NA TURE 



[August i, 1907 



spreads out, and is separated from the Antarctic region by 

 a very narrow channel. By go'ng down to great depths 

 our problem is very much simplified. We find that the 

 surface of the earth can be divided into continental and 

 oceanic regions of approximately equal area by a curve 

 which approaches a regular geometrical shape. By smooth- 

 ing away the irregularities we obtain the curve shown in 

 Fig- 3. which exhibits the surface as divided up into a 

 continuous continental region and two oceanic regions — 

 the basin of the Pacific Ocean and the basin of the Atlantic 

 and Indian Oceans. We may take our problem to be this : 

 to account on dynamical grounds for the separation of the 

 surface into a continental region and two oceanic regions 

 which are approximately of this shape. 



The key of the problem was put into our hands four 

 years ago by Jeans in his theory of gravitational instability. 

 If there are any differences of density in different parts 

 of a gravitating body, the denser parts attract with a 

 greater force than the rarer parts, and thus more and 

 more of the mass tends to be drawn towards the parts 

 where the density is in excess, and away from the parts 

 where it is in defect. In every gravitating .system there 

 is a tendency to instability. In a body of planetary dimen- 

 sions this tendency, if it were not checked, would result 

 in a concentration of the mass either towards the centre 

 or towards some other part. But concentration of the 

 mass means compression of the material, and it cannot 

 proceed very far without being checked by the resistance 

 which the material offers to compression. There ensues a 

 sort of competition between two agencies : gravitation, 

 making for instability, and the el.astic resistance to com- 



Fig.3. 



pression, making for stability. Such competing agencies 

 are familiar in other questions concerning the stability of 

 deformable bodies. A long thin bar set up on end tends 

 to bend under its own weight. A steel knitting-needle a 

 foot long can stand up ; a piece of thin paper of the same 

 length would bend over. In order that a body may be 

 stable in an assigned configuration there must be some 

 relation between the forces which make for instability, the 

 size of the body, and the resistance which it offers to 

 changes of size and shape. In the case of a gravitating 

 planet we may inquire how small its resistance to com- 

 pression must be in order that it may be unstable, and, 

 further, in respect of what types of displacement the 

 instability would manifest itself. If we assign the con- 

 stitution of the planet, the inquiry becomes a definite 

 mathematical problem. The greatest difficulty in the 

 problem arises from the enormous stresses which are 

 developed within such a body as the earth by the mutual 

 gravitation of its parts. The earth is in a stale which is 

 described technically as a state of " initial stress." In 

 the ordinary theory of the mechanics of deformable bodies 

 a body is taken to be strained or deformed when there is 

 any stress in it, and the strain is taken to be porportional 

 to the stress. This method amounts to measuring the 

 strain or deformation from an ideal state of zero stress. 

 If the ideal state is unattainable without rupture or per- 

 manent set or overstrain, the body is in a state of initial 

 stress. The commonest example is a golf ball made of 

 india-rubber tightly wound at a high tension. Now the 

 problem of gravitational instability can be' solved for a 

 planet of the size of the earth oil the suppositions that 

 the density is uniform and the initial stress is hvdrostatic 

 pressure. If the resistance to compression is sufficientlv 

 NO. 1970, VOI. 76] 



small the body is unstable, both as regards concentration 

 of mass towards the centre and as regards displacements 

 by which the density is increased in one hemisphere and 

 diminished in the other. A planetary body of sufficiently 

 small resistance to compression could not exist in the form 

 of a homogeneous sphere. It could exist in a state in 

 which the surface is very nearly spherical, and the mass is 

 arranged in a continuous series of nearly spherical thin 

 sheets, each of constant density ; but these sheets would 

 not be concentric. They would be crowded together 

 towards one side and spaced out on the opposite side some- 

 what in the manner shown in Fig. 4. The effect would 

 be a displacement of the centre of gravity away from the 

 centre of figure towards the side where the sheets are 

 crowded together. How small must the resistance to 

 compression be in order that this state may be assumed 

 by the body instead of a homogeneous state? The answer 

 is that, if the body has the same size and mass as the 

 earth, the material must be as compressible as granite. 

 Granite, as we know it at the earth's surface, is not a 

 typically compressible material. A cube of granite 10 feet 

 every way could be compressed from its volume of 1000 

 cubic feet to a volume of 999 cubic feet by pressure applied 

 to every part of its surface; but according to the recent 

 measurements of .Adams and Coker the pressure would 

 have to be rather more than two tons per square inch. 

 A homogeneous sphere of the same size and mass as the 

 earth, made of a material as nearly incompressible as 

 granite, could not exist ; it would be gravitationally un- 

 stable. The body would take up some such state of 



Fig.4. 



Fiq.5. 



aggregation as that illustrated in Fig. 4, and its centre 

 of gravity would have an eccentric position. 



Now how would an ocean rest on a gravitating spheie 

 of which the centre of gravity does not coincide with the 

 centre of figure? Its surface would be a sphere with its 

 centre at the centre of gravity (Fig. 5). The oceanic region 

 would be on one side of the sphere and the continental 

 region on the other side. It was pointed out many years 

 ago by Pratt that the existence of the Pacific Ocean shows 

 that the centre of gravity of the earth does not coincide 

 with the centre of figure. There is no necessity to invoke 

 some great catastrophe to account for the existence of the 

 Pacific Ocean, or to think of it as a kind of pit or scar 

 on the surface of the earth. The Pacific Ocean resembles 

 nothing so much as a drop of water adhering to a greasy 

 shot. The force that keeps the drop in position is surface 

 tension. The force that keeps the Pacific Ocean on one 

 side of the earth is gravity, directed more towards the 

 centre of gravity than the centre of figure. An adequate 

 cause for the eccentric position of the centre of gravity 

 is found in the necessary state of aggregation which the 

 earth must have had if at one time it was as compressible 

 as granite. The theory of gravitational instability accounts 

 for the existence of the Pacific Ocean. 



But we can go much further than this in the direction of 

 accounting for the continental and oceanic regions. We 

 keep in mind the eccentric position of the centre of gravity, 

 and try to discover the effect of rotation upon a planet 

 of which the centre of gravity does not coincide with the 

 centre of figure. The shape of a rotating planet must be 

 nearly an oblate sphiroid ; but the figure of the ocean 

 would, owing to its greater mobility, be rather more 



