94 



MR. W. A. RICHARDSON OF THE PETROLOGY [vol. lxxix, 



plane (let it be EF) on which the stress is most oblique, or, in 

 other words, along which the shearing stress is a maximum. 1 

 Further, symmetry requires that there shall be another plane of 

 maximum shear, E', E' in the figure. In three dimensions there 

 will be surfaces of maximum shear, either pyramidal or conical, 

 according as the specimen is cubical or cylindrical. Under similar 

 conditions of loading, homogeneous test-cubes of Portland cement 

 break into six pyramids meeting with their apices at the centre 

 of the test-cube, and such broken test-pieces may be compared 

 with cone-in-cone concretions described by C. A. White, 2 in 

 which all the cones radiated from a centre, with their 

 apices all pointing towards that centre. 



In applying such an analysis to explain cone-in-cone, we are 



probably not concerned 



Eig. 8. — Element from a growing ' beef- with mechanical defor- 



vein subjected to principal stresses mation (since there is no 



p ^ q. optical sign of strain), 



ip but with the influence 



» E ' \y E B of the state of stress on 



the course of ciwstalli- 

 zation. The inclination 

 of the perfect rhombo- 

 hedral cleavage to the 

 vertical must make the 

 calcite-fibres extraordin- 

 arily sensitive to the 

 influence of the shear. 

 Where master shear - 

 planes were established, 

 fibres already formed 

 might be fractured; but, 

 more probably, the ac- 

 tion would be to inhibit 

 growth in such a way 

 that the fibre could not 

 cross such a plane. The 

 actual spacing of the planes set up would be influenced by many 

 factors, but chiefly by boundary conditions. The appearance of 

 secondary surfaces within the more prominent surfaces is some- 

 times seen when slabs, instead of cubes, are used as test-specimens. 

 And, therefore, the establishment of cones within cones would be 

 due to the formation of new shear-surfaces as thickness increased. 



By way of comparison, it is interesting to note that the extreme 

 tenuity of asbestos -fibres has been correctly explained by the 

 combination of prismatic growth with perfect prismatic cleavage, 

 and the platy character of satin-spar by the presence of the perfect 

 brachvpinacoidal cleavage. Thus all cross-fibre veins have 



1 A. Morley, ' Strength of Materials ' London, 1908, p. 14. 



2 Amer. Jonrn. Sci. ser. 2, vol. xlv (1868) p. 401, 



