14 Stromeyer, Explosions of Steam Pipes. 



where q is the weight of the spring, Q the weight which 

 will produce an extension of one inch, and 386-4 is the 

 acceleration due to gravity in inches. It was found some- 

 what difficult to time the oscillations of the spring before 

 its vibrations are changed into undulatory ones, but there 

 seem to be about four complete vibrations in five seconds, 

 which is in fair agreement with the value found above. 



This spring will also show very clearly that several 

 positive or negative changes of motion can travel together 

 along its length, independently of each other. This is a 

 matter of great importance, for it supports the views often 

 expressed by Dr. Konig, whose recent death we all 

 deplore, that musical timbre is as much a matter of the 

 shape of sound-waves as of combination of several 

 systems of undulatory waves, a view underl\'ing 

 Helmholtz's analyses. 



As a sudden change of motion is quite contrary to 

 our ideas of acceleration, an additional explanation of the 

 phenomena exemplified in this spring is perhaps not out 

 of place. A force imparts a given velocity to a given 

 mass in a given time. If the force is of a fixed intensity, 

 then the velocity will also be fixed, provided the mass and 

 time are proportioned to each other. Now, the mass of 

 the very extreme end of the spring can be imagined to be 

 infinitely small, therefore, the time in which it acquires or 

 changes its velocity under the influence of a definite 

 pressure must also be infinitely small. 



From the above it is, I think, now quite clear that, 

 when an elastic body suddenly comes to rest, the pressure 

 exerted by it can be calculated b)' the formula already 

 found 



and the duration of the pressure is 

 L 



