HYDRODYNAMICS. 



551 



Huid-. 



ITE 

 XIX 



1'.'. 



so is to cause the water to descend through the space 

 C %, it will of course rise in the other branch to the 

 height ef, so that Ae = Cg. Upon withdrawing the 

 piston, the elevated fluid in MS will descend in order 

 to recover its level ; the fluid in PO will also rise above 

 its natural level, and again descending, a series of os- 

 cillations will be performed by the fluid similar to those 

 of a pendulum, the surface AB vibrating between ef 

 and i f. and the surface CD between g h and -/ %. On 

 account of the friction of the water, however, against 

 the sides of the tube, the height C / will not be so great 

 a* A e ; and consequently, from the same cause, the os- 

 cillations will gradually diminish like those of a pendu- 

 lum, till the water resume its state of equilibrium. 



It is obvious from the Figure, that the force which 

 produces the oscillations is the weight of the column of 

 fluid efy i, or twice the column AB fe, which is to the 

 whole weight of the fluid column as 2 A * to ANOD, or 

 as At to the length of a pendulum EF, Fig. 13 which 

 describes arcs Fl equal to A e, or to one half of the os- 

 cillating column. Consequently since the length of the 

 oscillating column ANOD is a constant quantity, the 

 force which produces the oscillations is proportional to 

 the space described by the water, and therefore the os- 

 cillations are isochronous. 



Since the force by which the pendulum is made to 

 describe the small arch FI is to the weight of the pendu- 

 lum as FI is to FE, or as A * : EF; and since the force 

 which make* the water oscillate is to the weight of the 

 whole water in the same ratio, the oscillations of the 

 pendulum and of the fluid being produced by the same 

 MfCMf must be performed m equal times. 



Con. The oscillation; of a column of fluid will be 

 to the square roots of the length of the co- 

 Far as this is true of the pendulum, it 

 must be true also of the oscillating fluid, which follows 

 the same laws. See MECHANIC*. 



PROP. If. 



proportional U 



luinn of fluid. 



Those who wish to study farther the subject of the 

 oscillation of fluids, are referred to the Pnnctpia of Sir 

 Isaac Newton, lib. ii. Prop. 45, 46. and to Bossut's 

 Trait e Tknriijme el Exprrimmtnt if Hydrodymim imie, 

 lit. 179^, where they will find 



i. chap. ix. p. 4O3. edit. 



a genera] method of determining the oscillations of wa- 

 ter in a syphon of any form, with an application of the 

 method to a cylindrical syphon, and to a rectilineal sy- 

 phon composed of three tubes, two vertical, and one 

 horizontal. The subject is also treated in Bernoulli's 



Work*, torn. iii. p. 1*5, and in Hutton's Mathematical 



Tract*, vol. iii. p. 350. 



Undulation 

 of Wares. 



The undulations of waves are performed in the same "*'"' 

 time as the vibrations of a pendulum, whose length is PLATE 

 equal to AC or BD, Fig. 14. the breadth of the wave, CCCXIX. 

 or the distance between two adjoining eminences or* 1 ' 8 ' l *" 

 depressions. 



Let ABCDE represent the section of two waves. 

 It is obvious that the eminences A, C must descend, by 

 the force of gravity, or a force equal to the weight of 

 the elevated portion, and that the undulations are per- 

 formed like the oscillations of water in a syphon, the 

 highest parts AC becoming the lowest, while the low. 

 est BD become the highest. Hence, if we take a pendu- 

 lum, whose length is equal to half the distance between 

 A and C, or B and D, the parts A, C will descend so as to 

 be the lowest in the time of one oscillation of the pen- 

 dulum, and in the time of another oscillation they will 

 become the highest parts ; that is, the pendulum will 

 make two vibrations in the time of one undulation, or 

 the time that one of the summits C has described a 

 space comprehended between two adjacent summits. 

 And as a pendulum, whose length is four times that of 

 the preceding, oscillates once in the same time that it 

 oscillated twice, it follows that the waves perform their 

 oscillations in the same time as a pendulum, whose 

 length is equal to* AC or BD, the breadth of a wave. 

 Hence a wave 3| feet broad, will have a velocity of 

 S feet in a second ; and a wave 18 inches broad will 

 have a velocity of 26.538 inches per second. 



The preceding doctrine of the oscillation of waves 

 was first published by Sir Isaac Newton, in lib. ii. 

 prob. 44. of the Prmcipia. As the motion of waves, 

 however, is partly circular, Sir Isaac considered his 

 theory as only an approximation. M. La Place, in the 

 Memoir* of the Academy of Science* for 1776, has ap- 

 plied to this subject, particularly to rectilineal waves, 

 the general laws of the motion of fluids, and obtained 

 some interesting results, of which we have given a ge- 

 neral account in our History of HYDRODYNAMICS. La 

 Grange has treated the subject in a general manner in 

 the Berlin Memoir* for 17&6, and M. Poisson and M. 

 Cauchy have more recently written upon the same sub- 

 ject. The reader will find a general account of their 

 labours in the History of HVDKODYNAMICB, p. 418, 423. 

 The same subject nas likewise been treated by Dr 

 Thomas Young, with his usual ability, in his Lectures 

 o* Natural I'hilosuphy, vol. ii. p. 63. 



PART III. ON HYDRAULIC MACHINERY. 



1 HEterm HVDRAILK MACHINERY, is, in strict propri- 

 ety of language, applicable only to those machines which 

 are driven by the force of water, whether it descends 

 by its own weight, or act* by it* impulsive power when 

 in motion, or exerts a force in virtue of it* re-action. It 

 ha*, however, been applied in a mere extended senne, 

 so a* to include wrious machine*, by which water is 

 rawed M projected. The application ol wind, and the 

 force < as the moving power of machinery, 



!u.. Ii ciued under ME< MANIC*, and tl 

 portant application of tc..m will bi ^reat 



lengUi uudcr the separate wtcle of STIAM Engine. 



As pumps and fire engines are pneumatical machine*, Hydraulic 

 they will be described under the articles PNEUMATICS Machinery, 

 and PUMP. '-y*> 



CHAP. I. 

 ON WATER WHEELS. 



Tut usual method of employing water as the mov- 

 ing power of machinery, is to upply it to the circumfe- Wheels, 

 rence of wheel*, from the axis or uletree of which the 



