On Monday, February 6th, 1804.

At Northumberland, (Pennsylvania), which had of late years been the place of his residence-died

The Rev. JOSEPH PRIESTLEY, L. L. D. F. R. S.

He was choser.

CAL SOCIETY

January, 17

It was resolved i

That a

an Eulogium or and that a spec inst. at 6 P. M. shall deliver it.

Benjamin Sm of the Society, by the resolve o

END OF PART FIRST.

TRANSACTIONS

OF THE

AMERICAN PHILOSOPHICAL SOCIETY, &c.

VOL. VI, PART II.

No. XXXII.

Appendix to a Memoir on the Mississippi, No. XXX. of the 1st part of this Volume.-By William Dunbar, of the Natchez, communicated by the Author, through the President of the Society.

Read October 5th, 1804.

ALTHOUGH the memoir was not intended to convey opinions upon the theory of rivers, yet as it contains observations and remarks, which are at variance with the doctrines delivered to us by several of the most eminent mathematicians of Europe, it may seem that a short apology is necessary.

This subject has been treated by mathematicians of the first order in Italy, France and Germany, but more especially the former; and generally such partial views only have been taken of the subject, as have furnished them with the amusement of an elegant application of calculus. The theorems of Guglielmini have been held in the highest estimation, and, perhaps unfortunately for the progress of science, prevail too generally at this day. The theory of spouting fluids issuing from

A

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 absurdities, 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 exists a current at the rate of 8 feet per second (5 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 16 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 immensely 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

a velocity of 3 inches per second will just begin to work upon clay, and that of 3 feet will sweep along shivery angular stones of the size of an egg, and as according to our theory, the evil ought to be perpetually upon the encrease, in as much as the velocity augments with the depth, it must have resulted that by such incredible velocities as are deducible from the theory, the bowels of the earth must have been long since torn up, and this globe have been no longer a fit habitation for man: a system so pregnant with consequences contradictory to the order and regularity which are the result of the laws of nature, must be abandoned. Without the aid of philosophy it must have been remarked by every common observer, that the most furious torrent (directed into a new channel) after breaking up and tearing every thing before it, does at length fashion its own bed, in respect to breadth and depth, so as to be perfectly adapted to the momentum of its waters; it is no longer a furious torrent, but a mild placid stream. Nature aims continually at an equilibrium; in rivers which have for a course of ages occupied the same channel, the accelerations and resistances are so perfectly counterpoised, that a complete equability of current takes place for a great extent (i. e.) so far as the regimen of the river has established itself; abrasion at the bottom of the river ceases; this can only be the consequence of reduced velocity, contrary to our theory, which demands velocity encreasing with the square-root of the depth. Mathematicians and engineers who have calculated upon so false a theory have been most egregiously disappointed in their expectations; a canal was projected to supply the city of Edinburg with water, the celebrated M'Laurin calculated the quantity it ought to deliver, and the no less celebrated Desaguliers who was to conduct the enterprise, and whose theoretick principles were somewhat corrected by experimental knowledge, reduced to nearly one half the calculation of the former; the work was executed to the satisfaction of both, and the result was, that the actual quantity of water delivered was of that calculated by M'Laurin and of that of Desaguliers.

The great improver of the Steam-Engine, Mr. Watt, informs us, that a canal of 18 feet wide at the surface, 7 feet

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 middle; 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.

66

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 corresponds 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 bottom 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 performed near the bottom of rivers against the stream, and in descending they almost float upon the surface; a curious account of the latter is given by Bartram in his 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.