126 Mr. II. Mallet on the Origin and Mechanism of 



as have by cooling already arrived at such a degree of rigidity as 

 no longer to permit of such movements. 



The upper surface film first arrives at that temperature at 

 which its rigidity becomes sufficient to prevent its yielding to the 

 contractile strains in orthogonal directions and in the plane of 

 its thickness in any way, except by its splitting up into much 

 smaller surfaces which can draw off from contact with each other. 

 We have assumed the mass isotropic — that is, contracting alike 

 in all three dimensions for equal decrement of heat. The plates 

 into which the rigid film tends to separate must therefore be 

 symmetric and similar, and such as while in contact at their 

 edges form the continuous film. What, then, determines the 

 form of each of these separated plates ? The tension between 

 all the particles of a rigid film, such as we have supposed, con- 

 tracting alike in orthogonal directions in reference to the plane 

 of the film, can obviously be met by its subdivision in two direc- 

 tions only, namely by two sets of fissures transverse to any two 

 horizontal axes — that is, by division of the film into square plates 

 of a certain size ; and this at first sight would seem to be the sim- 

 plest mode in which the necessary relief to tension could be pro- 

 duced. It is not, however, the form into which the film actually 

 does separate ; for, as we see in nature, the normal form of the 

 prisms of basalt is hexagonal, and the film which we are con- 

 sidering is but the elemental top or boundary of these prisms. 

 What, then, determines the hexagonal rather than the square 

 splitting up, or initiates the hexagonal rather than the square or 

 other polygonal columnar structure ? This important question 

 seems to have been but insufficiently examined by previous 

 writers. 



There are but three forms all equal and similar to each other 

 into one of which a surface can be divided leaving no vacancies, 

 viz. the equilateral triangle, the square, and the regular hexa- 

 gon, as in fig. 1 ; and into one or other of these, therefore, 



Ft C.I 

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