Reduce 2250 livres to South- the quotient will be Spanish, or

Reduce 2153 liv. 1613 so. to olina currency. Irish money. 20

DUODECIMALS,

OR CROSS MULTIPLICATION,

IS a Rule, made use of by workmen and artificers in casting up the contents of their works.

Dimensions are generally taken in feet, inches and parts.

Inches and parts are sometimes called primes, seconds, thirds, &c. and are marked thus; inches or primes (') seconds ("), thirds ("), fourths (""), &c.

This method of multiplying is not confined to twelves; but may be greatly extended: For any number, whether its inferiour denominations decrease from the integer in the same ratio, or not, may be multiplied crosswise; and, for the better understanding of it, the learner must observe, that if he multiplies any denomination by an integer, the value of an unit in the product will be equal to the value of an unit in the multiplicand; but if he multiplies by any number of an inferiour denomination, the value of an unit in the product will be so much inferiour to the value of an unit in the multiplicand as an unit of the multiplier is less than an integer.

Thus, pounds, multiplied by pounds, are pounds; pounds, multiplied by shillings, are shillings, &c. shillings, multiplied by shillings are twentieths of a shilling; shillings, multiplied by pence, are twentieths of a penny; pence, multiplied by pence, are 240ths of a penny, &c.

RULE.

1. Under the multiplicand write the corresponding denominations of the multiplier.

2. Multiply each term in the multiplicand, beginning at the lowest, by the highest denomination in the multiplier, and write the result of each under its respective term, observing, in duodecimals, to carry an unit for every 12. from each lower denomination to its next superiour, and for other numbers accordingly.

3. In the same manner multiply all the multiplicand by the primes or second denomination in the multiplier, and set the result of each term one place removed to the right hand of those in the multiplicand.

4. Do the same with the seconds in the multiplier, setting the result of each term two places to the right hand of those in the multiplicand.

5. Proceed in like manner with all the rest of the denominations, and their sum will be the answer required.

EXAMPLES.

3. How many square feet in a board 17 feet 7 foot 5 inches wide?

inches long, and I

Ans. 24ft. 10′ 11′′ 12 feet 10 inches

4. How many cubick feet in a stick of timber long, 1 foot 7 inches wide, and I foot 9 inches thick ?

Ans. 35ft. 6′ 8′′ 6""

5. How many cubick feet of wood in a load 6 feet 7 inches long, 3 feet 5 inches high, and 3 feet 8 inches wide? Ans. 82ft. 5' 8" 4"

6. There is a house with 4 tiers of windows, and 4 windows in a tier; the height of the first tier is 6ft. 8' ; of the second, 5ft. 9′; of the third, 4ft. 6'; and of the fourth, 3ft. 10; and the breadth of each is 3ft. 5; how many square feet do they contain in the whole ?

The two following questions are Sexcessimals.

Ans. 283ft. 7'

7. If 2 places differ in longitude 2° 12′; what is their difference of

time?

Mult. 2° 12' 00" 00"

by

3′ 59′′ 20" the time in which the sun passes through 1°

8' 46" 32" Answer.

8. Two places differ in longitude 31° 27′ 30′′; What is the difference, in time, of the sun's coming to the meridian of those places, the sun passing through 15° in an hour?

31° 37' 30"

4' 00" In 4' of a solar day, or day of 24 hours, the sun passes 1o

2° 6' 30" 00′′ Answer.

9. Multiply