I want to know how many stones are therein ?
Answ. 204 stone.

10. How many boxes, each to hold 12b. may be filled out of a hogshead of tobacco containing 74C.?

Answ. 70.

11. Received from Jamaica 56 hogsheads of sugar, each 120. 1yr. 10fb. (100, being their Čut) how many Cwt. here of 112 ? Answ. 617C. 2qrs.

12. Imported from Rotterdam 46 bales of cloth, each containing 24 pieces, and each piece 42 ells Flemish; how many yards were therein? Answ, 34776 yards.

13. In 150000 crusadoes, each 400 reas, 1000 reas to a milre of 5s. 6d. how many pounds sterling?

3d.

Answ. 155001.

14. In 5067. 12s. 6d. how many Portugal reas at 20 for Answ. 810600.

CHAP VII.

THE RULE OF THREE DIRECT.

THE method of finding a fourth proportional, from

Tthree numbers given, is called by some the Rule of

Proportion; by others the Rule of Three, because 3 numbers are given to find a fourth; and again, the Golden Rule for its extraordinary use.

In practical questions where three (applicate) numbers are given to find a fourth proportional; the greatest difficulty will be in stating the question, or abstracting the numbers out of the words in the question, and placing them down in their proper order.

Now

Now two of the three given terms are homogeneal, or of the same kind, one of which * asks or moves the question, and is to be put in the third place, the other number of the same kind in the first; and the remaining number in the second, being of the same name or kind with the fourth required. For instance,

If 3 yards cost 9 shillings, what will 6 yards cost at the same rate or proportion?

Here the first clause (if 3 yards cost 9 shillings) assigns or supposes the rate; then follows the question, what will 6 yards cost? Consequently the numbers must be ranged` thus; by the rule, viz.

The numbers being thus stated, the rule for the operation is as follows:

If the first number be 1, the answer or fourth is found by multiplying the second and third: And if the second or third be 1, the fourth will be found by dividing the other number by the first.

* Asks or moves the question) The term which moves the question bath generally some words like these before it, viz. What will? What cost? How many? How far? How long? or How much?

Otherwise by varying the stating, as follows:

qu.) or 2. Inversely. 3. Alternately.

1. Directly (

That is when the fourth number is found, if it be made the first of another stating, the third given number the second; the second the third; and we work by the general rule, if the answer be the first given number, the work is right other ways.

These things being premised, I intend to lead the learner gradually through the varieties of this excellent rule, in the sundry cases following.

The fourth number is always found in the same name which the second is given in, or reduced to; which if it be not the highest denomination of its kind, reduce it to the highest when it can be done.

Application and Reason.

Let the following question be proposed, viz. If 1b. of sugar cost 7d what will 112. come to?

Multiplying the third 112 by 7 the second, I find the product 784, which is the fourth number sought, since the first number is one, I say it is 78 pence, the same name with the second number, as is self-evident (I think) from the least consideration of the nature of the question:

for

for if 1. is equivalent to 7d. 112. of the same must be worth 112 times as much, viz. 112 times 7d. viz. 784 pence. But then since accompts are kept in pounds, shillings and pence, and payments made in coins which are calculated in shillings and pence, or pounds,

shillings and pence, it is

proper that these pence be brought inte pounds by Reduction, and then the answer will be 37. 5s. 4d. 2. Ě. I.

Examples.

Quest, 1. What cost 327 yards of canvas, at 8d. ' yard ? Answ. 101. 18s.

2. What will 17 tons of tallow come to at 251. the ton? Answ. 4251.

3. At 7s.

b. what cost 128. of tea?

Answ. 44/ 16s.

4. What cost 139 barrels of barley, at 6s. barrel? Answ. 411. 14s.

5. How much is the price of 1781. of merchandize, at 17d..? Answ. 121. 12s. 2d.

6. What cost 1727b. of rice, at 9 farthings t.
Answ. 161. 3s. 93d.

Case II.

When the second number is of divers denominations, bring it to the lowest mentioned, and the fourth will be found in the same name, to which the second is reduced, which reduce back to the highest possible.

Examples.

Let it be required to find what 178 yards of linen will cost, at 4s. 8d. yard?

7. What is the amount of 324 pieces, at 2s. 8d. piece? Answ. 431. 17s. 6d.

8. How much will 120C. come to, at 18s. 6d. Cwt ? Answ. 1111.

9. What will 24 yards of broad cloth cost, at 15s. 3d. ' yard? Answ. 181. 6s.

10. Bought 39C. of butter, at 17. 5s. 6d. Cwt. what comes it to? Answ. 491. 14s. 6d.

11. If I hold 120 acres of land, at 14s. 6d. acre, what is my yearly rent? Answ. 871.

12. If I expend one week with another 27. 13s. 51d. week, what is my expence in 52 weeks? Answ. 138. 19s. 10d.

Case III.

If the first and third be of different names, or one or both of divers denominations, reduce them both to one denomination, that is, to the lowest mentioned in either.

13. What quantity of brandy can I get for 187. 19s. at s. gallon? Answ. 1 hogshead,