210 



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 difficulties attending the mathematical theory of 

 hydraulics, so much has already been done, by the assistance of practical 

 investigations, that we may in general, by comparing the results of former 

 experiments 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 beginning of the 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 appli- 

 cation of the theory of hydraulics to practical cases, and to affect the 

 modes of calculation so materially, that it will require to be discussed, here- 

 after, 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 t 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 ascending 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 from a height of 1 

 foot, be caused to act in any manner 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 determination of 

 the motions of fluids, and that in many cases it becomes necessary to sup- 

 pose 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 

 proper 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 assumed by Bernoulli, without either demonstration, or even the 

 appearance of perfect accuracy, is this, that all the particles of a flui4 in 



* Horologium Oscillatorium, Pars 4, Hypoth. 1. 

 f Hydrodynamica, 4to, Strasb. 1738. 



