292- Major-General Sir Howard Douglas mi 



be defined to be the quotient obtained by dividing the area of 

 the transverse section of the stream expressed in square inches, 

 by the boundary or perimeter of that section, diminished by the 

 breadth of the upper surface of the stream, in hnear inches. To 

 those not very famihar with algebraical formulae, it is rather 

 difficult to apply formula (1.) to practical purposes, and there-^ 

 fore attempts have been made to simplify it for the use of prac- 

 tical men, without sacrificing much of its accuracy. For this 

 purpose, Robison, in his Works on Rivers, vol. ii. page 444, 

 adopts the second form of Du Buat, who, in p. 63, reduces it to 

 English inches, and it becomes 



307(VT-0 1) o.3(^,_,.^ . (,.^ 



/y/6_hyp.log.x\/6 + l . 6 ^^ ) y / 



from which he deduces a table that is easily applied. Sir How- 

 ard Douglas proceeds to a farther simplification, and in a note, 

 p. 17, adopts 



y = ^-^^ = m.t^l ........ (3.) 



This, though less accurate, will be sufficient for many practical 

 purposes. 



In page 20, we meet with some very interesting and useful 

 remarks, relative to the action of water on the beds of rivers se- 

 lected from Du Buat. This gentleman found — 



" by experiment, that the greatest velocities which the various substances 

 expressed below can resist without moving, are 



Velocity at bottom, 

 per second. 



6 inches. 



4 

 7 



12 

 24 

 36 



Fine sand, .... 



Coarse, angular, rough sand, 



/Fine, the size of grain of anniseed, 

 Gravel, < Mean, the size of a pea, 



I Coarse, the size of a bean, 

 Pebbles, an inch in diameter. 

 Angular stones, the size of an egg^ 



" These results shew the velocities required to cleanse or deepen canals of 

 any kind from any deposit, or accumulations of either of the substances 

 given above ; and for military purposes, it may be of service to remark, that i 

 this furnishes useful data to enable us to judge of the consistency of the bot- , 

 torn, which it is not always possible to do experimentally, by merely niea- 

 surihg the velocity of the current at the surface, and thesn referring to the 



