MR. CLERK MAXWELL OX THE DYNAMICAL THEORY OF GASES. 
53 
increases the displacement, 
f=et£+c,-*. 
showing that F tends to a constant value depending on the rate of displacement. 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 experi- 
mentally. In viscous solids T may be several hours or days, and then E is easily mea- 
sured. 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 equi- 
librium 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 elasti- 
city, or “ rigidity ” of the gas, but this resistance gives way and diminishes at a rate de- 
pending on the amount of the force and on the nature of the gas. 
Suppose the molecules to be confined in a rectangular vessel with perfectly elastic 
sides, and that they have no action on one another, so that they never strike one another, 
or cause each other to deviate from their rectilinear paths. Then it can easily be shown 
that the pressures on the sides of the vessel due to the impacts of the molecules are per- 
fectly independent of each other, so that the mass of moving molecules will behave, not 
like a fluid, but like an elastic solid. Now suppose the pressures at first equal in the 
three directions perpendicular to the sides, and let the dimensions «, b, c of the vessel 
be altered by small quantities, lb, Ic. 
Then if the original pressure in the direction of a was p, it will become 
1 6a U 8c\ 
i_ a“T - 7; 5 
sr if there is no change of volume, 
showing that in this case there is a “ longitudinal ” elasticity of form of which the coeffi- 
cient is 2p. The coefficient of “Rigidity” is therefore —p. 
