The Unsteady Motion of Viscous Liquids. 
551 
Hence we derive 
8 ju plv 
(3) 
These equations are only true, however, for steady motion; 
that is to say, these equations only hold when the flow has taken 
place for a length of time sufficient to permit the velocity to 
have become constant. 
In case the motion in the capillary tube begins from a condi¬ 
tion of rest and is allowed to increase under the influence of a 
constant difference in pressure between the ends of the tube, we 
must consider v as a variable defined by the differential equa¬ 
tion 
( 1 ) 
Solving this linear equation we obtain 
(5) 
This gives the velocity at any instant after the commencement 
of the motion. This equation is analogous to Helmholz’s equa¬ 
tion of self-induction in the theory of electric currents, as is 
readily seen from the following form of Helmholz’s equation: 
(6) 
in which L is the coefficient of self-induction. 
If instead of the liquid flowing from one reservoir into 
another through a capillary tube, the liquid is permitted to 
flow from a single reservoir into an empty capillary tube, l will 
no longer be a constant but will be a variable. The equation 
(4) above must be replaced by 
(7) 
