This section is from the book "The Engineer's And Mechanic's Encyclopaedia", by Luke Hebert. Also available from Amazon: Engineer's And Mechanic's Encyclopaedia.
This is no sooner done than the water is constrained to become again stationary, by which the momentum is lost, and the valve and weight again become superior, and fall, thus reopening the orifice, and permitting the water to flow again; and as the pressure of the water and the weight of the valve each alternately preponderate, the valve is kept in a constant state of vibration, or of opening and shutting, without any external aid whatever. Such is the principle upon which the motion of the water in the pipe q q is produced; but the motion generated cannot be instantly annihilated; and it is not only of sufficient power to raise the valve s, but likewise to burst open the lower end of the pipe q q, unless a sufficient vent be provided, by which this accumulated force can escape. Accordingly a second valve u is placed near the lower end of these pipes, and is made to open upwards into an air vessel w, with a discharging pipe x, and, consequently, whenever the valve s is closed, the water which would other wise have flowed from the orifice r now opens the valve u and enters the air vessel, until the spring of the continued air overcomes the gradually decreasing force of the momentum, when the valve u closes, and that at s opens to permit the water to make a second blow or pulsation, and in this way the action of the machine continues unceasingly, without any external aid, so long as it is supplied with water and remains in repair.
A small running stream is necessary for this machine, as the water at o should be kept at one constant elevation to ensure the perfection of its action. A much greater quantity of water likewise escapes at the orifice r between the pulsations than can be raised in the delivery pipe x, particularly if it extend to any considerable height, for the comparative quantity of water discharged through x, and permitted to run to waste at r, must always depend upon the respective perpendicular heights of the pressing column o v and the delivered or resisting column w x, and the rapidity of the pulsations will likewise depend upon the same circumstances. Mr. Millington, from whose Epitome of Natural Philosophy the above description is taken, and who has erected several of these machines in different parts of England, which gave great satisfaction, in order to show their efficacy gives the following particulars of one, which, at the time when he wrote, had been in constant use for about two years. The reservoir o is a basin of about 10 feet square and 2 feet deep, formed partly in limestone rock, and partly in brickwork, the supply of water being from a natural spring. The pipe q q is of cast iron, 14 yards long, and 2 inches in diameter.
The piece at the end, containing the air vessel and the valves, is about fifteen inches long; the valves 11/2 inch each in diameter, and made of brass; contents of the air vessel, about 1 gallon. The height from the surface of the water at o to its point of discharge at r, is 6 feet 4 inches, measured perpendicularly. The delivery pipe x is of lead, 1 inch in diameter, and proceeds horizontally under the ground 104 feet, and then rises perpendicularly to the height of 54 feet 3 inches above the discharge valve at r, where it delivers the water into a large cistern. The water is thus raised 47.11 inches above the surface of the spring which supplies it, and this by a fall of only 6 feet 4 inches. So circumstanced, the valve s makes about 50 vibrations, or opens 50 times in a minute, when it loses about two quarts of water, and injects nearly a quarter of a pint into the elevated cistern at each pulsation; the water lost being to that which is raised nearly as 17 to 1. This may appear a small quantity of water, but when it is recollected that the machine is at work night and day (unless purposely stopped), and furnishes six quarts of water every minute, this will be found to be a supply adequate to a very large household establishment.
The construction above described is, however, incomplete, as, owing to the mutual incorporation which takes place between air and water, the successive quantities of water that are impelled into the air vessel would soon absorb the whole of the air contained in it, and it would cease to afford that elasticity which is indispensable to the working of the machine. This was discovered in France by M. Montgolfier, who added an improvement to the machine by introducing a very small shifting valve, opening inwards into the lower part of the air vessel, but kept shut by a small spring. This is shown in the separate shaded figure above the last described, and represents an improved form of the air vessel. This valve is self-acting, and effectually prevents the escape of any air or water from the air vessel; but when the water is thrown back by the shutting of the valve s, it produces an instantaneous vacuum at the end of the pipe q, upon which the shifting valve opens, and admits a sufficient quantity of the external air into the air vessel to keep it constantly replenished, and by this simple addition the water ram is hindered continuous in its action.

The cut on page 725 represents a machine for raising water, the invention of Mr. Rudolph Cabanal, engineer, of Melina-place, Westminster-road. It consists of a series of troughs fixed one above another in a frame-work, and s, inclined in contrary directions that each trough is united at one of its ends with the trough next below it, and at the other end with the trough next above it. The lower part of this frame-work forms the segment of a circle, and rests upon a horizontal plane; so that with a very slight impulse the whole machine is put into a rocking motion; the lowest trough is thereby made to dip at each oscillation into a reservoir of water, which enters the trough through valves at the bottom; these opening only upwards, the water cannot return. As the next oscillation raises the end that was before depressed, the water runs along the trough to the opposite side of the machine, where it is discharged into the depressed end of the trough above it; from this second trough it is at the next oscillation thrown into the third trough; then from the third to the fourth at the following oscillation: in like manner it ascends each trough successively by the alternate rocking of the machine, until the water is raised ana discharged at the required height.
 
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