Dictionary of Arts and Sciences. In Plate 94, A, B, D, fig. 7, are the three legs upon which it is placed; when shut up, they form one round rod, and are kept together by three rings: these legs are jointed to a brass frame E, on the top of which is a male screw, screwing into a female screw within the projection a of the plate F. Within the top of a, figs. 4 and 7, is a hemispherical cavity to contain the spherical ball, fig. 5: this ball has a male screw d on its top, which screws into a female screw b, fig. 6, in the plate G, fig. 7 and fig. 6, the ball is put up through an opening e, fig. 4, and screwed to the plate, fig. 6; so that the upper plate G can move in any direction within certain limits by the play of the ball in its socket; to confine the upper plate G when it is set in any direction, four screws, HHHH, figs. 4 and 7, are employed; they work in tubes firmly fixed to the plate F, and are turned by their milled heads; the upper ends of these screws act against the under side of the plate fig. 6, as shown in fig. 7; so that when the plate G is required to be moved in any direction, it is done by screwing up one screw and screwing down the opposite tillit is brought to the proper inclination; then by screwing up both together, the plate is firmly fixed. The ball, fig. 5, has a conical hole fthrough it, to receive an axis which is screwed fast to the bottom of the compass-box, I, fig. 7; a screw screwed into the end of this axis prevents its being lifted out, and at the same time leaves it at liberty to turn round independent of the ball, fig. 5. On each side of the compass-box, I, is a bar KK, on the end of which are fixed two forked pieces IO, called the Y's (from their resemblance to that letter), carrying the telescope M. One of these (0) is capable of being raised or lowered by means of a milled-headed screw N, which works through a collar in the lower end of the tube g; the rest of the tube has a triangular hole through it, in which slides a bar k, which is part of the Y; O the female screw is cut within this bar, and the screw works into it, so that by turning the milled head one way, the Y is raised, and by reversing the motion, it is lowered. The axis which connects the compass-box and the other apparatus, has a collar upon it just above where it enters the ball, fig. 5, which is embraced by a clamp P, fig. 6, which is closed by a screw C, so as to hold the collar of the axis quite tight; and when the screw is turned back, its own elasticity opens it so as to allow the axis of the compass-box to turn round freely within it; on the opposite side of the clamp is a projecting arm, carrying the nut m of the screw Q, which screw works in a stud n, fixed to the upper plate G, figs. 7 and 6: by this means, when G is loosened, the telescope can be turned quite round, but when it is fastened, it can only be moved by turning the screw Q. The level-tube Z is fastened to the under side of the telescope by a screw q at one end and a bar at the other: the use of these are to adjust it so that it shall be exactly parallel to the axis of he telescope-tube. The level, as best ex plained in the section, fig. 1, is a tube of glass ss, nearly filled with spirits of wine, but so as to leave a bubble of air in it; if the tube is of exactly the same diameter in every part, the bubble will rest in the middle of the tube when it is level. In some of the best levels made by Ramsden, the inside of the tube is bent into a segment of a circle, 100 feet diameter, and the inside is ground, which causes the bubble to adhere together; if the tube is straight, it is liable to divide into several small ones. The internal parts of the telescope are explained in fig. 1: RR is the external tube of brass plate; within this slides another tube ss; it has two glasses v, w, screwed into the outer end, called object-glasses, and it has two divisions . y, called diaphagram, with small holes in them; their use is to collect the prismatic rays with which the objects would otherwise be tinged; the tube ss has a rack t fixed nearly in the middle of it, which takes into a pinion on the axis of the milled head T, figs. I and 7; by turning this, the glasses v, w, can be moved nearly to, or farther from, the eye to adjust the focus; to the tube Rat are fixed the cross wires, whose intersection is exactly in the centre of the tube. The manner of fixing these is explained in fig. 3: A is a brass box, which fits into the end of the telescopetube, and is held there by four small screws; within this box is placed a brass plate B, carrying the wires, which are fastened by screwing four screws down upon their ends; when the plate B is in the box, a ring D is screwed in upon it, which prevents its falling out, but at the same time leaves it at liberty to move about in the box; the sides of the box, and also the telescope-tube, has four rectangular holes in it, through which four screws are passed into the edges of the piece B, so as to hold it in any pesition: these screws come through the external tube, and have square heads, to be turned by a key, so as to adjust the interactions in the centre: the box A has a female screw in the front, into which is screwed the eye-piece W; 3 is the tube which is screwed to the telescope; within this slides a tube, containing two glasses 4, 5; by sliding the glasses in or out of the tube 3, they can be adjusted so as to adapt their focus to the cross wires. This eye-piece is convenient on account of its shortness; but as it reverses the objects, it is sometimes more convenient to use the eye-piece fig. 2. which is much longer, but does not reverse objects. a is the tube which is screwed to the telescope; within this slides another tube bb, having at one end a tube dd, containing two glasses ef, and a diaphagram g, and at the other end a tube hh, containing two glasses ik, and a diaphagram: m is a cap screwed on to the end to prevent the tubes coming out. When the instrument is to be carried, the level is unscrewed from the legs and packed in a case; the legs are shut up and kept so by the rings, as before described. The manner of using this instrument is as follows: When the difference of level between any two places is required, the observer with the level goes to the highest of the two, and his assistant goes to the lowest with the target, which is a long pole of wood with a groove in it, in which slides a small rod carrying a round piece of wood, called a sight, which is to be observed through the telescope: the observer opens the legs of the instrument, and sets them on the ground; the level is next screwed to them at E, as shown in fig. 7; the telescope is then brought nearly to a level by the screws HHHH, as before described; the screw c is then turned so as to release the clamp P, fig. 6; and the telescope is turned about, so as to point to the target; the clamp P is then closed, the observer looks through the telescope, and by turning the nut T, the focus is adjusted: the screw Q is then turned till the cross wires are brought to coincide with the object, in an horizontal plane; he then takes his eye from the telescope, and works the screw Ń till he brings the bubble of air in the level-tube exactly in the middle, which shows that the telescope is perfectly horizontal; the observer then makes signals to the assistant to raise or lower the sight on the slider of the target, till it is brought to coincide with the intersection of the cross wire, which shows that the telescope and the sight of the target are on the same level; the height which the sight is from the ground where the target stands, deducted from the height the telescope stands from the ground, is the difference of level required. LEVEL TOPPED, in botany. See FASTI GIATE. LE/VELLER. 8. (from level.) I. One who makes any thing even. 2. One who destroys superiority; one who endeavours to bring all to the same state of equality (Collier). a LEVELLING, the art or act of finding line parallel to the horizon at one or more stations, to determine the height or depth of one place with respect to another; for laying out grounds even, regulating descents, draining morasses, conducting water, &c. Two or more places are on a true level when they are equally distant from the centre of the earth. Also one place is higher than another, or out of level with it, when it is farther from the centre of the earth; and a line equally distant from that centre in all its points, is called the line of true level. Hence, because the earth is round, that line must be a curve, and make a part of the earth's circumference, or at least be parallel to it, or concentrical with it; as the line BCFG (Plate 93, fig. 10), which has all its points equally distant from A, the centre of the earth, considering it as a perfect globe. But the line of sight BDE, &c. given by the operations of levels, is a tangent, or a right line perpendicular to the semidiameter of the earth at the point of contact B, rising always higher above the true line of level, the farther the distance is, is called the apparent line of level. Thus, CD is the height of the apparent level above the true level, at the distance BC or BD; also EF is the excess of height at F, and GH at G, &c. The difference, it is evi dent, is always equal to the excess of the secant of the arch of distance above the radius of the earth. The common methods of levelling are sufficient for laying pavements of walks, or for conveying water to small distances, &c.; but in more extensive operations, as in levelling the bottoms of canals, which are to convey water to the distance of many miles, and such like, the difference between the true and the apparent level must be taken into the account. Now the difference CD between the true and apparent level, at any distance BC or BD, may be found thus: By a well-known property of the circle, (2AC + CD) : BD : : BD : CD ; or because the diameter of the earth is so great with respect to the line CD at all distances to which an operation of levelling commonly extends, that 2AC may be safely taken for 2AC + CD in that proportion without any sensible error, it will be 2AC: BD :: BD ̊: CD, which therefore is BD2 BC2 Or 2AC 2AC nearly; that is, the difference between the true and apparent level, is equal to the square of the distance between the places, divided by the diameter of the earth; and consequently it is always proportional to the square of the distance. Now the diameter of the earth being nearly 7958 miles; if we first take BC 1 mile, then BC2 = 1 the excess becomes of a mile, which 2AC 7958 is 7-962 inches, or almost eight inches, for the height of the apparent above the true level at the distance of one mile. Hence, proportioning the excesses in altitude according to the squares of the distances, the following table is obtained, showing the height of the apparent above the true level for every 100 yards of distance on the one hand, and for every mile on the other. great multitude; for, being unacquainted with the correction answering to any distance, they only levelled from one twenty yards to another, when they had occasion to continue the work to some considerable extent. This table will answer several useful purposes. Thus, first, to find the height of the apparent level above the true, at any distance. If the given distance is in the table, the correction of level is found on the same line with it: thus at the distance of 1000 yards, the correction is 257, or two inches and a half nearly; and at the distance of 10 miles, it is 66 feet 4 inches. But if the exact distance is not found in the table, then multiply the square of the distance in yards by 257, and divide by 1,000,000, or cut off six places on the right for decimals; the rest are inches: or multiply the square of the distance in miles by 66 feet 4 inches, and divide by 100. 2diy, To find the extent of the visible horizon, or how far can be seen from any given height, on a horizontal plane, as at sea, &c. Suppose the eye of ano bserver, on the top of a ship's mast at sea, is at the height of 130 feet above the water, he will then see about 14 miles all around. Or from the top of a cliff by the sea-side, the height of which is 66 feet, a person may see to the distance of near 10 miles on the surface of the sea. Also, when the top of a bill, or the light in a light-house, or such like, whose height is 130 feet, first comes into the view of an eye on board a ship, the table shows that the distance of the ship from it is fourteen miles, if the eye is at the surface of the water; but if the height of the eye in the ship is 80 feet, then the distance will be increased by near eleven miles, making in all about twenty-five miles indistance. 3dly, Suppose a spring to be on one side of a hill, and a house on an opposite hill, with a valley between them, and that the spring seen from the house appears by a levelling instrument to be on a level with the foundation of the house, which suppose is at a mile distance from it; then is the spring eight inches above the true level of the house; and this difference would be barely sufficient for the water to be brought in pipes from the spring to the house, the pipes being laid all the way in the ground. 4th, If the height or distance exceed the limits of the table, then, first, if the distance be given, divide it by 2, or by 3, or by 4, &c. till the quotient come within the distances in the table; then take out the height answering to the quotient, and multiply it by the square of the divisor, that is, by 4, or 9, or 16, &c. for the height required: so if the top of a hill is just seen at the distance of 40 miles, then 40 divided by 4 gives 10, to which in the table answer 664 feet, which being multiplied by 16, the square of 4, gives 10613 feet for the height of the hill. But when the height is given, divide it by one of these square numbers 4, 9, 16, 25, &c. till the quotient come within the limits of the table, and multiply the quotient by the square root of the divisor, that is by 2, or 3, or 4, or 5, &c. for the distance sought: so when the top of the peak of Teneriffe, said to be almost three miles, or 15,810 feet high, just comes into view at sea, divide 15,840 by 225, or the square of 15, and the quotient is 70 nearly; to which in the table answers by proportion nearly 10 miles; then multiplying 102 by 15, gives 154 miles and §, for the distance of the hill. All that has been previously stated has been said without any regard to the effect of refraction in elevating the apparent places of objects. But as the operation of refraction in incurvating the rays of light proceeding from objects near the horizon is very considerable, it can by no means be neglected, when the difference between the true and apparent level is estimated at considerable distances. It is now ascertained (see REFRACTION) that for horizontal refractions the radius of curvature of the curve of refraction is about seven times the radius of the earth; in consequence of which the dis. tance at which an object can be seen by refraction is to the distance at which it could be seen without refraction, nearly as 14 to 13, the refraction augmenting the distance at which an object can be seen by about a thirteenth of itself. By reason of this refraction, too, it happens, that it is necessary to diminish by 4 of itself the height of the apparent above the true level, as given in the preceding table of reductions. Thus, at 1000 yards, the true difference of level when allowance is made for the effect of refraction, will be 2:570 —:367 .20203 inches. At two miles it would be 32 - 14 = 272 inches; and so on. = M. Prony lias given at the end of his Architecture Hydraulique a table computed on this principle, extending from 50 to 6000 French toises, and showing, in three distinct columns, the difference between the true and apparent levels, first without regarding refraction, next considering it, and then a column showing the difference of the results. This table is almost entirely useless; yet the author of the article Levelling in the Encyclopædia Britannica has faithfully transcribed it without acknowledgment; and as it would seem, without being aware, that on account of the different ratios subsisting between the French toise and the radius of the earth, and six English feet and the same measure, the table as given in English is too inaccurate to be de pended upon, even were it of use. To find the height H of a mountain, its angle of apparent elevation (E), the are A of a great circle of the earth included between the foot of the mountain and the place of the observer, and the apparent angle C made at the top of the mountain between the plumb-line and the apparent first place of the observer on the earthi's surface, M. Lambert gave this theorem, R being the radius of the earth: R sin (90+E—A) R+ H = : sin (C-A) whence H is immediately found. Other for mulæ are deduced by M. Laplace for the same purpose ; but they are too complex to be inserted here. |