ME. ROBERT MALLET ON VOLCANIC ENERGY. 
211 
quantity of matter to be extruded is proportionate to the difference between their 
internal or external surfaces respectively, or as 
(2r7 : (2R/) 2 . 
In dealing with these enormous volumes, this relation affords a convenient method of 
determining the volume of matter that must be extruded from the shell. 
Table II. 
1 . 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
Thick- 
ness 
of 
shell. 
Diameter 
of 
nucleus. 
Volume of 
nucleus. 
Volume of 
contracted nucleus. 
Reduction 
in yolume 
due to heat 
lost. 
Radial con- 
traction in miles. 
Volume of 
extruded 
matter. 
Radial 
contraction 
in inches. 
miles. 
miles. 
100 
7715 
240440392958- 15 
240440392956-6793 
0000000007806 
0-07663643 
00004945 
200 
7515 
22221176499215 
222211764990-67939 
0-00000000836 
0-15374 
00005296 
1-470602 
400 
7115 
188592463139 15 
18859246313767939 
0-00000000928 
0-34636 
0-00058995 
800 
6315 
131882013356-15 
131882013354-67939 
00000000106 
0-758199 
0-0006716 
The results arrived at are seen at one view in Table II. On examining the Table, 
it will be seen that the diminution in volume of the nucleus is constant whatever be the 
thickness of the shell, for the obvious reason that the absolute reduction in temperature, 
and therefore the absolute contraction in volume, are inversely as the mass of the nucleus 
acted upon by the constant refrigeration, 777 cubic miles of melted ice; but the radial 
contraction is greater as the volume of the nucleus is smaller. Recalling from the 
author’s paper of 1873 the result that (15579 of a cubic mile of crushed mean rock is the 
amount annually necessary for the maintenance of the volcanic activity of our globe at 
present (an amount which the author believes to exceed the actual truth), and viewing 
such crushed rock as the same thing with the extruded matter of the shell, it will be 
seen that, on the suppositions we have made, the thickness of the solid shell of our globe 
necessary for the support of its volcanic activity must exceed 400 miles, and that with 
a thickness of shell of 800 miles the annual volume of the extruded or crushed rock 
exceeds by about one half the quantity required to support volcanic activity. As the 
rigid shell is and has been for ages in a state of elastic compression by tangential thrusts, 
it is easily perceived that any increase, however slowly taking place, in these compressive 
strains must be promptly responded to by disturbances in the mechanical equilibrium 
of the shell itself. Some minute portion of these may perhaps still be disposed of in 
small partial thickenings of the shell itself, giving rise to slight secular variations in level, 
such as have been observed in Scandinavia and Greenland ; but these expiring remains of 
ancient mountain-building are relatively so minute that they may be disregarded here. 
The reliability of the conclusions here arrived at is of course only proportionate to the 
admissibility of the suppositions made upon which they depend. In so far, however 
they tend to support the author’s views as to the nature and origin of volcanic heat and 
