3. To New Jersey, Pennsylvania, Delaware, and Maryland currency.

Rule. To the Canada, &c. sum add one half.

Reduce £100 Canada, &c. to New Jersey, &c.

2)100
+ 50

£150 Answer.

4. To South Carolina and Geor. gia currency.

Rule. From the Canada, &c. sum deduct one fifteenth.

Reduce £100 Canada, &c. to South Carolina, &c. 15=3×5)100

3)20

6 13 4

£93 6 8 Answer.

5. To English Money. Rule. From the Canada, &c. deduct one tenth.

Reduce £100 Canada, &c. to English money. 10)100

10

£90 Answer.

6. To Irish Money.

IX. To reduce Livres Tournois.

1. To New Hampshire, Massachusetts, Rhode Island, Connecticut, and Virginia currency.

Rule. Multiply the livres by 2: Divide the product by 35, and the quotient will be pounds. Or, Multiply the livres by 8: Divide

Rule. From the Canada, &c. the product by 7, and the quo

deduct one fortieth.

tient will be shillings.

Reduce 1750 livres to NewHampshire, &c. currency.

1750

Or, 1750

4. To South Carolina and Geor- Bullion, that is, they are bought and

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.

*The reason of this rule is evident by considering the denominations below the integer, as fractional parts of the integer, and multiplying as in Vulgar Fractions. Thus inches or primes are 12ths of a foot, seconds are 12ths of an inch, or 144ths of a foot, and so on. Then feet multiplied by inches would give inch3 6 3 6 es, for 2 feet X 6 inches; inches by inches give seconds, for 12×12= 12 12 18 1246 12 14412x12=12x12=12x12+

18

6 12X12

1

6

1 inch and 6"; inches in

6 3

18

12

6

1

6

to thirds gives fourths, for 12144-12×144 12×144+12×144-144+1728 -1 and 6", and so on.

A similar process will show the correctness of the Rule, when the denominations do not decrease uniformly by 12 or any one number, as in pounds, shillings and pence, where 1 shilling would be of a pound, and 1 penny, of a pound, and so on.

20

Note. It is evident that when the denominations decrease by any one number, as 12, the denomination of the product is the sum of the denominations of the factors. Thus primes into primes give seconds, 2 being the sum of 1+1, the denominations of the factors, seconds into thirds give fifths, 24345; second to fourths give sixths, and so on.

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.

3. How many square feet in a board 17 feet 7 inches long, and 1 foot 5 inches wide?

Ans. 24ft. 10' 11"

4. How many cubick feet in a stick of timber 12 feet 10 inches long, 1 foot 7 inches wide, and 1 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? Ans. 283ft. 7