1920-21.] Stable Flow of a Fluid in a Uniform Channel. 147 
. TTOL 
Sill — 
K (l 
2 CL , 7 TX TTOL 
cosh — — cos — 
= 0 . 
The slip at the boundary therefore attains a maximum value of ^ cot ^ 
when x = 0 and falls off exponentially as x increases, becoming zero as 
| x | ->oo . The maximum velocity of slip may likewise be written, of 
course, ~~ tan Associating this with the conditions for stability and 
ZCt ZC6 
instability (30) in the form 
=— UAcot 2 J^, it follows that for a stable 
7 r 2a 
16/?/ It 
system the maximum velocity of slip is always less than U cot , and 
7 r a 2a 
for an unstable system the slip is always greater than this quantity. The 
fact that as the passage is made from the stable to the unstable region the 
tendency to slip increases, should be associated with the remarks in § 5 of 
this paper relative to the insufficiency of experimental evidence on the 
question of slip at the boundary when turbulent flow has set in. 
{Issued separately December 13, 1921.) 
