Report of Messrs, Humphreys and Abbot. 205 
In order to understand the signs prefixed to the numbers in 
the foregoing table, it must be observed that the authors have 
tabulated the differences as corrections, not as errors. That is, 
each number must be applied to the result of the particular 
computation to which it relates, with the sign as written. Thus, 
the first number in the Chezy-Young formula, viz: +2°6888 
indicates that this amount must be added to the value of v which 
the formula gives, in order to make it equal to the observed 
velocity, 59288. The formula gives 3:2400, and 3-2400+2-6888 
=5°9288. This mode of exhibiting results, though it makes 
the comparative error striking, fails to convey an sreanar im- 
pression of the comparative approach to truth, which is a different, 
and practically more important thing. Let us take, for illustra- 
tion, the first four examples, with the results by several of the 
old formule and the new. 
; 2. 3 4, 
Vel. observed, 59288 58869 4:0838 39175 
Chezy-Young, $2400 29702 1°3365 1:4253 
Dubu 27468 2°4495 06796 07702 
irard, 48148 43183 14181 15587 
Prony-Eytelwein, 8°5314 8-2285 1-3960 14955 
Prony- Wei : 3°5044 32663 1:4613 1:5593 
Young, 32741 2°9869 1:2516 13455 
St. Venant, 35907 38-1867 13804 14766 
et, 30451 2°7369 10786 | 1°1545 
Humphreys and Abbot, 5°8908 56444 87745 39117 
Rhine, the Tiber, &c., than upon the Mississippi; though upon 
€ Mississippi itself, their results show great discrepancies. 
There is, however, one curious exception in the case of small 
Streams. Numbers 17 and 18 are examples upon the feeder of 
the Chesapeake and Ohio Canal near Washington. The follow- 
the results: 
are the 
= 4: 2. 1. 2, 
Vel. observed, 8-0823 2°7227 || Prony-Weisbach, 47199 47050 
: Chezy-Young, 42858 42633 || Young, 44069 43830 
Dubust, 47363 47084 || St, Venant, ~ 46793 4°6180 
Girard é Ellet, - 45096 4 
Prony-Eytelwein, 47056 46803 || Humphreys and Abbot, 31032 3-0821 
