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RULE. Multiply the principal, in cents, by the number of days, and point off five figures to the right hand of the produet, which will give the interest for the given time, in shillings and decimals of a shilling, very nearly.
A note for 65 dollars, 31 cents, has been on interest 25 days; how much is the interest thereof, in New-England currency? $ cts,
qrs. Ans. 65,31=6531 X25=1,63275=1 72 REMARKS.- In the above, and likewise in the preceding practical Rules, (page 127) the interest is confined at six per cent. which admits of a variety of short methods of casting; and when the rate of interest is 7 per cent. as established in New-York, &c. you may first cast the interest at 6 per cent. and add thereto one sixth of itself, and the sum will be the interest at 7 per cent. which perhaps, many times, will be found more convenient than the general rule of casting interest.
Required the interest of 751. for 5 months at 7 per cent.
7,5 for 1 month.
£. s. d.
37,5=1 17 6 for 5 months at 6 per cent.
Ans. £2 3 9 for ditto at 7 per cent.
A SHORT METHOD FOR FINDING THE RUBATE OF ANY GIVEN SUM, FOR MONTHS AND DAYS.
RULE. Diminish the interest of the given sum for the time by its own interest, and this gives the Rebate very nearly
1. What is the rebate of 50 dollars for six months, at 6 per cent. ?
8 cts. The interest of 50 dollars for 6 months, is 1 50 And, the interest of 1 dol. 50 cts. for 6 months, is 4
Ans. Rebate, $1 46 2. What is the rebate of 1501. for 7 months, at 5 per cent. ?
nterest of 150l. for 7 months, is 4 mterest of 4l. 7s. 6d. for 7 months, is
Ans. £4 4 11 nearly. By the above Rule, those who use interest tables in their counting-houses, have only to deduct the interest of the interest, and the remainder is the discount.
A concise Rule to reduce the currencies of the different
States, where a dollar is an even number of skillinges, to Federal Money.
RULE I. Bring the given sum into a decimal expression by inspection, (as in Problem I. page 87) then divide the whole by ,3 in New-England and by ,4 in New-York currency, and the quotient will be dollars, cents, &c.
1. Reduce 541. 8. 3 d. New-England currency, to Federal Money.
93)54,415 decimally expressed.
Ans. $181,38 cts. 2. Reduce 79. 118d. New-England currency, to Fede. ral Monev.
78. 111d.=$0,399 then, ,3),399
Ans. $1,33 3. Reduce 5131. 16s. 10d. New-York, &c. currency, to Federal Money.
4. Reduce 19s. 534. New-York, &c. currency, to Federal Money.
,)0,974 decimal of 19s. 54d. }
$2,434 Ans. 5. Reduce 641. New-England currency, to Federal Money.
,3)64000 decimal expression.
8213,334 Ans. Note. By the foregoing rule you may carry on the decimal to any degree of exactness; but in ordinary practice, the following Contraction may be useful.
RULE II. To the shillings contained in the given sum, annex 8 times the given pence, increasing the product by ?; then divide the whole by the number of shillings contained in a dollar, and the quotient will be cents.
1. Reduce 45s. 6d. New-England currency, to Federal Money.
6x8+2 =50 to he annexed,
758 cents.=7,58 2. Reduce 21. 10s. 9d. New-York, &c. currency, to Federal Money.
9x8+2=74 to be annexed. Then 8)5074
Or thus, 8)50,74
1 Scts. Ans. 634 cents.=6 34
86,34 Ans. N. B. When there are no pence in the given sum, you niust annex two cyphers to the shillings; then divide as before, &c.
3. Reduce Sl. 58. New-England currency, to Federal money.
31 58. -65%. Then 6)6500
Ans. 1083 cents.
SOME USEFUL RULES,
FOR FINDING THE CONTENTS OF SUPERFICIES AND
SOLIDS. SECTION I. OF SUPERFICIES. The superficies or area of any plane surface, is composed or made up of squares, either greater or less, according to the different measures by which the dimensions of the figure are taken or measured :-and because 12 inches in length make 1 foot of long measure, there fore, 12x12=144, the square inches in a superficial foot, &c.
ART. I. To find the area of a square having equal sides.
RULE. Multiply the side of the square into itself, and the product will be the area, or content.
EXAMPLES 1. How many square feet of boards are contained in the floor of a room which is 20 feet square ?
20x20=4n0 feet, the Answer. 2. Suppose a square lot of land measures 26 rods on each side, how many acres doth it contain ?
Note.-160 square rods make an acre.
36r. the Answer. ART. 2. To measure a parallelogram, or long square.
RULE, Multiply the length by the breadth, and the product will be the area, or superficial content.
1. A certain garden, in form of a long square, is 96 ft. song, and 5-1 wide; how many square feet of ground are contained in it? Ans. 96 x 54=5144 square feet.
2. A lot of land, in form of a long square, is 120 rods in length, and 60 rods wide; how many acres are in it? 120X60=7200 sqr. rods, then 720 = 45 acres. Ans.
3. If a board or plank be 21 feet long, and 18 inches oroad; how many square feet are contained in it? .
18 inches=1,5 feet, then 21x1,5=31,5 Ans.
Or, in measuring boards, you may multiply the length in feet by the breadth in inches, and divide by 12, the quotient will give the answer in square feet, &c.
Thus, in the foregoing example, 21X18+12=31,5 as before.
4. If a board be 8 inches wide, how much in length will make a square foot :
RULE.—Divide 144 by the breadth, thus, 8)144
Ans. 19 in. 5. If a piece of land be 5 rods wide, how many rods ir length will make an acre ?
Rule.--Divide 160 by the breadth, and the quotient will be the length required, thus, 5)160
Ins. $2 rod; in length. ART. 3. To measure a Triangle. Definition.--A Triangle is any three cornered figure which is bounded by three right lines.
RULE. Multiply the base of the given triangle into half its perpendicular height, or half
the base into the whole perpendicular, and the product will be the area.
1. Required the area of a triangle whose base or longest side is 32 inches, and the perpendicular height 14 inches.
32x7=224 square inches, the Answer. 2. There is a triangular or three cornered lot of land whose base or longest side is 51} rods ; the perpendicular from the corner opposite the base measures 44 inds; how many acres doth it contain:
51,5X22=1133 square rods,=7 acres, 13 rods.
*A Triangle may be either right angled or oblique : in either case the teacher can easily give the scholar a right idea of the base and perpendicular, by marking it down on a slatp. paper, &c.