GEOPHYSICS, a F. BECKER 
81 
ON THE EARTH CONSIDERED AS A HEAT ENGINE 
By George F. Becker 
UNITED STATES GEOLOGICAL SURVEY. WASHINGTON 
Presented to the Academy, December 4, 1914 
Imagine that the earth soHdified in such a way that fluid equilibrium 
were perfectly preserved and that the exterior were perfectly smooth, 
presenting an ideal equipotential surface of uniform temperature. Sup- 
pose that the only differences between different portions of this surface 
were in the diffusivity (that there are large variations in the diffusivities 
of different rocks, the pubHshed determinations clearly show). For 
simpKcity's sake, suppose that a certain square area had a uniform 
diffusivity smaller than that of the surrounding surface. It is evident 
that this square would cool more slowly than the adjacent portions, 
and by reason of the slower escape of heat it would develop a shght 
relative elevation — provided indeed that the material of the globe con- 
tracted in cooling as almost all substances actually do. Furthermore, 
the relative contraction of the surrounding mass would bring to bear a 
pressure on all four sides of the square, and this pressure would extend 
downward as far as the difference of temperature was sensible. Such 
a pressure might even suffice to rupture the rock within the square. 
Indeed the order of magnitude of the difference in temperature needful 
to induce rupture is easily estimated. 
Let M be the Young's modulus of the rock composing the square, P 
the lateral pressure on any face and e the elongation. Then by definition 
Me = P 01 e = P/M. The crushing load for the best granite is about 
1000 kilograms per square centimeter, and the average Young's modulus 
found by H. Nagaoka^ for 5 granites is 25 X 10^^ dynes or 254800 kg. 
per square centimeter, only about half as great as that given by Everett 
for glass. This would indicate at the breaking point e = 0.004, very 
nearly. Now the linear expansion between 0*^C. ani 100°C. of mineral 
substances such as glass, quartz, topaz, etc., is not far from 0.08, or some 
20 times the value for e just found. Hence a difference of temperature 
between the square and the surrounding area of the order of 5°C. would 
be enough to produce rupture in the square column imagined. 
Thus a difference in diffusivity would bring about an intumescence on 
the surface of the globe followed by the formation of four systems of 
joints which in the simple case supposed would cross one another at right 
angles at the surface and dip at about 45° in four directions. ^ These 
joints are equivalent to voids, which as I have recently shown may in 
extreme cases approach 6.73 percent of the volume.^ Thus a further 
