152 



T. G. BONNET ON COLUMNAR, FISSILE, 



caused shells to be formed, they would be spherical, because the 

 sphere is, for au equal volume, the figure of least area, and there- 

 fore of least resistance ; and as its surface is at every point at right 

 angles to the radius, there is no tangential component to the central 

 force, and thus the whole of it is effective in rupturing. Thus a 

 hexagon is the figure which w T ill result from uniform contraction in 

 two dimensions, a sphere from contraction in three dimensions. 



But now, supposing that the contraction is mainly in one dimen- 

 sion, or, to put it otherwise, suppose that all the points lying in one 

 surface in a body are in a state of uniform strain in one direction, 

 naturally there would be a tendency to rupture along a surface at 

 right angles to the strain. Suppose, for example, a number of tiles 

 placed on a floor were subjected to strains perpendicular to the floor, 

 they would naturally split parallel to it. Something analogous to 

 this happens in the cooling of an igneous mass, where heat is lost 

 from a surface (suppose the upper). The strains in a horizontal 

 direction, due to contraction, are at once eased by the formation of 

 joints, more or less regular ; but if the loss of heat from the surface 

 be rather rapid, there will be a strong normal strain, which will not 

 be relieved thus, and so slabs or tabulae will be broken off by a kind 

 of exfoliation ; and the more the adjacent particles in a straight line 

 normal to the cooling surface differ in temperature, as will be the 

 case in rapid cooling, the more frequent will these cross joints be. 

 Thus the mass near the surface is generally platy or tabular. 



The matter may be expressed, perhaps, rather more simply in 

 another way. Suppose a body contracting uniformly towards a 

 point within it, and its particles incapable of differential motion ; 

 then if rupture takes place, a series of spherical shells, concentric 

 with this point, will be formed. Suppose now (the law remaining 

 the same) this point bo in the surface of the body ; then it will 

 break in concentric hemispherical shells. Suppose the point towards 

 which contraction takes place be outside, still the body will break 

 into segments of large concentric spheres whose curvature will 

 become less and less as the point becomes more remote, the limit 

 being, of course, a plane when the distance of the point is infinite. 

 Head, for a force causing contraction to a point, loss of heat from a 

 surface causing contraction, and the case remains the same. When 

 heat was lost with tolerable uniformity throughout any part of the 

 mass, spheroids both large and small would be formed ; when it was 

 lost from a more or less plane surface, but from certain points on it 

 more than others (which is equivalent to what would happen when 

 cooling had advanced a little distance within a lava-stream, owing 

 to either superficial irregularities or surface-fissures), curved cross 

 joints and cur vitabular joints would be formed; and when cooling 

 was taking place uniformly from all the points of a plane surface, 

 then platy or tabular forms would result. It must also be remem- 

 bered that the form of the exterior surface would greatly modify 

 these results; for, speaking generally, all points of equal tension 

 would lie in surfaces parallel to the exterior one, whatever it might 

 be. Still, the principle of least action would cause a certain svin- 



