V. The Gravitational Stability of the Earth. 



/>>/ A. E. H. LOVE, F.K.S., Sedleian Professor of Natural Philosophy in the 



University of Oxford. 



Received February 16, Read March 14, 1907. 



CONTENTS. 



PART I. 



Page 



Introduction 171 



Statement of the mathematical problem 174 



Solution of the differential equations by means of spherical harmonics 178 



Adjustment of the harmonics to satisfy the boundary conditions 188 



The frequency equation and the condition of gravitational instability 191 



Instability in respect of radial displacements 193 



Instability in respect of displacements specified by harmonics of the first degree 197 



Stability in respect of displacements specified by harmonics of the second and third degrees . . 202 



Summary of the solution of the mathematical problem 210 



Application to the problem of the gravitational stability of the earth (propagation of earth- 

 quake shocks) 213 



PART II. 



A past state of gravitational instability as a reason for the existing distribution of land and 



water 217 



Illustration of the nature of a hemispherical distribution of density 218 



Effect of rotation upon a planet with such a distribution of density 221 



Effect of certain external forces 225 



The problem of the shape of the lithosphere 225 



Spherical harmonic analysis of the distribution of land and water 226 



The continental blocks and oceanic regions as expressed by means of spherical harmonica of the 



first, second, and third degrees 236 



Geological implications of the theory 238 



PART I. 

 INTRODUCTION. 



1. IF in a gravitating body there occurs a displacement which involves alteration of 

 density, there must be a tendency for the material to move towards the places where 

 the density is increased, and away from the places where the density is diminished. 

 The effect of this tendency, if it were not held in check, would be to accentuate local 

 VOL. ccvn, A 417, Z 2 31.5.07 



