346 Mr. Mallet on the Physical Conditions 



rounding air, which is propagated outwards, in all diretions, in spherical shells or waves, 

 moving with uniform velocity, which is about equal to that of sound in air, but with a 

 continually decreasing range of pulse or amplitude of wave oscillation. As the distance from 

 the point ofexplosion increases, the quantity of elastic matter in motion, at any moment after 

 the explosion, must, in accordance with the general mechanical law of the conservation of 

 vis viva, be equal to that in the original spherical generating wave, to whose volume 

 that of every subsequent spherical shell must be equal also at the same phase of the wave, 

 or at the instant of equal density. The surface of each spherical shell increases in the ratio of 

 R-, and if the entire phase of the wave (i.e. the oscillation to and fro) be 2a, the impulse 

 at any point of the surface of any spherical shell, at the distance R from the origin, is pro- 

 portional to -r — =-. 

 Za it- 



The shock, or overturning power of the elastic wave, or, what is the same, the energy 

 of the explosion in overthrowing objects, is at every point around (above the earth's 

 surface, upon which we may suppose the shell to explode) inversely proportionate to the 

 squai-e of its distance from the focus of explosion. In fact, it follows the law of light, and 

 sound in air. But the amplitude of the wave is originally proportionate to the weight 

 of powder exploded. A determinate extent of oscillation is necessary to overturn or destroy 

 any given object, whether it be to overturn a wall or to break a window ; therefore, any 

 such object will be overthrown by imequal quantities of powder at distances greater as the 

 quantity is greater. This is the power of demolition in any radial direction round ; and 

 as this power acts alike within a circle having this for its radius, and whose area is propor- 

 tionate to R\ the total power of demolition, therefore, of any shell varies directly as the 

 square of the weight of powder exploded. 



Comparing, then, the 13-inch and 36-inch shells, the total power of demolition is as 

 12-: 480°, or as 144: 230400, or as 1 : 1600; and equal demolition will take place at radial 

 distances from the point ofexplosion, greater in the ratio of 40 : 1. Nor can it be con- 

 cluded from this, that the extent and character of demolition would only be that of forty 

 13-inch shells: for it is obvious that the explosion of the 36-inch shell will be capable of 

 overturning or destroying objects which the explosion of a 13-inch shell, or of any number 

 of successive 13-inch shells, however great, could never move at all. 



The missile power of the shell as against fixed objects (and such shells are not intended 

 to act against troops, but against the material, buildings, and other essentials of fortified 

 places, or against shipping) depends upon the total weight of fragments, and on the dis- 

 tance to which they are projected ; the latter will vary about as the vtv, the exploded 

 powder, for a given weight of shell; hence, in the 13-inch and 36-inch shells, as 

 190 X %/l2: 2486 x ^480, or as 665:54443, or as 1:81. In this respect, therefore, 

 the large shell is above eighty times as destructive as the largest now employed. 



