Page:The New International Encyclopædia 1st ed. v. 04.djvu/633

CHECK. 551 CHECKING. A CBECKERED BEETLE. provides that if the crossing is afoompanied with the words 'not negotiable,' a person taking the check shall not have, and shall not be capable of giving, a better title than that of the person from whom he took it. In most respects other than those mentioned above, checks are governed by the rules which apply to bills of exchange. Consult the authori- ties referred to under Negoti.ble Instruments. CHECKERBERKY. See Gacxthebia and rAi{Tuiiii:K- Berry. CHECKERED BEETLE. . beetle of the serricorn pentamerous family Clcrida>, so named because of its variegated markings. Many of them are ant-like in form and movement. The adults are found on flowers, such as Spirea alba, and on trunks of trees, where they subsist on nectar and sweet sap. The lar- vae live under bark, and feed on wood- boring lar'ae, even penetrating into the Innrows in search of them. Some infest the hives of bees, where they devour the young bees, burrowing their way from cell to cell, and still others feed on dead animal matter. A sj-nopsis of tlw Xorth American spe- cies, by J. L. Le Conte. will be found in the Aniinls of the Lvceum of Natural History of Xew York, Vol. V. (New York, 1849). CHECKERS (OF. escheqiiier. from ML. .tcacuriiiiii. chess-board, from scacci, chess, from Pers. shah, king), or Dr.wght.s (Dutch drntit, Gcr. TrachI, burden, from AS. drnynn, to draw. Ger. trngen, to carry). A game played with 'men' on a checkered board, made square, di- vided into sixty-four equal square spaces, col- ored alternately black and white. The draughts or checkers are circular and Hat. There are many varieties of checkers — Chinese, English, Polish. Spanish, Italian, and Turkish. The game is also found among the native tribes of the interior of New Zealand. In France it is called let; dames, from its having been a favorite game with ladies: in Scotland the draught-board is called the dam- brod. Two persons play this game, each having a set of twelve men — one set black, the other white. The men may be placed either on the black or white squares, but they must all be placed on one color only. In England it is usual to play upon the white squares, with a black square to the lower right, and in Scotland upon the black, with a white square to the lower right. The men may be moved diagonally only, and by one square at a time. If an enemy's man stands in the way. no move may take place un- less there be a vacant square beyond into which the piece can be lifted. The man leaped over is then taken and removed from the board. The ob- ject of the game is to clear the board of the enemy's men. or to hem them in so that they cannot be moved, and whichever party does so first wins the game. .s no piece can move more than one step diagonally at a time, there can be no taking till the antagonists come to close quarters, and the advancing of them cautiously into each other's neighborhood is the chief art of the game. When a man on either side has made his wav. either bv taking or bv a clear open path, to the opposite side of the board, he is entitled to be 'crowned,' which is done by placing another man on the top of his man. Crowned men nuiy move either backward or forward, but always diagonally and by one square at a time, as before, and this additional power gives a great advantage to the player who owns the greatest number of 'kings.' and i;sually decides the game in his favor. Joshua Sturges's work, entitled The (luUle to the Game of Draughts, first printed in 1800, edited by Kean and last published in 18!)2, is the standard authority. The rules and many diagrams will be found in Spalding's Home Library (Xew Y'ork ) . CHECKING. In arithmetic, one of the old- est and best methods of checking the results of operations in decimal arithmetic is known as casting out nines. It originated at an early date among the Hindus, and from them it ])assed to the Arabs. Proofs for this rule appear in the works of Avicenna in the Teuth Century. Luca Pacioli (1494) adds this check to his work on division, pointing out cases in which it fails. Its use in elementary schools has been neglected more on the Continent of Europe than in Eng- land, and not until recently has the method been seriously urged by American teachers. The pro- cess may be best explained by an example. Required to check the multiplication, 3.5 X 34 = 1190: (1) Dividing 3.5 by 9, the remainder is 8; (2) Dividing 34 by 9, the remainder is 7; (3) Dividing 56 (the product of 7 and 8) by 9, the remainder is 2 : (4) Dividing 1190 by 9, the remainder is like- wise '2. But 2 = 2: therefore the product, 1190, is cor- rect. According to a proposition in the theory of numbers, the remainder arising from dividing a number by 9 (called the excess) is the same as that arising from dividing the sum of the digits by 9. Hence, the above remainders mav be obtained thus: (1) 3-f 5 = 8; (2) 3+ 4 = 7; (3) 5 + 6=11 = 9 + 2.- (4) 1 + 1 + 9 + = 9 + .2 ,' but 2 = 2 as before. In the case of addition, the excess in the sum is equal to the excess in the sum of the excesses of the addends. Thus, in 635 + 234 = 869, 6 + 3 + 5 = 9 + 5. 2+ 3 + 4 = 9 + 0, 8 + 6 + 9 = 2X9 + 5, but 5 + = 5; therefore the sura 809 is correct. From the identity of division, dividend = di- visor X quotient + remainder, it appears that the excess in the first member must equal that in the .second. Hence, the check for division is made to depend upon that for addition and nmltiplication. Tims, in 8765 = 42 X 208 + 29, 8 + 7 + 6 + 5 = 2X9 + 8, -4 + 2 = 6, 2 + + 8 = 9 + /, 2 + 9 = 9 + 2, -6X1 + 2=8; but 8 = 8, therefore the division is correct. In practice, the sum of the digits is rarely found. As soon as the addition produces 9, this is rejected, and so on. Thus, in 180136. 6 + 3 = 9, 1+0 + 8 = 9: hence. 1 is the excess. If the result obtained from any operation dif- fers from the true result by a multiple of 9, the check evidently fails, as is also the case if the result differs from the true re.silt by having certain digits interchanged. These cases, how- ever, rarelv occur. Anv number could be chosen