320 Lord Ray leigh : Acoustical Notes. 



the walls behave as insulators. For a circular aperture in a 

 thin wall c is equal to the diameter of the aperture. If there 

 are several apertures, well separated from one another, c is 

 equal to the sum of the diameters, or as we may write it, 



c^=d 1 + d 2 + d s + , (2) 



Hence, if the first aperture acting alone give the funda- 

 mental tone, the first and second together the octave, the first 

 three together the twelfth and so on, we have so far as 

 relative magnitudes are concerned, 



^ = 1, ^ + ^ = 4, ^4-^ + ^ = 9, &c; 

 or 



d { \d 2 :d i =1:3:5 (3) 



The ratios (3) may give some idea of the proportions, but 

 for many reasons — among them the neglect of the thickness 

 of the walls — they are only roughly applicable. There is no 

 reason for insisting on a circular form of* aperture ; indeed, 

 when the aperture is large, an elongated form lends itself 

 better to closure by a finger. Extreme cases excluded, the 

 effectiveness of an aperture depends mainly upon its area. 



When, as would be especially likely to happen in the case 

 of the fundamental tone, a simple aperture would be very 

 small, it may be well to replace it by a channel of finite 

 length. If R be the radius of a tube of circular section and 

 L its length, 



ttR 2 



c- 



L + ^ttR' 



(4) 



from which it will be seen that the area of aperture may 

 be much increased as compared with what would be admissible 

 ifL = 0. 



Two compound resonators on this principle have been 

 constructed. The first was made from the upper part of a 

 glass bottle which had been cut off square near the neck. 

 Over the wide opening a rather stout zinc plate was cemented 

 through which the various apertures were bored. Through a 

 cork, fitted into the neck, passed a short piece of brass 

 tubing, by means of which and a suitable india-rubber pro- 

 longation connexion between the ear and the interior of the 

 resonator was" established. In tuning the instrument it is 

 necessary to begin with the lowest tone and care must be 

 taken to complete the adjustment of each aperture, or channel, 

 before the next is attempted. Further details are hardiy 

 required. If the resonance is improved by shading an 

 aperture with the ringer, it is a sign that the aperture is 

 already too large. If on the other hand the resonance 



