Report of Messrs. Humphreys and Abbot. 23 
By assuming for the change of stand, or the rise of the river, 
a hypothetical value, the new slope and new mean velocity may 
be computed; from which, in turn, a calculated value of the rise 
may be obtained. Thus by a a simple system of trial and error, 
the true value of the rise will easily be determined; and the 
resolution of involved equations avoided. Ina similar manner, 
the depression of level, or the fall of the river, may be ascer- 
tained, in case any determinate portion of its waters be with- 
drawn by opening a new o 
The treatment of this raced Pr by the authorities generally 
has the advantage over this of being greatly more simple; but 
it = also the disadvantage of not in the least representing 
- natur 
statements embrace, in brief, the substance of the con- 
seibatione of this valuable report to the advancement of hy- 
draulic — and the basis of the new methods of practice 
which its authors have introduced. In estimating the effects of 
bends in the stream, they have adopted the principle of Dobe 
derived from observations on the flow of water in pipes, whi ch 
makes the loss of living foree proportional to the sum of the 
squares of the sines of the bending; the total amount of curva- 
ture being divided into angles below forty degrees. The agree- 
ment of the results of computation, upon this principle, with 
those of the observations instituted to test its correctness is very 
close, and is entirely satisfactory. 
Whoever claims to have discovered a new law of nature, or a 
processes by 
the results which follow from its application in cases where 
ductions from it may be tested by direct observation, or by the 
degree of their accordance with other truths already known. 
This has been anticipated by the authors of this report, and 
they have accordingly peprinore in the amplest form, the mate- 
rial for applying either of the tests above suggested. We can 
only indicate in outline the ee of the material, referring 
those who would sift it thoroughly to the report itse tself. 
Measurements of the daily discharge’ of the river were con- 
tinuously made for periods of twelve months at Carrolton, Louis- 
iana, of eleven months at Columbus, Kentucky, of ten months at 
Vicksburg, and one and a half months at Natchez. Similar ob- _ 
servations were made upon the Arkansas at Napoleon, for eleven 
months; and, besides these, many others less protracted were 
e upon n the main river and its tributaries and outlets, from 
the Ohio to the Gulf. These measurements required the deter- 
_ mination of the cross-section and mean velocity at each ee 
_ for every day. The cross-sections were determined by sound ings 
