284 Mr. Mallet on the Pliyskal Conditions 



1°. A tangential pressure producing a splitting strain, in extension, 



perpendicular to the radius. 

 2°. A compression of the metal in the direction of the radius, which adds 

 to the extension due to the tangential strain, and is greatest at the 

 interior surface, g, p, d. 

 S'. A longitudinal strain producing extension, parallel to the axis, and 

 nearly equal for any part of the same transverse section of metal. 

 Both the latter forces tend to increase the effective energy of the 

 first. 

 The measure of tension at the interior circumference, is the pressure per 

 square inch, times g, d. But, in accordance with Hooke's law, ut tensio sic vis, 

 the resistance opposed to this pressure, by the extensible and compressible 

 elastic metal, is proportionate to the pressure, which is greater for the interior 

 lamina of metal than for any other further removed from the axis. The metal, 

 therefore, of the interior of the gun is the most stretched, and the resistance 

 afforded by any two successive laminaj, whose distances from the axis are D' 

 and D, are as D- to D'^. 



The exterior portions of the solid thickness of the gun bear proportionably, 

 therefore, but a very small share of the strain from the exploded charge. 



Were the nature of the material by possibility such, that its measure of 

 tenacity were accompanied either by infinite extensibility, or by none at all, 

 then the measure of resistance would be the same for each successive, indefi- 

 nitely thin lamina, and would be simply equal to the entire cross section of 

 metal, or to twice p, f. 



274. The limit, therefore, at which no addition of thickness to the exterior 

 of a gun adds anything to its resisting power, is reached as soon as the maxi- 

 mum pressure per square inch upon the interior equals the resistance of its metal 

 at the point of rupture, for at this point the interior lamince tear asunder, while 

 those exterior to them remain whole, to be in succession ruptured by a further 

 application of pressure, which now acts with a greater moment, because upon 

 a greater internal diameter, by the depth of the rent opened, added to the caliber. 

 This result is indicated by every formula proposed for the resistance of cylin- 

 ders underpressure. 



e - -~ Morin. ( 1 ) 



