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BACK-Staff, an instrument formerly used for taking the sun’s altitude at sea; being so called be. cause the back of the observer is turned towards the sun when he makes the observation. This instrument is also called Davis’s Quadrant. It consists of two co-centric arches of box-wood, and three vanes, the arch of the longer radius being of 30°, and that of the shorter of 60, forming together 90°, or a quadrant. BALANCE, in Mechanics, a pe. culiar application of the lever, in order to determine the difference or equality of weights in heavy bodies; and, consequently, their masses or quantity of matter. There are various kinds of balances; the principal of which, however, are the common balance, the bent lever balance, the Roman balance, and the Swedish or Danish balance. Balances also receive other denominations, according to the circumstances under which they are employed, or the principles on which they act, as assay balance hydrostatic balance, &c. Assay BA1, Ance, a very delicate balance used for determining the exact weight of minute bodies, in the different processes of assaying, and of frequent use and application in chemical analysis: for a description of which, see Gregory's Mechanics, vol. ii. p. 94; Nicholson’s Journal, 4to. vol. v. p. 303; see also the Annales de Chemie, xxxvi. 50. Bent Lever BALANCE. This instrument operates by a fixed weight at the end of a bent lever, supported on its axis in a pillar, and having a scale suspended from the other extremity. Common BALAN co, or Scale-beam. This instrument is too well known to need any particular description; it consists of a lever with equal arms, at the extremity of each of which is attached a scalo, and before loading it with any weights the whole ought to preserve a perfect equilibrium; and this equiliwrium, Aust arise from an exact

distribution of the weight of each arm and scale of the balance, as well as from the equal length of the former; for on this depends the accuracy of its action. Professor Playfair has the following remarks on the accuracy of the balance. “1. It should rest in a horizontal position when loaded with equal weights. 2. It should have great sensibility. 3. It should have great stability; that is, when disturbed, it should quickly return to a state of rest. That the first requisite may be obtained, the beam must have equal arms, and the centre of suspension must be higher than the centre of gravity. Were these centres to coincide, the beam, when the weights were equal, would rest in any position, and the addition of the smallest weight would overset the balance, and place the beam in a vertical situation, from which it would have no tendency to return. The sensibility, in this case, would be the greatest possible; but the other two requisites of level and stability would be entirely lost. The case would be worse, if the centre of gravity were lower than the centre of suspension, as the balance, when deranged, would make a revolution of no less than a semi-circle. When the centre of suspension is higher than the centre of gravity, if the weights be equal, the beam will be horizontal; and if they be unequal, it will take an oblique position, and will raise the centre of gravity of the whole, making the momentum on the side of the lighter weight equal to that on the side of the heavier, so that an equilibrium will again take place. “The second requisite is the sensibility of the balance, or the smallness of the weight, by which a given angle of inclination is produced. If a be the length of the arm of the balance, and b the distance between the centre of suspension and the centre of gravity, P the load in either scale, and the weight of the beam, the sensi- - a. bility of the balance **EGFTW * it is therefore greater, the greater the length of the arm, the less the distance between the two centres, and the less the weight with which the balance is loaded. “Lastly. The stability or the force with which the state of equiiibrium is recovered, is proportional to (2P+W)b, the denominator of the preceding fraction. “ The diminution of b, therefore, while it increases the sensibility, lessens the stability of the balance. The lengthening of a will, however, increase the former of these quantities, without diminishing the latter. By means of these formular, one balance may be made having exactly the same sensibility and stability with another; it is only required that the ratio of the iengths of the arms should be the same with that which is compounded of the ratios of the distances of the centres of gravity and suspension, and of the weights of the beams.” Compound BALANce, is a combi’ nation of several balances employed in weighing very heavy bodies. Danish BALANce, is a sort of steel-yard, in very general use in various parts of the continent of Europe; the principle of its action being as follows: It consists of a bar of iron, or batten of wood, having a heavy lump or knob at one end, and a scale or hook at the other. The goods to be weighed are placed in the scale, or suspended from the hook, and the whole is then balanced on a piece of cord, by sliding the latter about to and fro till the equilibrium obtains; and the weight of the body is then indicated by the graduated divisions of the instrument, which are thus computed : Put the whole length = d, the distance of the cord from the knob = z, the weight of the knob = a, and the weight in the scale or on the hook = w.

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3, &c. th. the distance a or AC, for each of those weights, will be determined. Suppose, for example, the whole length = 30 inches,

and the weight A = 2fb.; then, substituting these numbers for a and d, and the numbers 1, 2, 3, &c. for tt', we shall have the following series: at := 20, 15, 12, 10, &c. w- 1, 2, 3, 4, &c. We give this merely as the principle of computation; in real practice, of course, the weight of the bar, and the place of its centre of gravity, must enter into the calculation, which will render it a little more complicated. See Gregory’s Mechanics, vol. ii. Hydrostatic BALA Nce, is an instrument contrived for determining accurately the specific gravity of bodies, both solid and fluid ; of which there are various constructions. See HY drost Atic Balance. Roman BALANce, or Steel-yard. See STEEL-yard. BALAN ce of a Clock, or Watch, is that part which by its motion regulates and determines the beat. BALANce, in Astronomy, is the same as LIBRA, which see. BALL, in a popular sense, is any spherical body, whether natural or artificial. BALLISTIC Pendulum, a machine invented by Robins, for ascertaining the velocity of military | rojectiles, and consequently the force of fired gunpowder. It consists of a large block of wood suspended vertically by a strong horizontal iron axis, to which it is connected by a firm iron stem. Now to determine the velocit with which a ball is projected, the pendulum is so situated that the ball impinges directly against it, and causes it to vibrate through a certain arc, which being accucurately observed, the velocity of projection is computed as follows: Let the weight of the pendulum E ov

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tres of oscillation, gravity, and gyration, and P the point of impact; also let Q be a weight, which, collected in the point P, a given force applied to P will generate the same angular velocity as if it \vere applied against the pendulum itself in the point P.

This equivalent weight q = to X SG X So * × SR’.

S be T SD?

Again, let w represent the velo. §ty communicated to the point P, and r the required velocity of the ball. Then the block of wood being considered as non-elastic, the laws of collision gives the fol. lowing proportion; viz.

q + p p = ~ : v, whence
q + p

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And here, site p and q are known, it only remains to assign the velocity v, which has been Communicated to the point P, from having given the angle through which the pendulum is impelled by the stroke. or this purpose, make So = s, SP = d., then ihe velocity acquir: ed by the centre of oscislation in a pendulum, which describing from rest any arc of a circle has arrived at its sowest point, is equal to that acquired by a heavy body, which has descended freesy froń. rest by the acceleration of gravi. ty, through a space equal to the versed sine of the arc described by the pendulum. In like man. ner, if any given velocity be com. municated to the centre of oscillation of a pendulum when quiet. cent, it will rise through an arc whose versed sine is equal to the space through which a body falls freely from rest, in order to acquire that velocity. , Let, then, b represent the versed sine of the angle described by the pendulum to radius = 1, then will the centre of oscillation O, describe an arc during its motion, the versed sine of which = s b; and consequently, if we represent 16% feet by g, the central velocity of . O = V4gbs feet no second, and the velocity o 41bda

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BAROMETER, an instrument for measuring the weight of the atmosphere and its variations, in order principally to determine the changes of the weather, the heights of mountains, and other eminences, &c. The barometer is founded up: on the Torricellian experiment. Torricelli filled a glass tube, about three feet long, with quicksilver; . and having sealed it hermetically at one end, he immersed the other in an open vessel of the same fluid. He found that the mercury descended in the tube, and finally settled at the height of about twenty-nine and a half Roman inches, and this, whether the tube was vertical or inclined, according to the known laws of hydrostatical pressure. This experiment was repeated and diversified in various ways, with tubes filled with other fluids, and the result being the same in all, except so far as relates to their specific gravities, the weight and pressure of the air were established beyond the possibility of doubt. The real cause of the suspension of the mercury in the tube, and of water in pumps, was thus admitted to be the atmospheric pressure, and repeated observations were made, connected with this subject; from which it was discovered that the column of mercury varied considerably in its height, at different times, and this variation was soon observed to be followed by changes of the weather. This led to far. ther and more accurate observations, and various alterations and improvements were suggested in the form and construction of the barometer, or weather-glass, as it is sometimes called, in consequence of its use , in determining the changes in the weather.

Common BARometer. This is a ; tube, open at one end, and

ermatically sealed at the other,

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having its diameter about onethird or one-fourth of an inch, and its length thirty-three or thirtyfour inches. It is filled with purified mercury so justly as not to have any air over it, nor any bubbles *::::::: to the sides of the tube, which is best done by means of a small paper or glass funnel, with a capillary tube. The orifice of the tube, filled after this manner, so as to overflow, is then closely pressed by the finger, so as to exclude any air between it and the mercury; this done, invert the tube, and immerse the finger and end thus stopped, into a bason of like purified quicksilver, and in this position withdraw the finger, and the mercury will descend in the tube to some place between twenty-eight and thirty-one inches above the surface of ine mercury in the bason, these being the limits between , which it always stands near the surface of the earth or sea. Instead, however, of the detached vessel, the modern barometer tubes are curved at the bottom, and terminate in a bulb, which ought to be as big as it can be conveniently made, in order that the variation in the altitude of the mercury in the tube may affect, as little as possible, the depth of that in the bulb. The barometer tubes, under either of the above forms, are now to be enclosed in a wooden case or frame, to prevent their being broken, and the vessel or bulb, though open to the air, must be secured from dust; and thus far the construction will be completed. Next measure from the surface of the mercury to 28 inches and 31 inches; dividing the spaces between them into inches and tenths, which are marked on a scale placed against the side of the tube; and these tenths are again subdivided into hundredth parts of an inch, by means of a sliding index carrying a vernier or monius. In the common barometers, called weather-glasses, the lowest limit is marked stormy, and the highest point is marked on one side very dry for summer, and on the other, “; hard frost for winter. To the

next half-inch below the highest point are annexed set fair, on the one side, and set frost on the other. At the height of 30 inches, fair is marked on one side, and frost on the other. At the height of 294 inches is marked changeable, both for summer and winter; and at 29 inches, rain on one side, and snow on the other. At 28% inches, much rain on one side, and much snow on the other; the lowest division being marked stormy, as we have before observed. The bore of the tube should be large (not less than one-fourth of an inch), in order to prevent the effects of the attraction of cohesion. If a cistern be used as a reservoir for the stagnant umercury, it should be at least ten times the diameter of the tube, that the addition or subtraction of the mercury contained between the greatest and least altitudes, may not sensibly affect its depth. In order more effectually to preserve the lower surface at the same height from the divisions on the scale affixed to the instrument, a floating gage has been applied, by means of which the same screw that renders the barometer portable, regulates

the surface of the mercury in the

cistern, so that it is always at the place from whence the divisions on the scale commence. The tube should be preserved free srom dust till it is used ; and for this purpose it may be hermetically sealed at both ends, and one end may be opened with a tile, when it is to be filled. The mercury should be pure; and inay be purged of its air by previously boiling it in a glazed earthen pipkin covered close ; and when the tube has been uniformly heated, and rendered eiectrical by rubbing it, the hot mercury should be poured into it in a regular current, through a glass funnel, with a long capiliary tube, so that the air may not have room to pass between the parts of the quicksilver. Another circumstance, that requires attention in the construction and use of barometers, is the temperature of the air; for unless this remains the same, the diumen

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sions of a given quantity of mercury will be variable; and the altitude of the mercury will be an uncertain measure of the weight of the atmosphere, because it is dilated by heat, and contracted by cold, when probably its weight, and ressure are unchanged. M. de uc attended particularly to this circumstance, and contrived to estimate the effects of heat on the quicksilver in the barometer, when it is used for accurate observation, by means of the thermometer; the scale of which is divided in such manner as to indicate, with little labour of calculation, the correction to be made on account of heat. The interval between the freezing and boiling points (answering to six lines of the barometer) is divided into 96 equal parts; each of which corresponds to the sixteenth of a line in the motion of the mercury in the barometer dilated by heat, which must be added to, or subtracted from the height of the mercury in the barometer, for every degree of the variation of the thermoineter so graduated. As soon as it was observed that the different heights of the mercury indicated by the barometer were, in some measure, connected with the state of the weather, and that it might be applied to the purpose of a weather-glass, many attempts were made to render the changes in it more sensible, whereby to measure the variations in the weight of the atmosphere the more accurately, which attempts have given rise to a great number of barometers of different structures, deviating from the simplicity of the common barometer, and frequently much less accurate. Diagonal BARom ETER. This acts on the same principle as the common barometer above described, except, that the upper end of the tube is bent at about an angle of 45° from the vertical, whereby the scale of variations is increased in about the ratio of three to two, or more accurately, in the ratio of the diagonal of a square to the length of its side. If the upper end be bent in a greater angle, the scale of variation will be so much *. more increased; but in prac7

tice it is not found convenient to have the angle much exceeding 45°. Horizontal BARom grer. This consists of a tube bent at right angles, having a pretty wide cylindrical part at the upper end of the vertical leg, which is hermetically sealed, the horizontal leg being open, where, however, the mercury cannot run out, being opposed by the pressure of the atmosphere, the variations of which are indicated by a scale attached to that branch of the instrument. Marine BARom ETER. This instrument is intended to be used on shipboard, being contrived so as not to be affected or injured by the motion of the vessel. It consists of a double thermometer, or two tubes half filled with spirits of wine; the one sealed at both ends, with a quantity of air included; the other sealed at one end only. The former of these is af. fected only by the temperature of the air; but the other, both by the external temperature, and by the variable pressure of the atmosphere. Hence, considering the spirit thermometer as a standard, the excess of the rise or fall of the other, beyond the former, will shew the increase or decrease of the pressure of the atmosphere. Pendant BA Rometer. This instrument is rather pretty than use. ful. It consists ...P. comical tube placed vertically; its upper and smallar extreme is hermetically sealed, and its larger and lower end open : it has no vessel or cistern, its conical figure supplying that defect. Portable BAROMETER. This is so constructed that it may be carried from one place to another without damage or derangement. The end of the tube is tied up in a leathern bag, not quite full of mercury, which, being pressed by the air, forces itself into the tube, and keeps suspended at its proper height. This bag is usually enclosed in a box, through the bottom of which passes a screw, by means of which the mercury may be forced to the upper end of the tube, and prevented from breaking it by dashing against the top,

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