448 FOURTH REPORT — 1834. 



admirable work on Hj'drodynamics shows abundant proofs of the 

 great sagacity with which he investigated everj^ question relative 

 to the motions of waters through orifices and pipes ; but his 

 experiments on artificial canals are unsatisfactory from his hav- 

 ing omitted the consideration of the depth. 



The investigations of Bernoulli seem to have formed the 

 groundwork of the French school ; for although he adopted 

 the opinion of Guglielmini, with regard to the analogy between 

 the motion of a river and the motion of a fluid escaping from a 

 vessel, yet his theory of the law of the velocity, however absurd 

 its application to the gradations of velocity in a river, is correct. 

 Although the science of hydrodynamics had acquired a high 

 degree of perfection at this period, it was nevertheless confined 

 to the hypothesis of the parallelism of filaments, in which all the 

 points of the same filament move in one and the same direction*. 

 It was desirable to express the motion from a given point in a 

 fluid in any direction. This problem was resolved by D'Alem- 

 bert, who discovered equations on two principles, namely, 

 that a rectangular canal, taken as a fluid mass, is in equilibrio, 

 and that a portion of a fluid, in changing its position, preserves 

 the same volume when the fluid is incompressible, or dilates 

 according to a given law when the fluid is elastic. This pro- 

 found and ingenious investigation was published in his Essai 

 sur la Resistance des Fluides in the year 1752, and afterwards 

 perfected in his Opuscules Math^matiques. 



Euler, in his Memoires des Acaddmies de Berlin et de St. Pe- 

 tersbourg, and La Grange, in the year 1781, exhausted all the 

 resources of geometry for the same object, but without any ap- 

 plicable result. It was not until the year 1781, when M. Bossut 

 published his Traits TMorique et Experimental, that the theory 

 of hydrodynamics was made subservient to experiment. 



M. Bossut divides his work into two volumes, theoretical and 

 experimental : the first explains the general principles of hydro- 

 statics and hydraulics according to the previously established 

 theory ; the second contains a vast number of experiments on 

 practical hydraulics ; on the motion of water through orifices, 

 pipes, and rectangular canals. 



In the case of a rectangular canal of 105 feet in length, a con- 

 siderable diiference between the natural and artificial expendi- 

 tures, arising from the friction of the sides of the canal and of 

 the atmosphere, was found to prevail: also a very considerable 

 swelling or rise of the water between the two extremities of the 

 canal ; but without any diminution of the expenditure in a given 

 time, although the reverse is the case in pipes. He also found 

 that with the same initial velocity of the fluid, canals which are 



