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the sum of the former (23,) abating two nines, leaves 5 also. Hence the addition is right. Compound Addition is the collecting several quantities of different denominations into one sum. Place the same denominations to stand directly under each other. Add up the figures in the lowest denomination, and find how many ... units of the next higher denomination are contained in their sum. Write down the remainder, and carry these units to the next higher denomination ; which add up in the same manner as before ; and proceed thus through all the , different denominations to the highest.
A DLition of Intermediate Decimals, is the finding the sum of any number of circulating decimals.
1. Reduce all the decimals to their equivalent fractions; and the sum of these will be the answer required ; or,
2. Carry on the repetends till they all begin and end their periods of circulation in the same lines, and let the circulation of each be carried two figures beyond this place; then add them up as in the former rule, observing not to set down any thing in the first two places; only carry the proper namber from them to the conterminous period; and the result will give the true period of circulation in the sum required.
In this example, the periods of circulation do not commence together 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 their proper signs. And this is generally divided into the following cases. 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.
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
Note. When the quantities are reduced to their lowest terms, or simplest form, and have different indices and numbers, they can only be added together, by means of the sign + placed between them. Thus, V 18 + V108 = 3 V2+6V3, 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 additive 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, a's — pro + q2 = a, is an ad fected equation, having three different powers of the unknown quantity ar entering into its composition. Such equations are distinguished from simple, which involve but one power. ADHESION, in Philosophy, is a species of attraction which takes place between the surfaces of bodies, whether similar or dissimilar, and which, in a certain degree, connects them together; differs from cohesion, which, uniting particle to particle, retains together the component parts of the same mass. The power of adhesion is proportional to the number of 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 ower 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 .
exposed to the fire, produces a vehement blast of wind. AEOLUS’S Harp, an instrument so named from its producing agreeable harmony, merely by the action 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 two pieces of wainscot, about half an inch high and a quarter of an inch thick, to serve as bridges for the strings; and within side, at each end, glue two pieces of beech, about an inch square, of length equal to the width of the box, which are to sustain the pegs; into these fix as many pins, such as are used in a harpsichord, as there are to be strings in the instrument, 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. AERA, in Chronology, is the same as Epoch, and means a fixed point of time, from which to begin a computation of the succeeding years. AERA also means the way or mode of accounting time. Thus, we say, such a year of the Christian aera, &c. Christian AERA. 1t 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. AERIAL, 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 the greater the distance at which they are viewed. AEROGRAPHY, a description of the air or atmosphere, its nature, composition, limits, dimensions, properties, &c. AEROLITHS, a name given to those solid semi-metallic substances which fall from the atmoshere. The descent of such bodies •+. been long reported ; but the fact was not confirmed till within a few years. The larger sort of these stones have been seen as luminous bodies, to move with great velocities, descending in oblique directions, and frequently with a loud hissing noise, resembling that of a mortar-shell when projected from a piece of ordnance ; they 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. One of the most remarkable and distinguishing characteristics of these stones is, that they perfectly resemble each other; at the same time, that they are totally different from any known terrestrial substance. They present, in all cases, the same appearance of semi-metallic matter, coated on the outside with a black incrustation. The stone which fell at TAgie in France, in 1803, was found to con. tain 54 parts of silica * . . . oxyde of iron • * magnesia - oxyde of nickel sulphur lime ave been analized rly the same results. gravity of these
bodies is also found to be nearly the same, being about 3.400, or nearly 3} times that of common Water.
These general and constant characters strongly indicate a common origin, and various hypotheses have been advanced to account for them. Some have attributed them to terrestrial, and others to lunar, volcanoes; they have again been supposed to be concretions actually formed in the regions of our atmosphere; while others have considered them as small planets circulating about the sun or earth, which coming in contact with our atmosphere, take fire from the resistance and friction they experience in passing through it.
With regard to the first supposition, viz. that these stones proceed from terrestrial volcanoes, it will be sufficient to observe, that no remarkable eruption has been known to happen at or near the time of their fall, and that such bodies have been found at the distance of some thousand miles from any known volcano ; beside the inimense force that would be necessary to project bodies, some of them of many hundred weight, to so great a distance, far exceeds any force that we can conceive to arise from volcanic eruptions. The theory, that they proceed from
volcanoes in the moon, has cer
tainly a much greater degree of probability. The same force that would project a body from the moon to the earth, would not, if it were exerted at the earth’s surface, send the same body to the distance of ten miles; in consequence of the superior mass of our planet, and density of its atmosphere. It is readily computed, that a body projected from a fa. vourable spot on the moon's sur. 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 centré of attraction, and consequently into the sphere of the earth's ac. tivity; whence it must necessarily either fall to our surface, or circu
\ late about us as a satellite. The time that a body, so projected,
moon 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 aerostatic machines; and on account of their
round figure, air-balloons. The 1.
person who navigates them is called an apronaut. would be in its passage from the
The fundamental principles of this art have been long known ; although the application of them to practice seems to be altogether a modern discovery. These chiefly relate to the §t, 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 decreases, 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 dimimution 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 dilated, 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