6b S. YOKOTA! A METILOD Of DETERMINING THE CROSS-SECTION 
APPENDIX. 
Using Ganguillet and Kutter’s Formula, the discharge Q per second 
for any form of section is given by 
ch 
= KERN INH 
Do = 
where = vI(K + —_ ) and ce =nk. 
1 
But @ = = so that 
p 
A? 
(ee 
Re ar ae 
/ AS 
€ =; ee fe 
or, © ae) c?A4— 2cc’QA’p + Q?(ce2p?—Ap) =0. 
Taking the variation of A with respect to p, we have 
dA 2cc'QA?—2e?Q*p+Q7a 
dp” 40° A®—4eee’Q Ap —Q?p 
Now, inserting the relations (4) and (5), this becomes after reduction, 
> 2nk+ Vk’b 
Bie dep = beer pes 
tok+ 3 vk’b 
Op 
The variation of A with respect to p being thus determined in terms 
of b of the standard section, let 
B Cc KN eT: 
ABCD in Fig. 1 be the standard section for a given discharge Q, and EF 
the new water surface. From D draw DG perpendicular to EF, meeting 
itat G. Join BG and let it intersect AD at H. From H drop perpendi- 
cular HJ on EF meeting it at J. Then if we draw JK parallel to the 
side line DC, the area EBKJ==area ABCD. 
rom the intersecting point L of CD and EF, take LM=:2DL on EF. 
Draw the perpendicular MN from M on BC, intersecting it at N. From 
Nöon NM, take NP 2, Join PY andi draw NERH EN 
y 
op 
to PJ, intersecting EF at S. 
