60 1) Mr. Gr. F. Becker on the Gudermannian 



to the direction o£ force by somewhat more than 45°, and 

 specimens broken by pressure would have faces at less than 

 45° to the axis. As a matter of fact, rupture at sensibly 45° 

 occurs only in brittle substances such as glass, which break 

 when the deformation is extremely small. The scrap-heap 

 of any testing shop shows that mild steel and similar 

 materials under tension part on surfaces standing at less 

 (instead of more) than 45° to the direction of stress, and that 

 crushing produces partings at more (instead of less) than 45° 

 to this direction. Prof. J. A. Ewing has summarized the 

 experimental data as showing that the partings in crushed 

 cast iron stand at about 55° to the axis of stress, and those 

 in steel under tension at about 25° to this axis, pointing out 

 that these substances distinctly do not yield on planes of 

 maximum tangential stress *. Observations of my own on 

 rocks, colloids, and pseudosolids as well as on metals show 

 similar relations. The actual partings vary from 45° in the 

 same sense as do the planes of maximum tangential strain, 

 and vary with the plasticity of the material in the same sense 

 as does the position of these planes. 



Everything known to me is consistent with the theory that 

 not merely the ruptures produced in most materials by 

 testing-machines take place on planes of maximum slide 

 or load, but also the joints, faults, and slaty cleavage of 

 rocks f . 



For geophysical purposes it is thus vital to find tan w or /3 



* Enc. Brit, lltli ed. vol. xxy. p. 1016. 



t Although indiarubber is a substance witli very anomalous elastic 

 properties, it seems to me that the behaviour of various preparations of 

 rubber affords valuable suggestions. Thus an ordinary rubber band, 

 made of raw rubber with some 10 per cent, of sulphur and vulcanized, 

 may be stretched to about 8 times its length, but beyond this point is 

 almost as inextensible as a bit of twine. For the buffers of railway 

 carriages and* similar purposes rubber is mixed with something like 

 35 per cent, of mineral matter for the express purpose of limiting the 

 deformation of which it is capable. This addition changes the Young's 

 modulus, as it evidently must, and it is also clear that a block of such 

 rubber cannot yield to pressure elastically beyond the point at which 

 the mineral particles are forced nearly into contact. Although the 

 elastic limit is much reduced by the addition of mineral matter, the 

 elasticity is not materially impaired ; for such springs often do duty for 

 a considerable number of years. Now a real elastic solid might be con- 

 ceived as a mixture of particles almost incapable of deformation with a 

 substance ideally elastic or capable of indefinite stretching and dilatation. 

 Such a mixture would have a definite and possibly small elastic limit, 

 but would be perfectly elastic within this limit. Above the elastic 

 limit it must either break or yield through a permanent readjustment in 

 the distribution of the contained inelastic particles which might be 

 conceived as of molecular dimensions. 



