260 Mr HOPKINS ON AERIAL VIBRATIONS 



The phenomena above mentioned, agree with those observed by 

 Mr Willis, and described in his paper on the Vowel sounds, pub- 

 lished in the Transactions of this Society, Vol. III. The manner 

 however in which his experiments (having a different object from 

 mine) were conducted, render them unfit for the verification of any 

 of our mathematical results in this subject. 



34. From what I have above stated, respecting the difficulty of 

 making the plate vibrate with certain lengths of the tube, it is manifest 

 how we may avail ourselves of this phenomenon, in the determination 

 of the value of X, corresponding to any particular mode of vibration 

 of the plate, supposing those particular lengths of the tube can be 

 ascertained with sufficient accuracy. Now this can be done almost 

 as accurately as the position of a node can be determined by the 

 vibrating membrane, and consequently the value of X may thus be 

 found. For if A and 4 denote two observed values of /, we shall have 



— = , n being a whole number easily ascertained. (See Arts. 30, 31.) 



35. Though I have had frequent occasion to speak of this displace- 

 ment of the nodes in the open tube, from the positions assigned to them 

 by the common theory, I have hitherto said nothing as to the ex- 

 perimental determination of its magnitude. The most direct way of 

 accomplishing this, is to determine the actual positions of the nodal 

 points by means of the vibrating membrane ; but this method becomes 

 inconvenient when the diameter of the tube is small, as, for instance, 

 less than an inch. Those which I have used most commonly are 

 from 1.3 in. to 1.5 in. diameter. If the tube be larger than this, it 

 will generally be too large to admit of the extreme section of it 

 being placed entirely upon the same ventral segment of the plate, 

 as is always desirable, (see Art. 29) ; and if much smaller it becomes 

 necessary to make the surface of the membrane so small as to be 

 inconvenient, in order that it may not bear too great a ratio to the 

 area of the section of the tube, in which case the presence of the 

 membrane might be supposed to render the vibrations in the tube 

 materially different from what they would otherwise be. 



