446 PROFESSOR CHALLIS, ON ATMOSPHERIC TEMPERATURE 



By equating these two values of p we obtain, 

 dp 



(by the foregoing equation,) 



pdx 



Sx 

 Now -J- is the rate at which the density at the distance x is 



transferred to the distance x + Sx, and is equal to the velocity of 



the particles + the velocity of propagation. 



dv 

 dx 



J7 



pdx 



Therefore the velocity of propagation = -^- . 



If the given state of density be propagated with the uniform 

 velocity b, it follows that 



dv , dp 

 dx ~ 'pdx' 



an equation applicable to uniform propagation under whatever circum- 

 stances it takes place. By integration, v = b . Nap. log p, assuming that 

 V = 0, when /> = 1. 



Supposing the medium to be such that p = b'p, the propagation is 

 known to be uniform and equal to b. Therefore for this medium 



T' — ^- ~T~ • Hence the relation between the velocity and density is 



