L_^ 



170 F. II. Lahee — Dodecahedral Jointing. 



as the result of the regular inward advance of successively 

 cooler planes, for each of which the temperature is uniform 

 throughout. 



If, on the other hand, we conceive of a solid which is losing 

 heat equally in all directions and in such a way as to be sub- 

 jected to a homogeneous strain, six-way fracture will develop 

 instead of the three-way fracture of the cooling surface, and 

 the resulting geometrical form will be a dodecahedron instead 

 of a hexagon. 



As hexagonal fracture may be illustrated by considering a 

 series of equal tangent circles compressed uniformly from all 

 directions in the same plane, so dodecahedral jointing may be 

 experimentally demonstrated by subjecting a group of equal 

 tangent balls, arranged in superposed horizontal layers, to 

 equal pressure from every direction. Those spheres which 

 were originally in contact with twelve others will, it is true, 

 be dodecahedral ; but whether they become regular rhombic 

 dodecahedra or forms which, to borrow from crystallography, 

 resemble a regular rhombic dodecahedron twinned parallel to 

 an octahedral face, will depend on whether the centers of the 

 balls of a given horizontal layer w T ere above the centers of the 

 spaces, or of the spheres, of the second layer below. In either 

 case, prior to the compression, the conditions of unoccupied 

 space and of equal distance between the centers of spheres will 

 be fulfilled. 



The literature appears to be lacking in references to the par- 

 ticular kind of jointing described. Much of the work on this 

 subject was done several decades ago. At that time hexagonal 

 jointing received considerable " attention and was correctly 

 explained as the result of uniform strain in a surface. Spher- 

 oidal structure, which was shown by Bonney to be often unre- 

 latedto fracture systems, was, however, held to be the analogous 

 phenomenon in a solid, and perlitic structure was consigned to 

 the same catagory. Bonney thus states his views :* " A hexa- 

 gon is the figure which will result from uniform contraction in 

 two dimensions, a sphere from contraction in three dimen- 

 sions." The case in point, however, leads to the conclusions : 

 (1) that hexagonal columnar jointing is caused by equal tension 

 in all directions in a surface at right angles to which the 

 strain is differential ; and (2) that uniform contraction in a 

 solid must, under corresponding conditions of homogeneity, 

 give rise to dodecahedral jointing. The sphere cannot be the 

 exact analogue of the hexagon. 



Cambridge, Mass. 



* Bonney, T. G., On Columnar? Fissile, and Spheroidal Structure. Quart. 

 Jour. Geol. Soc, Lond., xxxii, p. 152, 1876. On this subject see also 

 Jukes, J. B., and Geikie, A., Student's Manual of Geology. 3d ed., 1872, 

 pp. 182, 183, 311; Mallet, E., Phil. Mag., Ser. 4, vol. i, pp. 122, 201; 

 Scrope's Volcanoes of Central France, p. 92; Iddings, J. P., The Columnar 

 Structure in the Igneous Bock on Orange Mountain, New Jersey, this Jour- 

 nal, (3), xxxi, p. 321, 1886, and Iddings, J. P., Igneous Bocks, N. Y., 320, 

 1909. 



