286 Cilley — Fundamental Propositions in the 



satisfying the demands of mechanics in this connection. It 

 would be absurd to maintain in the face of known facts that 

 the earth had arrived at its present condition simply through 

 elastic distortion, and therefore that its condition could be 

 deduced from consideration of the elastic distortions of a 

 sphere originally free from all forces and all stresses and 

 strains. Nothing is more certain than that innumerable flows 

 and slips have occurred, and that, if the earth could be relieved 

 of all gravitational force and could stand the resulting change 

 of strains, it would then be found in a condition of great 

 primary stress and strain. It has been assumed, to overcome 

 the difficulties of the ordinary explanation which neglects these 

 evident facts, that the moduli of elasticity are not constant,, 

 but are immensely greater under great stress than under the 

 stresses with which we are familar. This is quite possibly true 

 and would greatly help out the old theory, but it certainly is 

 not the only and complete explanation, in fact no explanation 

 can be complete which does not take into consideration the 

 possible differences between actual states of stress and strain 

 and the changes in stress and strain under applied forces, at 

 present alone considered by the theory of elasticity. This i» 

 also true of many other problems in speculative science which 

 would take new shape and become comprehensible by aid of 

 the idea of primary and actual states of stress and strain. 



Here closing our illustrations, there still remain some special 

 considerations worthy of attention, among which we may note 

 the following. 



Primary stresses and strains are in their essence no different 

 from any other stresses and strains. They need be of no larger 

 amounts, they no more involve consideration of the higher 

 powers of the strains, than in the case of the changes in stress 

 and strain produced by applied forces, and they are governed 

 by the same stress-strain relations. These stress- strain relations 

 are fixed purely by the physical constitution of the body at 

 each point. The one peculiarity of the primary stresses is that 

 they are not the concomitant of external forces, appearing 

 and vanishing as these are applied and removed, and balanced 

 against them, but on the contrary may exist independently of 

 the external forces and are balanced among themselves. For 

 this reason primary stresses may properly be characterized by 

 the name " self-balancing stresses." And the peculiarity of 

 primary strains is that they are not necessarily factors in the 

 distortion of a piece under external forces, but may exist with- 

 out any such forces and without any necessary relations to dis- 

 placements such as the strain- displacement relations of the 

 usual theory. 



