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We begin on the right hand, and multiply the multiplicand through, first by the primes of the multiplier, then by the feet of the multiplier, thus: 3'x7=txt=ite of a foot, which is 21"=1'9''; we write down the 9", and reserve the l' for the next product; again, 14f.x3'=14x
=t of a foot, which is 42'; now adding in the 1', which was reserved from the last product, we have 43'= 3f. 7', which we write down, thus finishing the first line of products.
Again, we have 2f.x7=2x7=24 of a foot, which is 14'=1f. 2'; we write the 2' under the primes of the line above, and reserve the 1f. for the next product; 2f. x 14f.=28f., to which, adding in the 1f. reserved from the last product, we have 29f., which we place underneath the feet of the line above. Taking the sum, we find 32f. 9' 9'', for the answer.
From the above we infer, that if we consider the index
of the feet to be 0, then the denomination of each product will be denoted by the sum of the indices of the factors.
Thus, feet by feet, produces feet ; feet by primes, produces prinies ; primes by primes, produces seconds, &c.
Hence, to multiply a number consisting of feet, inchus, seconds, &c., by another number consisting of like quan tities, we have this
Place the several terms of the multiplier under the cor. sesponding ones of the multiplicand. Beginning at the right hand, multiply the several terms of the multiplicand by the several terms of the multiplier successively, placing the right-hand term of each of the partial products under its multiplier ; then add the partial products together, observing to carry one for every twelve, both in multiplying and adding. The sum of the partial products will be the answer. Repeat this Rule.
103. Before the adoption of Federal money in this country, accounts were generally kept in the denominations of English money. Different States considered the pound as having different values, as given in the following
$1 in England=4s. 6d.=£, called Sterling money. 1 in South Carolina ? =4s. 8d. = £7, called Georgia
? Georgia I currency. 1 in Canada ] = 5s.=t, called Canada cur
Nova Scotia S rency. [New England States Virginia
=6s.=£*, called New $1 in Kentucky
England currency. (Tennessee
How were accounts kept before the adoption of Federal money? Did all the Stater estimate the pound at the same value? What fraction of a £ is $1 in Sterling money? What part of a £ is $1 in Georgia currency? What part of a t is $1 Canada currency? What part of a £ is $1 New England currency? What part in Pennsylvania cur rency? What part in Now York currency?
104. To reduce Federal money to pounds, shillings, and pence, we obviously have this
Multiply the sum in Federal money by the value of $1 expressed in the fraction of a pound, as given in the above Table ; the product will be pounds. If there are decimals of a pound, they must be reduced to shillings and pence by Ruie under Art. 99.
What is the fraction by which we multiply Federal money to reduce it to Sterling money? What fraction do we multiply to reduce it to Georgia currency? What is the fraction for Canada currency? What fur New England currency? What for Pennsylvania currency? What for New York currency? If in the product there are decimals of a pound, how do you dispose of them ?
1. Reduce $100.20 to the different currencies, as given in the preceding Table.
£ s. d.
25 10 Canada currency. Ans. $100-20=
30 1 2 New England currency
( 40 1 77 New York currency. 2. Reduce $37.37 to the different currencies
£ s. d.
8 14 4.72 Georgia currency.
9 6 102 Canada currency. Ans. $37.37 = 1 4 2.64 New England currency
14 0 3:3 Pennsylvania currency.
| 14 18 11:52 New York currency. :) 3. Reduce $1000 to equivalent values in the different currencies.
[ 225 Sterling money.
105. To reduce a sum in either of the above currencies o Federal money.
It is obvious, that by inverting the fractions which ex. press the value of $1 in pounds, as given in the preceding