JULY 4, 1907] 



NA rURE 



THE SHAPE OF THE EARTH.' 



THE most promising' suggestion towarf's a 

 dynamical explanation of the distribution of 

 land and water on the surface of the globe is to be 

 found in the theory of gravitational instability pro- 

 pounded by Jeans in 1903. There is always a 

 tendency in gravitating matter, if homogeneous, to 

 condense towards a centre, or towards an axis, or in 

 some more complex fashion. If the matter is hetero- 

 geneous, there is always a tendency for the density 

 to increase where it is above the average and to 

 diminish where it is below the average. Such 

 changes of density imply compression of the material, 

 and they are resisted by the elastic force with which 

 the material resists compression. In the case of a 

 planet we may ask two questions : How small must 

 the resistance to compression be in order that sensible 

 condensations may take place? In respect of what 

 changes of density can instability manifest itself? 

 The answers depend greatly upon the size and mass 

 of the planet, and they depend also upon its constitu- 

 tion. 



Whatever the internal constitution of a planet may 

 be, it is certain that, owing to the mutual gravitation 

 of its parts, great stresses will be developed within it. 

 A direct method of attacking the problem of gravi- 

 tational instabilitv for a planet in such a state of 

 stress was proposed by I.ord Rayleigh in igo6. The 

 development of this method leads to the result that 

 a homogeneous spherical planet, of the same size 

 and mass as the earth, could not exist unless the 

 resistance to compression of the material of which it 

 is composed were at least half as great as that of 

 steel. If the resistance were less than a quarter of 

 that of steel (so that the substance was less com- 

 pressible than mercury but more compressible than 

 glass) such a planetary body would be unstable, both 

 as regards concentration of mass towards the centre 

 and also as regards displacements by which the 

 densitv is increased in one hemisphere and diminished 

 in the opposite hemisphere. No matter how small 

 the resistance to compression might be, the body 

 would not be unstable as regards any other type of 

 displacements. If the resistance to compression were 

 small enough for a spherically symmetrical state of 

 aggregation to be unstable, the density of the super- 

 ficial portions would be less than the mean density, 

 and the centre of gravity would not coincide with the 

 centre of figure. If the planet were at rest under no 

 external forces, a shallow ocean resting upon it would 

 be drawn permanently towards the side nearer the 

 centre of gravity, so that there would be a land hemi- 

 sphere and a water hemisphere. 



The average resistance to compression of the 

 materials of which the earth is composed can be 

 deduced from the observed velocity of propagation of 

 earthquake shocks, and it is found to be decidedly 

 greater than that of any known materia! at the 

 surface — a result clearlv associated with the increase 

 of resistance under great pressure. There is, there- 

 fore, no tendency to gravitational instability at the 

 present time; but the actual excess of the mean 

 density over the density of surface rocks, and the fact 

 that a very large proportion of the land lies within 

 a great circle having its centre in south-eastern 

 Europe, suggest that the resistance to compression 

 was once much smaller than it is now. This sug- 

 gestion offers a possible dynamical explanation of the 

 fact that the centre of gravity does not coincide with 

 the centre of figure, and the maintenance of the 

 Pacific Ocean on one side of the globe is due to the 

 eccentric position of the centre of gravity. 



1 Based up" n a raper on " The Giavilational Stability of the Earth," by 

 rof. A. E. H. Love, F.R.S., read before the Royal Society on March 14. 



The actual shape of the lithosphere, or rocky 

 nucleus of the earth, and its situation relative to the 

 geoid, or the equipotential surface which coincides 

 with the surface of the ocean, are due to many 

 causes, of which the eccentric position of the centre 

 of gravity is one. Other important causes are the 

 rotation and the attraction of the moon. The moon 

 was once very near the earth, and the day and the 

 month were once nearly equal. The earth was then 

 drawn out towards the moon nearly into the form 

 of an ellipsoid with three unequal axes. The direct 

 result of the rotation and the attraction of the moon 

 would be to give to the lithosphere the shape of an 

 ellipsoid differing slightly from the ellipsoidal figure 

 of the geoid. If the centre of gravity coincided with 

 the centre of figure, the lithosphere would protrude 

 from the geoid near the North and South Poles and 

 in two equatorial regions at the opposite ends of 

 the longest equatorial diameter of the lithosphere. 

 If the density v,'ere in excess on one side of a 

 diametral plane and in defect on the opposite side, 

 the effects of the rotation, and of those irregularities 

 of attraction which are due to the ellipsoidal figure, 

 would be greater where the density was greater, and 

 the surface of the lithosphere would consequently be 

 deformed in such a way that the deviation from the 

 ellipsoidal figure could be expressed mathematically 

 by means of a spherical surface harmonic of the 

 third degree. The ellipsoidal deviations from 

 sphericity are expressed by harmonics of the second 

 degree, and the eccentric position of the centre of 

 gravity is equivalent to a deviation from symmetry 

 expressed by harmonics of the first degree. We can 

 therefore account theoretically for the presence of 

 harmonics of these three degrees in the formula for 

 the shape of the lithosphere and its situation relative 

 to the geoid. 



Now it is known that the actual contour-line at 

 mean-sphere-level (1400 fathoms below sea-level) 

 divides the surface of the globe into two regions of 

 equal area — the continental block and the oceanic 

 region. The continental block is practically con- 

 tinuous, and there are two great ocean basins, one 

 containing the deep parts of the Atlantic and Indian 

 Oceans, and the other the deep part of the P,-icific 

 Ocean. A spherical harmonic analysis of the distri- 

 bution of land and water, account being taken of the 

 submerged portions of the continental block, yields 

 the result that the actual outlines of the great ocean 

 basins at mean-sphere-level coincide very approxi- 

 mately with one of the contour-lines of a certain 

 spherical harmonic containing terms of the first, 

 second, and third degrees, but no terms of any higher 

 degree. . 



it appears, therefore, that the shapes and relative 

 situations of the great ocean basins, and their posi- 

 tions relative to the polar axis, can be described, at 

 least approximately, in the statement that the litho- 

 sphere is an ellipsoid with three unequal axes, having 

 its surface deformed according to the formula for a 

 certain spherical harmonic of the third des-ree. and 

 displaced as a whole relatively to the geoid in the 

 direction towards south-eastern Europe. The dis- 

 placement of the surface as a whole is accounted for 

 by the eccentric position of the centre of gravity, and 

 this eccentric position can be regarded as a survival 

 from a past state in which the resistance to com- 

 pression was too small for a spherically symmetrica! 

 configuration to be stable. The ellipsoidal fia;ure is 

 accounted for partly by the rotation and partly as a 

 survival from a past state brought about by the 

 attraction of the moon at the time when the day 

 and the month were nearly equal. The deformation 

 of the ellipsoid according to the formula for a 

 spherical harmonic of the third degree is accounted 



NO. 1966, VOL. 76] 



