MancJiesUr Memoirs, Vol. Iv. {\C)\\\ No.%^. S 



example. In each case we should deal with the difference 

 of two stress systems. The practical difference is that we 

 cannot handle the massive structure. 



In the case of the substance of the Earth, there can be 

 no justification for assuming the whole stress system to be 

 elastic, although a part of it may be so treated. 



General Principles. 



In text-books on Elasticity and in numerous investi- 

 gations on that subject, elastic equilibrium " under bodily 

 forces " is treated in a method far from satisfactory, 

 except as descriptive of displacements consistent with 

 elastic stress. The method is to assume that the whole 

 stress system is elastic, and to form equations which can 

 to some extent be solved, and to state that difficulty arises 

 in satisfying the surface-conditions. This method hides 

 what may be the real question at issue, and throws upon 

 the surface-conditions difficulties which may have been 

 introduced by the initial hypothesis, because the stress 

 system is not an elastic stress system. 



I write this paper to propose a different order of treat- 

 ment, in which the solution of the elastic equations may 

 be convenient and desirable, but will not be the prime 

 essential. It will be necessary to show by examples 

 that the method proposed is a feasible one. 



The method is first to solve formally the statical stress 

 equations " under bodily forces " for a body of the shape 

 under consideration. There will be three equations con- 

 necting the six elements of the stress, and the solution will 

 give the six elements of the stress in terms of the force 

 system and three quantities conditioned by the form of 

 the bounding surfaces. The stresses so found must satisfy 

 such structural conditions as may apply to the case : the 



