EXPLOSION

(Lat explosio.) In Natural Philosophy,asudden and violent expansion of the parts of any Explosion differs from expansion in this, that whereas the former is always sudden, and only of momentary duration, the latter is the effect of some gradual and continued power, acttag uniformly for some considerable lime See Expansion j Matter, Properties op. EXl'ONENT, in Algebra, is used in various senses; thus we say the exponent of a power, the exponent of a rank, the exponent of a ratio. The exponent of a power is a number or algebraic character expre ing the degree or elevation of the power to which the quantity is raised. For example, in the expre ion a*, 4 is the exponent, denoting that a is raised to the fourth power. Intheexpre jn the exponent m is indeterminate, as it may repre-;<tiy number whatever. The exponent may also be fractional, in which case it denotes not the power, but the root of the quantity; thus a* denotes the third or cube root of a Or it may be negative, in which case it denotes the quotient that ariseB from the division of unit by the quantity raised to that power; for example, o-n is the same thing as —. The earliest writers on algebra denoted the powers of an numbers by an abbreviation of the name of the power. Harriot repeated the quantity, and for <H wrote aaa a; the present convenient system was introduced by Des cartes. i'onent of a rank is the number or place of any term in a series; thus, in the series of uneven numbers, 1,3. 5. 7. 9, II. 13, 15, Ac, 7 is the exponent of the rank of the term 13, because 13 is the 7th term from the commencement. \ponent of a geometrical ratio is the quotient that arises from dividing the consequent by the antecedent of the ratio. Thus, in the ratio of 2 to 8, the exponent is ^ = 4; and in the ratio of 8 to 2, the exponent is f = |- mathematicians, however, consider logarithms as the pxnonents of ratios. [s. 449]