192 APPENDIX TO A MEMOIR 



orifices with velocities in the ratio of the square-roots of the 

 respective columns, has been applied without modification to 

 every motion of water. Mariotte, Varignon and Guglielmini 

 have made it the basis of complete systems of hydraulicks. 

 Varignon has composed many analytical memoirs upon this 

 theory; and Gravesande, Musschenbroek and Belidor deliver no 

 other principles: Guglielmini has (in addition to this theory) 

 introduced something not very intelligible on the energy of 

 deep waters, which he considers as the cause that rivers are not 

 stagnant at their mouths, where there is, as he supposes, no 

 declivity of surface. 



Theories formed by ingenious men, without any regard to 

 experiment, have too frequently led their authors into absurdi- 

 ties, and it is surprising that a theory so contrary to fact in the 

 most familiar and obvious circumstances, should have met with 

 so much attention : to defend it must involve its advocates in 

 an inextricable dilemma: it results from this theory, that at one 

 foot under the surface of the most sluggish stream, there ex- 

 ists a current at the rate of 8 feet per second (5i miles per hour) 

 exceeding that at the surface; so extraordinary a case must 

 have been long since familiar to boatmen, but it is well known 

 that if a person on board of a boat floating down the stream, 

 thrust his hand and arm at full length under the surface, he 

 will find the water (relatively) as still as a mill-pond; it cannot 

 be supposed that river-navigators would have so long neglected 

 to take advantage of so favorable a circumstance; oars and sails 

 would have ceased to be necessary for descending great rivers; 

 the velocity (from theory) at the small depth only of about \6 

 feet below the surface, exceeding that at the surface 32 feet 

 per second, if we permit a drag of proper construction to sink 

 to that depth, connected with a vessel, she would be drawn 

 along with a velocity, exceeding that at the surface about 22 

 miles per hour. Again, however minute the velocity may be 

 at the surface, that at the bottom of a deep river would be im- 

 mensely great: what shall we think of that of the gulf stream? 

 or even of the Mississippi, where the depth is supposed to be 

 50 fathoms, and which would produce 140 feet per second, little 

 short of one hundred miles per hour? now as it is known that 



