130 On the Transmission, in one direction, of Sound through Air. 



suppose, where k = ae 2« ,f + cc. 

 But 



therefore, since // (ox 2 ) = 0, we must have // (k) — 0, and there- 

 fore 



that is, one of the equations of our solution must be of the form 



a conclusion the consequences of which have been already pointed 

 out. 



On the whole, therefore, it appears that the pair of equations 



'o« "\w 



«<} 



constitute the most general solution of which the equations (2) 

 and (1) are susceptible when the motions are not small. But 



« x = — , where D denotes the density of equilibrium. Hence, 



as it is clearly impossible that we shall always have the relation 

 between the velocity and density indicated by the equation 



-= + loo- £. 



when the motions are not small, it follows that the equations 

 (2) and (1) must be considered defective in their representa- 

 tion of the motion. 



6 New Square, Lincoln's Inn, 

 March 1873. 



