Se ye at a a Nac ia are lia 
VISCOSITY OF WATER BY THE EFFLUX METHOD. 109 
other components of motion consequently becoming zero. The 
equation 
du dp 
a ¢ nit kab a _ — fy = 0 ( a) 
p( dt da ee ides 
with similar expressions in Y, y, v, and 7, 2, w,—in which y* 
denotes as usual Laplace’s operator, p the density of the fluid, X 
ete., the components of the external impressed forces per unit of 
mass and u, v, w the components of velocity in the directions a, 
y, z—reduce under the circumstances indicated to one, viz. that 
above written. The condition of the conservation of volumes or 
the equation of continuity becomes du/dx=0, and that of steady 
motion is du/dé=0. Ina circular section u is clearly a function 
of r and ¢ only: using therefore cylindrical codrdinates, in which 
case the operator, thus restricted, becomes 
dr? ry "ar 
o oe ae oe. er 
The left hand side of this equation does not involve r nor the 
right hand «, hence each must bea constant,—A say. If therefore 
the difference of pressure in two sections the distance Z apart be 
P, the left hand side of this last equation gives 
1 
Sar ot a 
and the right hand side : 
a = 1Ar?+B logr+C’ 
and ©’ being arbitrary constants, As the velocity at the 
—_a of the pipe where r=0, is finite, B’ must be zero: substi- 
tuting therefore the above value of A in the expression for u, and 
remembering in regard to the constant C’ that when r= &, the 
radius of the pipe, «=0, there being no slip at the boundary, we 
have for the velocity at any point in the section at the distance r 
from its centre 
ai a ae a 2 
—- bs a ae a aS (15) es 
(2) is obtained by substituting the value of u in the 
