258 G. II Dnrvin- N//7,v.sv.v cinisri! hi thi' Fjllih hlj 



or purely a pressure. Treating pressures as negative tractions, 

 we may say that at any point of a stressed elastic solid there 

 are three mutually perpendicular directions along which the 

 stresses are purely tractional. The traction which must be 

 applied to an inter-face of a square centimeter in area, in order 

 to mail] tain equilibrium when the matter on one side of the 

 inter-face is removed, is called a principal stress, and is of 

 course to be measured by grams weight per square centi- 



If the three stresses be equal and negative the matter at the 

 point in question is simply squeezed by hydrostatic pressure, 

 and it is not likely that in a homogeneous solid any simple 

 hydrostatic pressure, absolutely equal in all directions, would 

 ever rupture the solid. The effect of the equality of the three 

 stresses when they are positive and tractional is obscure, but 

 at least physicists do not in general suppose that this is the 

 cause of rupture when a solid breaks. 



If the three principal stresses be unequal, one must of course 

 be greatest and one least, and there is reason to suppose that 

 tendency of the solid to rupture is to be measured by the 

 difference between these principal stresses. 



In one very simple case we know that this is ao, for if we 

 imagine a square bar, of which the section is a square centi- 

 meter, to be submitted to simple longitudinal tension, then two 

 of the principal stresses are zero (namely, the stresses perpen- 

 dicular to the faces of the rod), and the third is equal to the 

 longitudinal traction. The traction under which the rod 

 breaks is a measure of its strength, and this is equal to the 

 difference of principal stresses. 



If, at the same time, the rod were subjected to great hydro- 

 static pressure the breaking load would be very little, if at all 

 affected ; now the hydrostatic pressure subtracts the same 

 quantity from all three principal stresses, but leaves the differ- 

 ence between the greatest and least principal stresses the same 

 as before. 



Difference of principal stresses may also be produced by 

 crushing. 



In this paper I call the difference between the greatest and 

 least principal stresses the "stress-difference," and I say that, 

 if calculation shows that the weight of a certain inequality on 

 the su nam oi the earth will produce such and such stress- 

 difference at Bach ;md such a place, then the matter at that 

 place must be at least as strong as matter which will break 

 when an equal stress-difference is produced by traction or 

 crushing. 



1 shall usually estimate stress-difference by metric tonnes (a 

 million grams), per square centimeter, or by British tons 



