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LECTURE XXIII. 



ON THE THEORY OF HYDRAULICS. 



Having considered the principal cases of the equilibrium of fluids, both 

 liquid and aeriform, we proceed to examine the theory of their motions. 

 Notwithstanding the dithculties attending the mathematical theory of hy- 

 draulics, so much has already been done, by the assistance of practical inves- 

 tigations, that we may in general, by comparing the results of former experi- 

 ments with our calculations, predict the effect of any proposed arrangement, 

 without an error of more than one fifth, or perhaps one tenth of the whole: 

 and this is a degree of accuracy fully sufficient for practice, and which indeed 

 could scarcely have been expected from the state of the science at the begin- 

 ning of thfl last century. Many of these improvements have been derived from 

 an examination of the nature and magnitude of the friction of fluids, which, 

 although at first sight it might be supposed to be very inconsiderable, is 

 found to be of so much importance in the application of the theory of hy- 

 draulics to practical cases, and to affect the modes of calculation so materially, 

 that it will require to be discussed, hereafter, in a separate lecture. 



There is a general principle of mechanical action, which was first distinctly 

 stated by Huygens, and which has been made by Daniel Bernoulli the basis of 

 his most elegant calculations in hydrodynamics. Supposing that no force is 

 lost In the communication of motion between different bodies, considered as 

 belonging to any system, they always acquire such velocities in descending 

 through any space, that the centre of gravity of the system is capable of as- 

 cending to a height equal to that from which it descended, notwithstanding 

 any mutual actions between the bodies. The truth of this principle may 

 easily be inferred from the laws of collision, compared with the properties of 

 accelerating and retarding forces. Thus, if an elastic ball, weighing 10 

 ounces, and descending froitt a height of 1 foot,be caused to act in any maanc*- 



