Hydrostatic Pressure and Conditions of Rupture. 77 



to stand more pressure on the inside than the tensile test 

 limit, even if the walls of the cylinder are of: infinite thick- 

 ness compared with the bore. One can in cases like this, 

 where there is no yield up to the rapture-point, safely apply 

 the theory of elasticity in calculating the strain up to the 

 rupture-point. This means that no glass capillary ought to 

 be able to stand more than 500 atmos. Capillaries have 

 been found, however, which have successfully withstood 

 1000 atmos. The question of annealing is of great im- 

 portance here. Probably with more careful annealing it 

 would be possible to exceed this limit. In any event, the 

 circumferential extension, even when the pressure is only 

 1000 atmos., must be nearly twice the critical value under 

 rupture in tension. 



The manner of rupture described here, beginning at the 

 outside first, is not universal for all materials, but probably 

 holds only for those materials showing considerable plasticity, 

 There can be little doubt but that the rupture of glass cylinders 

 does begin at the inside, and one case in another substance 

 has been actually observed in which the rupture did travel 

 from the centre to the outside. A cylinder of transparent 

 gelatine, about 1 in. o. d. and cast with a concentric hole ^q in. 

 diameter, was ruptured by blowing into it. The rupture 

 took place exactly as the theory predicts ; it started at the 

 inner surface as a tear across an axial plane, and travelled 

 out slowly toward the outside as the interior was more and 

 more distended by blowing. 



It is worth while examining these bursting tests a little 

 further, for in this case we can make plausible to ourselves 

 why rupture does not occur at the inside, and so gain an 

 inkling of a much more general criterion than any of those 

 hitherto proposed which must always be satisfied when 

 rupture occurs. If we consider the state of stress at the 

 inside surface we shall find that initially as long as the 

 equations of elasticity hold, the stress consists of a pressure 

 across planes perpendicular to the radius, and a circum- 

 ferential tension which is greater than the pressure. When 

 the internal pressure becomes too great, however, the inner 

 layers yield plastically, the hole taking a set. During this 

 plastic yield the metal must be thought of as behaving like 

 an imperfect viscous liquid, tending to transmit pressure 

 hydrostatically in every direction. In consequence of the 

 tendency to equality of stress in every direction, the initial 

 circumferential tension becomes a circumferential com- 

 pression. The mean stress, therefore, at any point of the 

 interior surface becomes a compression after the plastic 



