134 Mr. J. C. Maxwell on the Dynamical Theory of Gases. 

 In a solid body free from viscosity, F will remain = ES, and 



^F — . 



dt ~ dt 



If, however, the body is viscous, F will not remain constant, 

 but will tend to disappear at a rate depending on the value of 

 F, and on the nature of the body. If we suppose this rate pro- 

 portional to F, the equation may be written 



dF dS_F 

 dt dt T' 



which will indicate the actual phenomena in an empirical man- 

 ner. For if S be constant, 



F=ESe~T 



showing 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 

 dt 



body which continually increases the displacement, 



showing that F tends to a constant value depending on the rate 

 of displacement. The quantity ET, by which the rate of dis- 

 placement must be multiplied to get the force, may be called the 

 coefficient of viscosity. It is the product of a coefficient of elas- 

 ticity, E, and a time T, which may be called the " time of relax- 

 ation }> of the elastic force. In mobile fluids T is a very small 

 fraction of a second, and E is not easily determined experimen- 

 tally. 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 per- 

 fect 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 por- 

 tions. 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 



