SUMMARY OF HYDRAULICS. S3 



fe twice the fquare of the depth, and the hydraulic mean depth 

 f of the aftual depth. He then inveftigates the difcharge of a 

 canal of which the bottom is horizontal. The velocity appears 

 in this cafe to be fomewhat greater than in a fimilar canal, of 

 which the bottom is parallel to the furface. 



The author remarks that the velocity is greater near the con- Velocities when 

 cave than the convex tide of a flexure : a circumftance probably curved 

 occafioned by the centrifugal force accumulating the water on 

 that fide. No general rule can be given for the decreafe of 

 the velocity in going downwards : but fometimes the maximum 

 appears to be a little below the furface. In the Arno the velo- at different 

 cities are at 2 feet below the furface, 39f inches; at 4, 38§; * 

 at 8, 37; at 16, 33f; at 17, 31. In the Rhine at 1 foot, 58 

 inches; at 5, 56; at 10, 52; at I5 t 43. As an approxima- 

 tion to the mean velocity, the author direcls us to deduct from 

 the Superficial velocity T j^ for every foot of the whole depth. 

 For inftance ; if the depth were 13 feet, and the fuperficial ve- 

 locity 5 feet, to take 4| as the average velocity of the whole 

 river. This can however only be true in large rivers : for in 

 the canal, meafured by Mr. Watt, the fuperficial velocity muft 

 be diminifhed nearly | for a depth of only 4 feet. And we may 

 in general come quite as near to the mean velocity by taking 

 ■gs of the fuperficial velocity ; although this may ftill differ ma- 

 terially from the true medium. But comparing this with the 

 former theorem for the velocity, which gives a refult oftener 

 above than below the truth, we may bring them both into a 

 form eafily recollected, thus; 



The fuperficial velocity of a river is nearly a mean propor- Conclfe deduo 

 tionai between the hydraulic mean depth and the fall in two J' r ° a " j? c ^ an y " 

 miles ; and the mean velocity of the whole water is, ftill more depth, 

 nearly, nine-tenths of this mean proportional. 



We may find a double confirmation of thefe principles in 

 Major Rennel's account of the Ganges (Phil. Tranf. 1781, 

 p. 87). 



He informs us that " at 500 miles from the fea, the channel Inftance in the 

 is 30 feet deep when the river is at its Ioweft ; and it conti- 

 nues at leaft this depth to the fea," that " a fe&ion of the 

 ground, parallel to one of its branches, in length 60 miles, was 

 taken by order of Mr. Haftings;" that " the windings of the 

 river were fo great as to reduce the declivity on which the 

 water ran, to lefs than 4 inches per mile;" that '* the medium 

 Vol. III.— September, 1802. D rate 



