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VI. The Influence of Flaws and Air-cavities on the Strength 

 of Materials. By J. Larmor, M.A., Fellow of St. Johns 

 College, Cambridge* . 



IN practical estimates of the strength of materials it is usual 

 to take the greatest compressive or tensile stress which 

 the material is found in experiment to sustain, and divide it 

 by a factor of safety to insure against sudden applications and 

 reversals of the load, and against flaws or sources of weakness 

 that cannot be foreseen. Among the latter, cavities or air- 

 bubbles in the material hold a place ; and these may also be 

 taken in a general way for purposes of calculation as the type 

 of flaws consisting of a defect or weakening which is confined 

 to a limited volume of the substance. 



Thus, in the case of a shaft transmitting a torque or couple, 

 the shearing-stress is annulled over the volume of the cavity, 

 and this may lead to greater than average shearing-stress in 

 some part of its immediate neighbourhood. In the case of a 

 column supporting a load, the supporting thrust is absent 

 over the part of the cross section occupied by the cavity, and 

 this defect of support must be compensated by a greater 

 thrust elsewdiere. 



When the cavity or flaw is at a great distance from the 

 surface of the casting compared with its linear dimensions, 

 the changes produced by it in the intensity of the stress are 

 the same at corresponding points, whatever be the dimensions 

 of the cavity. For when the latter is altered in linear dimen- 

 sions but not in form, and the displacement of the material at 

 corresponding points is altered in the same ratio, the com- 

 ponents of the strain will maintain their intensities unaltered at 

 corresponding points, and so will the components of the stress. 

 Thus the traction over the surface of the cavity will be un- 

 altered, and therefore remain zero; while the displacements 

 over the surface will be changed in the above ratio. The 

 practical statement of this principle of similarity is that the 

 effect which is produced by a cavity on the strength of a piece 

 under uniform stress is dependent on the form but not on the 

 size of the cavity, provided the distance of the nearest part of 

 the surface from it is at least two or three times its greatest 

 diameter. 



The amount of this increase of internal stress determines 

 the theoretical factor of safety which the possibility of a flaw 

 of the type in question w T ould necessitate : and it is possible 

 to arrive at an estimate for the case of spherical or cylindrical 



* Communicated by the Author. 



