DUNNAGE

Any light or loose material, as wool, ., used as a bed in the stowage of heavy articles. DUODECIMAL. {l^aX-dMoAecim, twelve.) Proceeding by twelves. The term is given to a rule or operation of arithmetic, by which the contents of any surface or solid are found by multiplying together its linear dimensions, expre ed in feet, inches, and lines, and is consequently much used by artificers in finding the contents of their work. The rule is also called cro multiplication, from the manner in which the operation is usually performed, and which is as follows: Suppose it were required to find the superficial content of a plank 12 feet 9^ inches long, and 3 feet 7 inches broad. Set down the two dimensions under each other, placing feet under feet, inches under inches, ., and for the half inch put down its equivalent 6 lines> as in the following example; — Now, since the feet are conceived to be units of measure, the inches are so many 12ths of unity, and ^e lines so many 12ths of a 12th, or 144th parts of unity. The units consequently form the first column, the 12tns the second, and the 144ths the third. Multiplying therefore the first line by 3 feet or 3 units, we get 38 feet, 4-12ths of a foot, and 6-144ths of a foot. Next, multiplying the upper line by 7-12ths, we get first the 6 lines or 6-144ths, multiplied ^7-12ths, equal to 42.1728ths, which is equal to 3i-144ths. Then the9-12ths multiplied by the7-12ths give63-144ths, which added to the 3^ make 66i-144ths, or 5-12ths and 6i-144ths; therefore 6£is placed in the third column, and the5-12ths carried on. Lastly, the 12units multiplied by the 7-12ths give 84-1 2ths, which added to the5-]2ths make 89-1 2ths, and this is equal to 7 units or feet and 5-12ths; consequently 7 is placed in the first column and 5 in the second. Adding the two products together, we get 45 feet, 10-12ths of a foot, and §-144ths of a foot. But in square or superficial measure the 144th part of a foot is an inch; and 10-I2ths = 120-144ths; consequently the result of the operation is 45 sq. feet and 120^ sq. inches. The operation is itself much simpler than the description or ejcplanation, which is found embarra ing to beginners; it would therefore, perhaps, be better to reject the rule altogether from elementary books of arithmetic; and, regarding the inches and lines as parts of a foot, to perform the operation by the ordinary rule of practice. [s. 382]