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circumference, so as to float perpendicularly inthe current. It is evident that the progress ofthe rod must be exactly that of the mean rate,or velocity of the current, since it is acted uponby every variation of velocity from the bottomupwards.

Of the Figure of the Beds of Rivers , and the

Formation, Nature, fyc. of their Sinuosities.

If the breadth at top, and area of the sectionof a river are given, the resistance of the bedto the current would be the least possible werethat section a semi-circle; because, in that case,the perimeter would be a minimum under thesame area. When the velocity, slope, and area,remain the same, the resistances in differentshaped sections, increase in proportion to theperimeter. If the area of the transverse sectionbe divided by the perimeter, the quotient iswhat M. Du Buat calls the mean radius: conse-quently the less the perimeter, the greater willbe the mean radius, and the less the resistance,*

* M. Du Buat (vol. i. p. G3) gives the following expressionfor the velocity of running water.

.. 297 (Vr— 0-1)

Y=-—- —- 0-3 (Vr—0-1)

b — hyp- log. b -f- 1 • 6

Where V denotes the velocity of the water in inches, persecond of time.

r = the mean radius, which is the area of the transverse sec-