a canton of Switzerland, bounded to the north by Swabia and the canton of Schaffhausen; to the south by the town and territory of Rappelweil and the cantons of Switz and Zug; to the east by the Thurgau, Toggenburg, and Utzach; and to the west by the three bailiages and county of Baden. It is about 65 miles from north to south, and 48 from east to west. With respect to its face, air, and soil, it is said to be an epitome of all Switzerland, as containing in its hills, valleys, plains, cornlands, vineyards, lakes, and rivers. Their wines have a tartness at first, but the longer they are kept the more agreeable they are. The other products are excellent fruits, corn, pasture, fine clay, chalk, several coloured earths, pit-coal, turf, and sulphur. There are also some mineral springs in the canton; and of the lakes, that of Zurich is the most considerable. The reformation was introduced here by Zuingleius in the year 1517. This canton is the first in rank, and inferior only to that of Bern in extent, power, and wealth; in consequence of which, its representatives preside in the general diets, when held in any place belonging in common to the cantons; and the affairs relating to the whole confederacy are transacted in its offices. Its quota, for the defence of the several members of the confederacy, is 1400 men. Of one of the two armies raised on these occasions, it nominates one of the commanders in chief, as Lucern does the other. Its revenue is said to be about 150,000 crowns a-year; of which, one year with another, two-thirds are expended in the charges of government, and the rest laid up in the treasury. It can bring 50,000 fighting men into the field at a very short warning.

capital of a canton of the same name in Switzerland, stands in a pleasant country, near where the river Aa issues from the lake that takes its name from the town, 23 miles from Schaffhausen, and 114 from Geneva. After having been ruined by Attila the Hun, it is said to have been restored by Thuricus, son of Theodoric king of the Goths, from whom it took the name of Thuricum, corrupted afterwards into that of Zurich. It is fortified in the modern way, and has wide ditches, faced with free stone. There are five arsenals in it, well stored with arms and artillery; an academy or college, having 15 professors; a museum, or chamber of rarities; a flatly town house, the pillars in the front of which are of black marble, flecked with white; and a town library. The sovereignty and administration of all affairs are lodged in the greater and lesser council, out of which are chosen the city officers, as the councils are out of the 13 companies of burghears. There are several other councils or colleges, each of which has its particular department. Here are a great variety of silk, woollen, linen, cotton, and other manufactures; this being the place of the greatest trade in all Switzerland. The town is well supplied with provisions by and from its lake. The streets are neat, and houses well built, but not magnificent. In the town library are several letters to Bullinger from lady Jane Gray daughter to the duke of Suffolk. In one of the arsenals is the figure of William Tell, dressed and armed armed in the ancient Swiss manner, with the cross-bow whence he shot the arrow that struck the apple off his child's head.

Both men and women are so fond of music, that there are few of them that cannot play on some instrument. If a burgher goes out of town, or a peasant enters it, without a sword, they are liable to be fined. No persons, whatever their rank or office may be, are exempted from the sum- mary laws. The burgomasters, who are the same as the advocates at Bern, have the title of excellence. The hospi- tals here are very neat and well endowed; but they do not affect the ridiculous vanity of lodging the poor in palaces. Not only in this town and canton, and other parts of Swit- zerland, but also among the Grisons, the ministers all preach covered. The country about the town is very pleasant and fruitful; for both which it is not a little indebted to the lake, that extends 24 miles in length, and about two or three in breadth. The water is of a green colour, suppo- sed to be owing to the melted snow that falls into it from the adjacent mountains. That part of it next Zurich is called the Lower Lake, and the other end the Upper. The cathedral, or great church here, is collegiate. The present city is said to owe its origin to a nunnery, founded by the emperor Lewis I near where the ancient Tigurum stood. E. Long. 8° 30'. N. Lat. 47° 20'.

What may be reckoned one of the greatest curiosities of Zurich is the pump invented and erected here by H. An- dras Wirtz, a temple worker of this place. The inven- tion shows him to be a person of very uncommon mecha- nical knowledge and sagacity. As it is a machine which op- erates on a principle widely different from all other hydrau- lic machines, and is really excellent in its kind, we presume that our readers will not be displeased with the account of it, although it be rather out of place here, and should have appeared in the article Water-Works.

Fig. 16. is a sketch of the section of the machine, as it was first erected by Wirtz at a dye house in Limmat, in the suburbs or vicinity of Zurich. It consists of a hollow cy- linder, like a very large grindstone, turning on a horizontal axis, and partly plunged in a cistern of water. The axis is hollow at one end, and communicates with a perpendicular pipe CBZ, part of which is hid by the cylinder. This cylinder or drum is formed into a spiral canal by a plate coiled up within it like the main spring of a watch in its box; only the spires are at a distance from each other, so as to form a conduit for the water of uniform width. This spiral partition is well joined to the two ends of the cylin- der, and no water escapes between them. The outermost turn of the spiral begins to widen about 3ths of a circum- ference from the end, and this gradual enlargement conti- nues from Q to S nearly a semicircle: this part may be called the Horn. It then widens suddenly, forming a Scoop or shovel SS'. The cylinder is supported so as to drop several inches into the water, whose surface is repre- sented by VV'.

When this cylinder is turned round its axis in the direc- tion ABEQ, as expressed by the two darts, the scoop SS' dips at V', and takes up a certain quantity of water before it emerges again at V. This quantity is sufficient to fill the taper part SQ, which we have called the Horn; and this is nearly equal in capacity to the outermost uniform spiral round.

After the scoop has emerged, the water passes along the spiral by the motion of it round the axis, and drives the air before it into the rising-pipe, where it escapes.—In the mean time, air comes in at the mouth of the scoop; and when the scoop again dips into the water, it again takes in some. Thus there is now a part filled with water and a part fil- led with air. Continuing this motion, we shall receive a second round of water and another of air. The water in any turn of the spiral will have its two ends on a level; and the air between the successive columns of water will be in its natural state; for since the passage into the rising pipe or Main is open, there is nothing to force the water and air into any other position. But since the spires gradually diminish in their length, it is plain that the column of water will gradually occupy more and more of the circumference of each. At last it will occupy a complete turn of some spiral that is near the centre; and when felt farther in, by the continuance of the motion, some of it will run back over the top of the succeeding spiral. Thus it will run over at K 4 into the right hand side of the third spiral. Therefore it will push the water of this spiral backwards, and raise its other end, so that it also will run over back- wards before the next turn be completed. And this change of disposition will at last reach the first or outermost spiral, and some water will run over into the horn and scoop, and finally into the cistern.

But as soon as water gets into the rising pipe, and rises a little in it, it stops the escape of the air when the next scoop of water is taken in. Here are now two columns of water acting against each other by hydrostatic pressure and the intervening column of air. They must compress the air between them, and the water and air columns will now be unequal. This will have a general tendency to keep the whole water back, and cause it to be higher on the left or rising side of each spire than on the right descending side. The excess of height will be just such as produces the compression of the air between that and the preceding column of water. This will go on increasing as the wa- ter mounts in the rising-pipe; for the air next to the rising- pipe is compressed at its inner end with the weight of the whole column in the main. It must be as much compressed at its outer end. This must be done by the water column without it; and this column exerts this pressure partly by reason that its outer end is higher than its inner end, and partly by the transmission of the pressure on its outer end by air, which is similarly compelled from without. And thus it will happen that each column of water, being high- er at its outer than at its inner end, compresses the air on the water-column beyond or within it, which transmits this pressure to the air beyond it, adding to it the pressure acting from its own want of level at the ends. Therefore the greatest compression, viz. that of the air next the main, is produced by the sum of all the transmitted pressures; and these are the sum of all the differences between the eleva- tions of the inner ends of the water columns above their outer ends: and the height to which the water will rise in the main will be just equal to this sum.

Draw the horizontal lines K'K r, K'K 2, K'K 3, &c. and m m, m m, m n, &c. Suppose the left hand spaces to be filled with water, and the right hand spaces to be filled with air. There is a certain gradation of compression which will keep things in this position. The spaces evidently decrease in arithmetical progression; so do the hydrostatic heights and pressures of the water columns. If therefore the air be dense in the same progression, all will be in hydrostatic equilibrium. Now this is evidently producible by the mere motion of the machine; for since the density and com- pression in each air column is supposed inversely as the bulk of the column, the absolute quantity of air is the same in all; therefore the column first taken in will pass gradually in- wards, and the increasing compression will cause it to occu- py precisely the whole right hand side of every spire. The gradual diminution of the water columns will be produced during the motion by the water running over backwards at It is evident that this disposition of the air and water will raise the water to the greatest height, because the hydrostatic height of each water column is the greatest possible, viz., the diameter of the spire. This disposition may be obtained in the following manner: Take CL to CB as the density of the external air to its density in the last column next the rising-pipe or main; that is, make CL to CB as 33 feet (the height of the column of water which balances the atmosphere), to the sum of 33 feet and the height of the rising-pipe. Then divide BI into such a number of turns, that the sum of their diameters shall be equal to the height of the main; then bring a pipe straight from L to the centre C. The reason of all this is very evident.

But when the main is very high, this construction will require a very great diameter of the drum, or many turns of a very narrow pipe. In such cases it will be much better to make the spiral in the form of a cork-screw, as in fig. 17—instead of this flat form like a watch-spring. The pipe which forms the spiral may be lapped round the frustum of a cone; whose greatest diameter is to the least (which is next to the rising pipe) in the same proportion that we assigned to CB and CL. By this construction the water will stand in every round so as to have its upper and lower surfaces tangents to the top and bottom of the spiral, and the water columns will occupy the whole attending side of the machine, while the air occupies the descending side.

This form is vastly preferable to the flat; it will allow us to employ many turns of a large pipe, and therefore produce a great elevation of a large quantity of water.

The same thing will be still better done by lapping the pipe on a cylinder, and making it taper to the end, in such a proportion that the contents of each round may be the same as when it is lapped round the cone. It will raise the water to a greater height (but with an increase of the impelling power) by the same number of turns, because the vertical or pressing height of each column is greater.

Nay, the same thing may be done in a more simple manner, by lapping a pipe of uniform bore round a cylinder. But this will require more turns, because the water columns will have less differences between the heights of their two ends. It requires a very minute investigation to show the progress of the columns of air and water in this construction, and the various changes of their arrangement, before one is attained which will continue during the working of the machine.

We have chosen for the description of the machine that construction which made its principle and manner of working most evident, namely, which contained the same material quantity of air in each turn of the spiral, more and more compressed as it approaches to the rising-pipe. We should otherwise have been obliged to investigate in great detail the gradual progress of the water, and the frequent changes of its arrangement, before we could see that one arrangement would be produced which would remain constant during the working of the machine. But this is not the best construction. We see that, in order to raise water to the height of a column of 34 feet, which balances the atmosphere, the air in the last spire is compressed into half its bulk; and the quantity of water delivered into the main at each turn is but half of what was received into the first spire, the rest flowing back from spire to spire, and being discharged at the spout.

But it may be constructed so as that the quantity of water in each spire may be the same that was received into the first; by which means a greater quantity (double in the instance now given) will be delivered into the main, and raised to the same height by very nearly the same force. Zurich.

This may be done by another proportion of the capacity of the spires, whether by a change of their caliber or of their diameters. Suppose the bore to be the same, the diameter must be made such that the constant column of water, and the column of air, compressed to the proper degree, may occupy the whole circumference. Let A be the column of water which balances the atmosphere, and b the height to which the water is to be raised. Let A be to \( \frac{A + b}{m} \) as 1 to m.

It is plain that m will represent the density of the air in the last spire, if its natural density be 1, because it is pressed by the column \( \frac{A + b}{m} \), while the common air is pressed by A. Let 1 represent the constant water column, and therefore nearly equal to the air column in the first spire. The whole circumference of the last spire must be \( \frac{1}{m} \), in order to hold the water 1, and the air compressed into the space \( \frac{1}{m} \) or \( \frac{A}{A + b} \).

The circumference of the first spire is \( \frac{1}{m} \) or 2. Let D and d be the diameters of the first and last spires; we have \( 2 : 1 + \frac{1}{m} = D : d \), or \( 2m : m + 1 = D : d \). Therefore if a pipe of uniform bore be lapped round a cone, of which D and d are the end diameters, the spirals will be very nearly such as will answer the purpose. It will not be quite exact, for the intermediate spirals will be somewhat too large. The conoidal frustum should be formed by the revolution of a curve of the logarithmic kind. But the error is very trifling.

With such a spiral, the full quantity of water which was confined in the first spiral will find room in the last, and will be sent into the main at every turn. This is a very great advantage, especially when the water is to be much raised. The saving of power by this change of contraction is always in proportion of the greatest compression of the air.

The great difficulty in the construction of any of these forms is in determining the form and position of the horn and the scoop; and on this greatly depends the performance of the machine. The following instructions will make it pretty easy.

Let A B E O (fig. 18.) represent the first or outermost round of the spiral, of which the axis is C. Suppose it immersed up to the axis in the water V V, we have seen that the machine is most effective when the surfaces K B and O n of the water columns are distant the whole diameter E O of the spiral. Therefore let the pipe be first supplied of equal caliber to the very mouth E e, which we suppose to be just about to dip into the water. The surface O n is kept there, in opposition to the pressure of the water column B A O, by the compressed air contained in the quadrant O E, and in the quadrant which lies behind E B. And this compression is supported by the columns behind, between this spire and the rising pipe. But the air in the outermost quadrant E B is in its natural state, communicating as yet with the external air. When, however, the mouth E e has come round to A, it will not have the water standing in it in the same manner, leaving the half space B E O filled with compressed air; for it took in and confined only what filled the quadrant B E. It is plain, therefore, that the quadrant B E must be so shaped as to take in and confine a much greater quantity of air; so that when it has come to A, the space B E O may contain air sufficiently dense to support the column A O. But this is not enough: For when the wide mouth, now at A e, rises up to the top, the surface of the water in it rises also, because the part A O o a is more capa- cious than the cylindric part OE eo which succeeds it, and which cannot contain all the water that it does. Since, then, the water in the spire rises above A, it will press the water back from O n to some other position m' n', and the pressing height of the water-column will be diminished by this rising on the other side of O. In short, the horn must begin to widen, not from B, but from A, and must occupy the whole semicircle ABE; and its capacity must be to the capacity of the opposite cylindrical side as the sum of BO, and the height of a column of water which balances the atmosphere to the height of that column. For then the air which filled it, when of the common density, will fill the uniform side BEO, when compressed so as to balance the vertical column BO. But even this is not enough; for it has not taken in enough of water. When it dipped into the cistern at E, it carried air down with it, and the pressure of the water in the cistern caused the water to rise into it a little way; and some water must have come over at B from the other side, which was drawing narrower. Therefore when the horn is in the position EOA, it is not full of water. Therefore when it comes into the situation OAB, it cannot be full nor balance the air on the opposite side. Some will therefore come out at O, and rise up through the water. The horn must therefore, if possible, extend at least from O to B, or occupy half the circumference; and, zephyr, it must contain at least twice as much water as would fill the side BEO. It will do little harm though it be much larger; because the surplus of air which it takes in at E will be discharged, as the end E of the horn rises from O to B, and it will leave the precise quantity that is wanted. The overplus water will be discharged as the horn comes round to dip again into the cistern. It is possible, but requires a discussion too intricate for this place, to make it of such a size and shape, that while the mouth moves from E to B, passing through O and A, the surface of the water in it shall advance from E to O n, and be exactly at O when the beginning or narrow end of the horn arrives there.

We must also secure the proper quantity of water. When the machine is too much immersed as to be up to the axis in water, the capacity which thus secures the proper quantity of air will also take in the proper quantity of water. But it may be erected so as that the spirals shall not even reach the water. In this case it will answer our purpose if we join to the end of the horn a scoop or shovel QRSB (fig. 19.), which is so formed as to take in at least as much water as will fill the horn. This is all that is wanted in the beginning of the motion along the spiral, and more than is necessary when the water has advanced to the succeeding spire; but the overplus is discharged in the way we have mentioned. At the same time, it is needless to load the machine with more water than is necessary, merely to throw it out again. We think that if the horn occupies fully more than one-half of the circumference, and contains as much as will fill the whole round, and if the scoop itself as much as will certainly fill the horn, it will do very well.

N.B. The scoop must be very open on the side next the axis, that it may not confine the air as soon as it enters the water. This would hinder it from receiving water enough.

The following dimensions of a machine erected at Florence, and whose performance corresponded extremely well with the theory, may serve as an example.

The spiral is formed on a cylinder of 10 feet diameter, and the diameter of the pipe is 6 inches. The smaller end of the horn is of the same diameter; and it occupies 2/3ths of the circumference, and it is 7 8/9ths inches wide at the outer end. Here it joins the scoop, which lifts as much water as fills the horn, which contains 4340 Swedish cubic inches, each = 1577 English. The machine makes 6 turns in a minute, and raises 1554 pounds of water, or 22 cubic feet, Zurich, 10 feet high in a minute.

The above account will, we hope, sufficiently explain the manner on which this singular hydraulic machine produces its effect. When every thing is executed by the maxims which we have deduced from its principles, we are confident that its performance will correspond to the theory; and we have the Florentine machine as a proof of this. It raises more than 2/3ths of what the theory promises, and it is not perfect. The spiral is of equal caliber, and is formed on a cylinder. The friction is so inconsiderable in this machine, that it need not be mended; but the great excellency is, that whatever imperfection there may be in the arrangement of the air and water columns, this only affects the elegance of the execution, causing the water to make a few more turns in the spiral before it can mount to the height required; but wastes no power, because the power employed is always in proportion to the sum of the vertical columns of water in the rising side of the machine; and the height to which the water is raised by it is in the very same proportion. It should be made to move very slow, that the water be not always dragged up by the pipes, which would cause more to run over from each column, and diminish the prelude of the remainder.

If the rising-pipe be made wide, and thus room be made for the air to escape freely up through the water, it will rise to the height assigned; but if it be narrow, so that the air cannot get up, it rises almost as slow as the water, and by this circumstance the water is raised to a much greater height mixed with air, and this with hardly any more power. It is in this way that we can account for the great performance of the Florentine machine, which is almost triple of what a man can do with the finest pump that ever was made; indeed the performance is so great, that one is apt to suspect some inaccuracy in the accounts. The entry into the rising-pipe should be no wider than the last part of the spiral; and it would be advisable to divide it into four channels by a thin partition, and then to make the rising-pipe very wide, and to put into it a number of slender rods, which would divide it into slender channels that would completely entangle the air among the water. This will greatly increase the height of the heterogeneous column. It is surprising that a machine that is so very promising should have attracted so little notice. We do not know of any being erected out of Switzerland except at Florence in 1778. The account of its performance was in consequence of a very public trial in 1779, and honourable declaration of its merit, by Sig. Lorenzo Ginori, who erected another, which fully equalled it. It is shortly mentioned by Professor Sulzer of Berlin, in the Sammlungen Vermischten Schriften for 1754. A description of it is published by the Philosophical Society at Zurich in 1766, and in the descriptions published by the Society in London for the encouragement of Arts in 1776. The celebrated Daniel Bernoulli has published a very accurate theory of it in the Edinburgh Commentaries for 1772; and the machines at Florence were erected according to his instructions. Baron Altromer in Sweden caused a glass model of it to be made, to exhibit the internal motions for the instruction of artists, and also ordered an operative engine to be erected; but we have not seen any account of its performance. It is a very intricate machine in its principles; and an ignorant engineer, nay the most intelligent, may erect one which shall hardly do anything; and yet, by a very trifling change, may become very powerful. We presume that failures of this kind have turned the attention of engineers from it; but we are persuaded that it may be made very effective, and we are certain that it must be very durable. Fig. 20. is a section of the manner in which the author author has formed the communication between the spiral and the rising-pipe. P is the end of the hollow axis which is united with the solid iron axis. Adjoining to P, on the under side, is the entry from the last turn of the spiral. At Q is the collar which rests on the supports, and turns round in a hole of bell-metal. ff is a broad flanch calf in one piece with the hollow part. Beyond this the pipe is turned somewhat smaller, very round and smooth, so as to fit into the mouth of the rising-pipe, like the key of a cock. This mouth has a plate ee attached to it. There is another plate dd, which is broader than ee, and is not fixed to the cylindrical part, but moves easily round it. In this plate are four screws, such as g, g, which go into holes in the plate ff, and thus draw the two plates ff and dd together, with the plate ee between them. Pieces of thin leather are put on each side of ee; and thus all escape of water is effectually prevented, with a very moderate compression and friction.