ELIJAH. 798 ELIMINATION. the marriage of Aliab with the Tyrian princess Jezebel. Klijah is rather abruptly introduced by the writer as the uiicoinproniising oppoueut of Ahab, to whom he declares that uo rain or dew is to fall save at the Prophet's declaration. A famine ensues, during which time Elijah is miraculously fed by ravens. The famine increases, and at last Ahab is forced to yield and give his consent to a contest between Elijah and the propliets of Baal. The latter call upon Baal to send down the rain, but in vain. When Elijah, however, appeals to Yahwch. lightning comes to consume the bullock which the Prophet had placed on an altar soaked with water. By the order of Elijah, the prophets of Baal are slain at the brook Kishon, and rain is sent by Yahweh. Such is the general char- acter of the Elijah stories, all intended to illus- trate the superiority of Yahweh over other gods. Ahab is represented as again led astray by .Jezebel, who continues the opposition to Elijah. At times the latter is portrayed nigh unto despair; but he is encouraged by Yahweh, who appears to him in the 'rustling of the breezes,' and while threatening destruction to Israel promises escape to those who do not bow the knee to Baal. Even though the story of his life as given in the Bible be considered as having legendarj- and mythical features, we see in Elijah one of the most striking figures in Helirew liis- tory — one whose attitude foreshadows important changes in the religious life of the people. He shares, however, many of the characteristics of the old-time seer, whose chief function it was to give oracles and to control the moods of the deity in whose service he stood. He wears a primi- tive dress — a robe of goat's or camel's hair with a leathern girdle. He is accompanied often by a guild of prophets, though at times he myste- riously disappears and seeks the solitude of the wilderness. So. during the great famine, it is in the wilderness that ravens bring him bread and meat every morning and evening, and it is again in a solitary spot of the wilderness beyond Beer- sheba that "his strength is miraculously restored to him through a cake and a cruse of water that suddenly appear and which sustain him for forty days. He is not connected with any sanctuary, and holds no position at the Court. His appear- ance is as sudden as his disappearance. His courage is unbounded, for those parts of the narrative which picture him denouncing King Ahab — as e.g. for the judicial murder of Na- both, I. Kings xxi. 17-20 (see Ahab) — rest upon historical ground that may be regarded as solid, even though details have been added to color the dramatic situation. The transfiguration of Elijah, which takes place in the presence of his disciple Elisha (II. Kings ii. 11), may be a strange touch illustrating the admixture of myth and legend. A fiery chariot with fiery steeds descends from above, and Elijah rides in the storm to heaven. An old storm mj-th, in which the rolling of the clouds is taken as por- traying the storm-god himself riding in his cliar- iot, may have been incorpor.ated into the story of the old prophet. The mantle of Elijah falls from him as he a.seends and it is picked up by Elisha. In this way the indication is given that Elisha is to continue the work of Elijah. See Ellsh.v. ELIJAH. An oratorio, first performed at Birmingham, England. August 26. lS4(i. the music of which is bv Me?idelssohn and the words by Bartholomew. The biblical passages repro- duced were selected by Shubring. ELIM'INANT. See Detebiuxa.nts ; Elim- IX.VTIOX. ELIMINATION (from Lat. climiiiare, to turn out of doors, from ex, out + liiitcn, thresh- old). A process by which, from a number of statements concerning several quantities, a sepa- rate statement concerning each is obtained. In a larger sense, it means the setting aside of all extraneous considerations — of everything not es- sentia! to the result. In algebra, elimination is the operation which causes a quantity or a let- ter common to two or more equations to disap- pear, thus reducing a given system of equations to one of a less number of unknowns. If three imknown quantities, for instance, are to be found from three independent equations, the first step is to form from the three given equations two new ones, so as to eliminate one of the un- known quantities. From these two equations an- other of t!ie unknown qmmtities is eliminated, giving one equation of one unknown quantity, the value of which is then found. In solving simul- taneous linear equations, the simplest methods are those of addition (or subtraction) and com- parison. In the former method the coefiicients of the unknown to be eliminated are made alike, or alike except in sign, and the two equations subtracted or added member to member, thus causing the unknown to disappear. In the lat- ter case each equation is solved for the chosen unknown in terms of the other unknowns, and these expressions for the same quantity equated one to another. In complicated equations, elimi- nation becomes difiicult and often impossible. Two methods for eliminating a single unknown from two consistent equations of any degree de- serve special mention. The first, known as S,vl- vester's dialytic method, will best be understood from an example : To eliminate x from the equation — a^x' + o~r^ + a,a? + «„ = b^' + b,x + 6„ = Multiplying the members of the first equation by X, and those of the second by x and x- suc- cessively, «e have — 03 ar" + (I, a-- + Oi a; -j- «„ = O3 X* + a-x" + a^x- + OoX ' =0 h,x-+b,x+h„ — 6, x' + b,x- + b„x - } ,a-< + b,r' + Kx'- = The .eliminant of the se five equal ions a-', or", x X is—
a. Oj <h Oo Oj 0.. "1 a„ n
b.
6,
..
=
6, 6, fco
h. 6> 6„
(See Deter5[in.
ts.)
This method may be applied to certain systems
of more than two equations. Euler also sug-
gested an ingenious method, as follows:
Given the equations:
Fix) = Ojor' + a,x= + Oja) -f ao =
Ux) = M' + Si'" +b., = a
These cauations. being consistent, have a com-
mon root, r. Hence —
X — r
T — r
