490 E. MALLET ON THE MECHANISM OF 



within a ring-formed embankment whose plan is a closed curve, is 

 normal to the embankment at any point, and is resolved into tan- 

 gential forces tending to pull asunder or rupture the mass transversely 

 to its circumference, as well as to push every part of it outwards 

 upon its base. The degree of cohesion which the material of a 

 circular embankment possesses is thus an important element of its 

 resistance to fluid pressure within it ; and such resistance in any 

 circular embankment of given section, material, and depth of cavity, 

 or of fluid pressure within, decreases with the increase of the 

 diameter or surface of the cavity within. There is, in fact, a close 

 analogy between the mechanical conditions of resistance of a circular 

 embankment aud those which resist bursting in a water-pipe, the 

 cylinder of an hydraulic press, or the chase of a cannon. The 

 resistance in these depends almost wholly on cohesion of the mate- 

 rial ; and it has been shown by mechanical authors that in a thick 

 tube, such as a cast-iron smooth-bore gun, the exterior portions of 

 the metal are greatly less strained by any expansive force from 

 within than are the interior portions next the cavity ; and as soon 

 as the pressure within that, whether liquid or gaseous pressure, 

 reaches the rupturing-point, i. e. exceeds the cohesion per unit 

 of section of the material at the interior surface, the thick 

 hollow cylinder begins to burst by fissures passing outwards from 

 the interior surface, extending in planes radial to and passing 

 through the axis of the gun or tube. After this point has been 

 reached, no increase of thickness can add to its strength or prevent 

 the formation of such fissures, because, as is obvious, the circum- 

 ferential strains at any distance from the inner surface are every- 

 where propartional to the normal pressures transmitted to the same 

 distance ; and as these pressures are only transmitted to any exterior 

 couche by the compression already sustained by those interior to it, 

 and as, in accordance with Hook's law, the resistance in all cohesive 

 bodies is proportional to the rupturing force acting upon them, so 

 the exterior portions of the gun or pipe are exposed to a much 

 smaller strain than are those within, and the strain is greatest at 

 the interior surface, where, as has been said, the tube first com- 

 mences to burst. 



The construction of modern ordnance in ringed structure, or in 

 two or more separate tubes, each grasping and therefore compressing 

 those within it with a certain amount of initial tension, is based 

 upon the conditions just stated. Were the cavity of a volcanic 

 crater an exact form of revolution, either a cylinder or a cone, and 

 were the materials composing the embankment around it perfectly 

 uniform, and the mass and slope such that the resistance was every- 

 where proportional to the depth of liquid lava filling it, fissures, if 

 formed by the liquid pressure, would be in true radial and vertical 

 planes, like those in which burst cannon are found to divide ; and 

 this would be so whether the cohesive resistance of the material of 

 the cone were great or small. Like fissures would take place if the 

 material of the cone or circular embankment were absolutely devoid 

 of cohesion, as if it consisted of an incoherent mass of sand or earth ; 



