NOTE.-In England a dollar contains In South Carolina and Georgia,

In Nova Scotia and the Canadas,

In New England,† Virginia, Kentucky,

and Tennessee,

In New Jersey, Pennsylvania, Delaware, and Maryland,

In New-York and North Carolina,

12)6000 d. 210) 5010s.

45

£ 25

4 6

4

8

5 0

NOTE. But for about thirty years past, North Carolina has estimated the dollar at ten shillings.

LESSON 31.

LESSON 35.

If 5s. make 100 cents, how If 100 cents make 6s. or 72d. many dollars will £52 15s. New England currency, how make? Ans 211 dollars.much will 100 dollars make in New England currency? c. Ans. £ 30.

S. cents. 8. £ 52 15

5: 100 :: 1055

5)105500

21100

20

1055

C.

d.

* Two ciphers annexed to multiply by 100.

+ New England is composed of the following states, viz. Vermont, New Hampshire, Commonwealth of Massachusetts, Rhode Island and Connecticut.

COMPOUND PROPORTION.

This is called the Double Rule of Three, or, Rule of Five. In this Rule five terms are given to find a sixth.

EXAMPLE.

If 4 men can reap 16 acres in 8 days, how many men can reap 48 acres in 4 days? Answer, 24 men.

The three first terms form a supposition, the fourth and fifth make a demand, and the sixth gives the answer.

As in simple Proportion, so in this; if more require more, or less require less, it is direct.

And, if more require less, or less require more, it is inverse.

"If the proportion is direct, the sixth term must bear such proportion to the fourth and fifth, as the third term bears to the first and second.

But if the proportion is inverse, then the sixth term must bear such proportion to the fourth and fifth, as the first bears to the second and third, or as the second bears to the first and third."

RULE FOR STATING.

Take those terms which form the supposition in the above example, and begin thus:

1. Let the principal cause of action be placed in the first term; as,

2. Let that which denotes time, distance, &c. be in the second term; as,

4 men:

8 days

:: 16 acres

3. Place the remaining number of the suppesition in the third term; as,

Then the work will stand thus:

4. Place the other two terms, which move the question, under those of the same name, thus:

See Lesson D. Card 31.

men. d. acres.

4: 48

KEY TO CARD No. 31.

5. If the blank fall under the third term, then multiply the first and second terms together for a divisor, and the other three for a dividend.

But, if the blank fall under the first or second term, then multiply the third and fourth terms together for a divisor, and the other three for a dividend, the quotient in either case will be the answer.

PROOF IS PERFORMED

By two statings in simple proportion.
OPERATION OF THE AFOREGOING EXAMPLE.

men d. acres.

We will suppose that the men reap during the time of 8 days; then say,

If 16 acres : require 4 men how many men will 48 acres require?

acres. men. acres.

256

Now say if 8 days require

many

12 men:: how
4 days require?
d. men.

men will

d.

8 : 12 :: 4

12

4)96(24 mėn.

In this last statement, the third term is less than the first and requires the fourth to be greater than the second, and shows that less requires more; therefore the propor16)192(12 men.tion is inverse.

16: 4 ::

48
4

16

.32

LESSON 1.

If 56 bushels of corn will By this operation we find how many bushels will supsupply 7 persons 4 months, that 48 acres require 12 men ply 46 persons 10 months? if they reap during 8 days. Answer, 920 bushels.