G. II. Darwin — Stresses caused in the Earth by 



inequalities. Although the questions of distribution and 

 magnitude of the stresses are thus independent, it will, in gen- 

 eral, be convenient to discuss them more or less simultaneously. 



The problem has only been solved for the class of superficial 

 ies called zonal harmonics, and their nature will now 

 be explained. 



A zonal harmonic consists of a series of undulations corru- 

 gating the surface in parallels of latitude with reference to 

 some equator on the globe; the number of the undulations is 

 estimated by the order of the harmonic. The harmonic of the 

 second order is the most fundamental kind, and consists of a 

 single undulation forming an elevation round the equator, and 

 a pair of depressions at the poles of that equator ; it may also 

 be defined as an elliptic spheroid of revolution, and the abso- 

 lute magnitude is measured b\ the ellipticity of the spheroid. 



If the order of the harmonic be high, say 30 or 40, we have 

 a regular series of mountain chains and intervening valleys 

 running round the sphere in parallels of latitude. 



For the sake of convenience I shall always speak as though 

 the equator were a region of elevation, but the only effect of 



;ing elevations into depressk 

 3ally 



metrically reverse the directions of all the stresses. 



The harmonics of the orders 2, 6, 10, etc., have depressions 

 at the poles of the sphere ; those of orders 4, 8, 12, etc., have 

 elevations at the pole. 



The harmonic of the fourth order consists of an equatorial 

 continent and a pair of •■'uvular polar continents, with an inter- 

 vening depression. That of the sixth order consists of an 

 equatorial continent and a pair of annular continents in lati- 

 tudes (about) 60° on one and the other side of the equator. 

 The eighth harmonic brings down these new annular conti- 

 nents to about latitude 45°, and a continents; 



A, above explained, the sphere is deformed into a spheroid of 

 revolution. The investigation also applies to the case of a 

 rotating spheroid, such as the earth, with either more or less 

 oblateness than is appropriate for the figure of equilibrium. 



It is remarkable that the stress-difference is the same all over 

 the surface. In the polar regions the stress-difference dimin- 

 ishes as we descend into the spheroid, and then increases 

 auain ; in the equatorial regions it always increases as we 

 descend. The maximum value is at the center, and there the 

 stress-difference is eight times as great as at the surface. 



