in Ancient Geography, a town of Boeotia, to the west of Thebes, or lying between Plateae and Thebe, where the Lacedemonians had a great defeat given them by Epaminondas and Pelopidas, the Theban generals. The Theban army consisted at most but of 6000 men, whereas that of the enemy was at least thrice that number; but Epaminondas trusted most in his horse, wherein he had much the advantage, both in their quality and good management; the rest he endeavoured to supply by the disposition of his men, and the vigour of the attack. He even refused to suffer any to serve under him in the engagement, but such as he knew to be fully resolved to conquer or die. He put himself at the head of the left wing, opposite to Cleombrotus king of Sparta, and placed the main streets of the battle there; rightly concluding, that if he could break the body of the Spartans, which was but 12 men deep, whereas his own was 50, the rest would be soon put to flight. He closed his own with the sacred band, which was commanded by Pelopidas; and placed his horse in the front. His right, from which he had drawn so many men, he ordered to fall back, in a slanting line, as if they declined to fight, that they might not be too much exposed to the enemy, and might serve him for a corps of reserve in case of need. This was the wise disposition which the two Theban generals made of these few but resolute forces; and which succeeded in every part, according to their wish. Epaminondas advanced with his left wing, extending it obliquely, in order to draw the enemy's right from the main body; and Pelopidas charged them with such desperate speed and fury, at the head of his battalion, before they could reunite, that their horse, not being able to stand the shock, were forced back upon their infantry, which threw the whole into the greatest confusion; so, that though the Spartans were of all the Greeks the most expert in recovering from any surprise, yet their skill on this occasion either failed them or proved of no effect; for the Thebans, observing the dreadful impression they had made on them with their horse, pushed furiously upon the Spartan king, and opened their way to him with a great slaughter.

Upon the death of Cleombrotus, and several officers of note, the Spartans, according to custom, renewed the fight with double vigour and fury, not too much to revenge his death as to recover his body, which was such an established point of honour as they could not give up without the greatest disgrace. But here the Theban general wisely chose rather to gratify them in that point, than to hazard the success of a second onset; and left them in possession of their king, whilst he marched straight against their other wing, commanded by Archidamus, and confining chiefly of such auxiliaries and allies as had not heartily engaged in the Spartan interest: these were so discouraged by the death of the king and the defeat of that wing, that they took themselves to flight, and were presently followed by the rest of the army. The Thebans, however, pursued them so closely, that they made a second dreadful slaughter among them; which completed Epaminondas's victory, who remained master of the field, and erected a trophy in memory of it. This was the conclusion of the famed battle of Leuctra, in which the Lacedemonians lost 4000 men, and the Thebans but 300.

**LEVEL** is an instrument which enables us to find a line parallel to the horizon, or concentric with the circumference of the earth, and to continue it to any distance:—to form a surface exactly level, having all its parts at equal distances from the earth's centre; or to find the difference of ascent between several places for the purpose of making roads, conducting water, draining low grounds, rendering rivers navigable; forming canals, &c. &c.

Among the great variety of instruments which have been invented for these purposes, the following are the most important and useful.

**Air-Level**, that which shows the line of level by Air-level, means of a bubble of air inclosed with some liquor in a glass tube of an indeterminate length and thickness, whose two ends are hermetically sealed. When the bubble fixes itself at a certain mark, made exactly in the middle of the tube, the plane or ruler wherein it is fixed is level. When it is not level, the bubble will rise to one end. This glass tube may be set in another of traps, having an aperture in the middle, through which the bubble of air may be observed. The liquor with which the tube is filled is oil of tartar, or aqua secunda; these not being liable to freeze as common water, nor to rarefaction and condensation, as spirit of wine is. This application of a bubble of air was the invention of Dr Hooke.

There is one of these instruments made with sights, which is an improvement upon that last described, and which, by a little additional apparatus, becomes more commodious and exact. It consists of an air level (fig. i.), about eight inches long, and seven or eight lines in diameter, set in a brass tube 2, with an aperture in the middle, C. The tubes are supported by a straight ruler a foot long; at whose ends are fixed two sights, 3, 3, exactly perpendicular to the tubes, and of an equal height, having a square hole, formed by two fillets of of brafs crossing each other at right angles, in the middle of which is drilled a very small hole, through which a point on a level with the instrument is observed. The brafs tube is fastened on the ruler by means of two screws; one of which, marked 4, serves to raise or depress the tube at pleasure, for bringing it towards a level. The top of the ball and socket is riveted to a little ruler that springs, one end whereof is fastened with a screw to the great ruler, and at the other end has a screw, 5, serving to raise and depress the instrument when nearly level.

The instrument just described, however, is still less commodious than the following one; for though the holes be ever so small, they will take in too great a space to determine the point of level precisely.

The instrument alluded to consists of an air-level, with telescopic sights. This level (fig. 2.) is like the last; with this difference, that, instead of plain sights, it carries a telescope to determine exactly a point of level at a great distance. The telescope is a little brafs tube, about 15 inches long, fastened on the same ruler as the level. At the end of the tube of the telescope, marked 1, enters the little tube 1, carrying the eyeglass and a hair placed horizontally in the focus of the object-glass, 2; which little tube may be drawn out, or pushed into the great one, for adjusting the telescope to different sights: at the other end of the telescope is placed the object-glass. The screw 3, is for raising or lowering the little fork, for carrying the hair, and making it agree with the bubble of air when the instrument is level; and the screw 4, is for making the bubble of air, D or E, agree with the telescope: the whole is fitted to a ball and socket. M. Huygens is said to be the first inventor of this level; which has this advantage, that it may be inverted by turning the ruler and telescope half round; and if then the hair is at the same point that it did before, the operation is just.

It may be observed, that one may add a telescope to any kind of level, by applying it upon, or parallel to, the base or ruler, when there is occasion to take the level of remote objects.

Dr Defaguliers contrived an instrument, by which the difference of level of two places, which could not be taken in less than four or five days with the best telecosopic levels, may be taken in a few hours. The instrument is as follows. To the ball C (fig. 3.) is joined a recurve tube BA, with a very fine bore, and a small bubble at top A, whose under part is open. It is evident from the make of this instrument, that if it be inclined in carrying, no injury will be done to the liquor, which will always be right both in the ball and tube when the instrument is set upright. If the air at C be so expanded with heat, as to drive the liquor to the top of the tube, the cavity A will receive the liquor, which will come down again and settle at D, or near it, according to the level of the place where the instrument is, as soon as the air at C returns to the same temperament as to heat and cold. To preserve the same degree of heat, when the different observations are made, the machine is fixed in a tin vessel EF, filled with water up to g h, above the ball, and a very sensible thermometer has also its ball under water, that one may observe the liquor at D, in each experiment, when the thermometer stands at the same height as before. The water is poured out when the instrument is carried; which one may do conveniently by means of the wooden frame, which is set upright by the three screws, S, S, S, (fig. 4.), and a line and plummet PP, (fig. 5.). At the back part of the wooden frame, from the piece at top K, hangs the plummet P, over a brafs point at N; M m are brackets to make the upright board KN continue at right angles with the horizontal one at N. Fig. 6. represents a front view of the machine, supposing the fore part of the tin vessel transparent; and here the brafs socket of the recurve-tube, into which the ball is forewed, has two wings at H, fixed to the bottom, that the ball may not break the tube by its endeavour to emerge when the water is poured in as high as g h.

After the doctor had contrived this machine, he considered, that as the tube is of a very small bore, if the liquor should rise into the ball at A (fig. 3.) in carrying the instrument from one place to another, some of it would adhere to the sides or the ball A, and upon its descent in making the experiment, so much might be left behind, that the liquor would not be high enough at D to show the difference of the level; therefore, to prevent that inconvenience, he contrived a blank screw, to shut up the hole at A, as soon as one experiment is made, that, in carrying the machine, the air in A may balance that in C, so that the liquor shall not run up and down the tube, whatever degrees of heat and cold may act upon the instrument, in going from one place to another. Now, because one experiment may be made in the morning, the water may be so cold, that when a second experiment is made at noon the water cannot be brought to the same degree of cold it had in the morning; therefore, in making the first experiment, warm water must be mixed with the cold, and when the water has stood some time, before it comes to be as cold as it is likely to be at the warmest part of that day, observe and set down the degree of the thermometer at which the spirit stands, and likewise the degree of the water in the barometer at D; then screw on the cape at A, pour out the water, and carry the instrument to the place whose level you would know; then pour in your water, and when the thermometer is come to the same degree as before, open the screw at top, and observe the liquor in the barometer.

The doctor's scale for the barometer is ten inches long, and divided into tenths; so that such an instrument will serve for any heights not exceeding ten feet, each tenth of an inch answering to a foot in height.

The doctor made no allowance for the decrease of density in the air, because he did not propose this machine for measuring mountains (though, with a proper allowance for the decreasing density of the air, it will do very well), but for heights that want to be known in gardens, plantations, and the conveyance of water, where an experiment that answers two or three feet in a distance of 20 miles, will render this a very useful instrument.

Artillery Foot-LEVEL is in form of a square, having its two legs or branches of an equal length; at a juncture whereof is a little hole, whence hangs a thread... and plummet playing on a perpendicular line in the middle of a quadrant. It is divided into twice 45 degrees from the middle.

This instrument may be used on other occasions, by placing the ends of its two branches on a plane; for when the thread plays perpendicularly over the middle division of the quadrant, the plane is assuredly level. To use it in gunnery, place the two ends on the piece of artillery, which you may raise to any proposed height, by means of the plummet, whose thread will give the degree above the level.

Carpenters and Paviors LEVEL, consists of a long ruler, in the middle of which is fitted, at right angles, another somewhat larger. At the top of this is fastened a thread, which, when it hangs over a fiducial line at right angles with the base, shows that this base is horizontal. Sometimes this level is composed of one board. See fig. 8.

Gunners LEVEL, for levelling cannons and mortars, consists of a triangular brass plate, about four inches high, (fig. 9.) at the bottom of which is a portion of a circle, divided only into 45 degrees; as this number is sufficient for the highest elevation of cannons and mortars, and for giving shot the greatest range. On the centre of this segment of a circle is screwed a piece of brass, by means of which it may be fixed or screwed at pleasure. The end of this piece of brass is made so as to serve for a plummet and index, in order to show the different degrees of elevation of pieces of artillery. This instrument has also a brass foot, to set upon cannons or mortars, so that when those pieces are horizontal, the instrument will be perpendicular. The foot of this level is to be placed on the piece to be elevated, in such a manner, as that the point of the plummet may fall on the proper degree; this is what they call levelling the piece.

Masons LEVEL, is composed of three rules, so joined as to form an isosceles triangle somewhat like a Roman A. At the vertex of this triangle is fastened a thread, from which hangs a plummet, that passes over a fiducial line, marked in the middle of the base, when the thing to which the level is applied is horizontal; but declines from the mark, when the thing is lower on the one side than on the other.

Plumb or Pendulum LEVEL, that which shows the horizontal lines by means of another line perpendicular to that described by a plummet or pendulum. This instrument, (fig. 10,) consists of two legs or branches, joined together at right angles. The branch which carries the thread and plummet is about a foot and a half long; and the thread is hung towards the top of the branch, at the point 2. The middle of the branch where the thread passes is hollow, so that it may hang free everywhere; but towards the bottom, where there is a little blade of silver, on which is drawn a line perpendicular to the telescope, the said cavity is covered by two pieces of brass, making as it were a kind of case, lest the wind should agitate the thread. For this reason the silver blade is covered with a glass G, in order that it may be seen when the thread and plummet play upon the perpendicular. The telescope is fastened to the other branch of the instrument, and is about two feet long; having a hair placed horizontally across the focus of the object-glass, which determines the point of the level. The telescope must be fitted at right angles to the perpendicular. It has a ball and socket, by which it is fixed to the foot, and was invented by M. Picard.

Reflecting LEVEL, that made by means of a pretty Mariotte's long surface of water representing the same object inverted which we see reflected by the eye; so that the point where these two objects appear to meet is a level with the place where the surface of the water is found. This is the invention of M. Mariotte.

There is another reflecting level consisting of a mirror of steel, or the like, well polished, and placed a little before the object-glass of a telescope, suspended perpendicularly. This mirror must make an angle of 45 with the telescope; in which case the perpendicular line of the telescope is converted into a horizontal line, which is the same with the line of level. This is the invention of M. Cassini.

Water LEVEL, that which shows the horizontal line by means of a surface of water or other liquor; founded on this principle that water always places itself level. The most simple water level is made of a long wooden trough or canal, whose sides are parallel to the base; so that being equally filled with water, its surface shows the line of level. This is the chorobates of the ancients. See CHOROBATA.

It is also made with two cups fitted to the two ends of a pipe, three or four feet long, about an inch in diameter, by means of which the water communicates from the one to the other cup; and this pipe being moveable on its stand by means of a ball and socket, when the two cups become equally full of water, their two surfaces mark the line of level.

This instrument, instead of cups, may also be made with two short cylinders of glass three or four inches long, fastened to each extreme of the pipe with wax or mastic. Into the pipe is poured some common or coloured water, which shows itself through the cylinders, by means of which the line of level is determined; the height of the water, with respect to the centre of the earth, being always the same in both cylinders. This level, though very simple, is yet very commodious for levelling at small distances.

De la Hire's level consists of two vessels filled with water, and communicating with each other by means of Hire's level, one or more tubes. A small cylindrical box made of thin copper or planished tin, and terminating below in an obtuse cone, floats in each of these boxes, which are kept in a vertical position by introducing into the cones a ball of lead or a quantity of mercury. One of the boxes carries the object-glass; and the eye-glass along with the cords wires are fastened into the other, but in such a manner as to be elevated or depressed by sliding in two grooves, in order that the axes of the lenses may be exactly level, which is effected by measuring a base. See Traité du Nivellement par M. Picard. The inconveniences attending this instrument arise from the difficulty of bringing the floating eye-glass into the same line with the axis of the object-glass, and of making the boxes settle in such a position that distinct vision may be procured through the telescope; for if the wires in the focus of the eye-glass be out of the axis, or at the smallest distance from the focus of the object-glass, the image will be both indistinct and deformed. In order that De la Hire's level may may be perfect, it is necessary that the boxes should be of the same weight and magnitude, that the boxes which contain the water should be put nearly on a level by means of a plummet, that the same quantity of water should be introduced, and that the object-glass should be kept at the same height with the eye-glass. These conditions, which are requisite to the perfection of the level, are too numerous and too difficult to be attained, to render this instrument of any use where accurate results are required.

These defects in De la Hire's level were partly remedied by M. Couplet, by inserting the object-glass and eye-glass into the same tube, and by placing this telescope loosely on two boxes which formerly floated at random on the fluid. He equalized the weight of these boxes by means of a quantity of small shot, and verified the instrument by putting one of the boxes beneath the object-glass, and the other beneath the eyeglass of the telescope. It is evident, however, that the accuracy of Couplet's level depends upon the equal distribution of the small shot contained in the boxes; for if it is distributed unequally, the box will be more depressed on one side than another, and consequently the intersection of the cross wires in the focus of the eye-glass, will either recede from, or approach to the surface of the water, according as the small shot is unequally distributed in the box which supports the eyeglass, or in that which carries the object-glass. Besides this source of error, considerable inconvenience might arise in practice from the want of connection between the telescope and the two boxes upon which it floats.

The level of Deparcieux is properly an improvement upon that of Couplet. It consists of two parts, a box ABCD of light wood, in which are placed two vessels of tin EFG, EFG filled with water. These vessels are each 10 inches long, 7 inches wide, and 4½ deep, and communicate by one or more tubes GE. The other part is composed of three tubes M, M, M, and of two boxes L, L, enclosed on all sides, having 8½ inches of length, 6 of breadth, and 4 of depth, and above these are foldered the three tubes. (Fig. 1, a vertical section, and fig. 2, a horizontal section of the instrument). The two outermost tubes are telescopes from 18 to 36 inches long, pointed in opposite directions to prevent the necessity of turning the level, and are necessary for its adjustment and verification.—A piece of lead weighing about two pounds is foldered to the bottom of each box L, L, and a weight P of half a pound is made to move towards Q or R by the screw RQ, in order to adjust the level by making one of the floating boxes sink deeper in the water than the other. This weight should be fixed to a small tin tube which can move easily within the greater one, and the foreword is turned by means of a handle similar to that which is used for winding up a clock. The whole instrument is thus covered with a case a b to prevent the wind from agitating the water.

In order to adjust the level, place the box ABCD adjusting it upon a table, and elevate one end or another by means of wedges till the intersection of the two cross wires in the focus of the eye-glass of one of the telescopes seems to fall upon a very remote object, each of these wires being moveable by screws so that their point of intersection can be varied. Then take the level out of the box ABCD, and invert its position, so that one of the tin

boxes EF may occupy the position which the other had before, and look through the other telescope. If the intersection of the wires falls upon the same object, their position is correct, and the axes of the telescopes are parallel; but if it falls at a distance from the object, the point of intersection must be shifted one-half of that distance towards the object, and the same operation repeated till the intersection of the hairs of one of the telescopes covers the same point of the object that is hid by the intersection of the hairs of the other telescope. When this happens, the axes of the telescopes will be exactly parallel.

The level is then placed upon its stand, which is fixed to the box at K, and a very remote object is examined with one of the telescopes, so as to find the point of it which is hid by the intersection of the wires. The level is then inverted, and the object examined with the other telescope. If the intersection of the wires covers the same point of the object as before, the level is adjusted, and the object is in the line of apparent level passing through the intersection of the wires. But if this is not the case, the weight P towards Q or towards R, according as the point of the object first examined is above or below the intersection of the wires, in order to make the image of the object rise or fall one-half of the distance between the points that are covered by the intersection of the wires in each observation. The operation is then repeated, till the intersection of the wires in both telescopes falls upon the same point of the object, in which case the axes of the telescopes will be exactly level, and the instrument properly adjusted. It is obvious that by moving the weight P from the position which it has when the level is adjusted, the axes of the telescopes will be inclined to the line of the level either above or below it according as the weight is moved to one side or another. Hence, by measuring a scale with a vertical object at its remote extremity, it may be easily found how many minutes or seconds correspond with a given variation in the position of the weight, merely by measuring the tangents on the vertical object; so that a scale may be engraved on the tube TT which will exhibit the angles of inclination to the line of apparent level, formed by the axes of the telescopes when the weight P has different positions.

The mercurial level lately invented by the ingenious Keith's Alexander Keith, Esq. of Kavelton, is founded on the mercurial same principle as the levels of De la Hire, Couplet, and Deparcieux, with this difference, that mercury is employed instead of water. A section of the mercurial level is represented in fig. 3, where A, A are two ob. Fig. 3. Long square cavities communicating by means of the channel MN. BB are two grooves hollowed out of the wood which contain the sights D, D', fig. 4, when fig. 4, the instrument is not in use. The sight D has a small hole in it, and the other is furnished with a cross hair. They are fixed into two pieces of ivory or hard wood, which are nearly of the same form as the cavities A, A, but a little smaller, so that they may go into the cavities without touching the sides. A quantity of mercury is then introduced into the communicating vessels A, A till they be about half full. The two sights are then placed in the cavities, and float on the horizontal surface of the mercury; consequently (Hydrodynamics, art. 34, 37) if the sights be of the same dimension and weight, a line joining the cross hair in D' and the small small hole in D will be level or parallel with the horizontal surface of the mercury. The instrument completely fitted up is represented in fig. 5, where D, D' are the sights, D being the sight to which the eye is applied. When there is a strong wind the level is covered with a cage, in which two holes are left opposite to the sights.—The preceding level might be improved by making the cross hair move up and down with a screw, and by engraving a scale on the side of the square aperture at D', whose divisions being subdivided by a scale on the circumference of the nut that moves the screw, would indicate to great accuracy the angle of inclination.

The following mode of constructing a level upon a new principle has occurred to the writer of this article. Let AB be a reflecting surface either of glass or water, and let MN be a straight ruler held above this surface; thus it follows from optical principles that the line MN will be perpendicular to the plane AB when the object MN and its image NM' appear in the same straight line to an eye placed at M. Hence, by the bye, we may ascertain the error of a square, by placing one of its sides upon the surface of a looking glass, and applying the eye to its extremity M; for if it is inaccurate, the image of the side MN will form an angle with MN, thus if m N be the side of the square, its image will be Nm'.

Now let VV be a vessel containing either water or mercury, and let VV be the surface of the fluid. This vessel must be firmly connected with the base CD and also with the vertical plane EF (perpendicular to CD) by means of the cross bars a b c d. The telescope AB is fastened to MN, another plane which rises perpendicular to the plane EF, and the plane MN is so connected with EF by means of screws, that its side MN may be made to vary its angle with the horizon, in any direction. The vessel VV, therefore, and the planes EF, CD remain fixed, while the telescope AB and the plane MN can vary their position relative to the other parts of the level. The telescope AB should be constructed as to answer the purpose of two telephones. It has an object-glass both at A and B, and also an eye-glass with cross wires at A and B; and these are so fitted into the tube that when the eye is applied to the end B, the object-glass at B, and the eye-glass at A with its cross hairs, may be turned to one side so as to have distinct vision with the remaining eye-glass at B and the object-glass at A. When the eye is applied to A, the eye-glass at B and the object-glass at A are moved out of the axis of the telescope for the same reason. This contrivance is for the purpose of avoiding the necessity of having two telephones. The cross hair in the focus of each eye-glass must be made capable of varying their position, so that the point of intersection may be shifted for the purposes of adjustment.

In order to adjust the instrument, place its base CD, upon a table, and move the telescope of the index MN till the image NM' is in the same straight line with MN. Then look through the extremity B at a distant object, and mark the point of it which is covered by the intersection of the wires. Invert the whole instrument so that the end A may be at B, adjust the index MN as before, and look through the telescope at the same object. If the intersection of the wires falls upon the same point of the object as formerly, the instrument is properly adjusted. But if not, the intersection of the cross wires in one of the eye-pieces must be varied, as in the adjustment of Deparcieux's level, till it covers the same point of the object that was covered at the first observation. When this happens, the instrument is duly adjusted, and may be used by placing the base CD upon a stand, and adjusting the index MN; for when this is done, the axis of the telescope will be in a line accurately horizontal.