On the Annual Water-discharge of Large Rivers. 269 
rivers, the water-discharge varies simply as the cube of the 
linear dimensions of the river. This may be readily deduced 
from the hydraulic theory of the preceding note; where we 
have 
Q@=2 xy, xd, | (2) 
gh eae be a constant depending on the configuration of the river 
basin only, and if the river section remain similar to itself at the 
place of observation, then A will vary as the square of the linear 
dimension, and y, will vary as the simple linear dimension; and 
therefore 
Qa hs (3) 
where h is a linear dimension of the river section.* 
The French expedition to Egypt, in 1799-1801, obtained the 
following results :— 
Cubic Meters per Second. 
1°, Maximum discharge in September, - 10247 
Minimum discharge in June, P . 678 
2°. The average of the two years’ measurements on the Nil- 
ometer at: Cairo give the following depths, measured from an 
arbitrary zero, to which I have added an unknown quantity, x 
to be found from theory and observation :— 
The Nilometer at Cairo, 1799-1801. 
, 
1. September, a EDA ae ¢. March,’ <, - 48 + 2. 
2. October, . yy RD ae a & April, . = dob e 
3. November, - 10h + m% 9. May, ; . 25 4+ 9, 
4, December, ee Pinas 10. June, - a Ae aera: 
5. January, . Ae Milf ssore ae ll. July, : 40 + a. 
6. February, » “O86 + x 12. August, . Sind + x. 
Let x be the unknown line, to be added to the depths measured 
from the arbitrary zero, to convert them into h (the hydraulia 
mean depth, or standard linear dimension of the river bed), 
If equation (3) be true, we have from the foregoing data— 
152423. 10247 | (4) 
94+aJ - 678 ’ 
from which we find 
x=63. q.p. 
* This quantity & may be regarded as the Hydraulic Mean Depth of writers on 
Hydraulics. 
