RULE, Carpenter's Joint, an instrument, usually of box, 24 inehes long, and 14 broad, each inch being subdivided into eight parts ; on the same side with these divisions is usually added Gunter's line of numbers. On the other side are lines of timber and board-measure, the first beginning at and continued to 36, near the other end ; the latter is numbered from 7 to 36, 4 inches from the other end. The division of the timber-line is formed from a consideration that 1,728 inches make a solid foot, in the following manner : thus, 9 is so placed against one of the divisions of inches, or parts on the other side of the rule, beginning from the right hand, that its square, which is Si inches multiplied by that number of inches and parts, must make 1,723 inches; which, dividing 1,728 by Si, must be placed against 211 from the right-hand ; and 10 must be placed against inches ; because 1,728, divided by the square of 10 or 100, gives &e. But, beeause a square, whose side is 1,2, &c., to 8 inches, requires more than 24 inches in length, as a mul tiplier, in order to produce 1,728 inches ; and since the length of the rule is only 24 inches, there is a table upon the left end of it, which supplies its defect of length. In

this table, the upper row of figures, viz., 1, 2, 3, 4, 5, 6, 7, 8, denotes inches, or the lengths of the sides of squares ; and the second and third rows are the correspondent feet and inches to make up a solid foot. It is made by dividing 144 inches by the squares of 1, 2, 3, 4, 5, 6, 7, S.

The line of board•measure is thus divided : suppose the division 7 to be marked ; divide 144, the number of inches in a square foot, by 7, and the quotient will he 201 inches ; whence the division 7 must be against 201 inches on the other. side of the rule. To mark the division 8, divide 144 by S, and the quotient, which is 18 inches, must he placed on the line of board-measure against IS inches on the other side, &c. But because the side of a long square, that is, 1, 2, 3, 4, 5 inches, requires the other side to be more than 24 inches, the whole length of the rule, there is a table annexed, formed by dividing 144 inches by each of the numbers in the upper row, and then each of the quotients by 12 to reduce into feet.