involved in the Construction of Artillery. 401 



!St vah 

 the corresponding pressure, 



and \i 1)1 be the greatest value of —which the metal can bear without Cracture, we get for 



n = mV/ck-. . (7) 



" This conclusion depends upon the following admissions: — First, that the extending 

 force bears a constant ratio k to the extension ; secondly, that the compressing force bears 

 a constant ratio k' to the compression ; and, thirdly, that fracture only occurs when the 

 extension has exceeded the limit m; but it remains still to be proved by experiment wlie- 

 therthe resistance to extension is diminished or increased by simultaneous compression in a 

 transverse direction, and vice versa. Judging from the fact, that the extension of a piece of 

 India-rubber produces a visible compression in the transverse direction, and vice versa, it 

 seems probable that the effect of either of these forces must diminish considerably the power 

 to resist the other; and, if this be so, the resistance of the tube will be lessened; it is, also, 

 conceivable that a very great compression might of itself produce fracture, i.e. disintegration, 

 without any extension ; or might (before reaching the crushing limit) make the material 

 more easily broken by a transverse tension. 



" Supposing these objections (which apply to all the common formula; for strength of 

 materials) can be disposed of, that k = 111, the expression for n assumes a very simple form : — 



, R- - r- 

 n = mk -J- ; .•.W<mk. (8) 



K' + ?'- ' 



" As respects gun barrels, it should be remembered, that the transmission of the strain 

 from the inner to the outer surface of a thick barrel occupies some time, which may, 

 perhaps, be sufficient to make a sensible increase of strength, by retarding the entire effect 

 until the ball has had time to leave the gun ; and that this same cause may produce a great 

 increase of the compression of the inner surface at the first instant of the shock. 



" In estimating the strength of tubes, it is not necessary to consider the fact, that fracture 

 usually takes place along one side first; it is possible that the opposite side may have pre- 

 cisely the same strength — in which case they might yield together. 



" On the Ejfect of Fluid Pressure upon the Tube. — 1°. Let the tube be supposed in 

 its original state free from any strain; let r and R be the radii of its inner and outer sur- 

 faces, and let a pressure of F tons per square inch be applied to the inner surface: the 

 effect of this pressure will be to extend the inner shell, and thereby cause it to press with 

 a force F' on the shell next to it, and so on to the outer surface. Now, if :r be the radius 

 of the inner surface of any of these shells, and .v + dx the radius of its outer surface (the 

 shell being supposed indefinitely thin), and if/,/' be the corresponding pressures, the internal 



