36 Mr. W. J. M. Rankiiie on the Theory of Sound. 



from the poles. 3. When the ci-ystal is magnetie, that dii*ection 

 which between tlie magnetic poles stands axial, between the elec- 

 tric poles stands equatorial. When the ciystal is diamagnetic, 

 the positions between the magnetic poles and electric poles arc 

 coincident. The same holds true for substances artificially com- 

 pressed. 



V. On the Theory of Sound, 

 By W. J. Macquorn Rankine, F.R.S.E. ^c* 



I TRUST that the following brief remarks may remove the 

 objections still entertained by Professor Potter f to my ex- 

 planation of Poisson's investigation of the velocity of sound 

 in air J. 



Professor Potter objects that I have asserted, without sufficient 

 groimds, that the variation of pressure is developable in terms of 

 the variation of density by means of Taylor's theorem, the coeffi- 

 cient of the first term being a finite quantity, 



e«.,^Vo=l+/8. 

 Po 



My grounds for this assertion are, that if the variation of 

 pressure is not so developable in tenns of the variation of den- 

 sity, or if 1+/3 is not a finite quantity, then the variation of 

 pressure con'esponding to an indefinitely small variation of den- 

 sity must be either null or infinite ; that is to say, either the 

 pressure must be a maximum or a minimum with respect to the 

 density, or the density a maximum or a minimum with respect 

 to the pressure. But this is not the case, for the pressure varies 

 continuously with the density ; therefore the variation of pressure 

 is developable in terms of the variation of density by Taylor's 

 theorem, and the coefficient 1 +^8 is a finite quantity. 



Professor Potter misconceives my meaning when he supposes 

 that I deny the existence of unsymmetrical waves of sound. My 

 remarks were intended to apply to waves, which, having been 

 originally symmetrical, become unsymmetrical as they advance, 

 like those on the surface of shallow water. 



LondoD, June 2, 1851. 



* Communicated by the Author. 



t Fourth Series, vol. i. p. 476. % Ibid. p. 410. 



