pa PHILOSOPHICAL SOCIETY OF WASHINGTON. 
directions, and the contractile force which produces cracks at 
certain distances in a given mass will exert itself equally in all 
directions over a surface uniformly subjected to the cooling forces, 
and will, at the instant of fracture, act towards centres, whose dis- 
tance apart is dependent on the rate of cooling. If the mass is per- 
fectly homogeneous the centres of contraction will be disposed over 
the surface with the greatest uniformity possible, that is, they will 
be equidistant throughout, and the resultant fractures will be in a 
system of hexagons. If from any irregularity in the composition 
or petrographic structure of the rock the contractile force acts un- 
equally in different directions, the form of the polygons will be less 
regular. 
The mutual influence of the forces producing different columns as 
they approach each other is readily understood from the foregoing. 
Take the case of two columns, S, S’, approaching one another (Fig, 
3,) and suppose the progress of the maximum strain to have reached 
a b, a’ b’, the forces producing contraction acting through a and a 
will meet and react on each other before those acting through } 
and 0’, so that the points of maximum strain at any given time will 
have advanced farther along the lines through a and a’ than through 
band b’. The lines of greatest strain will then beed and ¢’ d’, and 
the cracks normal to them will take the directions ¢ e and ¢ é, 
This will continue.-till they become parallel. 
If there were but two columns forming at equal rates they would 
curve symmetrically and continue in parallel directions‘and of con- 
stant width, but if one column progresses more rapidly than the 
