316 G. H. KNIBBS. 
and a fresh reduction of the whole of the experimental data, has 
been given at length in two earlier papers, viz., that of July 1895, 
and of September 1896, read before this Society.’ In obtaining 
the value of the constant, a rational solution of the problem of 
flow in circular, and elliptical cylinders, and slightly tapering cones, 
was reached, for the case of non-sinuous motion, 7.¢., motion such 
that each particle moves parallel to the axis of the pipe. 
The viscosity was defined in the paper above referred to,” as the 
ratio of the tangential resistance between parallel strata of fluid 
moving with different velocities, to the rate of variation of the 
velocity measured perpendicularly to the direction of motion. Thus 
it may be regarded as a measure of the resistance of the fluid to 
the distortions or shear, involved by the circumstances of flow. It 
was likewise shewn that the velocity of water in contact with a 
pipe is zero; and that the fall in pressure from point to point of a 
horizontal pipe is wholly the consequence of the resistances 
between the surfaces of the elementary coiixial cylinders into which 
the whole volume of the liquid may be conceived to be divided, each 
one of which is moving more and more rapidly, as the axis of the 
pipe is approached. This type of motion may be described as steady 
and rectilinear. When the motion is non-linear, but otherwise 
steady, that is to say, when equal volumes pass each section in a 
unit of time, the velocities of translation must be in some sense 
periodic, although the periodicity may, and really appears to be, 
somewhat irregular. When the mean velocity of translation past 
any section is constant, the flow may be called steady non-linear 
or uniform turbulent flow. 
3. Velocity in elliptical pipe with steady rectilinear flow— When 
the viscosity coéfficient for a fluid is known, the mean velocity 0 
RE TORRENS oe OO LG Cee 
1 The History, Theory, and Determination of the Viscosity of Water 
Vol. 
Visooaity veg Water ae the Efflux Method.—Journ. Roy. Soc . N.S.We 
Vol. xxx., pp. 186 
2 Loc. cit., p. 88. 
