THE FLOW OF WATER IN WOOD-STAVE PIPE. 
51 
No. V H 
logV 
logH 
272 5. 942 0. 5144 0. 77391 
9.7133] 
273 6.127 .6426 
.7873 
fSum=4. 7756 
9.8079 
fSum=58. 8637 
274 6. 190 . 6154 
.7917 
1 Mean =. 7959 =b v 
9. 7892 
lMeaii=9.8106=b H 
275 6. 312 . 6938 
.8001 
1 Anti-log mean 
9. 8412 
] Anti-log mean 
276 6.436 .7237 
.8086 
[ =6. 250 
9. 8595 
[ =0. 6466 
277 6.516 .7155 
. 8140; 
9. 8546, 
278 6.693 .7700 
.8256 
fSum=3.4915 
9. 8865^ 
fSum=39. 8249 
279 6.852 .7490 
.8358 
J Mean = .8729=a v 
9. 8745 
|Mean= 9.9562=a H 
280 8.222 1.061 
.9150 
1 Anti-log mean 
10. 0257 
1 Anti-log mean 
281 8.223 1.092 
. 9151. 
[ =7.463 
Sum= 
10. 0382j 
[ =0. 9040 
Sum= 
8.2671 
=98. 6886 
Mean= 
. 8267= 
=c v Mean= 
= 9.8689= 
=c H 
Anti-log mean= 
6.710 
Anti-log mean 
=0. 7393 
The center of gravity of the whole series thus comes at such a point 
that there are 4 points below and 6 points above c. Then 
a v -c v = .0462, and a H -c H = .0873; 
whence : 
c v -b v = .0308, and c H -b H = .0583; 
0.0462 ^ 0.0873 _6 
0.0308 0.0583 4 
When the above ratios are in inverse proportion to the number of 
observations in the respective zones the three points found lie in the 
same straight line and approve the mathematical operations. 
The exponent of V in formula 17 is the inclination of the line acb 
and is equal to the tangent of the angle formed by the curve and the 
axis of V. Thus 
a H — b H .1456 
a v — b^ 
.0770 
= 1.891 =z. (See No. 51, column 17, Table 3.) 
The intercept m is found as follows : Since log m = log H — z log V 
(from formula 18, p. 49), by using the coordinates of the center of 
gravity c 
log m = 9.8689 -(1.891 X 0.8267) 
log m = 8.3056, therefore m = 0.02021 
In the same manner the exponent of V for each of the pipes 
underscored in Plate YII was determined, being found to vary from 
1.53 for No. 36 to 2.31 for No. 42. Any general law of variation in 
this exponent was not considered in their formulas by Moritz, Wil- 
liams and Hazen, or the writer, although Ha<zen sees a tendency for 
the exponent to increase with the size of the pipe, 1 while Williams 
later offered the deductions mentioned on page 11. Simultaneous 
values of diameter and exponent were plotted on logarithmic paper. 
i Trans. Amer. Soc. Civ. Engin., oi (1903), p. 320. 
f 
