320 



Dr. 0. Burton on Plane and Spherical 



Fk. 2. 



fc 



cylindrical tube (or, if we 

 please, is a portion of an "un- 

 limited rigid plane). All the 

 air to the right of A is initially 

 at rest and of uniform density, 

 and then A is impulsively set in 



motion, and kept moving to the right with uniform velocity v. 

 Consider the speed with which the disturbance generated by 

 A advances into the still air to the right ; it is evident that 

 in all cases the front of the disturbance must advance faster 

 than A. Take, then, the case in wdiich 



v > a, 



where a is the propagation-velocity of infinitesimal disturb- 

 ances. Two alternatives present themselves : — 



(i.) If velocity and density are always either constant or 

 continuously variable in the direction of propagation, the rate 

 of propagation at any point will, in accordance with known 

 principles, be 



v 



dp 



and therefore at the front of the disturbance, where u — and 

 p = the " undisturbed " density, the velocity of propagation 

 will be simply = a ; that is, less than the velocity with which 

 A is advancing. Obviously this will not do. 



(ii.) If velocity and density are not always either constant 

 or continuously variable, that is, if one or more surfaces of 

 discontinuity are being propagated through the air, we are 

 met by the difficulty explained in the last section. 



4. A simple mechanical analogy will help to indicate the 

 actual motion. A number of equal spheres, of the same 

 material throughout, are capable of sliding without friction 



Fig. 3. 



{l](i>=<oXl>=0==(><>= 



along a straight bar (fig. 3) , and are connected together by a 

 number of very weak and exactly similar springs (not shown), 

 so that when there is equilibrium they are equally spaced 



