an instrument for drawing ellipses. The trammel is an instrument that has long been known and used for describing ellipses. On the principle of the trammel, Mr Farey constructed his elliptograph in a form much more commodious for drawing. Mr Farey's elliptograph is represented at fig. 5. Plate LXXIX. The circle A slides between the two parallel rulers D E. The circle B slides between two parallel rulers F G, at right angles to the former. In this way, if a line, joining the centres of the circles, is made to revolve, M, the extremity of that line, will describe an ellipse in the same manner, as the extremity E of the line C D E, fig. 1, does in the trammel. The elliptograph may be considered as a trammel, in which the pins C and D, fig. 1, are enlarged into the circles A and B, fig. 5. The pinion at K, fixed to one of the arms of the lower circle, acting on a rack screwed to the upper circle, serves to alter the distance of the centres of the circles A and B, and, by so doing, this pinion serves to vary the eccentricity of the ellipses which the instrument describes. When the centres of the circles A B coincide, the describing pen M draws a circle. When the centres are removed from each other, and on the circles being turned round, an ellipse is described by the pen; and when the distance of the centres is increased, the eccentricity of the ellipse is increased. When the pen is at the centre it describes a straight line, continually moving to and fro on that line when the circles are turned round. The two circles are fixed together by screws, and can only be made to slide the upper circle over the lower by the action of the pinion K. The pinion at L moves a rack, by which the describing pen M, which draws the ellipse, is brought nearer to the centre, for the purpose of drawing a small ellipse; and removed farther from the centre of the ellipse, when a large one is to be drawn. The size of the ellipse may be increased as far as the size of the instrument will admit. The pair of rulers D E are placed below the pair F G, as is seen in fig. 6. The instrument, when used, is held upon the paper with the thumb and a finger of the left hand at the nuts N O, and the circles are moved by applying the right hand to the pins f, the pen M, pressing by its weight on the paper, then describes the ellipse.

Fig. 7 shows H the socket for the compasses, with the centre pin on which the socket moves; and the pinion L and rack h for moving along the frame g between the bars; and the other pinion K for separating the circles.

The ruler P has two points to fix the instrument to the paper. The ruler is united to the frame by screws, which serve to adjust the position of the instrument after the ruler has been fixed to the paper.

By means of the elliptograph, any ellipse can be described, of which the long and short axis are given, provided it does not exceed the size of the instrument. When an ellipse is to be described, draw on the paper the longer and shorter axis, bisecting each other; place the instrument on the paper so that the centre of the four rulers appears to coincide with the centre or the intersection of the two axes of the ellipse; fix the instrument in this situation by the points that go into the paper: by the pinion L move the pen to one extremity of the short axis of the ellipse; turn the circles half round to see if the pen comes to the other end of the short axis; if it does not, adjust the error one-half, by moving the pen by the pinion L, the other half by moving the frame on the paper; continue this adjustment till the pen, setting out from the one end of the short axis, arrives in a half revolution at the other end. Next, by means of the pinion K, bring the pen to one end of the long axis of the ellipse; turn the circles half round, and if the pen reaches the other extremity of the long axis of the ellipse, the instrument is rectified; if not one half of the error is to be corrected by moving the circles by the pinion K, and the other half by moving the instrument to a side on the paper by means of the nuts N, O. The instrument is now adjusted, and the pen resting on the paper traces the ellipse required when the circles are turned round by the handles.

An instrument similar to the elliptograph has been employed for engraving ellipses on copper plates, for Engraving and for dividing these ellipses accurately, so as to give the perspective representation of a circle divided into equal parts, both in the case where the distance of the eye is limited, and in the orthographic projection. The Society for Encouraging Arts rewarded Mr Farey with their gold medal for his invention, and a description of the elliptograph is contained in the thirty-first volume of the Transactions of that Society.

EMBANKMENT, a mound, or wall of earth, or other materials, used as a defence against the inundations of rivers, or the extraordinary flux of the sea.

The great value of alluvial soil to the agriculturist, no doubt, gave rise to the invention of banks, or other barriers, to protect such soils from the overflowing of their accompanying rivers. The civilized nations of the highest antiquity were chiefly inhabitants of vallies and alluvial plains; the soil, moisture, and warmth of which, by enlarging the parts, and ameliorating the fruits of the vegetable kingdom, afforded to man better nourishment, at less labour than could be obtained in hilly districts. The country of Paradise, and around Babylon, was flat, and the soil a saponaceous clay, occasionally overflowed by the Euphrates. The inhabited part of Egypt was also entirely of this description. Historians inform us, that embankments were first used by the Babylonians and Egyptians, very little by the Greeks, and a good deal by the Romans, who embarked the Tiber near Rome, and the Po for many stadia from its embouchure. The latter is perhaps one of the most singular cases of embankment in the world.

The oldest embankment in England is that of Romney Marsh, as to the origin of which, Dugdale remarks: "that there is no testimony left to us from any record or historian." (History of Embanking and Draining.) It is conjectured to have been the work of the Romans, as well as the banks on each side of the Thames, for several miles above London, which protect from floods and spring tides, several thousand acres of the richest garden ground in the neighbourhood of the metropolis.

The commencement of modern embankments in England took place about the middle of the seventeenth century, under Cromwell. In the space of a few years previously to 1651, 425,000 acres of fens, morasses, or overflowed muddy lands, were recovered in Lincolnshire, Cambridgeshire, Hampshire, and Kent; and let at from 2s. 6d. to 30s. an acre. (Harte's Essays, p. 54, 2d edit.) Vermuyden, a Fleming by birth, and a colonel of horse under Cromwell, who had served in Germany during the thirty years war, was the principal undertaker of these works. The works of this sort constructed in our own times will be found described in the Agricultural Reports of the maritime counties, especially of Lincolnshire, by Arthur Young.

Previous to entering on the detail of the different descriptions of banks for the purpose of embanking, we shall here observe, that the pressure of still water against the sides of the vessel containing it, being as its depth, it follows, that a bank of any material whatever, impervious to water, whose section is a right angled triangle, and the height of whose perpendicular side is equal to that of the water it is to dam in, will balance or resist this water, whatever may be the breadth of the surface of the latter; and, therefore, that as far as width or extent is concerned, it is just as easy to exclude the Atlantic Ocean as a lake or a river of a few yards in width.

1. THE EARTHEN WALL (fig. 1. Plate LXXIX.) is the simplest description of embankment, and is frequently erected by temporary occupiers of lands on the general principle of enclosing and subdividing, which is sometimes made a condition of tenure between the landlord and tenant. This wall applies to lands occasionally, but rarely overflowed, or inundated; and is set out in a direction generally parallel to the river or shore. Its base is commenced on the surface from two to five feet wide, regularly built of turf on the outsides, with the grassy sides underneath. The middle of the wall is filled up with loose earth. The wall is carried up with the sides bevelled towards the centre, so as to finish in a width of one foot or eighteen inches at five or six feet in height. In the inside of such walls, and at the distance of three or four feet, a small open drain is formed, as well to collect the surface water of the grounds within, as that which, in time of floods, will necessarily oose through a wall of this construction. The water so collected is let through the wall by tubes, or tunnels of boards, with a valve opening outwards on their exterior extremity. Such a tube and valve is represented by fig. 2. When the flow of water from without approaches, it shuts the valve, which remains in this state till the flood subsides, when the height of the water within being greater than that without, it presses open the valve and escapes. Walls and valves of this kind were erected about the year 1800, on the estate of the Earl of Galloway near Wigton by Mr Hannah, tenant for life of Cue farm; and by Mr Hutchinson, tenant for thirty years of Merscheid farm, on the Solway Firth. (Farmer's Magazine.) They are common enough in the drier parts of the feney districts of Lincolnshire and Cambridgeshire; and in Caernarvonshire 1800 acres were, in 1804, completely protected in this way on the estate of Tre Madoc by the proprietor, who has since made greater efforts in embanking, to be afterwards described.

2. THE EARTHEN MOUND (fig. 3.) is the most general description of embankment, and as it is executed at considerable expence, is only undertaken by such as have a permanent interest in the soil. This barrier applies to sea lands overflowed by every spring tide, and to alluvial plains inundated by every flood. It is set out in a direction parallel to the shore, and to the general turns of the river, but not to its minute windings; and it is placed farther from or nearer to the latter, according to the quantity of water in time of floods, the rapidity of the current from the declivity of the bed, the straight course of the stream, and the intended height of the bank. The two sides of such a mound are generally formed in different slopes. That towards the land is always the most abrupt, but can never be secure if more so than 45°; that towards the water varies from 45° to 15°; the power of the bank to resist the weight of the water, as well as to break its force when in motion, being inversely as its steepness. The power of water to lessen the gravity of bodies, or, in other words, to loosen the surfaces over which they flow or stand, is also lessened in a ratio somewhat similar.

The formation of such a mound consists merely in taking earth from the general surface of the ground to be protected, or from a collateral excavation, distant at least the width of the mound from its base line, and heaping it up in the desired form. The surface is then in general cases covered with turf, well rolled in order to bind it to the loose earth. The earth of such mounds is generally wheeled by barrows; but sometimes it is led by carts placed on a wooden roller instead of wheels, which, with the treading of the horses, serves in some degree to consolidate the bank.

The excavation within serves the same purpose as the open drain in the earthen wall, and similarly constructed sluices or valves are introduced on a larger scale. Sometimes also the interior water is drawn off by windmills, and thrown over the mound into the river. This is very common in Huntingdonshire, and might be greatly improved on by employing steam-engines for entire districts, one of which, of a ten horse power, would do the work of twenty mills, and this in calm weather, when the latter cannot move.

Embankments of this description are the most universal of any, and their sections vary from a scalene triangle of ten feet in base, and three feet in height, as on the Forth near Stirling, and the Thames at Fulham, to a base of 100 feet, and a height of ten feet, as in the great bank of the Ouse, near Wisbeach. The great rivers of Germany and Holland are embanked in this way, when so far from the sea as to be out of the reach of the tide; as the Vistula at Marienwerder, the banks of which, near Dantzig, are above fifteen feet in height; the Oder, the Elbe, &c. All these banks are closely covered in every part with a grassy surface, and sometimes ornamented with rows of trees.

But, near the sea, where such banks are washed by every tide when the course of the wind is towards the shore, and by all land floods and spring-tides, grass is only to be found on and near their summits. The rest of the bank is bare, and to preserve it from the action of waves, currents, and the stones, pieces of wood, and other foreign matters which they carry with them, the surface is covered with gravel, reeds, or straw, kept down by pieces of wood; faggots, wicker hurdles, nets of straw-ropes, or any other contrivance, according to the situation, to prevent the washing away of the bank. It is common to attribute to these coverings the power of breaking the force of the waves; but this power depends, as we have already stated, on the slope of the bank and its smoothness; and the use of the surface covering, and of the constant attention required to remove all obstacles which may be left on it by floods and tides, is to prevent the loosening power of the water from wearing it into holes. For this purpose, a sheet of canvass or straw-netting is as good, whilst it lasts, as a covering of plate-iron or stone pavement.

All banks whatever require to be constantly watched in time of floods or spring-tides, in order to remove every object, excepting sand or mud, which may be left by the water. Such objects, put in motion by the water, in a short time wear out large holes. These holes, presenting abrupt points to the stream, act as obstructions, soon become much larger, and if not immediately filled up, turfed over, and the turfs pinned down, or the new turfs rendered by some other means not easily softened and raised up by the water, will end in a breach of the bank. A similar effect is produced by a surface formed of unequal degrees of hardness and durability. The banks of this description in Holland, at Cuxhaven, and along the coast of Lincolnshire, are regularly watched throughout the year; the surface protection is repaired whenever it goes out of repair; as is the body of the bank in the summer season.

Mound with Puddle-Wall.—It generally happens that the earth of such banks is alluvial, and their foundation of the same description; but there are some cases where the basis is sand, silt, or gravel; or a mud or black earth, as in some parts of Cambridgeshire and Lincolnshire, which does not easily become so compact. Here it is common, before beginning the bank, to bring up what is called a puddle-ditch, or section of clay, in the centre of the highest part of the mound in the direction of its length, and of three or five feet wide, according to the depth of the silt and the intended height of the bank. When the clay of this puddle-ditch is well worked, either by men's feet or clay rammers, the bank will be perfectly impervious to water, and if against a mild stream or shore, need not contain such an accumulation of earth as where the imperviousness of the bank to water depends chiefly on the mass of materials. An important point to attend to in this variety of mound is, to found the section, or wall of clay, so deep as to be in contact with a stratum either by induration, or its argillaceous nature, impervious to water.

Mounds with reversed slopes, (fig. 4.)—In some cases of embanking rivers, as where they pass through parks, it is desirable to conceal, as much as possible, the appearance of a bank from the protected grounds, less able to break the force of waves. Here the mound is simply reversed, the steepest side being placed next the water. It is proper to observe, that such banks are not so strong by the difference of the weight of the triangle of water which would rest on the prolonged slope, were it placed next the river, and are more liable to be deranged in surface in proportion to the difference of the slopes.

Mound faced with stones.—This is the same species of mound, with a slope next the water of forty-five or fifty degrees, paved or causewayed with stones or timber. In Holland this pavement or causeway is often formed of planking or bricks; but in England generally with stones, and the mortar used is either some cement which will set under water, or, what is better, plants of moss firmly rammed between them. The objection to such banks are their expence, and their liability to be undermined invisibly by the admission of the water through crevices, &c. They are, therefore, chiefly used where there is little room, or where it is desirable to narrow and deepen the course of a river.

Mound protected by a wicker hedge.—This is a Dutch practice, and, where appearance is no object, has the advantage of not requiring watching. Wicker-work, however, subjected to the strain of waves, will be obviously less durable than where it lies flat on the ground, and can only decay chemically. This wicker hedge is sometimes a series of hurdles supported by posts and struts; but generally in Britain it is a dead hedge or row of stalks wattled or wrought with bushes presenting their spray to the sea or river. Besides placing such a hedge before a bank, others are sometimes placed in parallel rows on its surface; the object of which is to entrap sand, shells, and sea-weeds, to increase the mass of mound, or to collect shells for the purpose of carrying away as manure.

The sea wall (fig. 5.) is an embankment formed to protect abrupt and earthy shores or banks of rivers, and consists of a wall, varying in thickness, and in the inclination of its surface, according to the required height and other circumstances. Belidor in his Traité de Hydraulique, has given the exact curve which the section of such a wall ought to have, in order to resist loose earth, and which is somewhat greater than what we have given in the figure referred to, where the earth behind the wall is supposed to be chiefly firm. Some fine examples of such walls, for other purposes, occur in the CALEDONIAN CANAL, and perhaps the finest in the world are the granite walls which embank the Neva at Petersburg, the construction of which may serve as an example of a river case with a foundation of soft bog earth. A space of the river, say 100 feet long, and 20 wide along shore, being inclosed by a double row of piles, and filled in with loam in the usual way, the water is pumped out, and the ground excavated about ten feet deeper than the margin of the bed of the river. Poles are then inserted nearly as close as they can be put in, and driven to their full length. When finished this foundation occupies a breadth of from 12 to 18 feet, generally 15. The tops of the piles are now cut level, and covered with planks, and on this is raised a mass of brick-work for five or six feet, sloping on both sides as it ascends towards the centre line of the wall. In the course of rising six or seven feet, it is narrowed to five feet, and is within five feet of the bed of the margin of the river. Here the granite facing begins in immense blocks, and is continued at a slope of 15° from the perpendicular till it reaches the surface of the intended pathway. Here the wall from three feet is narrowed to an upright parapet, eighteen inches wide; and at four feet of height it is finished in a projecting coping of Finnish granite. The voids on each side of the wall are now filled with earth, the pavement on the land side (generally narrow) completed, and the piles removed, and another length taken in to repeat the operation.

There is another mode, adopted in Petersburg, of building under water by driving the piles and cutting them over level with a machine, and then sinking caissons of brick-work. This mode, however, is unsuitable for sea walls in general, which ought to be founded as deep as possible, and, at all events, under the bed of the water. The motion of the Neva is so slow as hardly to render this worth attending to.

In Britain, such walls are fortunately rare; for in proportion as it is agreeable and flattering to self-love to protect or gain lands never before cultivated, it must be mortifying to be obliged to protect such as have long been subjected to agriculture, and where success can only be said to have a negative advantage.

Embankments for fixing Drifting-sands, Shells, or Mud.—In several tracts of coast, the sea at ordinary tides barely covers a surface of sand; and these sands in dry weather, during high winds, are drifted and blown about in all directions. Great part of the north shores of the Solway Frith, of Lancaster Bay, and of the coast of Norfolk, is of this description. Mr Young, in his Farmer's Letters, informs us, that a considerable part of the county of Norfolk was drift-sand, even as far inland as Brandon in Suffolk, before the introduction of the turnip culture; and Harte (Essay I.) states, that some of what is now the richest land in Holland, was, about the middle of the sixteenth century, of this description. The suggestion of any mode, therefore, by which, at a moderate expence, such tracts could be fixed, and covered with vegetation, must be deemed worthy of a place in this article.

The mode which nature herself employs is as follows: After the tides and wind have raised a marginal strip of sand as high as high water mark, it becomes by degrees covered with vegetation, and chiefly by the Elymus arenarius, Triticum juncceum, various species of Juncus, and sometimes by the Galium verum. With the exception of the first of these plants (the leaves and stalks of which are manufactured into mats and ropes in Anglesea, and the grain of which is ground and used as meal in Ireland), they are of no other use than fixing the sands, which, being composed in great part of the debris of shells, expand as they decay, and contribute to raising the surface still higher, when the fibrous roots of good grasses soon destroy the others.

To assist nature in fixing drift-sands, it is only necessary to transplant the Elymus, which is to be had in abundance in almost every sandy coast in Britain; and as it would be liable to be blown away with the sands, if merely inserted in the common way, it seems advisable to tie the plants to the upper ends of willow or elder rods, of two or three feet in length, and to insert these in the sand, by which means there is the double chance of the grass growing, and the truncheon taking root. The elder will grow exposed to the sea breeze, and no plant throws out so many and such vigorous roots in proportion to its shoots.

The mode by which such sands were fixed in Holland was by the formation of wicker work embankments, and by sticking in the sands branches of trees, bushes, furze, &c. in all directions. These obstructed the motion of the sands, and collected masses of sand, shells or mud, and sea-weeds around them, which were immediately planted with some description of creeping grass; or, what was more frequent, covered with a thin coating of clay, or alluvial earth, and sown with clover.

Though the most certain and least expensive mode of gaining such lands be undoubtedly that of seconding the efforts of nature, by inserting bushes, and planting the Elymus in this way, yet it may sometimes be desirable to make a grand effort to protect an extensive surface, by forming a bank of branches, which might, in a single or in several tides, be filled with sand and shells. It is evident, that such a bank might be constructed in various ways; but that which would be most certain of remaining firm, and effecting the purpose, would be one regularly constructed of framed timber, the section of which would resemble a trussed roof; each truss being joined in the direction of the bank by rafters, and the whole inside and surface stuck full of branches. To retain it firm, piles would require to be driven into the sand, to the upper parts of which would be attached the trusses. The height of such a barrier would require to be several feet above that of the highest spring-tides; and the more its width at base exceeded the proportion of that of an equilateral triangle the better.

A more economical mode, and one, therefore, suited to a less extensive scale of operation, is to intersect a sandy shore in all directions, with common dead, or wicker work hedges, formed by first driving a row of stakes six or eight feet into the ground, leaving their tops three or four feet above it, and then weaving among these stakes, branches of trees, or the tops of hedges. The Dutch are said to weave straw ropes, and thereby to collect mud in the manner of warping. This mode being little expensive, seems to deserve a trial in favourable situations; and, in so doing, it must not be forgotten, that much depends on the immediate management of the surface, after it is in some degree fixed. In an extensive trial of this sort at present in progress, on the west coast of Scotland, under an English gentleman, seeds and roots are baked in a mixture of loam and dung in the gravel, and then formed into masses, and scattered over a sandy surface. These, from their weight, will not, it is thought, be moved by the water or the wind; but becoming more or less covered with sand, the mass will be kept moist, and the seeds and roots will grow, and, fixing themselves in the soil, will in time cover the surface with verdure. The experiment is ingenious, and we hope will be crowned with success.

Embankments for straightening the Course of Rivers.—Where a river in a fertile valley is very circuitous in its course, land may be gained, and a more rapid efflux of the water produced, by straightening its course. The best plan in general for effecting this is, to find an entirely new bed or course for the river; otherwise, when it passes alternately through new soil, and through a part of its old bed, its action on surfaces which are so different in regard to induration ends, if great care is not taken, in holes and gulleys in the new bank, which require to be constantly filled up with loose stones thrown in, and left to be fixed by the pressure and motion of the water.

The embankment used in straightening the course of rivers is almost always the mound, with a clay wall in the centre, varying in width according to the depth of the different parts of the old bed of the river which it has to intersect. The materials for these banks are obtained from excavations for the new bed.

The pier, called the Protecting Pier, is to be considered as a species of embankment, whose object is to prevent the increase of partial breaches made in the banks of rivers, by accidental obstructions during floods. A tree or branch carried down by a stream, and deposited, or accidentally fixed or retained in its banks, will repel that part of the stream which strikes against it, and the impulse (counteracted more or less by the general current) will direct a substream against the opposite bank. The effect of this continual action against one point of the opposite bank is, to wear out a hole or breach; and the protecting pier is placed so as to receive the impulse of the substream, and reverberate it to the middle of the general stream. If this pier is not placed very obliquely to the substream, as well as to the general stream, it will prove injurious to the opposite bank, by directing a subcurrent there as great as the first; and, indeed, it is next to impossible to avoid this; so much so, that Mr Smeaton, in every instance in which he was consulted in cases of this sort, recommended removing the obstacle where that could be done, and then throwing loose stones into the breach. A perfect bed of a river would be a perfect half cylinder, and therefore we are decidedly of opinion that Mr Smeaton's mode is the best, as tending to maintain, as much as possible, this form. Mr Marshal (Treatise on Landed Property) has treated on piers of this description at considerable length; but a very little reflection will show, that they are more likely to increase than to remedy the evil they are intended to cure. We have seen the injurious effects of such piers on the Tay and the Dee, and on a part of the Jed near Crailing they are so numerous, that the stream is, to use a familiar phrase, bandied about like a football, from one shore to the other; behind every pier an eddy is formed, and if the stream does not strike it exactly, a breach in the bank. Many of these piers have, in consequence, been taken down.

The use of such piers can only be justified where the obstruction, from ill-neighbourhood or some such cause, cannot be removed from the opposite bank; or where, as is sometimes the case, it arises from an island of sand or gravel thrown out by the river near its middle, and which, however absurd it may appear, the interested parties cannot agree as to who may remove it. The case of buildings also being in danger may justify such a pier for immediate protection; but, if such breaches are taken in time, a few loads of loose stones will effect a remedy without the risk of incurring or occasioning a greater evil.

Such piers are frequently constructed of wicker work; either a mere wicker hedge projecting into the water, as is common where the rivers are of slow motion,—as in England, and particularly on the Thames, Tame, and Severn; or a case of wicker work filled with stones, as is common where the motion is rapid,—as in Scotland, and particularly on the Esk, Tweed, Tay, and Clyde.

Embankments to serve as Roads are generally mounds without clay walls, carried through countries liable to be overflowed, without reference to protecting any part from water, through lakes or marshes, or across straight of the sea, &c. The earth, in such mounds, is generally allowed to take its own slope on both sides, which is commonly from 40° to 45°, and the width at top is regulated by that of the intended road. The materials, when the mound is formed in a country merely liable to be overflowed, as in many parts of Lincolnshire and Huntingdonshire, are excavated from ditches, or taken from the surface on each side of the mound. In Holland, the roads formed on such mounds are bounded by rows of trees; a practice which, it is to be regretted, has not been more attended to in England, where accidents not unfrequently happen in the night, and particularly on the Boston and Wisbeach roads; both of which are formed in great part on such mounds, unprotected by hedges, rails, or trees. In passing through part of a lake, or strait, or marsh, the earth must, of course, be taken from the firm ground on the shores; and here the ground being generally soft below, the first operation is to lay a foundation, three or four feet thick, of branches or faggots of copeswood, in order that the mound may sink in a body. The next thing, the direction of the mound being marked out by a line of poles placed along its centre, is to begin at one end, and wheel, or cart on earth, throwing it down in the direction of the bank, and raising it to its proper height and width; leaving the slopes at the sides to

PLATE LXXIX.

Fig. 1. Fig. 2. Fig. 3. Fig. 4. Fig. 5. Fig. 6. Fig. 7.