= 
a 
Report of Messrs. Humphreys and Abbot. 201 
formula of Dubuat, with a modification of the constant, to 
represent very nearly the effect deduced from observation. This 
formula is (with the constant divisor reduced to English feet) 
in which sin?4 is the sum of the squares of the natural sines of 
the amount of bending, divided into angles not exceeding 86° 
or 40°. 
Dubuat derived this formula from observation on the flow of 
the expression for the effect of bends, 
co v? sin 74 
"Aah 
been made, resort was had to the maps, and an estimate of 
the amount of bending made by measurement on the map. As 
& rough test of the correctness of t determinations, an 
independent formula was constructed, on the ‘siaal that the 
as measured by an air line, and by the river. Denoting this 
difference in miles by M, it was found that sin?é rarely differed 
essentially from 0°34 M. A series of comparisons somewhat 
extended, upon stretches of the river varying from three miles 
to more than eighty miles in length, gave, for the total of the 
Aw. Jour, Scr.—Srconp Series, Vou. XXXVI, No. 107,—Sepr., 1863. 
26 : 
