210 Hydraulics of the Mississippi River. 
Then, assuming some definite value for x, obtain the numerical 
values of and s,,; the former from the equation given 
just above, and the latter from “i equation, 
a pets), 
in which the reciprocal of the parameter has the value belonging 
to the locality. This being done, v,, may be obtained from the 
equation for mean velocity alread y given, viz: 
oo5st t\? 
1=(0- 0388—(2 258 Lon ) . 
and with this value of v,, a value of x may be formed from the 
equation just found; 
Qy —40y 
— 
Win 
If this last value agrees with the i ee hbo the problem 
is solved. If not, a new supposition must e. But, as the 
true value always lies between the two reece values—that 
is, between the assumed one and the computed one—the approx- 
imation will be rapid. This method has been fess by the 
authors of the report to the calculation of many rises in the 
river, of which the particulars are given in the Sitdwitie table. 
The results are compared with calculations for the same rises 
from the formula of Mr. Ellet. The symbols A, and L in the 
table belong to Mr. Ellet’s formula, the manner of employing 
which it is not necessary here to ex slain 
The only criterion by which it is possible to judge of the value 
of hydraulic formule, is the degree of their accordance wit 
direct observation. We have no , principles of positive science, 
to which, in forming such estimates, we can confidently or safely 
ie Were it otherwise, we should long since have had 
rmule, concerning the truth of which there would be no room 
ie doubt. 3ut science is not in eng ee of the material for 
resources of anaiyeias are oecceal to tell us what aciodc! af 
force will be consumed in driving a liquid, with a given velocity, 
into the mouth ef a tube, or through the simplest orifice at 
can e in the side ‘of the containing vessel, we may W 1 + 
regard a problem affected by all the complex conditions which 
