BETWEEN" THE VISCOSITY OF LIQUIDS AND THEIR CHEMICAL NATURE. 407 
Definition of the Viscosity Coefficient. 
It lias already been stated that the time which a liquid takes to flow through 
a capillary tube, is, under certain conditions, a measure of its viscosity. The 
necessary conditions will be given at length subsequently. It will be sufficient here 
to indicate the meaning of viscosity, and the principles involved in measuring it. 
In the case of an ideal solid, the value of the fraction 
Force producing deformation 
Hef or Illation produced 
is a constant; whereas in the case of a liquid this ratio depends on the time during 
which the force acts. Determined for unit-time, the fraction may be taken in the 
case of a liquid as a measure of its viscosity or its resistance to change of form. 
The coefficient of viscosity is thus given by the expression 
_ Deforming force 
^ Deformation per unit time. 
Consider a quantity of liquid contained between two parallel planes of unit area at 
a distance 8 apart, and let a tangential force act on the liquid so that the planes 
move parallel to one another, and let the displacement of one plane relative to the 
other, which may be considered at rest, be S'. 
If the velocity of any stratum be assumed to be proportional to its distance from 
the fixed plane, then the deformation of the substance between the planes per unit 
time, or the rate of shear, is measured by the velocity of displacement of any stratum 
divided by its distance from the fixed plane, and thus by 8'/S, so that, if F be the 
tangential force per unit area acting on either of the planes, and exerted by the 
substance in resisting deformation, 
F 
“ ¥il’ 
If SyS = ], that is, if the displacement is equal to the distance from the fixed 
plane, p = F, and the coefficient of viscosity can then be defined. It is the force 
which is necessary to maintain the movement of a layer of unit area past another of 
the same area with a velocity numerically equal to the distance between the layei’s, 
when the space between them is continuously filled y^ith the viscous substance. Or 
7] may be defined as the tangential force which must be exerted on unit area of each 
stratum of liquid in order to maintain the flow when the velocity is changing in a 
* Different symbols have been used in different countries to indicate the coefficient of viscosity. In 
France e, in Germany //, and in this country have been commonly employed. The use of seems 
objectionable as it is now largely employed for the refractive index of a substance; it is also sometimes 
used to denote magnetic permeability and also the micro-millimeter. We therefore prefer, in conformity 
with German custom, to make use of >] to denote the coefficient of viscosity. 
