Proceedings of the American Philosophical Society. 33 



state of load, but that the tendency to fracture will be immensely greater 

 in the former case than in the latter. 



4. In producing the fracture of natural substances, which all depart 

 from the law of perfect elasticity as we approach the limit of fracture, the 

 ratio of the effect of instantaneous and accumulative action will vary 

 with the nature of the substance, never being less, for elastic bodies, than 

 2 to 1, nor for flexible than 4 to 1, and more usually approaching 3 or 4 

 to 1 for the former case, and 5 or 6 to 1 for the latter. 



5. Let a vase or conduit be acted upon by a load which is alone suffi- 

 cient to break it, and let this load be partly balanced by a small exterior 

 force : should the great interior force suddenly cease, the small exterior 

 action may crush the vase or conduit inward ; its energy in such case 

 being the sum of the interior and exterior forces. 



6. Should the interior force be a vibration of the kind already explain- 

 ed, and should the exterior action be extremely feeble, and act on a very 

 great mass, this extremely feeble action may crush the vase inward, with 

 a power that shall exceed in any degree the enormous action of the inte- 

 rior or explosive vibration. The comparison of the interior and exterior 

 actions is best effected in this case, by finding the modulus of elasticity 

 of a material spring that shall coincide most nearly in effect with the in- 

 terior tremor. For putting e and e respectively for the modulus of the 

 spring and of the support, and o" and o' for the deflections resulting 

 from the tremor acting alone, and the reaction as it does act, we have 



a' /e . 



— = \/ — , or, m other words, the deflection produced by the reaction, 



is to the deflection that would be produced by the interior tremor alone, 

 in the inverse proportion of the square roots of the moduli of tremor and 

 support. 



7. Combining what is here said with the known laws of fluids moving 

 in pipes, and whereby they necessarily produce hydraulic shocks, it fol- 

 lows, that any vessel connected with such a train of pipes, and plunged 

 at some little depth in a considerable mass of water, or other heavy fluid, 

 will occasionally be subject to a crushing and exterior force vastly greater 

 than the interior strain due to the constant head of fluid. 



In illustration of the principles thus developed, Mr. Bonnycastle details 

 some experiments, and mentions a phenomenon which occurred under 

 his own notice, and is analogous to the one described by Dr. Hare. In 

 making experiments on the propagation of sound through water, he had 

 occasion to cause an explosion of gunpowder within a hollow metallic 

 cylinder, open at the lower end, and immersed under the liquid ; and, 

 although the strength of the cylinder was abundantly sufficient to bear 

 the statical pressure of the surrounding water, he found it crushed inward 

 after the explosion. 



Vol. XL, No. ].— Oct.-Dec. 1840. 5 



