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and subtracting this equation from the preceding, we have

o=gx-1

a'2

a2 u2 —gh + 1 u2.

a' 2

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This expresses, according to the theory of fluid threads, the relation is due to the height am, is expressed by ty dx/2g (h' + x); which, hh', would give the between the velocity u and the difference between the weights of two being integrated between 0 and x = filaments of the fluid having unity for the base of each, and whose quantity of water discharged through the whole orifice in the time t. If the orifice were rectangular, y would be constant: suppose it = b; heights are h and x. When x=0, the equation becomes ou then the indefinite integral would be bt √ 2y ƒ (h' + x) * dx, or $ -gh+u2; or considering the orifice as infinitely small so that abt √2g (h' + x), which (between the said limits) becomes bt √/2g and the whole first term of the second member vanishes, we have (hh): and if the orifice extended from the bottom to the top of -gh+2; whence u = √2gh. the vessel, having then xh, or '= o, the expression would be. bt √2g.h. If a rectangular orifice of the same form and magnitude were situated at the bottom B, with its longer side (= h) horizontal, the breadth 6 being very small in this, and also in the preceding case, the quantity discharged in the same time t, the velocity of the effluent water being now equal in every part of the orifice, and being that which is due to the whole height h, would be expressed by bt √2g h3. The discharge found above is manifestly equal to two-thirds of this quantity.

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Now gh expresses the weight of a prism of fluid having unity for the area of its base and whose height is h, h being the vertical distance of the surface of the fluid from the centre of gravity of the orifice, which is called the "charge of water on the orifice; and this is the pressure of the fluid against a small orifice at the bottom of the vessel: but, while the height h is the same, the pressure is the same whatever be the position or inclination of the orifice: therefore 2 gh will express the velocity at the same depth, whether the orifice be at the bottom or side of the vessel. By the theory of dynamics this is equal to the velocity acquired by a body in descending by gravity through a height h, equal to that of the column of fluid, the orifice being infinitely small.

=

It may be concluded from the above theorem, that the velocity of a fluid spouting upwards through an orifice in a vessel would cause it to ascend to the level of the upper surface of that in the vessel, if the resistance of the air and of friction were abstracted. Hence we see that if q=waste of water per second, m = a constant coefficient, d the surface of the orifice; then q=mud=md √2gh. Now m is found to be always 62 in orifices with thin walls; hence Q=4.98 √h. In orifices with a cylindrical spout, 3 or 4 times the size of the orifice, we shall have u='82√2 gh, and the waste=Q='82d✔✅2 gh=6·58 √2 h. It follows, also, that the velocities of spouting fluids, at different depths below the upper surface, are proportional to the square roots of the depths; that the quantities of fluids discharged in equal times at different depths in the vessel, the latter being constantly full, are to one another in a ratio compounded of the areas of the orifices and the square roots of the depths; and the quantity of water which would be discharged in a given time t, through an orifice a in a vessel kept constantly full at the height h, is expressed by a' t √ 2gh.

The velocity u or 2gh expresses the length of a cylinder of water which would flow through the orifice in one second; consequently the time of discharging, from a cylindrical or prismatical vessel, the area of whose base is a and whose height is h, a quantity of water equal to that which the vessel will contain, the latter being however kept full during all the time that the water is flowing, will be found by making ah equal to a't√2gh; whence t (the time required) a h The value of g is 32:19 feet, or 386.28 inches; and in these a' 2g values of u and t it is evident that the areas and height must be of the same denomination as g.

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When a vessel is suffered to discharge itself gradually, the velocity of the effluent water diminishes continually. Now if x be the depth to which the water has descended at the end of the time t, h being the whole height when the vessel is full, h will be the height of the fluid at that time; and we shall have √ 2g (h x) for the velocity in the orifice. This may be supposed constant during the time dt, and then the quantity of fluid discharged in that element of time would be equal to a' dt √ 2g (h-x). In the time of this discharge the surface of the fluid will descend through the depth da; therefore the area of the upper surface being a, we have a da a' dt 2y (h- x), a dx and dt = If the vessel is an upright cylinder or prism, a'√2g (h—x)

=

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upper

2 a

a'√2g (√h−√h−x); which, when

3

In the second book of the 'Principia,' Newton shows that all the particles of water issuing from an orifice in a vessel do not pass perpendicularly to the side or bottom in which it is formed, many of them converging towards the orifice in every direction; so that after passing it they form a stream of diminished breadth, which he called the vena contracta. The section of the vena contracta may be taken as equal to 5-8ths of the actual orifice, as has been shown by Mr. Rennie, in his 'Report to the British Association,' for 1834.

M. Savârt has demonstrated the existence of certain eddies formed at

the orifice by the issuing jet, caused by some water above the orifice trying to get out and coming into contact with the resisting walls, and by some water below it being moved by the falling mass above it, thus producing a set of forces acting by couples. Hence the issuing water, although it always has its motion of translation perpendicular to the resisting surface, has, besides, a rotatory motion caused by these eddies. The irregularities of this rotatory motion then tend to cause a disintegration of each successive section; and hence, between the thicker or normal drops there come out smaller ones, thus forming an irregular stream of varying width. Savârt has shown that each drop is formed by an annular enlargement at the orifice, which is propagated along the jet and causes this disintegration by a succession of such pulsations. The number of these is probably directly as the velocity of the jet, and inversely as the size of the orifice. It is remarkable that these pulsations are continuous enough to cause a clear musical note; and if with any instrument we produce the same note near, the pulsations become very regular, but cause no change in the amount or velocity of emission. When the orifices are not circular, curious variations in the geometrical figures, representing the sections at different distances from the orifice, are produced.

When a

When, again, a rising column of water impinges against a horizontal plate, we have a remarkable appearance,-namely, a sort of disc of water, of which the interior is a transparent sheet, and the outer rim is a streaked space, along which lines of fluid stretch out and fall back in a very fine spray. The pulsations here, also, are very regular, and produce a musical sound. The relative size of the striated part to the whole varies with the position of the intercepting solid. certain distance is reached this part vanishes, and we have a wholly transparent sheet. The forms also vary very beautifully, according as the plate is perpendicular or oblique to the issuing jet. M. Savârt has also given some curious results on the subject of the clashing together of two liquid veins, which we have not room here to describe, but which will be found in the Annales de Chimie et de Physique,' vol. liv.; and a brief summary in Pouillet's 'Traité de Physique.'

We have been recently enlightened as to the phenomena of issuing jets by the researches of MM. Savary and Magnus. Bidone asserted that the spiral form of the jet was illusory; but Savary, when accounting for the curious dilations which he calls ventral segments, showed h-that the efflux itself gives a vibratory motion to the liquid vein, thus causing the protuberances in question. Prof. Magnus, in the Phil. Mag.' for February and March, 1856, regards every jet as composed of an indefinite number of united jets. He then examines the effect produced by the collision of two equal jets, coming centrally in opposite directions. These, as we should suppose from Savârt's experiments, spread out at the confluence into a flat plate perpendicular to the axes of the jets. When they meet obliquely, but centrally, they form a flat plate, not circular, but oval. This also we should imagine à priori; for the force of each jet may be resolved into two others, one parallel to the plane bisecting the angle between the jets, and the other perpendicular to it. The latter causes the elongation of the plate in a plane perpendicular to the direction of the force, as in the former case. When the water thus spreads out laterally, its motion does not cease, but the plate, by its cohesion, contracts in width, and collects into two new jets converging to one another. These then throw out a new plate perpendicular to the first, and the same process is repeated, forming thus a succession of elliptic plates in perpendicular planes, like the links of a chain.

a'√2g x=h, becomes t= and comparing this with the time in which an equal quantity would run off, the vessel being kept full, it will

be found to be double the latter.

Next, if it were required to determine the quantity of water which would flow through an orifice of finite magnitude when cut in the vertical side of a vessel which is kept constantly full, it must be observed that the velocity of the effluent fluid at different points in the depth of the orifice varies as the square root of the distance of the point from the upper surface. Now let A B (= h) be the vertical height of the water in a vessel in one side of which is formed the orifice whose axis is CB, and imagine the horizontal ordinates at m and n to be drawn

775

HYDRODYNAMICS.

Again, if two jets meet obliquely, but not centrally, the liquid plate is still formed, but it is no longer flat, being twisted by its cohesion with the unimpaired parts of the jets.

From these two last cases especially, Prof. Magnus has shown the formation of a single jet from an orifice to be due to the clashing of several jets at the vena contracta, thus throwing out between them a plate of an elliptic form, and so on throughout the whole liquid vein. The chain movement of the jet thus produced is easily converted into a spiral one by any slight impediment at the orifice, or by currents, even very slight, in the cistern, since all motion whatever of water in a cistern necessarily resolves itself into rotatory motion; because all other motions are destroyed by the sides of the vessel. Besides this, even when there is perfect stillness in the water of the cistern, rotation will take place at an orifice, by reason of the motion of the earth. This is well illustrated by Foucault's pendulum experiment. [GYROSCOPE.] It is evident from this, that everything on the earth's surface has two motions relatively to the earth-namely: one round the earth's axis in 24 hours; and another round an axis in itself, and parallel to the former, in the same period. The latter, in the case of a vessel of water, is resolved into two, one parallel to the liquid surface, the other perpendicular to it; neither being visible, because the vessel and everything else have the same motion. The horizontal rotation, in the latitude of Great Britain, will be about per minute, so that the liquid has the rotation about its vertical axis. This will be abundantly sufficient to show the cause of the spiral motion of the issuing jet. Prof. Magnus, by introducing a tranquilliser,—that is, a fan consisting of four radiating plates,-in order to destroy the effect of this rotatory motion on the jet, succeeded in showing that, in this case, no ventral segments or any other irregularities were produced,--perhaps not even the vena contracta; but the issuing column was perfectly smooth and uniform. M. Plateau, however (Phil. Mag., Oct., 1856), denies this statement, and shows, by reference to his celebrated method of destroying the action of gravity on fluid veins, that a liquid cylinder is in stable equilibrium when its length and diameter do not exceed the limit of 3 and 3.6, being in unstable equilibrium beyond this limit, so that it is ruptured spontaneously into a series of isolated spheres with alternating spherules. This effect of the formation of various sized spheres is well shown in the fusion of a platinum wire by a strong electric current. The wire is first elongated, and then, by the rupture of equilibrium of the parts, resolves itself, just as a liquid jet, into spheroidal particles.

Lastly, with regard to the formation of the vena contracta in such cases, we shall see that it must be formed, if we consider the theorem of Torricelli, as correctly representing the approximate velocity of any affluent jet. By this theorem, as before shown, we have the velocity at the orifice given by the equation v2=2gs, where s is the distance from the surface to the orifice. Now, g is about 32-2 feet for the

latitude of London: hence v2=64'4 x 8

.. v = 8·025 × √ 8.

But it is shown by experiment, that this theoretic velocity (given by
substituting any value for s proper for the vessel in question) is
14 times the actual velocity, or this latter is of the former; so that
we must reckon the actual height of the surface, not from the orifice,
but from the vena contracta itself, in which case Torricelli's theorem
is in accordance with experiment.

The distances, measured on a plane passing through the base of a
vessel, to which fluids will be projected from orifices at different
depths in its side, may be easily determined (the resistance of the air
being neglected) by combining the action of gravity on the particles of
fluid after they have left the orifice with the velocity communicated
to them in consequence of the pressure arising from the depth of the
orifice below the top of the column; and the path of the filament may
be shown, as in the theory of gunnery, to be a parabolic curve.

The results of experiments tend to show that, when the height of a
head of water in a vessel and the diameter of an orifice in its base or
side are given, the discharge of water through an ajutage, or tube
inserted in the orifice (its length not exceeding three or four times its
diameter), is to that through the simple orifice, nearly in the ratio of
12 to 11; and it is observed that, with a given diameter at its farthest
extremity, the tube which is formed to coincide as nearly as possible
with the natural figure of the vena contracta affords the greatest
discharge. When the tube is fixed vertically in the base of a vessel,
the effect is increased in proportion nearly to the length of the tube;
since the velocity at the lower extremity of the tube is that which is
due not merely to the height of the fluid above the base of the vessel,
but to the height above the extremity of the tube. Again, if a short
tube be applied horizontally to an orifice in the side of a vessel, the
part nearest to the vessel having the form of the vena contracta, and,
from the narrow part of the tube, diverging conically to the opposite
end, the discharge of water is found to be more abundant than from a
tube whose form beyond the vena contracta is cylindrical. For when
the water has filled the tube, the cylindrical stream through the
contracted part communicates its motion laterally to the rest of the
water, till it causes the whole to acquire the same velocity. The
quantity discharged in this case, compared with that discharged from
a cylindrical tube, is considered to be nearly in the ratio that the
diameter of the conical tube at its extremity bears to that of the vena

HYDRODYNAMICS.

776

contracta. The following is the result of some experiments on this
subject, showing the use of an ajutage :-

A vessel with a simple hole

A vessel with a pipe whose length=2
diameters of the hole

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A vessel with the same pipe inserted
only half way in the hole
When the bottom of the vessel = the
parabolic curve described by the
particles

With a bell-mouth added to this

discharged 62 quarts in 100 sec.

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It is customary to express the slope, or inclination, of a pipe or canal,
be the lower
case of a reservoir, as A B, having a conduit-pipe D E; let A A' be the
when uniform, by the quotient arising from the division of the vertical
height of one end above the other by the whole length. But, in the
surface of the water, and E, in the horizontal line F E,
is considered as the effective slope.
orifice of the pipe. Then, if A'G express the height due to the observed
velocity at E, G F will be the height necessary to overcome the friction in
the pipe, and

GF

DE

The passage of water through long pipes is greatly retarded by adhesion and friction in the interior, by the resistance experienced remaining stationary in the pipes when the latter are laid along a level where bends take place, and by the disengagement of air, which surface, or rising to the higher parts of any vertical bends, opposes an obstacle and sometimes entirely arrests the motion of the water. Experiments alone can, at present, afford information concerning the amount of the retardation in pipes of given lengths and diameters; and those which were conducted by the Abbé Bossut at Meziéres in 1779 was allowed to flow through pipes whose diameters were 1 inch and are the most complete of any which have yet been made. The water 2 inches, and whose lengths varied from 30 to 180 feet. They were chiefly of tin, and were inserted in the side of a reservoir in which the water during any experiment was always kept at one height; which was either 1 foot or 2 feet above the axis of the pipe. The general rules deduced from the experiments are, that the discharges in given times, with pipes of the same length and with the same head of water, are proportional to the squares of the diameters; and, when the square roots of the lengths of the pipes. In order to afford the means diameters are equal, the discharges are inversely proportional to the of obtaining by calculation the supply which may be expected from a pipe of given dimensions, it may be assumed that when a pipe is 30 feet long and 1 inch in diameter, the discharge at its extremity is or short tube, of the same diameter. The experiments made by M. about one-half of that which would be obtained from a simple orifice, from 280 to 2340 fathoms, and the diameters from 4 to 12 inches. Couplet at Versailles, in 1730, were with pipes whose lengths varied The pipes were of iron or stone, or of both combined, and they were bent in various directions both horizontally and vertically. A pipe whose length was 600 fathoms, and which was 12 inches in diameter, when the head of water was 12 feet, afforded a discharge amounting to about th; and a pipe of equal diameter, whose length was 2340 found that, in order to produce a continued discharge in a pipe, the fathoms, when the head of water was 20 feet, discharged only th, of head of water should be about 12 inches in 180 feet. that which would have been obtained from a simple orifice. Bossut

The motion of water in the bed of a river depends on the action of The descent by gravity takes place in congravity, by which the particles endeavour constantly to descend, and on the mobility of the particles, by which they are enabled to assume a level surface when at rest. form of its bed; since the molecules of water, which are in every part sequence of the difference, in a longitudinal section of the river, of a transverse section, have equal facilities of moving in the direction between the levels of any two points on its surface, whatever be the in which, from the general slope, the motion can take place. And, by the nature of an inclined plane, the accelerative force by which a particle is moved is to that of gravity as the difference of level between any two points at the surface in a longitudinal section is to the distance between those points on the surface. That the motive force of the molecules composing a river depends on the upper surface only may be easily admitted, when it is considered that the bed may have any inclination and any degree of irregularity, yet if the upper surface be horizontal the water will be at rest.

If the water of a river experienced no resistance from the sides and bed, its motion would go on continually accelerating from its source to its mouth, like a solid body falling by the action of gravity; and the consequence would be, that besides the destruction ensuing from the violence of the torrents in the lower lands, the moisture would be drawn from the soils in the upper regions, which would thus become incapable of supporting vegetable and animal life. The adherence of the particles of water to each other, and the friction against the beds, produce together a resistance which increases with the velocity of the current, and becomes at length equal to the accelerative force of the descent; and then a uniform motion is established.

But when a current is in a state of equilibrium, the velocities in account of the variations in the areas of those sections, through all of different transverse sections of the river may be very unequal, on

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Τ

which the same quantity must flow in the same time; since otherwise the equilibrium of the river would not be permanent. It follows that the products of the areas of the sections multiplied by the velocities in each must be equal to each other, and that the velocities in different sections must be inversely proportional to the areas of those sections. If the difference of level between any two points on the surface of a river or canal, in a longitudinal section, be equal to one inch, and if l, in inches, be the distance of those points on the surface, the slope of the river may be represented by. Then, since the accelerative power of gravity vertically, is to the accelerative power on any plane, as the length of the plane is to its vertical height; we shall have for the accelerative power in a river whose slope is Again, if the resistances to the motion of the fluid were, as is sometimes the case, nearly proportional to the squares of the velocities, so that the resistance might be represented by (m being constant, and v representing the mean velocity); then (because when water in a river moves uniformly, the resistance is, as in all like cases, equal to the accelerative force) we v2 9 should have whence v√ But the resistances in canals ī and rivers are not strictly proportional to the squares of the velocities; and it is found by experiment that, in one and the same bed, v {√l – hyp. log. √7+16} may be considered as constant, and may be represented by my. Also, in beds whose transverse sections differ both in area and figure, when the mean radius is represented by r (where

m

A

Fig. 2.

==

v2

m

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mg

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it is found by experiment that is constant and equal to √r-01 307 inches; hence √mg=307 (√r−0·1) and m=244 (√r−0·1)3 Consequently we obtain

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The mean velocity in any one section may be practically found, tolerably near the truth, by placing in it a rod of wood loaded at one end with a weight sufficient to allow it to float upright in still water. The greater velocity at the upper surface will make the rod incline towards the direction of the stream; and, consequently, when it has acquired a state of equilibrium, it will float in an oblique position: the top of the rod will move slower than the water at the upper surface of the river, and the bottom will move faster than that in the lower part. Hence the mean velocity of the water in that part of the breadth of the river may be considered as equal to 8 of the observed velocity of the rod. Often a Woltmann's drum is used, in which is a turning shaft, communicating by a screw-channel with a meter, and carrying four wings like a windmill. The experiment must be tried in different parts of the breadth of the river; and, in order to find the quantity of water which flows through the section in a given time, the area of the section must be obtained by measuring the breadth and sounding the depths at intervals across the river.

A knowledge of the velocity at the bottom of a river is of consider able use in enabling the hydraulic engineer to judge of the action of the stream on its bed; and it is evident that, to ensure permanency, the accelerative force of the water should be in equilibrio with the tenacity of the channel. The following table shows the superior limits

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Irregularities in the sides and beds of rivers, whether arising from natural causes, or produced by artificial obstructions, are the causes of currents setting obliquely across and of eddies being formed. These not only diminish the velocity of the water by creating impediments to its motion, but are sometimes seriously detrimental to the navigation, and to the stability of the structures which are founded in the bed of the river. When walls are made to project into the stream, the water striking them is forced to rise above its general level, on account of the obstruction; and is afterwards reflected towards the middle of the channel, with a velocity due to the rise thus produced. This current carries with it, by a lateral communication of motion, some of the water from the parts beyond the obstruction; the surface of the river being here, consequently, depressed, a portion of the water from the oblique current falls by gravity into the lower part, and thus a sort of whirlpool is formed at the place where the obstruction terminates. This process goes on continually; and the pressure upon the bed of the river under the whirlpool being diminished in consequence of the centrifugal force arising from the spiral motion, the water under the bed forces its way upwards, removing the gravel and sand, and frequently displacing the materials which form the foundation of the work there constructed.

When a body moves in a fluid at rest, its anterior surface being perpendicular to the direction of the motion; if an indefinitely thin lamina of fluid be supposed at every successive instant of time to be displaced, the resistance experienced by the moving surface may be considered equal to the weight of a column of the fluid whose base is the surface pressed, and whose height is that which is due to the velocity: that is to say, the resistance may be supposed to be equal to the pressure which would produce the same velocity at an orifice in the base or side of a vessel. A difference of opinion has however surface. For a vein of water issuing from a vessel and striking a plane existed respecting the amount of the pressure sustained by the moving surface at rest is shown by Newton ( Principia,' lib. ii., prop. 36), (and the fact seems to be confirmed by the experiments of Krafft and Bossut), to exert a pressure upon that surface equal to the weight of a column of water whose height is twice that which is due to the velocity. Du Buat, however, has proved that, even if such should be the case with respect to the central part of the impinging column of fluid, the mean pressure is less, on account of the lateral deviations of the exterior filaments, and the amount first stated above is that which is generally

assumed.

If the velocity be represented by v, the height due to that velocity v2 is equal to ; then a representing the area of the moving surface, 2g

a v2 and D the specific gravity of the fluid, we shall have D for the 2g pressure against, or the resistance experienced by that surface in moving through the fluid.

But when the anterior surface of the moving body is oblique to the direction of the motion, the resistance above found must be diminished on account of the inclination. Thus, let I be that inclination; the number of parallel filaments which act against a plane perpendicularly is, to the number which can act upon it in an oblique position, as radius (=1) is to sin. I. And by mechanics, the intensity of any force acting obliquely on any plane is a decomposed part of the whole force, and is to the latter in the ratio of sin." I to rad.2 (=1). Therefore the effective pressure against an oblique plane varies, as sin. 1; consequently when the moving plane is oblique to the direction of its motion, the resistance which it experiences is to be expressed by D sin.3 I.

a v

2g

If a cylindrical body, terminated in front by an equilateral cone, move through a fluid in the direction of its axis; it can easily be shown that the resistance experienced is one-fourth, and if the body be terminated in front by a hemisphere, the resistance is one-half of that which would be experienced by the same cylinder if it were terminated in front by a plane perpendicular to its axis.

When a prismatical body is placed in a stream of water the effort necessary to keep it immovable in the fluid is equal to the difference between the pressures in front and behind. The pressure in front is equal to the sum of the pressure produced by the moving water and of the dead pressure, as it is called, which takes place when the body is at rest in still water; and the pressure on the rear face is merely equal to this last. When a body of that kind is made to move in a fluid at rest, its progress is retarded by the same difference of the

pressures before and behind, and by the friction of the water against the sides. Additional causes of retardation are the heaping up of the water in front when the velocity is considerable, and a diminution of the pressure on the hinder face on account of the surface of the water there being depressed below the general level; a circumstance arising from the lateral communication of motion in fluids, by which the water, driven off from the front, and proceeding in a diverging direction on each side towards the rear, carries away with it from thence some of the water which should counteract in part the pressure on the front.

Mr. Scott Russell in the' Report of the British Association,' for 1835, and Mr. Macneill in the Transactions of the Institution of Civil Engineers,' have given the following laws for the resistance to boats moving on canals; but for the practical reading of these laws we must refer to STEAM-BOAT.

1. The rise or emergence depends on the velocity of the vessel.

2. The resistance depends on the velocity or magnitude of the wave which is generated.

3. The resistance increases rapidly as the velocity of the body approaches the velocity of the wave, and is a maximum when they are equal.

4. If the velocity of the body be greater than the velocity of the wave, the resistance diminishes; for the body is poised on the summit of the wave in stable equilibrium.

5. The velocity of the wave is independent of the breadth of the fluid, but varies as the square-root of the depth.

6. In every navigable river there is a velocity with which it is easier to ascend against the current, than to descend with it.

7. Vessels on the summit of the wave may move about 20 or 30 miles per hour.

With regard to the form of vessel best adapted to diminish this resistance, they add :

1. A cylinder will meet with less resistance in a fluid than a plate of the same dimensions as the end of the cylinder; and a cone with its butt-end foremost is better than either.

2. There is no fixed ratio of breadth to length which is best. The longer the better, but the breadth varies with the burden.

3. The section of greatest breadth should be always abaft the middle, about 3-5th of the length from the bow.

4. Lastly, the water-lines should be hollow, of the form called the "wave-form," first concave, then convex.

We may conclude this article with a notice of one of the many hydrodynamic engines, referring to separate heads, as indicated under HYDRAULICS, for other contrivances, in which the water is to be raised, or the force of water to be employed.

upper

The HYDRAULIC RAM, which was invented by Montgolfier at the close of the last century, and improved by his son, consists, independently of the feeding cistern, of a pipe which carries the water to the head of operations. This part consists of a short tube, at the upper part of which, as well as at the end, are two valves, the stop-valve, and the ascension-valve; the extremity is in a bell filled in its part with air, and its lower with water. The ascension-valve being closed, the water will come from the reservoir with increasing velocity. and leaving it by the stop-valve, will shut it: then, by the vis viva which it has acquired, it will strike the ascension valve, and open it, and so penetrating into the reservoir of air, will compress it, and make the water in the ascension-tube rise; then the elasticity of the air, and the weight of water in the ascension-pipe will, of course, absorb partly the vis viva acquired with the water and will give it a powerful motion; hence, by reason of the retrograde motion of the water, the ascensionvalve will shut, and there will be formed a partial vacuum under the stop-valve, which will open, and so on continually. Hence this machine, when once set in motion with a continual supply of water, will work by the momentum generated and destroyed for any length of time, if kept in repair.

The accompanying figure represents a vertical section of the improved construction. The water arrives from a cistern at a higher level, by the horizontal pipe A, over which is a circular opening containing a valve v, which acts as a stoppage valve, and is suspended by a stem. Further on the pipe ascends into a small reservoir c, called the air matrass; the air contained in it is compressed by the ascending water, while the lateral pressure of the water opens the valves v v', and enters the larger reservoir F, which it partly fills, and compresses the air confined in the other part of it. The reaction of this air on the surface of the water causes the water to ascend the force-pipe G. When the stoppage valve is down, as in the figure, the water overflows the opening above it, and passes into a waste reservoir, thereby producing a rapid increase in the velocity of the current in A, which, acting on the under surface of the valve, forces it up, and closes the opening by which the water escapes. This momentary confinement of the water causes it to force its way into the cylinder c, where it compresses the air and produces a reaction, which opens the valves v v', and a portion of the water enters the vessel F, and further compresses the air there. These resistances retard the current A, and relieve the stoppage valve from the impulse which raised it, so that that valve again falls, and the valves v v are closed. The water again escapes from the opening over the stoppage valve as shown in the figure, the current in A is again accelerated; the stoppage valve is once more closed, and

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gradually absorbed by water, the compressed air of the vessels c and F is liable to be carried away by the water up the force-pipe &, the effect of which would be to subject the machine to shocks which would destroy the uniformity of its action and injure its working parts. To prevent this, an air-valve is provided at s, which, opening inwards, admits air during the intervals when the stoppage valve is closed. The air in rushing through the valve s makes the sound like the sniffling of a person's nose, and is hence called a snifting valve. It may consist of a tube of capillary bore, and be left entirely open.

HYDRO-ELECTRIC MACHINE. [ELECTRICAL MACHINE.]
HYDROFERRIDCYANIC ACID. [FERRIDCYANIC ACID.]
HYDROFERROCYANIC ACID. [FERROCYANIC ACID.]
HYDROFLUOBORIC ACID. [FLUORINE.]
HYDROFLUORIC ACID. [FLUORINE.]
HYDROFLUOSILICIC ACID. [FLUORINE.]

HYDROGEN (H), an elementary body, which, as it is known only in the aëriform state, is usually termed hydrogen gas. From the earliest dawn of chemical science, elastic fluids have been known which had the property of burning on the approach of flame, and were confounded under the general name of inflammable air. As it was afterwards found that there was a difference in their densities, they were distinguished as light and heavy inflammable air; it is the former of these which is now called hydrogen. Hydrogen gas was first minutely examined, and the mode of preparing it in various ways stated, by Mr. Cavendish. [CAVENDISH, HENRY, in NAT. HIST. DIV.]

In nature, hydrogen is found in the free or uncombined state, as a constituent of volcanic gases. In comparatively small quantity it occurs associated with phosphorus, sulphur, carbon, and nitrogen, forming gaseous compounds; it is a constituent of nearly all the proximate principles contained in animals and vegetables; but united with oxygen, it constitutes th of the total weight of that familiar compound-water.

Hydrogen is always prepared from water. If the gas is required absolutely pure, the water is decomposed by a current of electricity, the hydrogen being collected from the negative pole of the decomposing cell, and, if necessary, dried by being passed through a tube filled with pieces of chloride of calcium. Another process, valuable because instructive, consists in passing a fragment of potassium or sodium up into a small quantity of water in a test tube, the remaining portion of wich is filled with mercury, and inverted over the mercury trough; the sodium rapidly attacks the water, combining with its oxygen to form oxide of sodium (soda), and displacing its hydrogen, which latter element, being gaseous, expels the greater part or all of the mercury from the tube. The following is the simple change that takes place :- Na + HO Water.

Sodium.

H

=

NaO + Soda.

Hydrogen.

For ordinary purposes, hydrogen is prepared by acting upon granulated zinc with diluted sulphuric acid. The zinc, covered with water, is placed in a bottle or other convenient vessel to which a cork can be fitted, and strong sulphuric acid is then poured in by means of a funnel, to which is attached a tube passing through the cork to the bottom of the bottle. The gas is rapidly disengaged, and passing through an exit-tube in the cork may be conveyed by flexible tubing into a gasholder, &c. [GASES, COLLECTION OF.] In this process, sulphate of zinc is formed, which remains in the generating vessel dissolved in the excess of water used.

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If it be required to produce hydrogen cheaply, though in a very impure state, it may be readily done by passing steam over iron borings heated to redness in a piece of iron gas-pipe. Under these circumstances the iron is converted into an oxide (Fe,0.), and the hydrogen set at liberty.

Hydrogen is an element. No amount of pressure causes it to abandon its gaseous condition. When pure, it is colourless, tasteless, transparent, and inodorous. It is the lightest body in nature, being sixteen times lighter than oxygen, and fourteen and a half times lighter than atmospheric air; its specific gravity is, therefore, 0-0692, air being taken as unity. One hundred cubic inches of it weigh only 2.14 grains. This gas extinguishes flame; but when it meets with a supporter of combustion, as oxygen, it burns readily, with a continuous but feeble flame, generating much heat. When mixed with half its volume of oxygen, and the mixture is ignited by a taper, or by throwing into it a small quantity of platinum black, immediate and loud explosion ensues, attended with the formation of water by the combination of the gases; hence the name hydrogen, or the water-producer, from dwp, "water," and yevvaw, "I generate." It is irrespirable for any length of time, but when inspired for a short period it renders the voice remarkably but not permanently shrill; it does not appear to be poisonous, for when mixed with a due proportion of oxygen it may be respired without inconvenience; when it proves fatal, it seems to do so by the mere exclusion of oxygen.

It is very sparingly soluble in water, 100 cubic inches taking up only about one inch and a half of the gas; nor is there any other liquid which is capable of dissolving it in notable quantity. Hydrogen, neither in the gaseous state nor in solution, possesses either acid or alkaline properties. In its combinations it is powerfully electro-positive, and chemically plays more the part of a metal than of a metalloid. In its separate state, hydrogen has not been applied to any very useful purpose; but on account of its extreme lightness it has been used to fill air-balloons; at present, however, coal-gas is substituted for aeronautic purposes, by reason of the facility with which it is obtained. This, however, from its greater density, requires much larger balloons than hydrogen gas.

When mixed with oxygen gas, and the mixture gradually burned in a small jet issuing from such a blowpipe as is described under DRUMMOND LIGHT, a temperature is produced sufficiently intense to melt platinum; and even if burned in the air, the oxygen of which serves as a supporter of combustion, a considerable degree of heat is generated.

When a very small jet of hydrogen gas is burned, the flickering nature of the flame causes musical sounds when a tube of glass or metal, or even of paper, is held over it. Such an arrangement is known as the hydrogen harmonicon, but any combustible gas will produce a similar effect.

The equivalent of hydrogen is 1, and its combining volume 2. Its combinations with other elements or radicals are called hydrides or hydrurets.

Hydrogen combines with oxygen in three different proportions, forming,

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1. Protoxide of Hydrogen, or Water (HO) will be treated of in a special article. [WATER.] 2. Binoxide of Hydrogen (HO). To prepare this compound, twelve parts of binoxide of barium, obtained by passing oxygen gas over baryta heated to low redness, are dissolved in two hundred parts of water containing as much hydrochloric acid as will saturate about fifteen parts of baryta. Solution having been effected by gentle stirring, the whole of the baryta is then precipitated by a slight excess of sulphuric acid, added drop by drop. Another twelve parts of binoxide of barium are now added, and the precipitation of the baryta effected as before. This process is continued until about one hundred parts of binoxide of barium are consumed, care being taken to keep the mixture well cooled, and to filter it after every other addition of the binoxide. A tolerably strong solution of binoxide of hydrogen is thus obtained, containing, however, much hydrochloric acid. The latter is removed by the addition of sulphate of silver, and the sulphuric acid thus introduced got rid of by carbonate of baryta. Finally, the solution is placed in vacuo over sulphuric acid for a few days, when the water evaporates and leaves the binoxide of hydrogen. The latter body also volatilises in vacuo, but far less quickly than water.

Binoxide of hydrogen thus prepared must be kept in long glass tubes, closed with stoppers, and surrounded with ice. Notwithstanding these precautions, however, it slowly decomposes into water and free oxygen gas. It is a colourless, transparent liquid, of sp. gr. 1-452. It is unaltered by a temperature 54 degrees below the freezing point of water. It has a harsh, bitter taste, bleaches litmus paper without reddening it, and when placed on the hand whitens the cuticle and produces violent itching. Heat rapidly decomposes it. Contact with most metallic oxides not only causes violent separation of oxygen, but at the same time the oxides themselves are reduced to the metallic state. Binoxide of hydrogen appears to combine with some of the hydrated

acids, as it is far less decomposable in their presence than when alone. Oxygenated water is a term that has been applied to binoxide of hydrogen, but is now usually restricted to the solution formed by saturating water with oxygen gas.

3. Teroxide of Hydrogen (HO). The gases that are evolved when water is decomposed by a current of electricity are well known to possess a peculiar odour. The body that communicates this property has for some years been called ozone (from ow, "I smell "); but it is only recently that M. Baumert has proved it to be the teroxide of hydrogen. The presence of hydrogen in this remarkable compound M. Baumert demonstrated by passing the gases (oxygen and ozone) evolved from the positive pole of a water-decomposing apparatus through a long drying tube containing pumice-stone moistened with sulphuric acid, and then through a tube the inner surface of which was coated with anhydrous phosphoric acid, and one portion of which was gently heated; water was thus produced, and made evident by the solution of the film of phosphoric acid on that part of the tube through which the gas was making its exit, while the film on the opposite part was quite unaltered.

Teroxide of hydrogen decomposes iodide of potassium, the excess of oxygen it contains-over and above that necessary to form water with its hydrogen-liberating its equivalent of iodine from the iodide of potassium, just as chlorine or bromine does. Taking advantage of this fact, M. Baumert ascertained the composition of ozone, prepared as above, by passing the gas for several hours through a weighed bulb apparatus containing iodide of potassium solution, with an arrangement for preventing loss of water by evaporation. The increase in weight after that time gave the quantity of ozone that had passed into the apparatus; an estimation of the iodate of potash formed, showed how much oxygen, exclusive of the elements of water, was contained in that weight of ozone, while the difference between the weight of the oxygen and the total increase in weight of the apparatus, gave the weight of water that had been formed from the decomposition of the The mean of three such experiments proved that the ozone in question was teroxide of hydrogen, thus :—

ozone.

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Other Compounds of Hydrogen.-With sulphur, selenium, iodine, bromine, chlorine, fluorine, and tellurium, hydrogen forms combinations called hydracids. With nitrogen, it forms the powerful salifiable base ammonia; and with phosphorus, arsenic, antimony, and potassium, it forms the several hydrides. A description of each of these compounds will be found under the name of the element with which the hydrogen is united.

HYDROKINONE. [KINONIC GROUP.]
HYDROLEIC ACID. [OLEIC ACID.]

HYDROMARGARIC ACID. [MARGARIC ACID.]
HYDROMARGARITIC ACID. [MARGARIC ACID.]
HYDROMELLON. [MELLON.]

HYDROMELLONIC ACID. [MELLONIC ACID.]

HYDRO'METER (üdwp, water, and μérpov, a measure) is an instrument for determining the relative densities or specific gravities of fluids. The principle of the hydrometer is this: It is known that when a body is immersed in a fluid, it loses as much of its weight as is equal to the weight of that portion of the fluid which it displaces. [HYDROSTATICS.] Thus, if a body suspended from the extremity of one arm of a balance be counterpoised by weights applied to the other arm, and while thus suspended it be immersed in a vessel of water, it will be found that one arm of the balance will preponderate, and that, in order to restore the equilibrium, as much weight must be applied to that arm from which the body is suspended as is equal to the weight of the water displaced. Hence, if the same body be immersed successively in two different fluids, the portions of weight which it will thereby lose will be directly proportional to the specific gravities of those fluids; because the diminution of weight is always equal to the weight of the fluid displaced, that is, to the magnitude of the body multiplied into the specific gravity of the fluid. The above supposes the body to be specifically heavier than the fluid. If it be lighter, it will float upon the surface, so that its tendency to descend, or its weight, will then be entirely counteracted by the fluid; from which it appears that, when a body floats upon the surface of a fluid, the weight of the portion of fluid displaced is equal to the entire weight of the body. Now, since the weight of the fluid displaced by a floating body is constant (being always equal to the weight of the body), whatever may be the density of that fluid, it is obvious that if we can determine how much of the body is immersed, we may immediately deduce the specific gravity of the fluid; because, when the weight is constant, the specific gravity varies inversely as the bulk.

Upon this principle is constructed the instrument known by the name of Sykes's hydrometer, which is that employed in the collection of the spirit revenue of Great Britain. It consists of a thin brass stem about six inches in length, passing through and soldered to a hollow ball of the same material, and about one inch and a half in diameter.

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