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IV. On the Stresses caused in the Interior of the Earth by the Weight of Continents 
and Mountains. 
By G. H. Darwin, F.R.S. 
Received June 11,—Read June 16, 1881. 
[Plates 19, 20.] 
Table of Contents. 
Introduction . 
Part I. The Mathematical Investigation. 
Page. 
187 
§ 1. On the state of internal stress of a strained elastic sphere... 188 
§ 2. The determination of the stresses when the disturbing potential is an even 
zonal harmonic . 191 
§ 3. On the direction and magnitude of the principal stresses in a strained elastic 
solid... 198 
§ 4. The application of the previous analysis to the determination of the stresses 
produced by the weight of superficial inequalities . 200 
§ 5. The state of stress due to ellipticity of figure or to tide-generating forces .. 201 
§ 6. On the stresses due to a series of parallel mountain chains . 205 
§ 7. On the stresses due to the even zonal harmonic inequalities. 208 
§ 8. On the stresses due to the weight of an equatorial continent. 211 
§ 9. On the strength of various substances ... 213 
§ 10. On the case when the elastic solid is compressible. 215 
Part II. Summary and Discussion . 218 
In this paper I have considered the subject of the solidity and strength of the 
materials of which the earth is formed, from a point of view from which it does not 
seem to have been hitherto discussed. 
The first part of the paper is entirely devoted to a mathematical investigation, based 
upon a well-known paper of Sir William Thomson’s. The second part consists of a 
summary and discussion of the preceding work. In this I have tried, as far as possible, 
to avoid mathematics, and I hope that a considerable part of it may prove intelligible 
to the non-mathematical reader. 
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