196 APPENDIX TO A MEMOIR 



favourable view in which the theory can be presented, but will 

 not avail its advocates; for it cannot be shewn that the vis iner- 

 tias of 16 miles of fluid can be overcome by a pressure of 16" 

 feet, with the energy required by the theory; on the contra- 

 ry, it is shewn by the experiments of M. Couplet at Versailles, 

 that water conveyed in a smooth horizontal tube of 18 inches 

 diameter and 43,200 inches in length, from a reservoir 12 feet 

 high, issued with a velocity of less than 40 inches per second, 

 (i. e.) less than f of the velocity deduced from the theory; 

 hence we see that the vis inertias of 43/200 inches of horizon- 

 tal water combined with the friction of a tube 18 French inches 

 in diameter, destroys ^ of the velocity which the theory calls 

 for ; and if we should concede (what the theorist cannot de- 

 mand) that of those 4, 4- are occasioned by the friction of so 

 large a tube, and only 4. left for the vis inertias of the water, and 

 that it be allowed that every succeeding 43,200 inches destroy 

 4. of the respective remaining velocities, we shall find that at the 

 end of the 16 miles, the velocity of the issuing fluid will be less 

 than |. inch per second. Were we to suppose a horizontal 

 pressure at a, derived from a head of water ef, proportioned to the 

 column f e, it is yet inconceivable that this should produce a 

 continued velocity in the direction a b; water like all other bo- 

 dies, when in a state of compression, will escape on the side of 

 the least resistance, and in place of producing a current in the 

 direction a b, against the vis inertias of 16 miles of fluid, will 

 escape by the shortest passage to the surface, and bubble 

 up at d, where it will form an elevation and encrease the 

 superficial velocity. Were we disposed to suppress these ar- 

 guments, and concede to the theorists the doctrine they have 

 endeavoured to establish, the consequence would be equally 

 ruinous of their system : let us therefore suppose that a current 

 is produced from a, to b, with a velocity of 32 feet per second 

 greater than at c; by. a parity of reasoning it will at g be 64 

 feet greater than at c, and so in continuation gaining at the rate 

 of 2 feet per second every mile ; hence a river running one hun- 

 dred miles, after it had gained the depth of 16 feet would run 

 with a superficial velocity of more than 200 feet per second : 

 had we assumed the depth of one foot only in the place of 16, 



