EXPLOSIVES. 378 EXPOSITION OF THE SACRAMENT. Manufacture of Explosives in the United States. The manufacture of explosives is now one of the most important of the chemical indus- tries in the United States. Its growth, as will be seen from the following table from the census of 1900, has been most rapid, and the 97 estab- lishments manufacturing explosives were located in 21 different States. In Pennsylvania alone there were 30 such factories, while the 7 manu- facturers of California produced over one-fourth of the amount made in the United States. In addition there were two factories belonging to the Government, which in 1900 produced 80,000 pounds of explosives, with a value of $60,506. That tin- production of explosives in the United States is not entirely for domestic consumption is shown by the fact that the exports of gun- powder in the year 1900 amounted to 1.612,822 pounds, valued at $197,438; while exports of all other explosives were valued at $1,694,166. Total Production and Value of Explosives. by Decades : 1840 to 1900 TEAR ■235 E « a y. 8 Capital Average number of Wage- earnei-B Products Pounds Value 1840 137 54 58 36 54 69 97 $875,S75 1,179.223 2,805.700 4,099,900 6,585,185 13.539.478 19,465,846 496 679 747 973 1.340 2.353 4,502 8,977,348 1850 SI 580 B2 1860 1870 4,237.539 1880 1K90 1900 "s&Mriisaa" 215,980,719 5,802,029 10,993,131 •16.950,976 • This value is for the explosive substances only. When materials of all kinds produced in these establishments are Included, the value is $17,125,918. See also statistics under Gunpowder; Dyna- mite. Literature. The great interest in military circles concerning explosives has led to the pub- lication of a periodical in London entitled Arms and Explosives. The Bureau of Ordnance of the United States War Department issues, at in- tervals. Notes on the Construction of Ordnance, which contains the latest information on ex- plosives, and Charles E. Munroe has published for many years a series of "Notes on the Litera- ture of Explosives," in the Proceedings of the United Stales Naval Institute. The monographs of the leading experts, such as Abel of England, Berthelot of France, Munroe of the United States, and Von l.enek of Austria, should lie consulted, in addition to which see the following, which are among the latest books on the subject: Cundill, A Dictionary of Explosives I revised ed. by J. II. Thompson,' London, 1895) ; Guttmann, Blasting: A Handbook for the I si of Engineers and Others Engaging in Minimi, Tun neling, Quarrying, etc. (Philadelphia, 1S92) ; Berthollet, Explosives and Their Power, translated from the French by Napier Hooke and William MacNab (London, 1892); Eissler, The Modern High Explosives (New fork, 1893, later ed., Lon- don, 1897) ; Munroe, Index to the Literature of pari i and ii. I Baltimore, 1893 1 : Guttmann, The Manufacture of Explosives: 1 ' and Practical Treatise on the History, the Physical and Chemical Properties, and the Manufacture o Explosives, with full bibliography of from 1 168 to 1895 (2 vols., London, i) ; Walke, Lectures on Explosives (New ind De Kalb, Manual of Explosives (Toronto, 1900). See Gunpowder; Guncotton; Dynamite; Nitroglycerin; Artillery; Ballis- tics ; Ordnance ; and Smokeless Powders. EXPO'NENT and EXPONENTIAL (from Lat. exponere, to set forth, from ex, out + ponere, to put). An exponent, in the primitive sense, is a number-symbol which shows how many equal factors enter into a power; e.g. in 2 3 , 3 is the exponent of 2 ; in a 5 is the exponent of a. The exponent affects only the letter or number adjacent to which it stands, ab 3 meaning <i66&. While the various forms and the theory of expo- nents have been matters of growth, the notation as now used was introduced into algebra by the mathematicians of the seventeenth century. Chu- quet had ( 1484) used exponents, but not with the same significance as at present, and a step toward the theory of the subject, including the use of fractional exponents, had long before been made by Oresme (fourteenth century) . Kepler (1619) speaks of Biirgi as having written for x, x x 3 , x* .... 1R, Is, lc, zz, . . . whereas he himself prefers 1, V, l u , 1'" Biirgi. however, wrote -,'J. for 16a; 2 , and }J Q for 20a!*. Harriot (q.v.) wrote x* for xx, x 3 for xxx. Wallis (1656) explained the expressions a?"" and x as indicat- ing the same as — n and./—. The theory of ex- ponents has gradually received extensions until it has become an important division of algebra. The following equations show the meanings of various exponents: a° = 1, a 1 —a; a- 2 = =-; ar" = —• a 2 a" a* := -j/a; aiT= {/a; a' = f a 2 . The fundamental laws of exponents in algebra (a m ) n = a n,n ; (abf = a"b" ; for all values of m and n. These operations are sub- ject to the associative law (q.v.), a m+,1+ f _ rt (m-l-n)+p . to the commutative law, a mJ " n+ = a< ,+n+m , and to the distributive law, a( m+0 ) p = a + " r '. In quaternions (q.v.) and certain other branches of modern mathematics the con- ventions as to exponents differ. Functions in which the variable or variables are involved as exponents are called exponential functions; e.g. a 1 = c, x* =6, 2 X = 8. In the last example x evidently equals 3. When such equations cannot be solved by factoring, it is best to apply logarithms (q.v.). Thus in 2* = 80, ■i • log2 = log80, and x = ^~ = 6.322. The log 2 12 +1-2-3 ~ r l-2v!-4 is called the exponential series. If x be taken as 1, the series gives e = 2.718281828 .... the base of (he hyperbolic logarithms (q.v.). EXPOSITION. See' Exhibitions, Indus- trial. EXPOSITION OF THE SACRAMENT. Tn the Roman Catholic service, the public exhibition of ih. Holy Sacrament, instituted with certain ceremonies for the veneration of the faithful. There ia evidence to warrant the belief thai as early as the fourteenth century the sacrament
