390 Major-General Sir Howard Douglas on 



merits performed by Du Buat, the following laws were disco- 

 vered: 



1. In small velocities, the velocity at the surface exceeds that 

 at the bottom in a very considerable ratio. 



2. This ratio diminishes in proportion as the velocity of the 

 current increases ; and, in very great velocities, approaches near- 

 ly to a ratio of equality. 



3. Neither the magnitude of the bed, nor the slope of the 

 river, changes this proportion when the mean velocity remains 

 the same. 



4. When the velocity at the surface is constant, that at the 

 bottom is constant also, whatever be the depth of water, or the 

 magnitude of the section. 



5. The mean velocity is an arithmetical mean between that 

 at the surface and that at the bottom. 



It is very difficult to determine the velocity at the bottom by 

 experiment ; and the proportion between it and the former dimi- 

 nishes as the mean velocity increases. Du Buat determined this 

 variation by experiment, and thence deduced the following 

 rule. To find the bottom and mean velocities^hen that at the 

 surface is known, take unity from the square root of the surface 

 velocity, expressed in inches, and the square of the remainder is 

 the velocity at the bottom. Half the sum of these two will give 

 the mean velocity. 



Ex. If the surface velocity in the middle of the current, be 

 25 inches per second, what is the bottom and mean velocity ? 

 Ans. V 25 — 1 = 5 — 1 rr 4, and 4'^ = 16 the bottom velocity ; 



therefore, ^ = 20 J the mean velocity. As the mean ve- 

 locity is most generally required, it may be found by the follow- 

 ing rule. From the observed surface velocity^ in the middle of 

 the stream, increased hy g, subtract the square root of the sur- 

 face velocity, the 7'emainder will be the mean velocity of the 

 wJiole section. From the same example as before, 25 J — V25 

 = 25i — 5 = 20 J, the mean velocity obtained more readily 

 than by the former rule. 



This discovery is of great importance, because the velocity of 

 the surface, in the middle of the stream, is easily measured, from 



