88 G. H. KNIBBS. 
above equation applies. The physical characteristic of such a 
flow in a cylindrical pipe, is that the motion of all particles i 
parallel to its axis, and points of equal velocity lie, if the section : 
bea circle, in the circumference of a circle concentric therewith, the | 
velocity of course diminishing with increase of distance from the | 
axis. The liquid may therefore be imagined to be divided into a | 
series of coiixial circular cylinders, and the internal friction tobe 
the sum of the resistances exercised by each cylindrical stratum 
upon the interior and more rapidly moving cylinder. It is this 
conception, viz. that of steady rectilinear motion, which, together 
with the consideration of the boundary condition, leads to “ 
formula written. ‘4 
5. Definition of Viscosity.—Navier,! in his treatise, gives an 
explanation rather than a definition of the meaning of 4 (€ 12 bis 
equations), which may be thus expressed :—If we imagine 4 ful 
to be divided into a series of planes parallel to some fixed plane 
the motion in each being identical in direction, and in velocit] ’ 
equal to its distance from the plane, then the constant 7 repre 
sents in units of weight, the resistance per unit of surface to the 
sliding of one stratum on another. Hagenbach’s? definition 18:— 
By viscosity we denote the force necessary to move with unifor | 
velocity and in a unit (second) of time a stratum of fluid on 
molecule in thickness and of unit surface, the distance of sais 
the latter being moreover dependent upon a particular concep?” 
as to the physical constitution of a fluid. The following is ptr 
posed as obviating these objections :—The coéfiicient of vise : 
expresses the ratio, per unit of surface, of the tangential resista 
between parallel strata of a fluid moving with different velocities 
to the rate of variation of their velocity measured perpendicul 
to the direction of movement. The resistance is ge 
supposed to vary as the difference of the velocity, an assump 
1 Mém. Phd des Sciences, t. 6, p. 416, 
* Pogg. Annal. Bd. 109, p. 425. The translation is nearly literal. 
