When the quantity is such a number, as that no two numbers in the table will produce it exactly: Then multiply by two such numbers as come the nearest to it; and for the number wanting, multiply the given price of one yard by the said number of yards wanting, and add the products together for the answer; but if the product of the two numbers exceed the given quantity, then find the value of the overplus, which subtract from the last product, and the remainder will be the answer.

Produces 39 18 9 price of 45 yards. Ans. $139-026

Add 1 15 6 price of 2 yards.

Ans. £41 14 3 price of 47 yards.

Note. This may be performed by first finding the value of 48 yards, from which if you subtract the price of 1, the remainder will be the answer as above.

When the quantity is any number above the Multiplication Table: Multiply the price of 1 yard by 10, which will produce the price of 10 yards: This product, multiplied by 10, will give the price of 100 yards; then, you must multiply the price of one hundred by the number of hundreds in your question; the price of ten, by the number of tens; and the price of unity, or 1, by the number of

units: Lastly, add these several products together, and the sum will be the answer.

EXAMPLES.

1. What will 359 yards of cloth, at S 4s. 74d.

mount to?

£ s. d.

}per {77c. im. per yard, a

0 4 7 price of 1 yard.

10

2 6 3 price of 10 yards.

10.

c.m.

⚫771

359

6939

3855

2313

23 26 price 100 yds. Ans. $276-789

3

69 7 6 price of 300 yards.

5 times the price of 10 yds.11 11 3 price of 50 yards. 9 times the price of 1 yd:= 2 1 7 price of 9 yards.

To find the value of one hundred weight: As 112 is the gross hundred, so 112 farthings are =2s. 4d. and 112 pence =9s. 4d. ; therefore, if the price be farthings, or not more than 3d. multiply 25. 4d. by the farthings in the price of 1 lb. or, if the price he pence, multiply 9s. 4d. by the pence in the price of 1 lb. and in either case, the product will be the answer.

42

21

21

Aus. 2.352

Answer £0 14 0 price of 1 Cwt. at 11⁄2 per lb.

s. d.

2. 1 Cwt. of tin at 24d. per lb.? 2 4 price of 1 Cwt. at 4d. per lb. 9 farthings in the price of 1 lb.

⚫03125

To find the value of a hundred weight, when the price of 1lb. is any number of pounds and shillings; or shillings, pence and farthings: Multiply the price of 1 lb. by 7, its product by 8, and this product by 2; which last product will be the answer required: for 7x8x2=112.

£94 19s. 4d.

4. 1 Cwt. at {16. 11} per lb, = {316 51c. 2m. }

13s. 4d.

$1 77 c.

}

£74 13s. 4d. 23186 663c.

} }

PRACTICAL QUESTIONS IN WEIGHTS AND MEASURES.

1. What is the weight of 4 hogsheads of sugar, each weighing 7cwt. 3qrs. 19lb. ? Ans. 31cwt. 2qrs. 20lb. 2. What is the weight of 6 chests of tea, each weighing 3cwt. 2qrs. 9lb.? Ans. 21cwt. 1gr. 26lb. 3. If I am possessed of 14 dozen of silver spoons, each weighing 3oz. 5pwt,-2 dozen of tea spoons, each weighing 15pwt. 14gr. -3 silver cans, each 9oz. 7pwt.-2 silver tankards, each 21oz. 15pwt. and 6 silver porringers, each 11oz. 18pwt. pray what is the weight of the whole? Ans. 181b. 4oz. 3pwt.

1pt?

4. In 35 pieces of cloth, each measuring 27 yards, how many yards? Ans. 9714 yards. 5. How much brandy in 9 casks, each containing 45gal. 3qts.. Ans. 412gal. 3qts. 1pt. 6. If I have 9 fields, each of which contains 12 acres, 2 roods and 25 poles; how many acres are there in the whole? Ans. 113A. 3r. 25p.

COMPOUND DIVISION*

IS the dividing of numbers of different denominations: In doing which, always begin at the highest, and when you have divided that, if any thing remain, reduce it to the next lower denomination, and so on, till you have divided the whole, taking care to set down your quotient figures under their respective denominations. INTRODUCTORY EXAMPLES.

• To divide a number consisting of several denominations by any simple number whatever, is the same as dividing all the parts or members of which that number is composed, by the same number. And this will be true when any of the parts are not an exact multiple of the divisor; for, by conceiving the number, by which it exceeds that multiple, to have its proper value by being placed in the next lower denomination, the dividend will still be divided into parts, and the true quotient found as before: Thus £41 178. d. divided by &, will be the same as £36 1178. 42d. divided by 6, which is equal to £5 15. 7d. as by the rule.

In the first example, having divided the pounds, the 4, which remains, is 4 pounds, which are equal to 30 shillings, and 17 in the shillings make 97; I then find 5 is contained 19 times in 97, and 2 over: I set down 19 under the shillings, and reduce the 2 shillings, which remain, into pence, and they make 24, and the 9 pence, in the question, added, make 33: Then how often 5 in 33; I find it 6 times, and 3 over: I set down 6 under the pence, and reduce the 3 pence, which remain, to farthings, and they make 12; then, how often 5 in 12; I find it to be twice: I therefore set down id. and the 2 which remains, is of a farthing, which I make no account of.

25. Suppose that two places lie east and west of each other, and it is found by observation that it is noon at the former 2 hours, 6′ 30" sooner than at the latter; how many degrees are they asunder? 4'2h. 6' 30" Reduce the hours and minutes to minutes, then, minutes divided by 4' give degrees in the quotient.*

31° 37' 30" Ans.

* Because 360°, the whole circumference of the earth, divided by 24, the hours in a day, give 15o for one hour or 60 minutes: and 60÷÷15—4′ for one degree.