380 The N.Z. -Journal of Science and Technology. [Dec. 
both length l and friction head li are the same, by the condition of the 
problem. 
We have from the second equation v 1 2 /r 1 = v 2 2 /r 2 =v 2 /r. Expressing 
v ± and v 2 in terms of v, we have v ± 2 = v 2 r 1 /r, and v 2 2 = v 2 r 2 /r. ‘From the 
first equation we have Av — Ajiq -j- A 2 v 2 , 
we have 
Av =. A t v V - 1 + A 2 
and substituting for i\ and v 2 
v . \/— 
r 
