and the Origin of Mountain Ranges. 205 



The circumferential rate of contraction of the sphere may be 

 conceived as gradually increasing from zero at the surface in suc- 

 cessive infinitesimal zones or shells, until the maximum contracting 

 shell is attained, when the circumferential rate of contraction again 

 diminishes, until practical zero is arrived at 150 miles below the 

 surface. 



In all these zones or shells the circumferential contraction is 

 equal throughout for each particular shell. What I have called the 

 circumferential contraction is equal throughout the circle, whereas 

 the radial contraction differs at every point and is practically con- 

 fined to TjV of the radius. 



What will happen is this : There will be one particular shell 

 which will have the same rate of circumferential contraction as the 

 average radial contraction taken from the point of intersection to the 

 centre of the sphere. At this zone or surface there will be neither 

 tension nor compression, no deformation in fact, and it is to this 

 zone that the name of level-of-no-strain has been applied. Above 

 the level-of-no-strain the shells will be in compression, beginning 

 at zero at the level-of-no-strain and finishing at the surface with the 

 maximum. Below, the shells will be in tension, beginning at zero 

 at the level-of-no-strain, increasing to a maximum at about 60 miles 

 deep, and then shading off to nothing, 150 miles below the surface. 



This is a short statement of the principle I was the first to 

 enunciate in chap. xi. of the " Origin of Mountain Ranges," pub- 

 lished in 1886, in which I showed that the shell of compression 

 could not be more than a few miles thick, or, to state it otherwise, 

 that the neutral zone or level-of-no-strain between the shell in 

 compression and the shell in tension could not be more than a few 

 miles below the earth's surface. 



I reproduce by the lantern the original diagram from the " Origin 

 of Mountain Eanges." From this it follows that symmetrical 

 secular cooling produces tensile strains in by far the larger bulk 

 of the earth already affected by such cooling. 



Previous to this demonstration it had been customary to look at 

 the globe as consisting of a rigid crust in compression adapting 

 itself to a shrinking nucleus without intermediate gradations. 

 Eeasoners desirous of explaining in this way the rugosities of the 

 earth's surface, and the great evidences of lateral pressure shown 

 by the folding of strata in mountain ranges, assumed whatever 

 thickness they thought necessary for their theory, one well-known 

 geologist even placing the crust in compression at 800 miles. The 

 idea that any part of the shrinking globe was in tension did not 

 seem to have occurred to any of the physicists or geologists who 

 paid attention to the subject. I may add, as a matter of private 

 history, that this conception, which had been floating about in my 

 mind for a long time, was jotted down by me in a note five years 

 before publication. 



Since my work appeared, Mr, C. Davison contributed a paper to 

 the Eoyal Society (read April 7th, 1887) entitled, " On the Distri- 

 bution of Strain in the Earth's Crust resulting from Secular Cooling," 



