Supplement to Loss and Gain.

1. What is Lofs and Gain ?

QUESTIONS.

2. Having the price at which goods are bought and fold, how is the Lofs or Gain estimated ?

3. To know how much a commodity must be valued at to gain or lose fo much per cent. what is the method of procedure?

4. How may questions in Lofs and Gain be proved?

EXERCISES.

1. A draper bought 100 yards of broadcloth for £56. I demand how he muft fell it per yard, to gain 15 in laying out 100? Ans. 12s. 10d. 2g. 206

2. Bought 30 hogfheads of molaffes, at 600 dollars; paid in duties 20,66; for freight $40,78; for porterage $6,05 and for infurance, $30,84. If I fell it at 26 dollars per hogfhead, how much shall I gain per cent. ?

Ans. $11,695.

THIS rule is particularly useful to Workmen and Artificers in cafting up the contents of their work.

Inches and parts are

Dimensions are taken in feet, inches and parts. fometimes called primes ('), feconds ("), thirds (""), and fourths ('''').

TABLE.

12 Fourths make 1 Third.

12 Thirds,

12 Seconds,

-

1 Second.

By this rule alfo may be calculated the folid contents of bodies, having the meafures of their different fides, and is very

1 Inch or Prime. ufeful, therefore, in measuring wood. 12 Inches or Pr. 1 Foot.

RULE.

1. Under the multiplicand write the correfponding denominations of the multiplier.

2 Multiply each term in the multiplicand, beginning at the loweft, by the feet in the multiplier, and write the refult of each under its refpective term, oblerving to carry an unit for every 12, from each lower denomination to its fuperior.

3. In the fame manner multiply the multiplicand by the inches in the multiplier, and write the refult of each term in the multiplicand thus multiplied, one place to the right hand in the product.

4. Proceed in the fame manner with the other parts in the multiplier, which if feconds, write the refult two places to the right hand; if thirds, three places, &c. and their fum will be the answer required.

'The more eafily to comprehend the rule, NOTE. Feet multiplied by Feet give

EXAMPLES.

1. Multiply 7 feet, 3 inches, 2 Seconds, by I foot, 7 inches, and 3 Seconds.

OPERATION.

F.

I. 11

7 3 2

7 3

3 2

feet-Feet multiplied by Inches give Inches.-Feet multiplied by Seconds give Seconds-Inches multiplied by Inches give Seconds.-Inches multiplied by Seconds give Thirds.-Seconds multiplied by Seconds give Fourths.

Here I multiply the 7f. 3in. 2" by the lf. in the multiplier, which gives feconds, inches and feet.

Next I multiply the fame 7f. 3in. 2" by the 7in. faying 7 times 2 is 14 which is once 12 and 2 over, which (2) I fet down one place to the right hand, that is in the place of thirds, and carry 1 to the next place, and proceed in the fame manner with the other terms. Laftly I multiply the multiplicand by the 3" fay ing 3 times 2 is 6 which I fet down two places to the right hand and fo proed with the other terms of the multiplicand. The fum of all the products

7. How much wood in a load which measures 10f. in length, 3f. 9in. in width, and 4ƒ. 8in. in height; and how much will it coft at 1 dol. 33cts. per cord? Ans. 1 cord, and 47 solid feet over; it will coft 1 dol. 81 cts. 8m.

Or, we may multiply by the feet as already directed, and for the inches, take fuch parts of the multiplicand, &c. as the inches are aliquot or even parts of a foot, as done in the rule of Practice.

8. How many fquare feet in a board of 16 feet, 4 inches in length, and 2 feet, 8 inches wide?

Here, in the first place I multiply the 16ft. 4in. by the feet (2) of the multiplier; the inches (8) not being an even part of a foot, I take fuch as are an even part; thus, 6in. is half a foot, therefore divide the multiplicand by 2 for 6 inches, and that quotient by 3, (2in. is of 6 inches) for 2 inches, all which being added, give the product of 16 feet, 4 inches multiplied by 2ft. din.

3

9. Another board is 18 feet 9 inches in length, and 2 feet, 6 inches wide, how many fquare feet does it contain?

By Practice.

Ans. 46f. 10in. 6′′.
By Duodecimals.

10. There is a flock of 15 boards, 12 feet 8 inches in length, and 13 inches wide; how many feet of boards does the stock contain?

By Practice.

Ans. 205 feet 10 inches.
By Duodecimals.

Supplement to Duodecimals.

QUESTIONS.

1. OF what use are Duodecimals? To whom more especially are they ufeful?

2. In what are dimensions taken ?

3. How do you proceed in the multiplication of Duodecimals?

4. For what number do you carry?

5. What do you obferve in regard to fetting down the product different from what is common in the multiplication of other numbers?

6. Of what term is the product which arises from the multiplication of feet by inches? Feet by feconds? Inches by inches? Inches by feconds? Seconds by feconds?

7. In what way can the operation be varied?