EXPLOSION

, a sudden and violent expansion of an elastic fluid, by which it instantly throws off any obstacle that happens to be in the way, sometimes with astonishing force and rapidity, as the Explosion of fired gun-powder, &c.

Explosion differs from expansion, in that the latter is a gradual and continued power, acting uniformly for some certain time; whereas the former is always sudden, and only of momentary or immensurably short duration. The expansions of solid substances do not terminate in violent explosions, on account of their slowness, and the small space through which the expanding substance moves; though their strength may be equally great with that of the most active aerial fluids. Thus we find that though wedges of wood, when wetted, will cleave solid blocks of stone, they never throw them to any distance, as is the case with gunpowder. On the other hand, it is seldom that the expansion of any elastic fluid bursts a solid substance without throwing the fragments of it to a considerable distance, with effects that are often very terrible.

The most part of explosive substances are either aerial, or convertible into such, and raised into an elastic fluid. Thus gun-powder, whose essence seems to consist in common air fixed in the nitre, or at least an air of similar elasticity, where it is condensed into a bulk many hundred times less than the natural state of the atmosphere; which air being suddenly disengaged by the firing of the gun-powder, and the decomposition of its parts, it rapidly expands itself again with a force proportioned to the degree of its condensation when fixed in the gun-powder, and so explodes, and produces all those terrible effects that attend the explosion. The elastic fluid generated by the fired gun-powder expands itself with a velocity of about 10,000 feet per second, and with a force more than 1000 times greater than the pressure of the atmosphere on the same base.

The Electric Explosions seem to be still much more strong and astonishing; as in the cases of lightning, earthquakes, and volcanoes; and even in the artificial electricity produced by the ordinary machines. The astonishing strength of electric explosions, which is beyond all possible means of measuring it, manifests itself by the many tremendous effects we hear of fire-balls and lightning.

In cases where the electric matter acts like common fire, the force of the explosions, though very great, is capable of measurement, by comparing the distances to which bodies are thrown, with their weight. This is most evident in volcanoes, where the projections of the burning rocks and lava manifest the greatness of the power, at the same time that they afford a method of measuring it: and these explosions are owing to the extrication of aerial vapours, and their rarefaction by intense heat.

Next in strength to the aerial vapours, are those of aqueous and other liquids. Very remarkable effects of these are observed in steam-engines; and there is one case from which it has been inferred that aqueous steam is even vastly stronger than fired gun-powder. This is when water is thrown upon melted copper: for here the explosion is so strong as almost to exceed imagination; and the most terrible accidents have happened, even from so slight a cause as one of the workmen spit- | ting in the furnace where copper was melting; arising probably from a sudden decomposition of the water. Explosions happen also from the application of water to other melted metals, though in a lower degree, when the fluid is applied in small quantities, and even to common fire itself, as every person's own experience must have informed him; and this seems to be occasioned by the sudden rarefaction of the water into steam. Examples of this kind often occur when workmen are fastening cramps of iron into stones; where, if there happen to be a little water in the hole into which the lead is poured, this will fly out in such a manner as sometimes to burn them severely. Terrible accidents of this kind have sometimes happened in founderies, when large quantities of melted metal have been poured into wet or damp moulds. In these cases, the sudden expansion of the aqueous steam has thrown out the metal with great violence; and if any decomposition has taken place at the same time, so as to convert the aqueous vapour into an aerial one, the explosion must be still greater.

To this last kind of explosion must be referred that which takes place on pouring cold water into boiling or burning oil or tallow, or in pouring the latter upon the former; the water however being always used in a small quantity.

Another remarkable kind of Explosion is that produced by inflammable and dephlogisticated air, when mixed together, and set on fire; a kind of explosion that often happens in coal mines, &c. This differs from any of the cases before mentioned; for here is an absolute condensation rather than an expansion throughout the whole of the operation; and could the airs be made to take fire throughout their whole substance absolutely at the same instant, there would be no Explosion, but only a sudden production of heat.

Though Explosions be sometimes very destructive, they are likewise of confiderable use in life, as in removing obstacles that could scarcely be overcome by any mechanical power whatever. The principal of these are the blowing up of rocks, the separating of stones in quarries, and other purposes of that kind. The destruction occasioned by them in times of war, and the machines formed upon the principle of Explosion for the destruction of the human race, are well known; and if we cannot call these useful, they must be allowed at least to be necessary evils.

The effects of Explosions, when violent, are felt at a considerable distance, by reason of the concussions they give to the atmosphere. Sir Wm. Hamilton relates, that at the explosions of Vesuvius, in 1767, the doors and windows of the houses at Naples flew open if unbolted, and one door was burst open that had been locked, though at the distance of 6 miles: and the explosion of a powder-magazine, or a powder-mill, it is well known, spreads destruction for many miles round; and even kills people by the mere concussion of the air. A curious effect of them too is, that they electrify the air, and even glass windows, at a considerable distance. This is always observable in firing the guns at the Tower of London: and some years ago, after an Explosion of some powder-mills near that city, many people were alarmed by a rattling and breaking of their china-ware. In this respect however, the effects of electrical Explo- sions are the most remarkable, though not in the uncommon way just mentioned; but it is certain that the influence of a flash of lightning is diffused for a great way round the place where the Explosion happens, producing very perceptible changes both on the animul and vegetable creation.

EXPONENT of a Power, in Arithmetic and Algebra, denotes the number or quantity expressing the degree or elevation of the power, or which shews how often a given power is to be divided by its root before it be brought down to unity or 1. Thus, the Exponent or index of a square number, or the 2d power, is 2; of a cube 3; and so on; the square being a power of the 2d degree; the cube, of a 3d, &c. It is otherwise called the Index.

Exponents, as now used, are rather of modern invention. Diophantus, with the Arabian and the first European authors, denoted the powers of quantities by subjoining an abbreviation of the name of the power; though with some variation, and difference from one another. The names of the powers, and the marks for denoting them, according to Diophantus, are as follow: viz. Names, Marks, which we now denote by

1, a, a², a³, a⁴, a⁵, a⁶, &c.

F. Lucas Paciolus, or De Burgo, for the root, square, cube, &c, uses the terms cosa, censo, cubo, relato (primo, secundo, tertio, &c), or the abbreviations co. ce. cu.; and R for root or radicality.

Cardan used the Latin contractions of the names of the powers; and other contemporary, as well as succeeding, authors, especially the Germans, as Stifelius, Scheubelius, Pelitarius, &c, used the like contractions, but somewhat varied, as thus:

But besides that way, the same authors also made use of the numbers as in the last line here above, and it was Stifelius who first called them by the name Exponent.

Bombelli, whose Algebra was published in 1579, denotes the res, or unknown quantity, by this mark <*>, and the powers by numeral Exponents set over it, thus: , &c. And

Stevinus, who published his Arithmetic in 1585, and his Algebra soon afterwards, has such another me thod, but instead of <*> he uses a small circle ○, within which he places the numeral Exponent of the power; thus ○0, ○1, ○2, ○3, &c: and in this way he extends his notation to fractional Exponents, and even to radical ones; thus ○1/2, ○1<*>, ○3/4, ○2<*>, &c.

Vieta after this used words again to denote the powers. Afterwards Harriot denoted the powers by a repetition of the root; as a, aa, aaa, for the 1st, 2d, and 3d powers. Instead of which, Des Cartes again restored the numeral Exponents, placing them after the root, when the power is high, to avoid a too frequent repetition of the letter of the root; as a³ a⁴, &c, as at | present. Also Albert Girard, in 1629, used the Exponents to roots, thus; √, √², √³, &c.

The notation of powers and roots by the present way of Exponents, has introduced a new and general arithmetic of Exponents or powers; for hence powers are multiplied by only adding their Exponents, divided by subtracting the Exponents, raised to other powers, or roots of them extracted, by multiplying or dividing the Exponent by the index of the power or root.—

So ; the 2d power of a³ is a⁶, and the 3d root of a⁶ is a².

This algorithm of powers led the way to the invention of logarithms, which are only the indices or Exponents of powers: and hence the addition and subtraction of logarithms, answer to the multiplication and division of numbers; while the raising of powers, and extracting of roots, is effected by multiplying the logarithm by the index of the power, or dividing the logarithm by the index of the root.

Exponent of a Ratio, is, by some, understood as the quotient arising from the division of the antecedent of the ratio by the consequent: in which sense, the Exponent of the ratio of 3 to 2 is 3/2; and that of the ratio of 2 to 3 is 2/3.

But others, and those among the best mathematicians, understand logarithms as the Exponents of ratios; in which sense they coincide with the idea of measures of ratios, as delivered by Kepler, Mercator, Halley, Cotes, &c.

EXPONENTIAL Calculus, the method of differencing, or finding the fluxions of, Exponential quantities, and of summing up those differences, or finding their fluents. See Calculus, Fluxions, and FLUENTS.

Exponential Curve, is that whose nature is defined or expressed by an Exponential equation; as the curve denoted by a^x = y, or by x^x = y.

Exponential Equation, is one in which is contained an exponential quantity: as the equation a^x = b, or x^x = ab, &c.

Exponential Equations are commonly best resolved by means of logarithms, viz, first taking the log. of the given equation: thus, taking the log. of the equation a^x = b, it is x X log. of a = log. of b; and hence x = (log. b)/(log. a)

Also, the log. of the equation x^x = ab, is x X log. x = log. ab; and then x is easily found by trial-and-error, or the double rule of position.

Exponential Quantity, is that whose power is a variable quantity; as the expression a^x, or x^x.

Exponential quantities are of several degrees, and orders, according to the number of exponents or powers, one over another. Thus, a^x is an Exponential of the 1st order, a^xy, is one of the 2d order, a^xyz is one of the 3d order, and so on. See Bernoulli Oper. tom. 1, pa. 182, &c.