276 Cilley — Fundamental Propositions in the 



As in the case of primary stresses, we may define actual 

 stresses as those which, applied to a portion of a body when 

 removed from the body but still subject to the same bodily 

 forces and at the same temperature, would reduce that portion 

 of the body to the form and proportions it had when in the body 

 when the body was subject to the given external and bodily 

 forces, — and the actual strains will be the corresponding strains. 



Actual stresses and strains are always real stresses and 

 strains. But the corresponding primary stresses and strains 

 may be fictitious because of such amount and character as to 

 make their separate existence physically impossible. Such a 

 state of affairs occurs when the removal of the bodily forces 

 and surface tractions would result in so considerable changes in 

 stresses and strains as to pass the elastic limits and lead to flow 

 or even rupture. Release from excessive compression would 

 involve such results, an illustration being found in the state of 

 stress and strain in the earth's interior, which will be further 

 considered presently. Certain states of stress and strain under 

 certain forces, then, can not be deduced from any physically 

 possible condition of the body when under other forces, nota- 

 bly when free, from all bodily and external forces, through 

 mere elastic distortion, but necessarily involve flow or even 

 rupture of the material in the course of the transformation. 

 This fact is one of the first importance in all attempts to apply 

 the theory of elasticity to the explanation of cosmic phenom- 

 ena. 



In the practical treatment of the question of actual stresses 

 and strains we are confronted with the facts that we are rarely 

 able to determine the actual state of stress and strain by non- 

 injurious observations, and that it is not permissible to cut the 

 body to pieces in order to determine them. So we are obliged 

 to make use of such knowledge as we possess of the history of 

 the body, supplement it with such non-injurious observations as 

 are possible and thence make the best guess we can as to the 

 probable state of stress and strain in the body under some 

 known condition as to outer and bodily forces. This guess 

 must conform to the general equations of equilibrium for 

 actual stresses and strains. Any state that satisfies them is, 

 (except for physical limitations) a possible state, while any 

 state not satisfying them can not possibly subsist as a state of 

 equilibrium. These equations, then, serve simply as guides, 

 furnishing criteria as to possible states of stress and strain. 

 But beyond this they cannot help us. 



Often it is reasonable to assume no stress and strain when 

 there are no applied forces, and such is, consciously or uncon- 

 sciously, the usual procedure. But in some cases we know 

 that either under no applied forces there are certain fairly 



