Lord Rayleigh's Acoustical Observations. 159 



with the bellows by lengths of india-rubber tubing. When 

 the bottles were sufficiently removed from one another, the 

 mutual influence was very small, being insufficient to prevent 

 the formation of slow and pretty steady beats of about four 

 seconds' period. This experiment shows that the mutual in- 

 fluence depends upon the proximity of the open ends of the 

 pipes, and not upon any effects propagated through the supply- 

 pipes leading from a common bellows. 



Some further remarks on this subject will be found in a 

 paper read before the Musical Association, Dec. 2, 1878. 

 Reference may also be made to some allied experiments by 

 Gripon*, with which I have only lately become acquainted. 

 They appear scarcely to extend to the case with which I have 

 principally occupied myself, namely that in which both pipes 

 are blown. M. Gripon had, however, anticipated me in the 

 experimental determination of the effect of a flange in modi- 

 fying the correction for an open endj of a pipe. 



Kettledrums. 



The theory of the vibrations of uniform and uniformly 

 stretched flexible circular membranes, vibrating in vacuo, has 

 been known for many years J. In practice deviations from 

 such theoretical results are to be expected, if only in con- 

 sequence of the reaction of the air, which must operate with 

 considerable force on a vibrating body exposing so large a 

 surface in proportion to its mass. In the case of kettledrums, 

 the problem is further complicated by the action of the shell, 

 which limits the motion of the air on one side of the membrane. 



From the fact § that kettledrums are struck, not in the 

 centre, but at a point about midway between the centre and 

 edge, we may infer that the vibrations which it is desired to 

 excite are not of the symmetrical class. I find, indeed, that 

 the sound undergoes little, if any, change when the central 

 point is touched by the finger. Putting therefore the sym- 

 metrical vibrations out of account, we have to consider the 

 parts played by vibrations of the following modes : — (1) that 

 with one nodal diameter and no nodal circle ; (2) that with two 

 nodal diameters and no nodal circle; (3) that with three nodal 

 diameters and no nodal circle ; (4) that with one nodal diam- 

 eter and one nodal circle, &c. The investigation proved to be 

 of greater difficulty than I had expected, partly in consequence 

 of the short duration of the sounds. Better ears than mine 



* Ann. d. Chun. iii. p. 371, 1874. 



t Phil. Mag. June 1877. 



% l Theory of Sound,' ch. ix. 



§ De Pontigny. Proceedings of the Musical Association, Feb. 1876. 



