examined is of about 25 inches diameter; and 



