286 Mr. Mallet on the Physical Conditions 



at which any further addition of metal will be iiseless, will be sooner reached 

 with a gun of cast-steel, than of any other applicable material — a deduction 

 full of important considerations, as respects the use of this supposed valuable 

 metal for artillery. 



277. Professor Barlow, in common with other investigators, assumes the 

 gun to part in two, at opposite ends of a diameter, at the same moment. This 

 is seldom, if ever, the case in reality, as we have seen (sections 7, 8) that in 

 practice, one part or other, is slightly defective, or weaker in some way, and 

 that fracture begins and takes place from one side ; for example, from D, the gun 

 opening out and turning out round a point -4, as a fulcrum, at the opposite side 

 and very near the exterior surface. 



There is, therefore, a moment to the forces of pressure and of resistance, 

 the former being Dx x Ac, and the latter ct x AD ; but this does not alter the 

 condition upon which the limit of rupture depends ; for if a farther thickness 

 be added to the gun, so that its external surface reaches the dotted line BF, 

 increasing its thickness fi'om / to F, the relation of the moments is un- 

 changed, or 



.4c -.bc-.-.AD: bE, 



with some slight change, however, in the position relatively, both of the centres 

 of resistant effort D and E, and of the fulcra of rotation A and b. 



278. Let us, hoAvever, now suppose a new condition. Let it be assumed 

 that the caliber of the gun, g, d, continues the same, and the maximum pressure 

 per square inch likewise, that the annular shaded space between the circles 

 A, / and g, p, were filled up with some perfectly hard substance, possessing 

 perfect mobility of its particles (as if it were filled with a fluid, for example, 

 which could be confined so as not to flow away), and that outside this, between 

 the circle a, /, and the dotted circle b, f, the annular space, represented the 

 section of a surrounding cylinder, of the same material as the gun was made of 

 before. 



The eflective resistance now produced by the square inch of metal is con- 

 siderably increased, merely by removing it further from the axis, and interpos- 

 ing the thickness 2^, f oi inert material ; for the internal pressure per square 

 inch remains the same as before, but its energy to extend the metal is reduced 

 in the ratio of A, D : b, e. 



I 



