the time of its
appearance at the lower end of the 16-in. pipe at _E_ was noted. The
time was 3 hours and 50 min.

This gave:

Area of 10-in. pipe = 0.5454 sq. ft.
" " 16 " " = 1.3960 " "
Length " 10 " " = 13,200 ft.
" " 16 " " = 47,500 "
Time, = 13,800 sec.

Let _x_ = velocity of flow in 16-in. pipe, in feet per second, then 2.56
_x_ = velocity of flow in 10-in. pipe, in feet per second.

From which:

13,200 47,500
------- + ------- = 13,800
2.56_x_ _x_

_x_ = 3.805

and 2.56_x_ = 9.740

The discharge is:

For the 16-in. pipe, 1.396 x 3.805 = 5.31 cu. ft. per sec.;
and, for the 10-in. pipe, 0.5454 x 9.74 = 5.31 cu. ft. per sec.

The question arose as to whether or not the particles of bran in the
water traveled as fast as the water flowed. It was also desired to check
by observation the relative velocities in the two pipes, as above
deduced.

_Test No. 2_.--To determine these points, a second test was made, on
March 31st, 1908, twenty days after the first one. In this test, green
aniline, red potassium permanganate, and bran were used. An observer
was placed at the end of the 10-in. line at _B_ (Fig. 2), and, by
letting a small quantity of water run from a relief-valve there, he was
able to note the time of the appearance of the colors and the bran.

The green was started in the upper end of the 10-in. pipe, at _A_ (Fig.
2), at 8.30 A.M. It appeared at _B_ in 22 min., and at _E_ in 3 hours and
52 min.

The red was started at 8.45 A.M. It reached _B_ in 21-1/2 min., but it
was so faded that the time of its appearance at _E_ could not be noted
exactly.

The bran was started at 9.00 A.M. It reached _B_ in 22 min., and
appeared at _E_ in 3 hours and 51 min.

From the average of these figures, the velocities were:

In the 16-in. pipe, 3.792 ft. per sec.
" " 10 " " 9.695 " " "

and the discharges were:

In the 10-in. pipe, 5.287 cu. ft. per sec.
" " 16 " " 5.293 " " " "

The application of the equation for equalized relative velocities, as in
the first test, gives:

Velocity in 16-in. pipe = 9.705
" " 10 " " = 3.791
Discharge of 16 " " = 5.292
" " 10 " " = 5.293

These last figures would check exactly, except for dropping figures in
the fourth decimal place.

The results of these two tests, considering that 20 d