VISCOSITY. 45 



statical equilibrium acts like an ideally clastic or ideally fluid mass. 

 Under these conditions the resistance winch a solid offers to deformation 

 is due entirely to its "rigidity," this term being defined in the theory of 

 elasticity as the degree of resistance winch a solid in permanent equi- 

 librium opposes to stresses tending to change its shape* Under this 

 definition india-rubber and tallow possess rigidity as well as cast iron, 

 but the modulus of rigidity of the metal is greater than that of the gum 

 or the tat. In short, rigidity is an essential property of solids. 



A highly viscous fluid subjected to a stress of brief duration presents 

 greal resistance to deformation. Thus, if the earth were substantially a 

 mass of sufficiently ultra-viscous fluids, it would behave to the attrac- 

 tions of the sun and moon sensibly like an infinitely rigid body, because 

 of the rapid change in the direction of these attractions. There are valid 

 grounds, however, tor the belief that the earth is really solid. 



The viscosity of rocks often controls the directions in which they yield 

 to stress. When two equal stresses acting on the same rock-mass change 

 their directions at different rates, that stress which rotates at the smaller 

 rate will encounter the smaller resistance and will produce the greater 

 effect, It has been shown in the earlier part of this paper that all rota- 

 tional strains are accompanied by relative tangential motion on two sets 

 of mathematical planes which rotate relatively to the mass at different 

 rates. The difference of their effects due to viscosity will be discussed 

 under the head of geological applications. 



Flow. — At least some solids in the so-called "stale of ease " (freedom 

 from internal partial constraint) almost completely recover their original 

 form after small strains when time is allowed to overcome the viscosity. 

 It is apparently true of all bodies, however, that when strained beyond 

 a certain limit short of rupture, they are permanently deformed. The 

 process by which this deformation is effected is termed flow, and the 

 limit at which a, substance initially in a state of ease begins to flow is 

 called the limit of solidity. When the limit of solidity differs hut little 

 from tin; ultimate strength, the substance is known as brittle. When 

 the limit of solidity is a fixed quantity, so that any excess of stress pro- 

 duces continuous flow, the mass is said to be plastic. When a continu- 

 ously increasing stress is needful to produce continuous How, the sub- 

 stance is said to be ductile, and in this case a " hardening " of the mass 

 attends the flow, as. for example, in the manufacture of wire. 



Plastic flow thus differs from ductile flow. 1 am not aware of any 

 phenomena which point decisively to. the existence of ductility and the 

 attendant hardening among rock masses, but it cannot he amiss to call 



*The word rigidity, as used in the theory of elasticity, lias nearly the same aning as stiffness 



in common parlance. 



