44 G. P. BECKER — FINITE STRAIN IX ROCKS. 



belo re strain will keep this direction during strain only when the mass 

 acts as if it rested on or against an inflexible support. 

 1 f this support is parallel to o x, either tan x = or : 



tan y. =llZJ = tan (90° -f 2 x ). 



Properties of Matter. 



Viscosity. — The ideal elastic substance is one which requires a perfectly 

 difinite stress to hold it permanently in any given state of strain at a 

 given temperature. This stress is wholly independent of previous states 

 of strain or rates of straining. Heal substances fulfill this definition only 

 under certain conditions, and careful experiments always show that the 

 more rapidly deformation is produced, the greater is the resistance to be 

 overcome. Thus a spring, suddenly stretched by a given weight, yields 

 rapidly to a certain extent and may seem to become stationary ; but 

 careful observation shows that is continues to yield slowly to the traction 

 for a time, though it ultimately comes to rest. If the material were 

 ideally elastic, it would immediately assume this ultimate state of strain- 

 and the fact that the attainment of equilibrium is gradual proves that 

 the original resistance is a function of the rate of deformation. Fluids 

 show similar phenomena. 



Viscosity is that property in virtue of which matter presents to stress 

 a resistance into which the rate of deformation enters as a factor. 

 Viscosity and shear are inseparable, and mere dilation is unattended by 

 viscous phenomena* The coefficient of viscosity of a substance is ceteris 

 paribus, the shearing stress required to produce the unit shear in the unit 

 time. The degree of viscosity is considered as increasing with this coeffi- 

 cient, so that sealing wax and tar are more viscous than water, and steel 

 is more viscous than lead or copper. 



Substances which yield indefinitely though slowly to stresses, however 

 small, are now known as viscous fluids. Those which in the course of 

 time reach statical equilibrium under the action of deforming stress, such 

 as tallow and steel, are called viscous solids. 



If stress is applied very slowly (or rather infinitely slowly) viscosity 

 does not come into play. Thus, a viscous solid or fluid in permanent 



* Viscous resistance is often likened to friction. Each is a dissipative resistance to tangential 

 motion, but there are marked differences between them. Friction exists only where there is 

 normal pressure, and is therefore wholly absent on the planes of maximum tangential strain in a 

 shear. Friction also has its maximum value when the surfaces between which it exists are at rest. 

 Viscous resistance opposes relative motion of surfaces between which there is no normal pressure 

 when the rate of motion is finite, bul vanishes when this rate is infinitesimal. Thus their is 

 rather an analog} than a similarity between viscosity and friction. 



