210 Mr. Mallet on the Physical Conditions 



which is the rate at which force itself is transmitted through its mass, becomes 

 not wholly unimportant. The formula 



in which d and /* are the density of mercury at zero, and the height of the 

 barometric column at 30 inches, expresses the velocity of sound in any solid 

 whose modulus of elasticity is E and density D (omitting the coefEcient for 

 heat due to compression), and also expresses the velocity with which any 

 impidsive force whatever is transmitted through the same solid. This transit 

 rate, then, is proportionate to i/eZ), and for 



Gun-metal, 



Cast-iron, 

 Wrought-iron, 

 Steel, . . . 



151 

 203 

 239 



258 



proportionate, omitting decimals, to the numbers severally annexed. The 

 actual velocity is great in every case, being, probably, not less than 11-090 feet 

 per second for cast-iron, as determined by Biot and Malus ; but it is observable 

 that its rate in gun-metal is not much more than J that in steel. Were it pos- 

 sible to have a gun of sufficient thickness, therefore, the impulsive effect of the 

 explosion might have reached its maximum and vanished altogether before the 

 strain visited on the interior portions had been transmitted to the exterior. 

 This cannot occur in practice, but in no case is the ivhole of the impulse trans- 

 mitted equally through the whole thickness of the gun, and the less as the 

 above numbers are smaller. There cannot be a doubt that this, coupled with 

 the ductility of gun-metal, is one of the causes why guns of that material bear 

 without destruction such heavy charges. 



135. Again, as cast-iron is a crystallized body, and its planes of crystal- 

 lization variously arranged, as already shown (Chapters 3 and 4), and the 

 elasticity of the integrant crystals probably different in different axes, it follows 

 that the same internal impulse will not be transmitted at the same rate through 

 the mass of the gun, in the directions of these rectangular axes. Hence probably 

 another reason why impulsive or shattering forces act so injuriously upon it. 



