370 T. C. CHAMBERLIN 



sphere of disruption — which is applicable to solid bodies as 

 distinguished from liquid bodies. 



The size of this sphere of disruption compared with the 

 Roche sphere depends, among other things, on the coefificient 

 of cohesion and the size of the body to be disrupted. The 

 coefificient of cohesion being the same, the sphere of disruption 

 IS relatively smallest when small bodies are to be disrupted, and 

 becomes larger as the size of the body increases until it is 

 sensibly as large as the Roche sphere. To illustrate this con- 

 cretely, let disruption be supposed to take place along a diamet- 

 rical section normal to the gravitative pull, dividing the body 

 into halves. Let the bodies to be disrupted be spherical and 

 homogeneous. The cohesion to be overcome will then obviously 

 vary as the areas of the diametrical sections, and these areas 

 vary as the squares of the radii of the bodies. But the masses 

 of homogeneous spheres vary as the cubes of their radii, and 

 the gravitative pull varies as the masses, modified by the differ- 

 ential tidal pull. It follows that mutual gravitation will more 

 effectively disrupt large bodies than small ones. The limit at 

 which the fragmentation of a solid body will take place will 

 therefore approach more and more closely that of a fluid body 

 as the size of the solid body becomes larger. For solid bodies 

 of considerable dimensions, as asteroids, for example, the limit 

 of disruption approaches sufficiently near Roche's limit to make 

 the difference negligible in a general discussion. This will appear 

 the more evident from the following numerical considerations. 



Experimental data as to the tensile strength of rock are very 

 limited, as the material is rarely used where tensile stresses are 

 involved, but all the results of experimental tests given in 

 Johnson's Material of Co?istructio/i fall notably below looo 

 pounds to the square inch, and this figure may be assumed as a 

 liberal representative estimate. The weight of representative 

 rock may be taken as -^-^ pound per cubic inch. The tensile 

 strength of an inch cube is therefore to its weight, at the surface 

 of the earth, as 10,000 to i. Using the same data, the tensile 

 strength of a mile-cube of rock is to its weight as i to 6.36, 



