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-
