102 Prof. Potter on the solution of the Problem of Sound, 



reading, forcibly impressed on his mind the necessity of consi- 

 dering the change in the distances of the centres of the atoms of 

 gases dm-ing their condensation and rarefaction, when the elastic 

 force and the heat and cold de\eloped were the subjects of study. 

 Such teaching could never be forgotten by a mathematician 

 studjaug the equations of fluid motion; but the method of 

 bringing the foi-ce of mathematics to bear on the subject was 

 not so eAddent, whilst still in the dark, though abundantly simple 

 when once known. 



We mav consider the air, as is usually done, to be a homo- 

 geneous fluid, with a cubical arrangement of its atoms, and that 

 it is not necessaiy to notice the heat made sensible by conden- 

 sations, or the cold by rarefactions ; because the velocity of sound, 

 as found from experiment, is not as yet known to vary with the 

 loudness or feebleness, the high or low pitch of the sound ; so 

 that we need to use only Boyle's (or Man'iotte's) law, that the 

 elastic force of a gas varies as its density, or inversely as its vo- 

 lume for a given mass. 



Using the ordinary notation, let 



2) = the pressure on a unit of area, measuring the elastic force 

 of the gas ; 



p = the density of the gas ; 



then by Boyle's \aw, p = Kp. 



lietpi, Pi, Y^ be the corresponding pressure, density, and vo- 

 lume of a portion of gas, and 2r, the distance of the centimes of 

 two contiguous atoms. 



Also let p', p', V, 2r' be the like quantities after a chaiige of 

 volume. 



We must attribute the volumes (2?-^)^ and (2r')^ to each atom 

 in the respective cases, by virtue of the cubical arrangement, and 

 we have 



p,- pr v - .•'^' 



or 



«'_„ it- "prf. 



r —ri ^3 ~" ^3 



_ AC. mass of an atom 



This is the law of the elastic force, in terms of the distance 

 (2?^) of the centres of the atoms, which is to be applied in inves- 

 tigating the diff'erential equation of the vibratory and undulatory 

 motions in an elastic medium. 



