C. Davison—Secular Straining of the Earth. 223 
Above this surface a change takes place. In this part of the 
earth’s crust each shell in a given time loses less heat than the shell 
below it, and consequently undergoes less stretching. The stretching 
thus decreases gradually and continuously towards the surface of 
the earth ; and it may be shown that at a certain point it vanishes 
altogether. 
To do this, we must consider the shells close to the surface of the 
earth. The outermost shell of all is not losing any heat. The 
layer between it and the nucleus, by cooling and contracting, is 
diminished in thickness, and tends to leave the shell unsupported. 
But, immediately this takes place, enormous lateral pressures are 
developed by the attraction of all the earth’s mass within; and the 
outermost shell is crushed and wrinkled until it rests completely on 
the mass below. In the same way, the shell next below the outer- 
most is crushed and folded, but not to so great an extent, for it does 
lose a certain small amount of heat, and the contraction due to this 
brings it a little nearer the mass on which it is obliged to rest. In 
the shell below this, the loss of heat is still greater (for the rate of 
cooling increases from the surface downwards), and the amount of 
folding still less, and so on. Thus the folding and crushing of the 
shells gradually and continuously diminish as the depth from the 
surface increases. 
We have now the following state of things. From the surface of 
greatest rate of cooling, stretching gradually diminishes outwards. 
From the surface of the earth, crushing and folding gradually 
diminish inwards. At some point between the surface of the earth 
and the surface of greatest rate of cooling, there must be a shell 
which is being neither stretched nor crushed. We may call it there- 
fore the “surface of zero-strain.” 
This surface plays an important part in the physical history of 
the earth. If the contraction theory be true, our loftiest mountain- 
ranges must be formed principally, perhaps entirely, of the material 
in the comparatively thin layer of rock outside it. Our earthquakes 
and volcanic eruptions probably originate at points above the surface 
of zero-strain. 
It would therefore be an interesting and important problem to 
determine, if we could, the depth of the surface of zero-strain; but, 
in the present state of our knowledge, it is impossible to do this 
accurately. Assuming, however, that the coefficient of dilatation and 
the rate of conductivity are the same at all temperatures, that the 
surface of the earth is a sphere, and that the stretching or folding of 
any shell is uniform all over that shell, I found, by an approximate 
method which it is hardly necessary to describe, that the surface of 
zero-strain was, or more probably will be, at a depth of five miles 
after an interval of 174,240,000 years since the earth solidified. 
This depth, on account of the method of calculation employed, is too 
great by a fraction of a mile, but we shall probably be well within 
the limits of error if we put it at between four and five miles. 
1 This period was adopted in order to simplify the calculations, and is well within 
the limits given by Sir W. Thomson. 
