6iO PHILOSOPHICAL TRANSACTIONS. [ANNO 1800. 



second, as double the breadth of the passage is contained in 1130 feet, and the 

 ear receives a perception of a musical sound, thus determined in its pitch by the 

 breadth of the passage. On making the experiment, the result will be found ac- 

 curately to agree with this explanation. If the sound is predetermined, and the 

 frequency of vibrations such as that each pulse, when doubly reflected, may coin- 

 cide with the subsequent pulse proceeding directly from the sounding body, the 

 intensity of the sound will be much increased by the reflection; and also in a less 

 degree, if the reflected pulse coincides with the next but 1, the next but 2, or 

 more, of the direct pulses. The appropriate notes of a room may readily be dis- 

 covered by singing the scale in it; and they will be found to depend on the pro- 

 portion of its length or breadth to 1 1 30 feet. The sound of the stopped diapason 

 pipes of an organ is produced in a manner somewhat similar to the note from an 

 explosion in a passage ; and that of its reed pipes to the resonance of the voice in 

 a room : the length of the pipe in one case determing the sound, in the other, in- 

 creasing its strength. The frequency of the vibration does not at all immediately 

 depend on the diameter of the pipe. It must be confessed, that much remains 

 to be done in explaining the precise manner in which the vibration of the air in an 

 organ pipe is generated. M. Daniel Bernoulli has solved several difficult problems 

 relating to the subject; yet some of his assumptions are not only gratuitous, but 

 contrary to matter of fact. 



6. On the Divergence of Sound. — It has been generally asserted, chiefly on the 

 authority of Newton, that if any sound be admitted through an aperture into a 

 chamber, it will diverge from that aperture equally in all directions. The chief 

 arguments in favour of this opinion are deduced from considering the phenomena 

 of the pressure of fluids, and the motion of waves excited in a pool of water. 

 But the inference seems to be too hastily drawn : there is a very material difference 

 between impulse and pressure; and, in the case of waves of water, the moving 

 force at each point is the power of gravity, which, acting primarily in a perpen- 

 dicular direction, is only secondarily converted into a horizontal force, in the 

 direction of the progress of the waves, being at each step disposed to spread equally 

 in every direction : but the impulse transmitted by an elastic fluid, acts primarily in 

 the direction of its progress. It is well known, that if a person calls to another 

 with a speaking trumpet, he points it towards the place where his hearer stands: 

 and I am assured by a very respectable member of the r. s., that the report of a 

 cannon appears many times louder to a person towards whom it is fired, than to 

 one placed in a contrary direction. It must have occurred to every one's observation, 

 that a sound such as that of a mill, or a fall of water, has appeared much louder 

 after turning a corner, when the house or other obstacle no longer intervened; and 

 it has been already remarked by Euler, on this head, that we are not acquainted 

 with any substance perfectly impervious to sound. Indeed, as M. Lambert has 

 very truly asserted, the whole theory of the speaking trumpet, supported as it is 

 by practical experience, would fall to the ground, if it were demonstrable that 



