18 How many yards of matting, that is half a yard wide, will cover a room that is 18 feet wide and 30 long?

answer 120 yards.

19 How wide must a lot of ground be to contain an acre, when it is 13 poles in length?

answer 11P. 4yds. 2ft. Oin. 2.b.c. 20 If, when the price of a bushel of wheat is 6s. 3d. the penny loaf weighs 9oz. what ought it to weigh, when wheat is at 8s. 2d. per bushel ? answer 6oz. 13dr. + 21 In what time will 600l. gain 50l. interest, when 801. would gain it in 15 years? answer 2 years.

Application.

1 If 3 quarters of a yard of velvet cost 7s. 3d. how many answer 28yds. 2gr. yards can I buy for 131. 15s. 6d. ? 2 If an ingot of gold weighing 9lb. 9oz. 12dwt. be worth 411l. 12s. what is that per grain?

answer 1d. 3 A borrowed of B 2501, for 7 months; and in return lends him 3007, how long ought B to keep it, that the interest of it may be equal to that of the first sum ?

answer 5mo, 25da. 4 If a person's income be 500 guineas a year, and he spend 19s. 7d. sterling per day; how much will he have saved at the year's end ? answer 167lb. 12s. 1d. sterling. 5 At 13s. 2d per yard, what is the value of a piece of cloth containing 52 English ells and Sqrs. ?

answer 481. 8s. 5d. 6 If 30 men can perform a piece of work in 11 days; how many men will accomplish another piece of work four times as large, in 12 days?

answer 110 men.

7 The rents of a whole parish amount to 1750l, on which is assessed 32l. 16s. 3d. what is that in the pound?

answer 4d. 8 Bought three tons of oil for 151l. 14s. 85 gallons of which being damaged, I desire to know how I may sell the remainder per gallon, so as neither to gain nor lose thereby ? answer 4s. 6d.ş 9 If the carriage of 5C. 14lb. for 96 miles be 32s. 6d. how far may I have 3C. 1gr. carried for the same money? answer 151M. sfur. 3P. 10 Bought 200 yards of cambric for 90l. which being damaged, am willing to lose 7. 10s. by the whole, at what rate then must it sell per ell English? answer 10s. 3d.3

11 If, for 48s. 225 C. be carried 512 miles, how many hundred weight may be carried 64 miles for the same money ? answer 1800C.

12 Bought a parcel of cloth, at the rate of 6s. 6d. for every two yards, of which a certain quantity was sold at the rate of 18s. 9d. for every five yards, and gained thereby as much as 180 yards cost; how many yards were sold?

answer 1170 yards.

13 A certain steeple projected upon level ground a shadow to the distance of 633ft. 4in. when a staff 3 feet in length, perpendicularly erected, cast a shadow 6ft. 4in. from hence the height of the steeple is required ?

answer 100 yards. 14 If 12 yards of yard wide stuff exactly line 8 yards of silk of another breadth; how many yards of the latter will line 24 pieces of the former, each piece containing 20 yards? answer 320 yards.

15 Laid out 1007. upon serges and shalloons; the value of the shalloons was 60l. and the quantity of serge 237 yards; also for every two yards of serge there were three of shalloon; how many yards of shalloon were there, and what was the value of one yard of each sort?

answer 355 yds. shalloon, 3s. 4d.+each per yard. 16 How many pieces of Holland, each 33 ells Flemish, 1gr. 2na. may be had for 118. 17s. 7d., when 4 ells English cost 11. 7s. 10d.? answer 16 pieces 33 ells 1qr. Ina. 17 A factor bought 64 pieces of Holland, which cost him 3521. at 5s. 6d. per ell Flemish; how many yards were there in all, and how many ells English in each piece?

answer 960yds. 12 ells each piece. 18 If a pole, perpendicular to the horizon, of 50ft. 11in. in length, when the sun is on the meridian, cast a shadow 98ft. 6in long; what is the breadth of a river, that, running due east and west within 20ft. 6in. on the north side of the foot of a steeple, 300ft. 8in. high, which at the same time casts the extremity of its shadow 30ft. 9in. beyond the answer 176yds. 2ft. 4in. 19 Of what length must a board be, that is 7 in. wide, to 'measure 20 square feet? answer 32 feet. 20. A and B depart from the same place, and travel the same road; but A goes 5 days before B, at the rate of 20

stream?

miles a day; B follows at the rate of 25 miles a day; in what time and what distance will he overtake A ?

answer 20 days and 500 miles.

21 If 50 gallons of water, in one hour, fall into a cistern containing 230 gallons, and, by a pipe in the cistern, 35 gallons run out in an hour; in what time will it be filled? answer 15h. 20min.

22 A certain cistern has four pipes; by the first it will be filled in 10 minutes, by the second in 20, by the third in 40, and by the fourth in 80; in what time will all four, running together, fill it? answer 5min. 20sec.

23 Astronomers compute the earth's orbit, or track which it describes round the sun in 365 days 6 hours, to be about 596900000 miles; how far then, per minute, must we be carried through the firmament by this wonderful motion ♪ answer 1134+ miles.

24 Isaac Newton, and others, have found, by nice experi ments, that sound flies at the rate of 1142 feet per second, and a person in health has about 75 beats of the artery or pulsations in a minute; now the breadth of a river is required, at one side of which A, firing a gun, B, directly opposite at the other, counts six pulsations at his wrist between seeing the flash and hearing the report?

answer 5481ft. or 1 mile 201ft. 25 If the report of a piece of ordinance be heard one. minute and three seconds after the flash was observed; the distance is required? answer 13 miles 5 furlongs,

T

THE DOUBLE RULE OF THREE.

HE Double rule of three is that, wherein five numbers or terms are given, to find a sixth, three of which are a supposition, and two a demand: and is either direct or inverse.

RULE FOR STATING.

Set the two terms of the supposition, which are like those of the demand, one under the other, in the first place; that of the same kind with the term sought in the second; and the two demanding terms in the third place, with the two correspondent

correspondent terms of the supposition and demand in the same line, and of one denomination; as in the subsequent examples, viz.

1 If three men in 4 days eat 5lb. of bread, how much will suffice 6 men for 12 days ?

If Sm.
4d. S

5lb.

S 6m.
12d.

2 If 3 men eat 5lb. in 4 days; in how many days will 6

men consume 30lb.

4da. 30lb.

To know whether the stating be direct or inverse: Consider the upper pair of extremes, and the lower, each separately with the middle term, as a stating of the single rule, and try them as taught in that rule: if both lines be direct, the stating is in direct proportion; but of inverse, if either pair of the extremes be so. Thus, the first example above is direct, and the second inverse.

DIRECT PROPORTION.

RULE..

Divide the continual product of the two last extremes and middle term by that of the two first, and the quotient will be the sixth term, or answer.

PROOF.

By two statings of the single rule of three.

Note. If either of the two first terms, or both, will divide, or can be divided by any of the three last, or by any other number, without remainder, the operation may be abbreviated by cancelling them, and using their quotients or aliquot parts in their stead.

EXAMPLES.

If three men in four days eat 5lb. of bread; how much will suffice 6 men for 12 days?

2 Suppose 4 men in 12 days mow 48 acres ; how many acres can 8 men mow in 16 days?

answer 128 acres.

3. If 12 oxen in 16 days eat 20 acres of grass; how many acres will serve 24 oxen 48 days ?

answer 120 acres. 4 If 10 bushels of oats be sufficient for 18 horses 20 days; how may bushels will serve 60 horses 36 days, at that rate? answer 60 bushels.

5 If 56lb. of bread be sufficient for 7 men 14 days; how many pound will suffice 21 men 3 days? answer 36lb. 6 If 8 men have 3l. 4s. for 4 days work; how much ought 48 men to receive for 16 days? answer 761. 168. 7 If 700 dols. in half a year raise 14 dols. interest; what will be the interest of 400 dols. for 5 years ? ans. 80dols. 8 If 112 acres of grass be mowed by 16 men in 7 days; how many acres may 24 men mow in 19 days?

answer 456 acres. 9 If 167. 18s. be the wages of 16 men for 8 days; what sum will 32 men earn in 24 days? answer 1017. 8s.

10 If 751 in 9 months amount to 781. 7s. 6d. at what rate per cent. is the interest computed ? answer 6l. per cent. 11 Suppose the wages of 6 persons for 21 weeks be 1201. what will be the hire of 14 persons for 46 weeks?

5 per cent. ?

answer 6131. 6s. 8d. 12 What is the interest of 2591. 13s, 5d. for 20 weeks, at answer 41. 19s. 10d4. 13 If 2 men can do 12 rods of ditching in 6 days; how many rods may be done by 8 men in 24 days?

4

answer 192 rods. 14 If the carriage of 8 C.wt. 128 miles cost 6,40; what must be paid for the carriage of 4 C.wt. 32 miles ? answer 80cts. 15 If 200lb. be carried 40 miles for 40cts. how much must be paid at that rate for the carriage of 20200lb. 60 miles? answer 60,60).

16 If the freight of 9 hogsheads of sugar, each weighing 12 hundred weight, for 20 leagues, cost 167. what must be paid for the freight of 50 casks of ditto, each weighing 24 hundred weight, 100 leagues? answer 921. 11s. 10d.

INVERSE