R I V 



The velocity will become nothing by making the declivity so small that 



-[^ur lo = Oi but if is lesa " wBno or than 



l^th of an inch to an English mile, the water will have sensible motion. 

 In the above formula R is called the radius of tJie section. 



2. In a river the greatest velocity is at the surface and in the middle 

 of the stream, from which it diminishes towards the bottom and sides, 

 where it is least ; and it has been found by experiment, that if v = velo- 

 city of the stream in the middle in inches, then the velocity at the bot- 

 tom is 



_2 W+l. 



3. The mean velocity, or that with which (were the whole stream to 

 move) the discharge would be the same with the real discharge, is equal 

 to half the sum of the greatest and least velocities, as computed in the 

 last Prop. Hence the mean velocity v V v _j_ . 



4. Suppose that a liver having a rectangular bed is increased by the 

 junction of another river equal to itself, the declivity remaining the 

 same ; required the increase of depth. 



Let the breadth of the river = b t the depth before the junction .= d t 

 and after it .r ; then 



- ^- - .. ~ t) - , a cubic, equation which can always 



be resolved by Cardan's rule. 



5. To find the fall of water under bridges, let the breadth of the river, 

 in feet b j the breadth between the piers c ; the velocity iu a se- 

 cond v ; ' ^.S^ig feet; then the fail of the liver will be 



Tims at London bridge b - 920, c = 2S6, reduced by the piks.to IDC^^ 

 v =. 3*4, hence, the fall is 4.739; by observation A75, ( Toa.^V Nat. 

 Phil) 



6. When the sections of a river vary, tha quantity of water remaining- 

 lh same, the mcaa velocities are inversely as the ai'eas of the sections,, 



7. The following Table abridged from Dr Robison serves at once to 

 compare the surface, bottom, and mean velocities in rivers according; to 



the principles of Arts, 2, 3, (Gregory.) 

 \ 



247 O 3 



