532 



SCIENCE 



[N. S. Vor,. XXVI. No. 669 



elastic resistance to compression, 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 resist- 

 ance to compression must be in order that 

 it may be unstable, and, further, in respect 

 of what types of displacement the insta- 

 bility would manifest itself. If we assign 

 the constitution of the planet, the inquiry 

 becomes a definite mathematical problem. 

 The greatest difficulty in the problem arises 

 from the enormous stresses which are de- 

 veloped within such a body as the earth by 

 the mutual gravitation of its parts. The 

 earth is in a state which is described tech- 

 nically 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 

 proportional to the stress. This method 

 amounts to measuring the strain or de- 

 formation from an ideal state of zero stress. 

 If the ideal state is unattainable without 

 rupture or permanent 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 ten- 

 sion. Now the problem of gravitational 

 instability can be solved for a planet of the 

 size of the earth on the suppositions that 

 the density is uniform and the initial stress 

 is hydrostatic pressure. If the resistance 

 to compression is sufficiently small the body 



is unstable, both as regards concentration 

 of mass towards the center and as regards 

 displacements by which the density is in- 

 creased in one hemisphere and diminished 

 in the other. A planetary body of suf- 

 ficiently small resistance to compression 

 could not exist in the fonn of a homo- 

 geneous 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 somewhat in the man- 



F13.4. 



Fig.B. 



ner shown in Fig. 4. The effect would be 

 a displacement of the center of gravity 

 away from the center of figure towards the 

 side where the sheets are crowded together. 

 How small must the resistance to compres- 

 sion be in order that this state may be as- 

 sumed by the body instead of a homo- 

 geneous 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 com- 

 pressible material. A cube of granite 10 

 feet every way could be compressed from 

 its volume of 1,000 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 



