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which are close on all sides. A tube AB, having a funnel at the top, passes through the uppermost vessel without commu-nicating with it, being soldered into its top and bottom. It also passes through the top of the under vessel, where it is likewise soldered, and reaches almost to its bottom. This tube is open at both ends. There is another open tube ST, which is soldered into the top of the under vessel and the bottom of the upper vessel, and reaches almost to its top. These two tubes serve also to support the upper vessel. A third tube GF is soldered into the top of the upper vessel, and reaches almost to its bottom. This tube is open at both ends, but the orifice G is very small. Now suppose the uppermost vessel filled with water to the height EN, Ee being its surface a little below T. Stop the orifice G with the finger, and pour in water at A. This will descend through AB, and compress the air in OQRP into less room. Suppose the water in the under vessel to have acquired the surface cc, the air which formerly occupied the whole of the spaces OPOR and KLEE will now be contained in the spaces OPCC and KLEE; and its elasticity will be in equilibrio with the weight of the column of water whose base is the surface Ee, and whose height is Ac. As this pressure is exerted in every part of the air, it will be exerted on the surface Ee of the water of the upper vessel; and if the pipe FG were continued upwards, the water would be supported in it to a height en above Ee, equal to Ac. Therefore, if the finger be now taken from off the orifice G, the fluid will spout up through it to the same height as if it had fallen through a tube whose altitude is en. So long as there is any water in the vessel KLN M there will be a discharge through the orifice: therefore the play of the fountain will continue whilst the water contained in the upper vessel, having spouted out, falls down through the pipe AB: the height of the water measured from the basin VAW to the surface of the water in the lower vessel OPQR is always equal to the height measured from the top of the jet to the surface of the water in the vessel KLMN. Now, since the surface Ee is always falling, and the water in the lower vessel always rising, the height of the jet must continually decrease, till it is shorter by the depth of KLMN, which is empty, added to the depth of OPOR, which is always filling; and when the jet is fallen so low it immediately ceases to play.

7. A machine designed to raise water to a great height for the irrigation of land, in such situations as have the advantage of a small fall, is described in Dr. Darwin's Phytologia: as it depends on the principle of Hero's fountain, it may properly be inserted here.

Fig. 4. pl. XIX. a, b, is the stream of water.

b, c, c, represents the water-fall, supposed to be 10 feet. d, e, are two leaden or iron vessels, containing a certain quantity of water, which may be computed to be about 4 gallons each.

f, g, h, i, k, l, are leaden vessels, each holding about two quarts.

o, p, two cocks, each of which passes through two pipes, opening the one and closing the other.

-q, r, is a water-balance, that moves on its centre s; and by which the two cocks o and p are alternately turned.

t, u, and w, x, are two air-pipes of lead, both internally one inch and a quarter in diameter.

`Y, z ; y, z ; Y, z; are water-pipes, each being one inch in diameter.

up

The pipe b, e, c, is always full from the stream a, b: the small cisterns g, i, l, and the large one d, are supposed to have been previously filled with water. The fluid may then be admitted by turning the cock o, through the pipe c, e, into the large cistern e. This water will press the air confined in the cistern e, the air-pipe w, x, and will force the fluid out of the cisterns g, i, l, into those marked h, k, and c.-At the same time, by opening B, the water and condensed air, which previously existed in the large cistern d, and in the smaller ones marked f, h, k, will be discharged at B.-After a short time, the waterbalance, q, r, s, will turn the cocks, and exclude the water, while it opens the opposite ones; the cisterns f, h, k, are emptied in their turns by the condensed air from the cistern d, as the water progressively enters the latter from the pipe b, c.

8. A very ingenious application of the same principle has been made in the celebrated Hungarian machine, at Chemnitz. The best account we have been able to obtain of this is the following.

In fig. 3. pl. XVIII. A represents the source of water elevated 136 feet above the mouth of the pit. From this there runs down a pipe D of four inches diameter, which enters the top of a copper cylinder B, 8 feet high, 5 feet diameter, and 2 inches thick, and reaches to within 4 inches of the bottom: it has a cock at I.*

This cylinder has a cock at g, and a very large one at N. From its top proceeds a pipe v EC two inches in diameter, which goes 96 feet down the pit, and is inserted into the top of another brass cylinder c*, which is 6 feet high, 4 feet diameter, and

In the figure these vessels are in form of parallelopipeds, and there are some pipes and cocks which are not referred to in this description: but this happens, because one diagram is made to serve for both the original machine, and Mr. Boswell's improvements mentioned directly after.

two inches thick: the latter containing about 83 cubic feet, which is nearly one half of the capacity of the former, viz. 170 cubic feet. There is another pipe ro of 4 inches diameter, which rises from within 4 inches of the bottom of this lower eylinder, is soldered into its top, and rises to the trough z which carries off the water from the mouth of the pit. This lower cylinder communicates at the bottom with the water o, which collects in the drains of the mines. A large cock p serves to exclude or admit this water: another cock m at the top of this cylinder communicates with the external air.

Now, suppose the cock I shut, and all the rest open: the upper cylinder will contain air, and the lower cylinder will be filled with water, because it is sunk so deep that its top is below the usual surface of the mine-waters. Shut the cocks g, N, M, P, and open the cock 1. The water of the source a must run in by the orifice J, and rise in the upper cylinder, compressing the air above it and along the pipe VEC, and thus acting on the surface of the water in the lower cylinder. It will therefore cause it to rise gradually in the pipe OF, where it will always be of such a height that its weight balances the elasticity of the compressed air. Suppose no issue given to the air from the upper cylinder, it would be compressed into one-fifth of its bulk by the column of 136 feet high; for a column of 34 feet nearly balances the ordinary elasticity of the air. Therefore, when there is an issue given to it through the pipe VEC, it will drive the compressed air along this pipe, and it will expel water from the lower cylinder. When the upper cylinder is full of water, there will be 34 cubic feet of water expelled from the lower cylinder. If the pipe or had been more than 136 feet long, the water would have risen 136 feet, being then in equilibrio with the water in the feeding pipe n by the intervention of the elastic air; but no more water would have been expelled from the lower cylinder than what fills this pipe. But the pipe being only 96 feet high, the water will be thrown out at z with a considerable velocity. If it were not for the great obstructions which water and air must meet with in their passage along pipes, it would issue at z with a velocity of more than fifty feet per second. It issues however much more slowly, and at last the upper cylinder is full of water, and the water would enter the pipe VE and enter the lower cylinder, and, without displacing the air in it, would rise through the discharging pipe OP, and run off to waste. To prevent this there hangs in the pipe VE a cork ball or double cone, by a brass wire which is guided by holes in two cross pieces in that pipe. When the upper cylinder is filled with water, this cork plugs up the orifice V, and no water is wasted; the influx at J now stops. But the lower

cylinder contains compressed air, which would balance water in a discharging pipe 136 feet high, whereas op is only 96. Therefore the water will continue to flow at z till the air has so far expanded as to balance only 96 feet of water, that is, till it occupies one-half of its ordinary bulk, that is, one-fourth of the capacity of the upper cylinder, or 42 cubic feet. Therefore 42 cubic feet will be expelled, and the efflux at z will cease; and the lower cylinder is about one-half full of water. When the attending work man observes this, he shuts the cock 1. He might have done this before, had he known when the orifice v was stopped; but no loss ensues from the delay. At the same time the attendant opens the cock N the water issues with great violence, being pressed by the condensed air from the lower cylinder. It therefore issues with the sum of its own weight and of this compression. These gradually decrease together, by the efflux of the water and the expansion of the air; but this efflux stops before all the water has flowed out; for there are 42 feet of the lower cylinder occupied by air. This quantity of water remains, therefore, in the upper cylinder nearly: the workman knows this, because the discharged water is received first of all into a vessel containing three-fourths of the capacity of the upper cylinder. Whenever this is filled, the attendant opens the cock p by a long rod which goes down the shaft; this allows the water of the mine to fill the lower cylinder, and the air to get into the upper cylinder, which permits the remaining water to run out of it. Thus every thing is brought into its first condition; and when the attendant sees no more water come out at N, he shuts the cocks N and M, and opens the cock 1, and the operation is repeated.

There is a very surprising appearance in the working of this engine. When the efflux at z has stopped, if the cock o be opened, the water and air rush out together with prodigious violence, and the drops of water are changed into hail or lumps of ice. It is a sight usually shown to strangers, who are desired to hold their hats to receive the blasts of air: the ice comes out with such violence as frequently to pierce the hat like a pistol bullet. This rapid congelation is a remarkable instance of the general fact, that air by suddenly expanding generates cold, its capacity for heat being increased.

The above account of the procedure in working this engine shows that the efflux both at z and N becomes very slow near the end. It is found convenient therefore not to wait for the complete discharges, but to turn the cocks when about 30 cubic feet of water have been discharged at z: more work is done in this way. A gentleman of great accuracy and knowledge of these subject took the trouble of noticing particularly the per

formance of the machine. He observed that each stroke, as it may be called, took up about three minutes and one-eighth; and that 32 cubic feet of water were discharged at z, and 66 were expended at N. The expence therefore is 66 feet of water falling 136 feet, and the performance is 32 raised 96, and they are in the proportion of 66 × 136 to 32 x 96, or of 1 to 0.3422, or nearly as 3 to 1. This is superior to the performance of the most perfect undershot mill, even when all friction and irregu lar obstructions are neglected; and is not much inferior to any overshot pump-mill that has yet been erected. When we reflect on the great obstructions which water meets with in its passage through long pipes, we may be assured that, by doubling the size of the feeder and discharger, the performance of the machine will be greatly improved; we do not hesitate to say, that it would be increased one-third: it is true that it will expend more water; but this will not be nearly in the same proportion, for most of the deficiency of the machine arises from the needless velocity of the first efflux at z. The discharging pipe ought to be 110 feet high, and not give sensibly less water. Then it must be considered how inferior in original expense this simple machine must be to a mill of any kind which would raise 10 cubic feet 96 feet high in a minute, and how small the repairs on it need be, when compared with a mill. And, lastly, let it be noticed that such a machine can be used where no mill whatever can be put in motion. A small stream of water, which would not move any kind of wheel, will here raise one-third of its own quantity to the same height; working as fast as it is supplied.

For these reasons, we think that the Hungarian machine eminently deserves the attention of mathematicians and engineers, to bring it to its utmost perfection, and into general use. There are situations where this kind of machine may be very useful. Thus, where the tide rises 17 feet, it may be used for compressing air to seven-eighths of its bulk; and a pipe leading from a very large vessel inverted in it may be used for raising the water from a vessel of one-eighth of its capacity 17 feet high; or if this vessel has only one-tenth of the capacity of the large one set in the tide-way, two pipes may be led from it; one into the small vessel, and the other into an equal vessel 16 feet higher, which receives the water from the first. Thus one-sixteenth of the water may be raised 34 feet, and a smaller quantity to a still greater height; and this with a kind of power that can hardly be applied any other way. Machines of this kind are described by Schottus, Sturmius, Leupold, and other old writers; and they should not be forgotten, because opportunities may offer of making them highly beneficial.