nd plumb playing on a perpendicular line in the middle of a quadrant. It is divided into twice 45 degrees from the middle. Fig. 7.

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 Paciers 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 Mariette's long surface of water representing the same object inverted which we see erected 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. Mariette.

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 leone 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 cross 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 must 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 12 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 soldered the three tubes. (Fig. 1. is 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 soldered 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 screw 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 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 base 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 engraven 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 Mr. Alexander Keith, Esq. of Ravelston, 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 oblong 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 these 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 Level 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 case, 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 mN 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 ab, cd. 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 so constructed as to answer the purpose of two telescopes. It has an object-glass both at A and B, and also an eyeglass 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 eyeglass at A with its cross hairs, may be turned to one side so as to have distinct vision with the remaining eyeglass at B and the object-glass at A. When the eye is applied to A, the eyeglass 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 telescopes. The cross hair in the focus of each eyeglass 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. Insert 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 eyepieces 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.