522 



THE FORMS OF TISSUES 



[CH. 



part above will shrink the more; and this will set up a horizontal 

 shear in the interior of the column, in addition to the existing 

 vertical tension. The principal stress, compounded of shear and 

 tension, will be neither vertical nor horizontal, but inclined 

 obhquely between the two. Now in a brittle substance, such as 

 glass or basalt, an advancing fracture tends to advance at right 

 angles to the principal tension. Where the surface of the column 

 meets the cool air the tension is parallel to the face, and the fissure 

 enters at right angles to the face, that is to say, horizontally; it is 

 for this reason that the ball-and-socket joint is found to have 

 a square lip. Once inside the boundary, however, the advancing 

 rift finds itself in a region where the principal stress is inclined, 



4 



/. 



t P 



3 



Fig. 201. (1) Diagram of the vertical and shearing stresses in a shrinking column 

 of basalt, (2) The same in the neighbourhood of the point P. (3) JSS' re- 

 sultant stress, and TT' direction of rupture. After F. W. Preston. 



slightly, to the vertical; the crack consequently bends down, the 

 downward tilt increases for a short distance and then approaches 

 the horizontal again, and the opposing surfaces of "ball and socket" 

 are thus defined. The crack often fails to complete its journey, and 

 leaves a core of rock unbroken in the middle of the bowl. 



The curved sides of the basin, its square lip, its flattened centre, 

 often incomplete, are thus all explained; and whether it be convex 

 or concave, dome or basin, merely depends on whether the cooling 

 or quenching came from above or from below. 



The basin, or bowl, will always be a shallow one. For if at 

 a point P, within the column, the vertical tension be /, and the 

 horizontal shear-stress be /,., then the direction of the principal 

 planes will be 2(/. == tan-^ (- 2fjf) ; so that, since / and /^ are both 

 positive, <f>j^ hes between 45° and 90°, while ^2 ^i^s between 135° 



