164 PROFESSOR 0. REYNOLDS OFT THE THEORY OF LUBRICATION 1 
aid cf the graphic method, has been introduced as Section III. Finally, the definite 
application of the theory to Mr. Tower’s experiments is given in Section IX. 
Sect ton II. —The Properties of Lubricants. 
9. The Definition ofi Viscosity. 
In distinguishing between solid and fluid matter, it is customary to define fluid as 
a state of matter incapable of sustaining tangential or shearing stress. This defini¬ 
tion, however, as is well known, is only true as applied to actual fluids when at rest. 
The resistance encountered by water and all known fluids flowing steadily along 
parallel channels, affords definite proof that in certain states of motion all actual fluids 
will sustain shearing stress. These actual fluids are, therefore, called in the language 
of mathematics imperfect or viscous fluids. 
In order to obtain the equations of motion of such fluids, it has been necessary to 
define clearly the property of viscosity. This definition has been obtained from the 
consideration that to cause shearing stress in a body it is necessary to submit it to 
forces tending to change its shape. Forces tending to cause a general motion, whether 
linear, revolving, uniform expansion, or uniform contraction, call forth no shearing 
stress. 
Using the term distortion to express change of shape, apart from change of position, 
uniform expansion, or contraction, the viscosity of a fluid is defined as the shearing 
stress caused in the fluid while undergoing distortion, and the shearing stress divided by 
the rate of distortion is called the coefficient of viscosity, or, commonly, the viscosity 
of the fluid. 
This is best expressed by considering a mass of fluid bounded by two parallel planes 
at a distance a, and supposing the fluid between these planes to be in motion in a 
direction parallel to these surfaces with a velocity which varies uniformly from 0 at one 
of these surfaces to u at the other. Then the rate of distortion is 
u 
a 
and the shearing stress on a plane parallel to the motion is expressed by 
f=V- .0) 
/x being the coefficient of viscosity or the modulus of the resistance to distortional 
motion. 
10. The Character of Viscosity. 
In dealing with ideal fluids, it is of course allowable to consider y. as being zero or 
having any conceivable value; but practically, as regards natural philosophy, the 
