8 Stromeyer, Explosions of Steam Pipes. 



case of a long elastic bar or plug, which is the subject we 



wish to deal with. 



In such a bar, P is the pressure exerted when a 



E .a 

 length /+«, is reduced to /, in other words P^jj-- 



where E is the modulus of elasticity, and the bar is 

 supposed to have unit cross section. Let in be the mass 

 of a bar of the length {l-\-a), [i being the mass per unit of 

 length, then we have 



w = ^.(/+a) and V= J '—^1—.^ J 



where V is the velocity of propagation of a pressure-wave 

 in the plug. 



That this is true for the whole bar of unit length, 

 as well as for its individual parts, is easily shown. 

 The shortening of a bar of unit of length, under a 



pressure P, is — • The work done, or energy stored, is 



P P 



— • -^ per unit cross section, and this is equal to the 

 2 E ^ 



product -— ^', which leads to identically the same result as 



above, and which means that the energy stored in a 

 stretched or a compressed bar when stationary, is equal 

 to the vis viva of the unstrained bar when released and 

 moving. 



We have now to ascertain the velocity W with which 

 the pressure-wave travels along the bar. It will differ, of 

 course, according as to whether we deal with the length / 

 of the shortened bar, or with l-\-a its natural length, for the 

 time / is the same in both cases. This time has already 

 been determined under the conditions that when free 

 successive elastic blocks are just touching, then 





