208 BR. Mallet—Origin.of the columnar structure of Basalt. 
The author then inquires why the last of these is normally 
the force found in nature. He traces this to the law of least 
action which governs the play of all natural forces whose final 
result is produced by the least possible expenditure of force. 
He shows that, in a contracting surface splitting up into equal 
areas, the expenditure of work will, for the equilateral trian- 
gle, the square, and the regular hexagon, be approximately as 
the numbers 1-000, 0°680, and 0519. This economy of force 
a but from the sides, and the more important conditions 
influencing the latter in nature are pointed out. 
Any one prism is coldest at its extremity, and its tempera 
ture increases along its length to the other end, where the 
splitting is still proceeding. The prism is hotter, also, for any 
transverse section, as we approach its axis, than about the ex- 
terior; differential strains in the longitudinal direction thus 
take place, by cooling and contraction, between the successive 
imaginary couches, taken from the exterior to the axis 0 
prism, which tend to cause the outer poriions of the prisms 1 
tear asunder at intervals in length dependent, like the diame 
ter of the prisms themselves, upon the relation subsisting be 
tween the coefficient of contraction and of extensibility at rup 
ture of the material. 
The prism contracts not only in its length, but in its diame 
ter; transverse fracture at its surface i is 
