THE DYNAMICAL THEORY OP GASES. 31 



which will indicate the actual phenomena in an empirical manner. For if S 

 be constant, 



shewing that F gradually disappears, so that if the body is left to itself it 

 gradually loses any internal stress, and the pressures are finally distributed as 

 in a fluid at rest. 



If -, is constant, that is, if there is a steady motion of the body which 

 continually increases the displacement, 



shewing that F tends to a constant value depending on the rate of displace- 

 ment. The quantity ET, by which the rate of displacement must be multiplied 

 to get the force, may be called the coefficient of viscosity. It is the product 

 of a coefficient of elasticity, E, and a time T, which may be called the "time 

 of relaxation " of the elastic force. In mobile fluids T is a very small fraction 

 of a second, and E is not easily determined experimentally. In viscous solids 

 T may be several hours or days, and then E is easily measured. It is possible 

 that in some bodies T may be a function of F, and this would account for 

 the gradual untwisting of wires after being twisted beyond the limit of perfect 

 elasticity. For if T diminishes as F increases, the parts of the wire furthest 

 from the axis will yield more rapidly than the parts near the axis during the 

 twisting process, and when the twisting force is removed, the wire will at first 

 untwist till there is equilibrium between the stresses in the inner and outer 

 portions. These stresses will then undergo a gradual relaxation ; but since the 

 actual value of the stress is greater in the outer layers, it will have a more 

 rapid rate of relaxation, so that the wire will go on gradually untwisting for 

 some hours or days, owing to the stress on the interior portions maintaining 

 itself longer than that of the outer parts. This phenomenon was observed by 

 Weber in silk fibres, by Kohlrausch in glass fibres, and by myself in steel wires. 

 In the case of a collection of moving molecules such as we suppose a gas 

 to be, there is also a resistance to change of form, constituting what may be 

 called the linear elasticity, or "rigidity" of the gas, but this resistance gives 

 way and diminishes at a rate depending on the amount of the force and on 

 the nature of the gas. 



