204 Mr. R. Mallet on the Origin and Mechanism of 



be very materially varied, whatever be the law of lateral cooling 

 which we may be at liberty to assume. In figs. 6 and 7 the thick- 

 ness of successive isothermal couches has been taken as equal, or 

 the volume of a unit length of each couche to vary as the square 

 of the radius^ thus giving the largest volume to the outside and 

 hottest couche. But if the thickness of the isothermal couches 

 be taken so as to give equal volumes per unit length to all the 

 successive couches from surface to centre, the curvature of the 

 cross fracture L Z M in fig. 7 is but little altered by the differ- 

 ence in the rate of cooling inferred, and approaches more nearly 

 to an elastic curve than that shown by fig. 7, which is not far 

 from that of a circle. If the thickness of the exterior couches 

 be supposed still less than in either of those cases, the effect upon 

 the curvature will be to cause it to approach more nearly to that 

 of an ellipse, so that the cup-shaped articulations would approach 

 more nearly to the form of a watch-glass. 



In the preceding considerations we have viewed as a sufficiently 

 near approximation that the hexagonal prism coincides with the 

 inscribed cylinder. But those portions of the prism exte'rior to 

 that cylinder have also to be considered ; and, as will be seen by 

 the dotted lines to the right of fig. 7 (representing in so far 

 an axial section of the prism taken through the angles of the 

 hexagon, in which the curve of transverse fracture has been 

 laid down on the principles already described), they present no 

 material difference as to the curvature where that approaches the 

 solid angles of the prism, from the same curve as laid down in 

 fig. 7 taken in a direction of section normal to the faces. 



In all that precedes we have supposed the cooling of the ba- 

 saltic tabular mass to take place from the top surface only, when 

 the convexity of the cross fractures will point downwards only. 

 But the cooling of such a tabular mass may take place either 

 from the top or bottom surface, or from both, in which cases the 

 convexity of the cross joints will point upwards at the lower 

 portions of the mass ; and in general the convexity of the cross 

 joints will point in the reverse direction to that in which the wave 

 of heat has been transmitted from any cooling surface of the mass. 

 It is obvious that the curvature of any cross joint must be less 

 in proportion as the diameter of the prism is less — that is to 

 say, as the difference in temperature at the time of fracture is less 

 between the exterior and axial portions of the prism. Hence in 

 very small prisms we should expect to find the transverse frac- 

 tures more nearly approaching to a direct transverse plane of 

 separation, as is actually seen to occur in the long and slender 

 prisms of the Rhineland basaltic country : but this will be better 

 referred to further on in considering the effect of want of homo- 

 geneity in the mass upon the form and positions of the vertical 

 and cross jointings. 



