194} APPENDIX TO A MEMOIR 



at bottom and 4 feet deep, runs with a velocity of 17 inches 

 per second at the surface, 10 at the bottom, and 14 in the mid- 

 dle; according to the theory, the velocity at bottom ought to 

 have been 16+17 or 33 inches in place of 10, abating the 

 effect of friction upon the bottom of the canal. 



A very few persons have thrown light on this subject by 

 some valuable experiments, none have been more successful 

 than the Chevalier Buat: aided by St. Honore, a young offi- 

 cer of Engineers, he has adapted analytical forms of expres- 

 sion conformable to the operations of nature. Buat measured 

 velocities at the surface and bottom of canals and rivers, and 

 has discovered the following laws. " In small velocities there 

 " is great disproportion between the surface and bottom ; and 

 "in very great velocities, the ratio approaches to equality; in 

 " general the following rule will solve the problem : Take unity 

 " from the square-root of the superficial velocity per second 

 " expressed in inches, the square of the remainder is the veloci- 

 " ty at bottom." Thus a velocity of one inch at the surface will 

 give no sensible velocity at bottom, but a velocity of 36 inches 

 at the surface, will give 25 inches at bottom; Watt's canal corre- 

 sponds with this law, and it is probable that the law holds good 

 in all artificial canals and rivers of moderate depth; but in 

 great and deep rivers, whose regimen is established, there is 

 great reason to believe that the velocities at bottom are much 

 less than would result from Buat's rule, because as has already 

 been observed, that so far from abrasion taking effect at the bot- 

 tom of such rivers, they are actually rising by a slow progress, 

 which is regulated by the protrusion of the cradle of the river 

 into the ocean. Many more arguments from fact might be 

 drawn in opposition to this theory; I shall only observe that it 

 is known to fishermen, that the migration of fishes is perform- 

 ed near the bottom of rivers against the stream, and in descend- 

 ing they almost float upon the surface; a curious account of 

 the latter is given by Bartram in liis account of St. John's river, 

 in East Florida. 



We shall now endeavour to shew that the theory is unphilo- 

 -sophical and contrary to hydrostatical laws. 



