involved in the Construction of Artillery. 2G3 



measured by tlie pressure P simply, and the limit of its equilibrium is established 

 by the ultimate strength of the body only; but when the pressure is applied 

 rapidly, or with velocity, its effect is measured by the square of the velocity, 

 Py', and equilibrium depends upon the range of elastic compressibility or 

 extensibility of the body, and, as long since explained by Dr. Young, upon its 

 modulus of force transmission; for if the velocity of impulsion, be to that of 

 force transmission, in a greater ratio than the coefficient of final compression or 

 extension at rupture, due to the material, bears to the length or depth of the 

 body compressed or extended, destruction of continuity must occur, since the 

 body is broken in successive infinitely thin couches., the time not being suf- 

 ficient to admit of the transmission of the force from the first point of contact, 

 beyond it to other or distant parts of the mass. 



So that if fjL be the modulus of force transmission (sect. 134), and that of 



final extension or compression at rupture, ^ = V, the velocity that shall insure 



fracture ; and as V^ = 2gh, the vis viva required for fracture is, 



^\P. (56) 



230. Thus, for wrought-iron we may assume the modulus offeree transmis- 

 sion at 13000 feet per second, and = 0'05, or ^. From which we find, that 

 the impulse of any perfectly rigid body, striking it with sufficient force, will 

 produce fracture (and not bending, however tough and good the iron), if its 

 velocity exceed 560 feet per second, or between one-third and one-fourth that of 

 a cannon-shot. Where the striking body is itself compressible (as is always more 

 or less the case), the velocity required will be rather greater, and the more so as 

 the compressibility is greater. Hence, in the case of impulse produced by the 

 mass of a highly compressible body, such as that of the elastic gas liberated 

 suddenly from the explosion of gunpowder, the velocity of its motion requires 

 to be enormous, in order to 2'>'''oduce fracture thus by its own inipidse only, — a 

 consideration by which we arrive at a clear conception of the almost incon- 

 ceivable velocity of development of the elastic matter from the explosion of 

 fulminating silver, and other such compounds, which produce fracture upon 



2 M 2 



