as applied to the Origin of Mountains. 315 



within the earth, if unresisted, would no doubt be proportional to 

 the loss of temperature at that point in that time, and this, 

 assuming the truth of our old equations, would be proportional to 

 the rate of increase of the temperature gradient at the point. We 

 thus obtain the simple conception that the contraction will increase 

 from the surface inwards to a certain depth and then diminish, 

 until the point is reached at which temperature becomes uniform 

 downwards. 



The distance of such a shell of maximum contraction below the 

 surface, estimated in the way already indicated, will be equal to 

 ■\/ht, where h is the coefficient of thermometrio conductivity, and 

 t the time from consolidation in years. This gives, assuming the 

 same data as before, a depth of 38 miles. (Mr. Eeade states that 

 the value is 50, which would be the depth after about 160,000,000 

 years.) 



From the fact of the existence of such a maximum-contracting 

 shell, Mr. Reade has deduced with perfect theoretical correctness, 

 so far as a homogeneous sphere is concerned, the necessary existence 

 of a level of no-strain. In other words, there should, theoretically, 

 be a shell, between the surface and this shell of maximum-contrac- 

 tion, which could contract with loss of temperature so as not to 

 exert any pressure on the underlying mass ; whilst all shells below 

 it would, in contracting, squeeze the interior, and all shells above it 

 would, owing to less rapid contraction, attempt to stand off from 

 lower shells, and would, in consequence of the force of gravity, be 

 put into a state of compression. 



It becomes then a very important problem to find the depth 

 below the surface at which this level of no-strain lies ; and this 

 appears to be easily attacked in the following manner. 



Choosing any shell at a given distance from the centre of the 

 earth, we can easily find, by the foregoing analysis, the radial 

 contraction which has taken place in one year in any of the shells 

 below it which suffer loss of temperature, and, by summing all 

 these separate contractions, we obtain the whole amount by which 

 the interior has attempted to draw itself away from our chosen shell 

 in that time. If we equate this amount to what would be the 

 radial contraction in one year of a sphere with radius equal to the 

 distance of the selected shell from the centre, and further suppose 

 the whole of this sphere to be contracting at the same rate as the 

 given shell, we shall find the distance of such a shell from the 

 surface. Working this problem out with our preceding assumptions 

 I obtain a distance of a little over a mile fi'om the surface. 1 have 

 felt it necessary to give the reasoning employed, as this result differs 

 from that found by Professor Darwin, as quoted in Mr. Eeade's 

 paper, and to whose high authority I should naturally attach great 

 weight; but I have not, unfortunately, had the opportunity of 

 referring to his paper. 



Assuming, however, that Professor Darwin is correct in estimating 

 the depth of this shell of no-strain at two miles below the surface, 

 I cannot think that the result has any but a theoretical interest. 



