FLUIDS IN MOTION.] MECHANICAL PHILOSOPHY. HYDRODYNAMICS. 



763 



we infer that the curve presented by the upper surface 

 of the fluid interposed between the plates, is an hyper- 

 bola. The curve ceases, of course, to be that of the hyper- 

 bola beyond the limits of capillarity. At a distance from 

 the junction of the plates, at which, the interval between 

 them exceeds about ^th of an inch, the curve will ter- 

 minate : there will still be an elevation of the liquid up 

 the side of each plate, but the line traced by its surface 

 will become a straight lino. 



Where the distance between the plates is ^oth of an 

 inch, the fluid, if water, is observed to rise 5 inches ; 

 and therefore where the distance between the plates 

 is -p^th of an inch, the rise of the water is 2i inches. 

 The elevation of the liquid is found to be quite inde- 

 pendent of the thickness of the glass : if the bore of the 

 tube, or the distance between the interior surfaces of 

 the plate, be the same, the elevation is unaffected by 

 the thickness, so that the quantity of matter in the glass 

 does not contribute to the ascent of the fluid ; and if 

 the interior surfaces of the plates, or the bore of the 

 tube, be coated with a film of oil, the capillary attraction 

 is destroyed. On this account, it has been inferred that 

 the attraction is exerted entirely by the surface of the 

 glass, nnd that the liquid must be in complete contact 

 with that surface, for the phenomenon to take place : 

 the attractive energy, it would seem, has no penetrating 

 power, it being stifled and rendered inoperative by the 

 interposition of even the thinnest lamina of oil or grease. 

 It may be remarked, too, that the elevation of the 

 i is not near so great between plates, as in a tube 

 whose diameter is equal to the distance of the plates : 

 the rise is something less than half as great in the former 

 case as in the latter. But this might be expected, as in 

 the tube, the thread of fluid is completely surrounded by 

 the glasH surface ; the same law, however, namely, that 

 the height of the fluid is inversely proportional to the 

 distance between the plates, is observed to have place. 



The fluids which, exhibit the phenomena here noticed 

 are exclusively the watery fluids, all of which rise to 

 different heights in the same tube ; and some of the 

 heavier rise higher than the lighter : spirits of wine, for 

 instance, rises only about f ths as high as water, which 

 of all liquids rises to the greatest height. Mercury, 

 however, does not rise at all ; on the contrary, the tube 

 and the plates seem to exercise a repellant energy, and 

 cause the mercury to descend : this is called capillary 

 repidsion. 



The diameter of a capillary tube is not found by actual 

 measurement ; the method recommended is this : Put 

 a known weight w of grains of mercury into the tube, 

 and let the length of tube it occupies be I inches ; then 

 representing the diameter of a transverse section of the 

 tube by d, we have for the volume of the mercury 

 d?lx '7854 ; and as a cubic inch of mercury, when pure, 

 weighs 3443 grains, we have 



1 : d?l X '7854 : : 3443 grains : w grains ; 



V/(T 3443^7854-) 



Whatever the force called capillary attraction and re- 

 pulsion may be, it is plain that it cannot be analogous to 

 that so universally diffused throughout the material 

 universe, and called the force of gravitation ; because 

 the intensity of this influence increases with the mass of 

 the body exercising it : whereas the capillary influence 

 is more like that of electricity, which, when in a state of 

 equilibrium, seems to be confined to mere surfaces. It 

 appears not improbable, therefore, that capillarity may 

 be a peculiar manifestation of electric force exerted by 

 the surface of the glass on the particles of liquid in its 

 immediate neighbourhood. 



CHAPTER V. 

 HYDRODYNAMICS. 



HYDRODYNAMICS treats of the motion of incompressible 

 fluids, and, as the name implies, more especially of 

 water. The consideration of compressible or elastic 

 fluids, whether in a state of equilibrium or of motion, 

 comes under the head of Pneumatics, a subject to which 

 the nest chapter will be devoted. But, from our limited 

 space, we are precluded from discussing these remaining 

 topics at any great length. This, however, is scarcely to 

 be regretted, for the physical laws which regulate the 

 motions of fluids are so imperfectly ascertained, that, 

 except in those few particulars which constitute the mere 

 elements of the subject, the investigations of hydro- 

 dynamics, founded on hypothetical data, are of little 

 practical value ; and sometimes even lead to results 

 clearly contradicted by experiment. We shall, therefore, 

 confine ourselves, in this brief summary, to those elemen- 

 tary portions of the mathematical theory which actual 

 experiment confirms, or where the practical obstacles to 

 such confirmation are clearly ascertained, and may be 

 estimated and allowed for: 



If water run through a pipe or other channel, always 

 filling it, the velocity of the fluid at any part will be 

 inversely as the area of the transverse section of the 

 channel at that part. For let A, A' represent the area 

 of any two transverse sections, the water being supposed 

 to run from A towards A'; then whatever quantity passes 

 through A in a given time, the same quantity must pass 

 through A' in that time ; since if a less quantity passed 

 through, then the fluid between the sections, always re- 

 maining full, would be condensed ; and if a greater 

 quantity passed through, the fluid between the sections 

 would be expanded, as the channel is always fulL As 

 each consequence is incompatible with an incompressible 

 fluid, it follows that equal quantities of fluid must pass 

 through A and A' in the same time. 



If, therefore, the velocity of the stream through A be j 



Fig. 185. 



v feet per second, and the velocity through A', ' feet per 

 second, we shall have 



At; = A.'v .'. A : A' : : v' : v ; 



that is, the velocities are inversely as the areas of the 

 sections. 



SPOUTIXG OF FLUIDS. The velocity with which 

 a fluid issues from a small orifice in the bottom or side 

 of a vessel, kept constantly full, is equal to the velocity 

 that would be acquired by a heavy body falling freely 

 through the height of the surface of the fluid above the 

 hole. 



Suppose the orifice A (Fig. 185) to be at the bottom of 

 the vessel, then the thin lamina of fluid covering the 

 orifice A is forced out by the action of gravity upon it, 

 and by the superincumbent pressure of the column of 

 fluid whose base is A and altitude A B. Conceive the 

 column A B to consist of n such 

 lamince, thus supposed to be 

 noted upon at A ; that is, calling 

 the thickness of the lamina ], 

 let A B = n then before mo- 

 tion, the statical forces or pres- 

 sures on A are its own weight, 

 and the weight or pressure of 

 the column AB, and these are 

 as 1 to n ; consequently the dy- 

 namical effect of these forces, 

 when motion takes place, must 

 be also as 1 to n. Now the dy- 

 namical effect, that is, the velo- 

 city generated in the lamina A, 

 in the time of falling through its 

 own thickness 1, regarding tliis time as the unit of time, 

 is 2 (DYNAMICS, page 730) : hence 



1 : : : 2 : 2n ; 

 therefore 2n is the velocity generated in the lamina A by 



