THE SOUNDS OF PIPES. 355 



certain experimentally the places of the nodes. Ber- 

 noulli himself had shown that this place was affected 

 by the amount of opening, and Lambert 8 had ex- 

 amined other cases with the same view. Savart 

 traced the node in various musical pipes under 

 different conditions; and very recently, Mr. Hop- 

 kins, of Cambridge, has pursued the same experi- 

 mental inquiry 9 . It appears from these researches, 

 that the early assumptions of mathematicians with 

 regard to the position of the nodes, are not justified 

 by the facts. When the air in a pipe is made to 

 vibrate so as to have several nodes which divide 

 it into equal parts, it had been supposed by acou- 

 stical writers that the part adjacent to the open 

 end was half of the other parts ; the outermost 

 node, however, is found experimentally to be dis- 

 placed from the position thus assigned to it, by a 

 quantity depending on several collateral circum- 

 stances. 



Since our purpose was to consider this problem 

 only so far as it has tended towards mathematical 

 solution, we have avoided saying any thing of the 

 dependence of the mode of vibration on the cause 

 by which the sound is produced ; and consequently, 

 the researches on the effects of reeds, embouchures, 

 and the like, by Chladni, Savart, Willis and others, 

 do not belong to our subject. It is easily seen that 



8 Acad. Berlin, 1775. 



9 Camb. Trans, vol. v. p. 234. 



A A2 



