210 
ME. KOBEET MALLET ON VOLCANIC ENEEGY. 
shell until its radius =r', the shell then, in following down after the contracted nucleus, 
must descend everywhere through a vertical height equal r—r'. 
The spherical shell having the original external and internal radii R and r must 
Eig. 2. 
accommodate itself to this descent so as to remain in contact with the diminished 
nucleus : it may do this in either of two ways ; it may increase in thickness, or R'— r' be 
greater than R—r; or the thickness R—r may remain constant, in which case, as the 
volume of the shell after descent is less than before, a certain portion of its volume must 
be extruded or got rid of in some way. In the earlier stages of our globe’s refrigeration, 
as explained in the author’s paper of 1873, the thickness of the descending shell did 
not remain constant, but was increased by external corrugations and wrinklings, and 
other like changes due to tangential pressure in that epoch of mountain-raising. But 
the epoch of mountain-building has practically ceased, the shell being too thick and 
rigid to admit of it. The thickness of the shell now must therefore be viewed as constant, 
and the accommodation of its volume to enable it to remain in contact with the con- 
tracting nucleus is produced by extrusion of some of its mass blown out to the surface 
by volcanic action. The difference in volume thus to be got rid of is the difference 
between 
w{(2R) 3 — (2r) 3 } and w{(2R') 3 -(2r') 3 } 5 
the constant n=^ beings ’5236, 
and as stated, the thickness of the shell remaining constant, the thickness of the ima- 
ginary spherical shell which measures the reduction in volume of the nucleus, or r—r r , 
must be = to the vertical descent of the external surface of the original or uncontracted 
shell, or 
r-r'=R-R' . 
and as the absolute thickness of both these imaginary spherical shells is small, the 
