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In this example, the periods of circulation do not commence to gether till after the seventh place of decimals; they are then carried on two places further, in order to ascertain what ought to be carried to the conterminous period; which in the present case is 1, as will appear from the above operation.

Note. There may arise cases in which it will be necessary to carry the circulation on to three or more places beyond the conterminous period, but in general two or three places are sufficient.

ADDITION, in Algebra, is finding the sum of several algebraical quantities, and connecting those quantities together with proper signs. And this is generally divided into the following cases.

their

Case 1. When all the indetermi nate letters are the same, and have the same sign.

Add the co-efficients of the several quantities together, and prefix before the sum the proper sign, whether it be plus or minus.

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7cx+15x+4cy-9y
3abc
(7c+15)x+(4c-9) y
3 abc

In the addition of Surds, reduce all the given quantities to their most simple form; then add the co-efficients of the radicals which 13y have the same index and the same 11y number.

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4x + 14x

7y

Thus,

+18a+ 18b Sums + 23x 31y

Case 2. When the quantities are the same, but have different signs.

EXAMPLES.

√8+√18=2√2+3 √/2=5√2 √/12+√27=2√3+3√/ 3=5/3 108a4+32a=3a 4a+24a

= (3a+24a.

=

Add all the like quantities together that have also the same sign, Note. When the quantities are and thus two separate sums will reduced to their lowest terms, or be obtained; then subtract the less simplest form, and have different of these from the greater, and pre-indices and numbers, they can fix before the remained the sign of the greater sum.

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Note 1. When the leading quantity of any algebraical expression has no sign, it is supposed to be affected with the sign +.

Note 2. Unlike quantities can only be added by means of the sign+placed between them.

In the addition of Algebraic

only be added together by means of the sign + placed between them.

Thus, 18+√108 = 3√2+6√3, cannot be reduced to a simpler form than that above; and the same with various others.

ADDITION of Ratios, is the same as composition of ratios;

thus, if a b c d ; then by addition, or composition, a+b: a=c+d: c or, a+b: b = c + d: d.

ADDITIVE, denotes something to be added to another, in contradistinction to something to be taken away, or subtracted. Thus, astronomers speak of additive equa

tions; and geometricians, of addi-exposed to the fire, produces a vehement blast of wind.

tive ratios, &c. &c.

ADFECTED Equation, in Algebra, is that in which the unknown quantity is found in two or more different degrees or powers; thus, x8 — px2 + qx=a, is an adfected equation, having three different powers of the unknown quantity r entering into its composition. Such equations are distinguished from simple, which involve but one power.

EOLUS'S Harp, an instrument so named from its producing agreeable harmony, merely by the ac tion of the wind. It is thus constructed: let a box be made of as thin deal as possible, of the exact length answering to the width of the window in which it is intended to be placed, five or six inches deep, and seven or eight inches wide; let there be glued upon it ADHESION, in Philosophy, is a two pieces of wainscot, about half species of attraction which takes an inch high and a quarter of an place between the surfaces of inch thick, to serve as bridges for bodies, whether similar or dissimi- the strings; and within side, at lar, and which, in a certain degree, each end, glue two pieces of beech, connects them together; differs about an inch square, of length from cohesion, which, uniting par- equal to the width of the box, ticle to particle, retains together which are to sustain the pegs; into the component parts of the same these fix as many pins, such as are mass. The power of adhesion is used in a harpsichord, as there are proportional to the number of to be strings in the instrument, touching points, which depends upon the figures of the particles that form the bodies; and in solid bodies, upon the degree in which their surfaces are polished and compressed. The effects of this power are extremely curious, and

in

many instances astonishing. Musschenbroek relates that two cylinders of glass, whose diameters were not quite two inches, being heated to the same degree as boiling water, and joined together by means of melted tallow lightly put between them, adhered with a force equal to 130 pounds: lead, of the same diameter and in similar circumstances, adhered with a force of 275 pounds; and soft iron with one of 300 pounds. Grains.

Gold adheres to mercury, with a force of

Silver

Tin

Lead'

Bismuth

Platina

Zinc

Copper

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Antimony Iron Cobalt 8 ÆOLIPILE, EOLIPILA, an instrument consisting of a hollow metalline ball, with a slender neck or pipe arising from it. This being filled with water, and thus

half at one end and half at the other, at equal distances: it now remains to string it with small catgut, or blue first fiddle-strings, fixing one end to a small brass pin, and twisting the other round the opposite pin. When these strings are tuned in unison, and the instrument placed with the strings outward in the window to which it is fitted, it will, provided the air blows on that window, give a sound like a distant choir, increasing or decreasing according to the strength of the wind.

ÆRA, in Chronology, is the same as Epoch, and means a fixed point of time, from which to begin a computation of the succeeding years.

ERA also means the way or mode of accounting time. Thus, we say, such a year of the Christian æru, &c.

Christian ERA. It is generally allowed by chronologers, that the computation of time from the birth of Christ, was only introduced in the sixth century, in the reign of Justinian; and is generally as cribed to Dionysius Exiguus. See Epoch.

ÆRIAL, Perspective, is that which represents bodies diminished and weakened in proportion to their distance from the eye; but it relates principally to the colours

of objects, which are less distinct, bodies is also found to be nearly the greater the distance at which the same, being about 3.400, or they are viewed. nearly 3 times that of common

ROGRAPHY, a description water. of the air or atmosphere, its nature, These general and constant chacomposition, limits, dimensions, pro-racters strongly indicate a comperties, &c. AEROLITHS, a name given to theses have been advanced to acmon origin, and various hypothose solid semi-metallic substan- count for them. Some have attrices which fall from the atmos-buted them to terrestrial, and phere. The descent of such bodies others to lunar, volcanoes; they had been long reported; but the have again been supposed to be fact was not confirmed till within concretions actually formed in the a few years. The larger sort of regions of our atmosphere; while these stones have been seen as lu- others have considered them as minous bodies, to move with great small planets circulating about velocities, descending in oblique the sun or earth, which coming in directions, and frequently with a contact with our atmosphere, take loud hissing noise, resembling that fire from the resistance and fricof a mortar-shell when projected tion they experience in passing from a piece of ordnance; they through it. are sometimes surrounded with a

blaze or flame, tapering off to a narrow stream at the hinder part, are heard to explode, and seen to fly in pieces. The velocity with which they strike the earth is very great, frequently penetrating to a considerable depth, and when taken up they have been, in some cases, found to be still hot, and bearing evident marks of recent fusion. Sometimes such falls have happened during a storm of thunder and lightning, at others, when the sky has been clear and serene; whence one may infer that these phenomena are unconnected with the state of the atmosphere.

tion, viz. that these stones proceed With regard to the first supposifrom terrestrial volcanoes, it will be sufficient to observe, that no reto happen at or near the time of markable eruption has been known their fall, and that such bodies of some thousand miles from any have been found at the distance known volcano; beside the immense force that would be necessary to project bodies, some of so great a distance, far exceeds them of many hundred weight, to any force that we can conceive to arise from volcanic eruptions. The theory, that they proceed from One of the most remarkable and tainly a much greater degree of volcanoes in the moon, has cerdistinguishing characteristics of probability. The same force that these stones is, that they perfectly would project a body from the resemble each other; at the same moon to the earth, would not, if it time, that they are totally differ- were exerted at the earth's sur ent from any known terrestrial face, send the same body to the substance. They present, in all distance of ten miles; in consecases, the same appearance of sequence of the superior mass of our mi-metallic matter, coated on the planet, and density of its atmosoutside with a black incrustation. phere. It is readily computed, The stone which fell at l'Aigle in that a body projected from a faFrance, in 1803, was found to con-vourable spot on the moon's surtain 54 parts of silica

36

.

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oxyde of iron
magnesia

oxyde of nickel
sulphur
lime

have been analized
rly the same results.
gravity of these

face, that is, from the centre of her disc opposite the earth, with a velocity about four times what is commonly given to a cannon-ball, or, about 8220 feet per second, would carry it beyond the centre of attraction, and consequently into the sphere of the earth's activity; whence it must necessarily either fall to our surface, or circu

late about us as a satellite. The time that a body, so projected, would be in its passage from the mioon to the earth, is also found to be three days; which is not so long but that it might retain its heat, particularly as it is doubtful whether in passing through a vacuum, or very attenuated medium, it would be possible for the caloric to escape, not to say that it might acquire a fresh accumulation of heat, by passing through the denser parts of our atmosphere. Add to this, that eruptions resembling those of our volcanoes have been frequently observed in the moon, and that her atmosphere is extremely rare, and consequently presenting but little resistance to projected bodies; and it will then be seen that this hypothesis, though at first sight apparently extravagant, is notwithstanding much more probable than the one we before examined. It must be acknowledged, however, that the explosions of which we have spoken, are difficult to account for upon this supposition. With regard to these bodies being concretions formed in the air, there is one principal objection, viz. that the velocity with which they strike the earth, estimated by the depth to which they have been known to penetrate, is so great as to indicate their having fallen from heights far exceeding the limits of the terrestrial atmosphere.

AEROLOGY, the doctrine or science of the air, and its phenomena, properties, good and bad qualities, &c.

AEROMETRY, the art of measuring powers and properties of the air; including the laws of motion, gravitation, pressure, elasticity, refraction, condensation, &c. of the atmospheric fluid.

AERONAUT, a person who sails or navigates through the air.

AEROSTATION, in the modern application of the term, signifies the art of navigating through the air, both in the principles and practice of it. Hence also the machines, which are employed for this purpose, are called ærostatic machines; and on account of their round figure, air-balloons. The

person who navigates them is called an aronaut.

The fundamental principles of this art have been long known; although the application of then to practice seems to be altogether a modern discovery. These chiefly relate to the weight, pressure, and elasticity of the air, its specific gravity, and that of the other bodies to be raised or floated in it. Any body which is specifically, or bulk for bulk, lighter than the atmospheric air, will be buoyed up by it, and ascend; just as wood, or cork, ascends in water; but as the density of the atmosphere decrea ses, this body can rise only to a height in which the surrounding air will be of the same specific gravity with itself: in this situation it will either float, or be driven in the direction of the wind or current of air to which it is exposed. An air-balloon is a body of this kind, the whole mass of which, including the covering, contents, and appendages, is of less specific gravity than that of the air through which it rises.

Heat is well known to rarify and expand, and consequently to lessen the specific gravity of the air to which it is applied; and the dimi nution of its weight is proportional to the heat. According to the scale of Fahrenheit's thermometer, 400, or rather 435, degrees of heat, will just double the bulk of a quantity of air. If, therefore, the air enclosed in any kind of covering be heated, and consequently di lated, to such a degree as that the excess of the weight of an equal bulk of common air above the weight of the heated air, is greater than the weight of the covering and its appendages, this whole mass will ascend in the atmosphere; till by the cooling and condensation of the included air, or the diminished density of the surrounding fluid, it becomes of the same specific gravity with the air in which it floats, and without renewed heat it will then gradually descend: If instead of heating common air, inclosed in any covering, and thus diminishing its gravity, the covering be filled with an elastic fluid lighter than atmos

pheric air, the whole mass will ascend as in the former case, and continue to rise till it attains an altitude at which the surrounding air is of the same specific gravity with itself.

an aperture at the bottom, the air was rarefied, and the bag ascended to the height of 70 feet. Various experiments were now made upon a large scale, which excited the public curiosity very greatly. An immense bag of linen, lined with paper, and containing upwards of 23,000 cubic feet, was found to have a power of lifting about 500 pounds, including its own weight. Burning chopped straw and wool under the aperture of the machine,

The idea of flying by means of wings and other contrivances, was certainly entertained by the ancients; and some accounts relate exploits of this kind having been performed; but still there is reason to suppose they are mere fictions, and that no means were ever pos-immediately occasioned it to swell, sessed for accomplishing this un- and afterwards to ascend into the dertaking till the invention of bal- atmosphere. In ten minutes it had loons, which dates no further back risen 6000 feet; and when its force than the conclusion of the last was exhausted, it fell to the ground century. Soon after Mr. Caven- at the distance of 7668 feet from dish's discovery of the specific the place it ascended.-Soon after gravity of inflammable air, it oc- this one of the brothers, invited curred to the ingenious Dr. Black, by the Academy of Sciences to rethat if a bladder sufficiently light peat his experiment at their exand thin were filled with this air, pense, constructed a large balloon it would form a maɛs lighter than of an elliptical form; and in a prethe same bulk of atmospheric air, liminary experiment, this machine and rise in it. This thought was lifted from the ground eight persuggested in his lectures, in 1767 sons who held it, and would have and 1768; and he proposed, by carried them all off, if more had means of the allantois of a calf, to not quickly come to their assisttry the experiment. Other em ance. Next day the machine was ployments, however, prevented filled by the combustion of 50 the execution of his design. The pounds of straw and 12 pounds of possibility of constructing a vessel, wool. The balloon soon swelled which when filled with inflamma- and sustained itself in the air, toble air would ascend in the atmos-gether with the burden of between phere, had occurred also to Mr. Cavallo, and to him belongs the honour of having first made experiments on this subject, in the beginning of the year 1782, of which an account was read to the Royal Society, on the 20th of June in that year.

But while aerostation seemed thus on the point of being made known in Britain, it was unexpectedly announced in France by two brothers, Stephen and John Montgolfier, natives of Annonay, and masters of a considerable papermanufactory there, who had turned their thoughts to this project as early as the middle of the year 1782. Their idea was to form an artificial cloud, by inclosing smoke in a bag, and making it carry up the covering along with it. In that year the experiment was made at Avignon with a fine silk bag; and by applying burning paper to

400 and 500 pounds weight. It was designed to repeat the experiment before the king at Versailles; but a violent storm of rain and wind happening to damage the machine, it became necessary to prepare a new one; and such expedition was used, that this vast balloon, near 60 feet in height and 43 in diame ter, was made, painted within and without, and finely decorated, in the course of four days and four nights. Along with it was sent a wicker cage, containing a sheep, a cock, and a duck, which were the first animals ever sent on such a voyage. The full success of the experiment was, however, prevented by a violent gust of wind, which tore the machine in two places near the top, before it ascended. Still it rose 1440 feet; and after remaining in the air about eight minutes, fell to the ground, at the distance of 10,200

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