273 LECTURE XXIII. 



on a similar ball of one ounce, so as to lose the whole of its motion, the smaller 

 ball will acquire a velocity capable of carrying it to the height of 10 feet. It is 

 true that some other suppositions must be made, in applying this law to the de- 

 termination of the motions of fluids, and that in many cases it becomes necessary 

 to suppose that a certain portion of ascending force or energy is lost, in conse- 

 quence of the internal motions of the particles of the fluid. But still, with pro- 

 per restrictions and corrections, the principle affords us a ready method of 

 obtaining solutions of problems, which, without some such assistance, it would 

 be almost impossible to investigate. The principal hypothesis which is assum- 

 ed by Bernoulli, without either demonstration, or even the appearance of 

 perfect accuracy, is this, that all the particles of a fluid in motion, contained in 

 anyone transverse section of the vessels or pipes through which it runs, must 

 always move with equal velocities ; thus, if water be descending through a 

 vessel of any form, either regular or irregular, he supposes the particles 

 at the same height to move with the same velocity ; so that the velocity of 

 every particle in every part of a cylindrical vessel 10 inches in diameter,, 

 through which a fluid is moving, must be one hundredth part as great as in. 

 passing through a circular orifice, an inch in diameter, made in its bottom. 

 It is evident that this cannot possibly be true of the portions of the fluid near- 

 est the bottom of the vessel, since the particles most distant from the orifice 

 must be nearly at rest, while those which are immediately over the orifice 

 ai-e in rapid motion; but still the calculations founded on the hj'pothesis 

 agree tolerably well with experiments. In this case the actual descent, in any 

 instant,may be estimated by the removal of the quantity discharged, from the 

 surface of the fluid to the orifice, since the intermediate space remains always 

 • occupied. The ascending force thus obtained is to be distributed throughout 

 the fluid, according to the respective velocities of its different portions; and it 

 may easily be shown, that when the orifice is small, the part which belongs to 

 the fluid in the vessel is wholly inconsiderable in comparison with the ascend- 

 ing force required for the escape af the small portion which is flowing through- 

 the orifice, and the whole ascending force may, therefore, be supposed t& 

 be employed in the motion of this portion; so that it will acquire the velocity 

 of a body falling from the whole height of the surface of the reservoir, or the 

 velocity due to that height. It appears also that very nearly the same velocity 

 is acquired by almost the first particles that escape from the orifice, so that 

 no sensible time elapses before the jet flows with its utmost velocity. 



