Ex. 30. Reduce 15 minutes 48.924 seconds to the decimal of a degree. Ans. .26359. Ex. 31. Find the values of .0432 of a week, and 3.116805 days. Ans. 7 h. 15 m. 27.36 s., and 3 d, 2 h. 48 m. 12 s. Ex. 32. What is the content of a rectangular field, the length of which is 13 chains 75 links, and the breadth 12 chains 10 links? Ans. 16 acres 2 roods 22 perches. Ex. 33. What is the height of a room containing 38223 cubic feet, its length being 21 feet, and breadth 173 feet? Ans. 10 feet. Ex. 34. How many hours will there be in the years 1844 and 2200 respectively, by the calendar? Ans. 8784, and 8760. ADDITION AND SUBTRACTION OF 46. To add or subtract quantities consisting of different denominations, write the parts which are of the same denomination one under the other, and operate separately on each, beginning with those of the lowest denomination. If the sum of a column be equal to, or exceed the number contained in an unit of the next superior order, put down the excess, if any, and add the number of the next higher denomination contained in that sum to the next column. Also, if in any column the number to be subtracted exceed the subtrahend, add to the subtrahend as many as make one of the next higher denomination, instead of borrowing 10 as in abstract numbers, then put down the difference and carry one to the next number to be subtracted. Ex. 1. Required the sum of the following quantities: Tons cwt. qrs. lbs. Oz. drs. and the difference £2. 18s. 4d. Ex. 4. Required the sum and difference of .6 of a pound, and .875 of a shilling. .6£. = 13s. 4d., and .875s. = 10d. Whence the sum =14s. 21⁄2d., and the difference =12s. 51d. Ex. 5. Find the difference between 17 lbs. 9 oz. 10 dwts. 21 gr., and 9 lbs. 10 oz. 19 dwts. 10 gr. of silver. Ans. 7 lbs. 10 oz. 11 dwts. 11 gr. Ex. 6. Collect into one sum 3 lbs. 5 oz. 7 dr. 2 scr. 16 gr. 13 lbs. 7 oz. 3 dr., and 9 lbs. 11 oz. 1 scr. 6 gr., apothecaries' weight. Ans. 27 lbs. 3 dr. 1 scr. 2 gr. Ex. 7. Required the sum and difference of 1 1-6 of a pound, Ans. The sum is 11s. 4d., and the difference 2s. Ex. 8. Required the sum and difference of .75 of a pound and .5 of a guinea. Ans. The sum is 1£. 6s. 8d., and the difference 3s. 4d. MULTIPLICATION AND DIVISION OF 47. To multiply a compound by a simple or abstract number, place the multiplier under the number of the lowest denomination of the proposed quantity; find the product of this and the given multiplier, and ascertain the number of units of the next higher denomination contained in it, put down the remainder, if any, and carry these units to the product of the multiplier and the number of the next higher order; then proceed with this as with the first product, and continue the process until the whole is multiplied. To divide a compound by an abstract number, place the divisor and dividend as in division of abstract numbers, then find how often the divisor is contained in the number of the highest denomination in the quantity proposed, put down the quotient and reduce the remainder to the next inferior denomination, adding to it the number of the same denomination in the given quantity; repeat the division and proceed with the remainder as before; and continue the process until the whole is divided. Ex. 1. Multiply 18£. 12s. 71d. by 5 Multiplying the given quantity by the numerator, and dividing the product by the denominator, we have Ex. 2. Divide 784£. 10s. into 48 parts. Ex. 3. Multiply 3 tons 5 cwt. 2 qrs. by 38. Ex. 5. Find the value of of 135£. 16s. 10 d. Ans. 90£. 11s. 3d. Ex. 6. What is the eighteenth part of 21 acres 24 perches? Ans. 1 acre 28 perches. Ex. 7. Multiply 5 hrs. 1 min. 19.2 sec. by 23, and divide Ans. 3 hrs. 43 min. 33.6 sec. the product by 31. THE COMPUTATIONS OF ARTIFICERS BY 48. Cross Multiplication is a convenient method of computing small areas and solid contents, and is principally used by artificers to estimate the superficial or solid contents of work done. The dimensions are commonly taken in feet, and parts decreasing in a twelve-fold ratio, termed primes, seconds, thirds, &c., which are distinguished by accents placed a little to the right above the numbers to which they belong; thus, 23 feet, 9 primes, 6 seconds, 4 thirds, &c, are written 23, 9, 6", 4", &c. It is also called Duodecimal Multiplication and Duodecimals; but the operations are not conducted in the duodecimal scale of notation, the digits of the several denominations not being connected with each other by the factor 12, though the denominations themselves are. The rule for conducting the operations of Cross Multiplication may be enunciated as follows. RULE. Write the terms of the multiplier under the corresponding terms of the multiplicand. Multiply every term in the multiplicand, beginning at the lowest, by each term in the multiplier successively, beginning with the highest, divide each product which is not of the denomination of feet by 12, and place the remainder |