VISCOSITY OF WATER BY THE EFFLUX METHOD. 113 
semidiameters to be 1/16 and their sum to be 17/16, € will be 1/17, 
hence the correction on Poiseuille’s value will be — 2? + Ge* — ete. 
= 0:00685 or about 1/146. 
12. Flow ina frustum of a right circular cone.—Not one of the 
tubes used by Poiseuille was exactly a right circular cylinder, and 
the assumption of a cylindrical form is doubtless always unsafe, 
for capillary tubes are probably always more or less irregular in 
section. We proceed to consider the law of flow in a frustum ofa 
right circular cone whose generatrix is nearly parallel to its axis, 
and more generally in a tube forming a series of conical frusta. 
Since the motion of all stream lines is sensibly parallel—in the 
case supposed—to the axis of the cone, it will be necessary to 
have regard only to the variation of velocity with change in the 
area of the right section, and thus to determine the fall in pressure 
in terms of the radii of the tubes. Let R, Rm, Ry denote respec- . 
tively the radius of the tube at the terminal of efflux, and pro- 
ceeding toward the point of influx, the radii of the terminals of 
any conical length of the tube ; and let also R, denote the radius 
of a right section of this conical length at the distance 2 from Ryn», 
« being measured therefore toward to point of influx, z.e. towards 
R,. Then if U be the the mean velocity at the efflux terminal 
of the tube, the radius there being R, the mean velocity U, at the 
transverse section whose radius is R,, will be 
Cee oe 2 (22) 
mw (hat key 
in which & denotes the tangent of the angle between the axis and 
side of the cone, may be positive or negative, and is expressed by 
the equation 
(f) 
n 
1, being the distance between the terminal sections of the frustum: 
under consideration, 
k= Ry ~ Rin 
L 
Equation (16) gives at once 
“o that substituting for U, its value by (22), and for 2; its 
H—July 3, 1895, 
