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canne very popular. Father Mersenne was apprised of it in 1644, and immediately conveyed an account of it to the philosophers of France; and Pascal, after some hesitation, adopted Torricelli’s idea, and devised several experiments for confirming it. One of these was to procure a vacuum above the reservoir of quicksilver, in which case he found the column sunk down to the common level; but this appearing to him not suf. ficiently powerful to dissipate the prejudices of the philosophers of the old school, he prevailed on M. Perier, his brother-in-law, to execute the famous experiment of the Puy-de-domme, who found that the height of the quicksilver, half way up the mountain, was considerablv less than at the foot of it, and still i. at the top : by this means the question was set to rest; as no doubt could any longer be entertained, that it was the weight of the atmosphere that counterpoised the column of quicksilver. The medium of all these is about as one to 832, or one to 833; when reduced to the pressure of thirty inches of the barometer, and the mean temperature of fifty-five degrees of the thermometer; or, by adding # to the last number, the proportion becomes one to 833}, or 3 to 2500; whence, upon the whole, we may conclude, that the density of air is to that of water as 3 to 2500; and, consequently, that a cubic foot of air weighs at a mean 14 ounces avoir
dupois; the weight of a cubic foot of water being 1000 ounces, and of a cubic foot of quicksilver 13,600 ounces. Elasticity of the Air.—It is another quality of this fluid, that it will yield to any pressure, by contracting its dimensions; and that, upon removing or diminishing the pressure, it will again return to its natural state or volume. This elastic force may be accounted the distinguishing property of air, the others which we have mentioned above being common to all fluids. Various experiments were soon instituted both on the continent and in England, with a view of ascertaining the specific gravity of the air, or §. average weight of
a given bulk of it compared with that of water. To prove the existence of this property of air, various experiments might be cited ; it will, however, be sufficient to mention one; which is, simply inverting an open vessel full of air in water; in which case, the resistance it offers to further immersion, and the height to which the water ascends within it, in proportion as it is further immersed, are proofs of the elasticity of the air contained in it. With regard to the degree of this elastic force, it has been shown, by the most satisfactory experiments, that with moderate pressure it is always proportional to the density of the air, and that the density is always as the compressing force ; whence also the elasticity of air is as the force by which it is compressed. Thus, if air is confined in a bent tube, one end being open and the other hermetically sealed, and quicksilver be poured in at the open end, it will be found that the spaces into which the air is compressed are always inversely as the weights by which it is food. and since these weights are the measures of the elasticity, therefore the elasticities are inversely as the spaces which the air occupies. It has been questioned, amongst philosophers, whether this elastic ower of the air is capable of being destroyed or diminished. Mr. Boyle could not discover that any state of rarefaction, which he was capable of producing, was sufficient for destroying this property. Colonel Roy, has shown that the particles of air may be so far removed as to lose a very great part of their elastic force : the same experiments show that moist air possesses the greatest elastic force; and that common air, in its natural state, is proportionally more elastic than when its density is considerably augmented by pressure. The elasticity of air may be so effected by a violent pressure as to require some time to return to its natural tone. The weight or pressure of the air, it is obvious, has no dependence on its elasticity; but would be the same whether it possessed that property
or not. But being elastic, it is necessarily affected by pressure, which reduces it into such a space, that the elasticity which re-acts against the compressing weight, is equal to that weight. The elasticity of the air exerts itself equally in all ways; and when it is at liberty, and freed from the cause which compresses it, it expands equally in all directions, in consequence of which it always assumes a spherical figure, in the interstices of the fluid in which it is lodged. This is evident in liquors placed under the receiver of an air-pump; for, by exhausting the air, at first there appears a multitude of exceeding small bubbles, like grains of fine sand, dispersed through the fluid mass, and rising upwards; and as more air is pumped out, they enlarge in size, but still retain their spherical figure. Tne expansion of air, by means of its elastic property, when only the compressing force is taken off or diminished, is found to be surprisingly great; it having been Xnown, in certain experiments, to expand itself into 13,679 times its original space, and this solely by its own natural power, without the application of fire. he elasticity of the air, under the same pressure, is increased by heat and diminished by cold, and that according to several very accurate experiments, at the rate of about one-435th P. for every degree of heat of Fahrenheit's thermometer. AlB-Gun, a pneumatic machine, which expels bullets or shot with great velocity and effect; its operation depends upon the elastic power of air, which we have seen above increases in proportion to the greater degree of condensation. Now the elastic power of fired gunpowder being equal to the pressure of 1000 atmospheres, or 1000 times greater than that of common air, it follows that in order to produce the same effect with an airgun as with a musket, the air must be compressed into onethousandth part of its natural bulk; and for all inferior degrees of condensation, the effect will be proportionally diminished; and
as the velocities with which equal balls are impelled, are directly as the square roots of the forces acuing upon them, we shall be able always to estimate the effect previous to any explosion taking place : thus, if n be the number of times the air is condensed, then as V 1000 : Vn = the velocity arising from the explosion of gunpowder to that arising from condensation. If, therefore, the air be condensed twenty times, its velocity will be about one seventh of that arising from fired gunpowder. In the air-gun, however, the reservoir of condensed air is commonly very large, in proportion to the tube which contains the ball, and its density will be very little altered by expanding through the narrow tube; and, consequently, the ball will be urged i. out by nearly the same uniform force with that of the first instant, and hence the exploding power of condensed air is much more considerable than appears from the preceding estimation, being little less than that of gunpowder, even under a condensation of ten times, provided the reservoir be of any considerable magnitude. AIR-Pipes, an invention intended for clearing the holds of ships, and other close places, of their foul air. AIR-Pump,a pneumatic machine, which is of great use, in explaining and demonstrating the properties of air. It was invented by Otto de Guericke, consul of Magdeburgh, about the year 1654; and though it has since been much improved in form, its principle remains the same. The principal use of the air-pump is to extract the air from a vessel, which in that state is said to be exhausted, and the degree of exhaustion depends upon the goodness of the machine. The vessel, which is called a receiver, is fitted to a plate on the air-pump, having a small orifice in the middle, which communicates by a tube with the barrels of the pump. These barrels are of metal, or of glass, in each of which works an air-tight piston, having a valve, which opens outwards when the piston is forced down towards the bottom of the barrel.
There is another valve to prevent the air from being drawn back into the receiver. The elasticity of the compressed air at the bottom of the barrel being greater than that of the external atmo. sphere, forces open the valve, and escapes; and when the piston is again raised, air from the receiver escapes into the barrel. The two barrels, act thus alternately, till the air in the receiver be so much exhausted as not to have elasticity sufficient for , forcing open the valves, and there the degree of exhaustion which the pump can produce terminates. In whatever manner or form this machine is made, its use and operation are much the same. The air in the receiver is diminished at each stroke of the piston, by the quantity of the barrel or cy. linder full, and thus repeating the operation again and again, the air is rarefied to any proposed degree, a mercurial gage showing at any time what the degree of exhaustion is. . But, supposing no vapour from moisture, &c. to rise in the receiver, the degree of exhaustion, after any number of strokes of the piston, may be determined by knowing the respective capacities sof the barrel and the receiver, including the tube of communica. tion. For as every stroke diminishes the density in a constant proportion, namely, as much as the whole content exceeds that of the cylinder or barrel, the sum of as many diminutions as there are strokes of the piston, will show the whole diminution by all the strokes. Thus if the capacity of the barrel be equal to that of the receiver, then, the barrel being half the sum of the whole content, half the air will be drawn out at one stroke; and consequently the remaining half, being dilated through the whole or first capacity, will be of only half the density of the first; in like manner, after the second stroke, the density of the remaining contents will be only half of that after the first stroke, that is only 4 of the original density: continuing this operation, it follows that the density of the remaining air will be after three
strokes of the piston, T's after four.
strokes, and so on, according to the powers of the ratio , ; that is, such power of the ratio as is de. noted by the number of the strokes. Universally, if s denote the sum of the contents of the receiver and barrel, and r that of the receiver only without the barrel, and n any number of strokes of the piston ; then, the original density of the air being 1, the density after n
- rn strokes will be 7, that is, the nth s
derive a rule for finding the number of strokes of the piston, necessary to rarefy the air any number of times, or to reduce it to a given density d, that of the natural air
being 1. For since (+)"— d, by taking the logarithm of this equa
that is, divide the log. of the proposed density by the log. of the ra. tio of the receiver to the sum of the receiver and barrel together, and the quotient will show the number of strokes of the piston requisite to produce the degree of exhaustion required. Some of the principal effects and phenomena of the air-pump are the following:—That, in the exhausted receiver, heavy and light bodies fall equally swift; so, a piece of metal and a feather fall from the top of a tall receiver to the bottom exactly together. That most animals die in a minute or two: but, however, that vipers and frogs, though they swell much, live an hour or two ; and after being seemingly quite dead, come to life again in the open air: that snails survive about ten hours; efts, or slow-worms, two or three days; and leeches five or six. That oysters live for 24 hours. That the heart of an eel taken out of the body continues to beat for good part of an hour, and that more briskly than in the air. That warm blood, milk, gall, &c. undergo a considerable intumescence and ebullition. That a mouse or other animal may be brought, by degrees, to survive longer in a rarefied air, than it does naturally. That air may retain its usual pressure, after it is become unfit for respiration. That the eggs of silkworms hatch in vacuo. That vegetalion stops. That fire extinguishes; the flame of a candle usually going out in one minute; and a char. coal in about five minutes. That red-hot iron, however, seems not to be affected; and yet sulphur or gunpowder are not lighted by it, but only fused. That a match, after lying seemingly extinct a long time, revives again on re-admitting the air. That a flint and steel strike sparks of fire as copiously, and in all directions, as in air. That magnets, and magnetic needles, act the same as in air. That the smoke of an extinguished luminary gradually settles to the bottom in a darkish body, leaving the upper part of the receiver clear and transparent; and that on inclining the vessel sometimes to one side, and sometimes to another, the fume preserves its surface horizontal, after the nature of other fluids. That heat may be produced by attrition. That camphire will not take fire; and that gunpowder, though some of the grains of a heap of it be kindled by a burningglass, will not give fire to the contiguous grains. That glow-worms lose their light in proportion as the air is exhausted, and, at length, become totally obscure; but on readmitting the air, they presently recover it again. That a bell, on being struck, is not heard to ring, or very faintly. That water freezes much more rapidly than in the open air, especially if the basin which contains it be floating in a chemical mixture, by wilich the vapour arising from the water can be absorbed. But that a syphon will not run. That electricity appears like the aurora borealis.
MATH E MATICAL AND PHYSICAL SCIENCE.
AIR-Wessel, is a name given to those metallic cylinders which are placed between the two forcing-pumps in the improved fireengines. The water is injected b the action of the pistons throug two pipes, with valves, into this vessel ; the air previously contained in it will be compressed by the water, in proportion to the quantity admitted, and by its spring force the water into a pipe, which will discharge a constant and equal stream; whereas, in the common squirting engine, the stream is discontinued between the several strokes. ALGEBRA, a general method of solving problems and questions, whether arithmetical or matilematical, by means of symbols which have no fixed or determinate values like the arithmetical figures, and which, by preserving their original form through all the steps of a calculation, however long, enable the calculator to deduce, from the solutions of particular problems general formulae for the solution of all problems of the same kind. The origin of algebra, like that of other sciences of ancient date and gradual progress, is not easily ascertainable. ‘The earliest treatise on that part of analytics, which is properly called algebra, now extant, is that of Diophantus, a Greek of Alexandria, who flourished about the year 350, and who wrote thirteen books, though only six “Arithmeticorum ” of thern are preserved. He is the only Greek author on algebra whose works have been handed down to us, though some traces of it appear in the writings of some authors much nuore ancient, as Archimedes, Euclid, Apollonius, &c.; and we know that Hypatia wrote a commentary on the work of Diophantus. By what means the Arabs became possessed of this art is not known ; but both the name and the science were transmitted to Europe, and particularly to Spain, by the Arabians or Saracens, about the year 1100, or probably a little earlier. Italy, however, took the lead in the cultivation of the science,
after its introduction into Europe. Leonardo Bonacci, of Pisa, has some allusions to it in his arithmetic written after his return from Africa and the Levant, in 1202. Froin his manuscript, Lucus Paccioli, or de Borgo, derived the rudinients of that knowledge which enabled him to compose his “Summa Arithmeticae et Geometriae Proportionumque et Proportionalitatum,” which was published in Italian at Venice, in 1494, and again in 1523. After this, algebra became more generally known and improved, especially by many in Italy; and soon after, the first rule was there found out by Scipio Ferreus, for resolving one case of a compound cubic equation. But this science, as well as other branches of mathematics, was, in an eminent manner, cultivated and improved by Hieronymus Cardan of Bonomia, a very learned author, who, in the year 1545, published a book containing the whole doctrine of cubic equations, which had been in part revealed to him by Nicholas Tartalea. The chief improvements made by Cardan, as collected from his writings, are stated by Dr. Hutton as follows: Tartalea communicated to him only the rules for resolving three cases of cubic equations, namely; a" + br= c, r* = br + c, and r3+ c = br; and he from thence raised a very large and complete work, laying down rules for all forms and varieties of cubic equations, having all their terms, or wanting any of them, and having all possi. ble varieties of signs; demonstrating all these rules geometrically ; and treating very fully of almost all sorts of transformations of equation, in a manner totally new. It appears, also, that he was well acquainted with all the roots of equations, that are real, both posi
tive and negative; or, as he calls them, true and fictitious; and that
he made use of them both occa
sionally. He also shewed that the
even roots of positive quantities
are either positive or negative;
that the odd roots of negative quan.
uo. are real and negative; but 3.
that the even roots of them are impossible or nothing, as to common use. He was also acquainted with the number and nature of the roots of an equation, and that partly from the signs of the terms, and partly from the magnitude and relation of the co-efficients. He knew that the number of positive roots is equal to the number of changes of the signs of the terms. That the co-efficient of the second terim of the equation, is the differ ence between the positive and negative roots: That when the second term is wanted, the sum of the negative roots is equal to the sum of the positive roots. How to compose equations that shall have given roots. That changing the signs of the even terms, changes the signs of all the roots. That the number of roots failed in pairs; or what we now call impossible roots, were always in pairs. To change the equation from one for m to another, by taking away any term out of it. To increase or diminish the roots of a given equation. It appears, also, that he had a rule for extraeting the cube root of such binomials as admit of ex traction ; and that he often used the literal notation a, b, c, d, &c. That he gave a rule for biquadratic equations, suiting all their cases; and that in the investigation of that rule, he made use of an assumed indeterminate quantity; and afterwards found its value by the arbitrary assumption of a relation between the terms. Also, that he applied algebra to the resolution of geometrical problems; and was well acquainted with the difficulty of what is called the Irreducible Case, in attempting the solution of which he spent a good deal of time. About the time that Cardan and Tartalea flourished in Italy, the science of algebra was cultivated
in Germany by Stifelius, and Scheubelius. Stifelius introduced the characters +, −, V, for plus, minus, and root, or radix, as he
called it. Also the initials 1,3,