b(2P-+W

;

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.

and hence, by substituting w = 1, 2, 3, &c. th. the distance a or AC, for each of those weights, will be determined. Suppose, for example, the whole length =30 inches, "Lastly. The stability or the and the weight A= 2lb.; then, force with which the state of equi-substituting these numbers for librium is recovered, is proportiona and d, and the numbers 1, 2, 3, al to (2P+W)b, the denominator &c. for w, we shall have the folof the preceding fraction.

lowing series:

x= 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.

"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 formulæ, one balance may be made having exactly the same sensibility and stability with another; it is only required that the ratio of the lengths of the arms should be the sanie with that which is coming accurately the specific gravity pounded of the ratios of the dis- of bodies, both solid and fluid; of tances of the centres of gravity which there are various construcand suspension, and of the weights tions. See HYDROSTATIC Balance. of the beams." Roman BALANCE, or Steel-yard. See STEEL-yard.

Compound BALANCE, is a combination 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:

Hydrostatic BALANCE, is an instrument contrived for determin

BALANCE 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 na.

tural or artificial.

It consists of a bar of iron, or batten of wood, having a heavy BALLISTIC Pendulum, a malump or knob at one end, and achine invented by Robins, for as

scale or hook at the other. The

goods to be weighed are placed in certaining the velocity of military the scale, or suspended from the rojectiles, and consequently the hook, and the whole is then basists of a large block of wood susforce of fired gunpowder. It con. lanced 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 =x, the weight of the knob = a, and the weight in the scale or on

the hook=w.

pended vertically by a strong horizontal iron axis, to which it is connected by a firm iron stem. Now to determine the velocity with which a ball is projected, the pendulum is so situated that the ball impinges directly against it, and causes it to vibrate through curately observed, the velocity of a certain arc, which being accuprojection is computed as follows: Let the weight of the pendulum

= w

= P

the weight of the bali
And let O, G, and R, be the cen

tres of oscillation, gravity, and This, therefore, will give us the gyration, and P the point of im-velocity of the ball the instant it pact; also let q be a weight, which, struck the pendulum; that is, the collected in the point P, a given required velocity, force applied to P will generate the same angular velocity as if it were applied against the pendulum itself in the point P.

Ρ

4lbd2

=

P

feet per second.

BAROMETER, an instrument for measuring the weight of the at

Again, let represent the velo-mosphere and its variations, in orcity 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 following proportion; viz.

q+p:p=x: v, whence
q + p
P

der principally to determine the changes of the weather, the heights of mountains, and other eminences, &c. The barometer is founded upon 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 And here, since p and q are He found that the mercury descendin an open vessel of the same fluid. known, it only remains to assigned in the tube, and finally settled at the velocity, which has been communicated to the point P, from having given the angle through which the pendulum is impelled by the stroke.

the height of about twenty-nine and a half Roman inches, and this, whether the tube was vertical or inclined, according to the known For this purpose, make SO=s, This experiment was repeated and laws of hydrostatical pressure. SPd, then the velocity acquir diversified in various ways, with ed by the centre of oscillation in tubes filled with other fluids, and a pendulum, which describing the result being the same in all, from rest any arc of a circle has except so far as relates to their arrived at its lowest point, is equal specific gravities, the weight and to that acquired by a heavy body, pressure of the air were establishwhich has descended freely from ed beyond the possibility of doubt. rest by the acceleration of gravi- The real cause of the suspension of ty, through a space equal to the the mercury in the tube, and of versed sine of the arc described water in pumps, was thus admitted by the pendulum. In like man-to be the atmospheric pressure, and ner, if any given velocity be com- repeated observations were made, municated to the centre of oscillation of a pendulum when quiet- which it was discovered that the connected with this subject; from cent, it will rise through an arc column of mercury varied consiwhose versed sine is equal to the derably in its height, at different space through which a body falls times, and this variation was soon freely from rest, in order to ac- observed to be followed by changes quire that velocity. Let, then, of the weather. This led to far. represent the versed sine of the ther and more accurate observaangle described by the pendulum tions, and various alterations and to radius=1, then will the centre improvements were suggested in of oscillation O, describe an arc the form and construction of the daring its motion, the versed sine barometer, or weather-glass, as it is of which sb; and consequently, sometimes called, in consequence if we represent 16 feet by g, the of its use in determining the central velocity of 0=√4gbs changes in the weather. feet per second, and the velocity 4lbd

Common BAROMETER. This is a glass tube, open at one end, and hermetically sealed at 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 284 inches, much rain on one side, and much snow on the other; the lowest division being marked stormy, as we have before observed.

having its diameter about one-next half-inch below the highest third or one-fourth of an inch, and point are annexed set fair, on the its length thirty-three or thirty-one side, and set frost on the other. four inches. It is filled with purified mercury so justly as not to have any air over it, nor any bubbles adhering 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 the mercury in the bason, these being the li-ry contained between the greatest mits between which it always stands near the surface of the earth or sea.

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 mercury, it should be at least ten times the diameter of the tube, that the addition or subtraction of the mercu

and least altitudes, may not sensibly affect its depth. In order more effectually to preserve the lower Instead, however, of the detached surface at the same height from vessel, the modern barometer tubes the divisions on the scale affixed are curved at the bottom, and ter- to the instrument, a floating gage minate in a bulb, which ought to be has been applied, by means of as big as it can be conveniently which the same screw that renders made, in order that the variation the barometer portable, regulates in the altitude of the mercury in the surface of the mercury in the the tube may affect, as little as pos- cistern, so that it is always at the sible, the depth of that in the bulb. place from whence the divisions The barometer tubes, under ei-on the scale commence. The tube ther of the above forms, are now should be preserved free from to be enclosed in a wooden case or dust till it is used; and for this frame, to prevent their being bro-purpose it may be hermetically ken, and the vessel or bulb, though sealed at both ends, and one end open to the air, must be secured may be opened with a file, when from dust; and thus far the con- it is to be filled. The mercury struction will be completed. should be pure; and may 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 electrical by rubbing it, the hot mercury should be poured into it in a regular current, through a glass funnel, with a long capillary tube, so that the air may not have room to pass between the parts of the quicksilver.

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 nonius. 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, very hard frost for winter. To the

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 dimen

an accident very likely to happen ter, considered as a weather-glass, without this precaution. Mr. Pa- have been very differently extrick, it seems, first had a contri-plained by various writers; and vance of this kind; but the porta-although we have reason to beble barometer has received vari-lieve, that the barometer never ous improvements since, of which, fails to indicate a storm, or any perhaps, the most complete is that very great change of weather, for described by De Luc, in his Re-some hours before it occurs; yet cherches. Improvements in this its variations afford no indications instrument have also been suggest- or prognostics that are absolutely ed by Sir G. Shuckburgh and Ge- certain, with respect to those less neral Roy, which were carried in- considerable changes, to which the to execution by Ramsden, with weather is subject in our variable farther improvements of his own. climate. With certain restrictions Sir H. Englefield, and Humboldt, they afford some ground for probathe celebrated traveller, have also ble conjecture; and these restricmuch simplified the structure of tions are to be determined merely the portable barometer; and an by the sagacity of long-continued improvement as important, per- observation and experience. Strict haps, as any other was suggested ly speaking, the height of the merby Professor Playfair; namely, cury in the barometer has no immaking the tube, as high as the mediate and necessary connection lowest range of the mercury, of either with rain or fair weather. iron, by which means the hydro-That its variable height is the im statical pressure, the most usual mediate consequence of the variacasuality in the use of this barometer, is, in a great measure, guarded against.

Reduced BAROMETER. This instrument is only three inches long, and shows the dilatations of the air in the receiver of an air-pump, for which purpose it is commonly employed.

ble pressure of the atmosphere, is a fact that admits of no doubt; but the causes of this variable pressure have not yet been fully and satisfactorily ascertained; and how far the state of the weather, in all its minute and sudden changes, depends upon it, is a question that is still to be determined.

The principal observations that have been made on the variations of this instrument, are summed up by Mr. Kirwan in the following particulars:

I. The more considerable elevations and depressions of the mercury in the barometer happen at a very short interval of time, in places very remote from each other. But the coincidence is more remarkable when the places differ only in latitude.

Wheel BAROMETER. This instru ment is meant to render the alterations in the air more sensible. Here the barometer tube has a large ball at top, and is bent up at the lower or open end, where an iron ball floats on the surface of the mercury in the tube, to which is connected another ball by a cord hanging freely over a pulley, the axis of which carries an index that traverses on a dial. The circumference of the dial is so fitted to that of the pulley, that the whole range of the mercury is equal to the former, and thus what is but one inch in the common barometer, extends to three or four inches in this. But then it must be observed, that the friction of the pulley and axis greatly obstructs IV. They are considerably smallthe free motion of the quicksilver. er in very elevated situations than This imperfection in wheel baro at the level of the sea. meters has been in some measure V. The mean height of the baroobviated by introducing two pul-meter at the level of the sea, in leys, moving on friction wheels. most parts of the globe hitherto The phenomena of the barome-examined, is about 30 inches.

II. The variations are far more frequent and extensive in the neighbourhood of the poles than in that of the equator.

III. The variations without the tropics are greater and more frequent in winter than in summer.