15. A merchant bought a bale of cotton containing 400 yd. 3 qr. Having sold 139 yd. 3 qr. 2 na. of this purchase, how many yards of the cotton remain on hand?

Ans. 260 yd. 3 qr. 2 na.

16. A speculator bought a tract of land containing 960 A. 2 R. 26 P. Having sold from the tract to the amount of 509 A. 3 R., how many acres of it remain unsold?

Ans. 450 A. 3 R. 26 P.

17. A merchant bought at one time 4 T. 19 cut. of hemp, at another 3 T. 2qr., and at another 1 T. 13 cwt. 3 qr. 10 lb. Having sold at different times to the amount of 5 T. 10 cwt. 1 qr. 20 lb., how much hemp has he still unsold?

Ans. 4 T. 2 cwt. 3 qr. 18 lb.

18. A person who undertook a journey of 900 miles, traveled the first day 39 m. 3 fur., the second 40 m. 7 fur., the third and fourth each 43 m. 6 fur. How many miles of his journey then remained to be traveled? Ans. 732 m. 2 fur.

19. A manufacturer put into one bale 335 yd. 3 qr. of cotton, into another 400 yd., and into two others each 421 yd. 1 qr. having sold to one person 100 yd. 2 qr. from the first bale, and 200 yd. from each of the others, how many yards remain ? Ans. 877 yd. 3 qr.

20. A gentleman's fortune is estimated at 10000£ sterling. If he give to each of his three sons 2000£, 15 s., and to his only daughter the remainder, what will be the daughter's portion? Ans. 3997£, 15 s.

21. A planter has one tract of land containing 3000 A., and two others containing each 1500 A. 1 R. 16 P. If he sell from the first tract 400 A. 2 R., and from the other two together 305 A. 3 R. 25 P., how many acres will remain to him?

Ans. 5294 A. 1 R. 7 P.

22. A miller bought at one time 200 bu. 3 pk. of wheat, at another 313 bu. 1 pk., and at another 194 bu. Having manufactured 405 bu. 1 pk. of these purchases into flour, what quantity of wheat has he still on hand? Ans. 302 bu. 3 pk.

34 gal. 3 qt. 1 pt. of

23. A grocer bought from one distillery brandy, from another 40 gal., and from another 31 gal. 1 qt. Having sold to the amount of 50 gal. 1 qt. remains unsold?

1 pt., what quantity Ans. 55 gal. 3 qt.

land; B has 100 A.

24. Farmer A has 300 A. 1 R. 40 P. of 2 R. 13 P. more than A, and C has 39 A. 10 P. more than B, while D has 75 A.2 R. 20 P. less than the other three together. How much land has B, C, and D, respectively?

Ans. B, 401 A. 13 P.; C, 440 A. 23 P.; D, 1066 A. 16 P.

Interval of Time between two given Dates.

$195. In subtracting a prior from a later date, add to the number of days elapsed in the month of the later date (when requisite,) as many as make the month of the prior date, and allow 12 months to a year.

EXAMPLE.

To find the interval between the 20th day of March, 1823, and the 10th day of April, 1848.

y. m. da.

1848 4 10

1823 3 20

25 0 21

March being the 3d, and April the 4th month in the year, we designate them by these numbers, respectively.

Since March has 31 days, 11 days of it remained after the 20th. Adding these 11 da., to the 10 da. of April, we have 21 da.; and it is plain that whatever number of months might intervene between the months of the two given dates, the surplus days would be found in a similar manner.

But 31-20+10=10+31—20; hence the 21 da. (and the surplus days in every case) will be found, most readily, by the direction above given. (§ 195).

§ 196. The interval of time, found as above, will include the particular day of the later date, but not that of the prior one.

Thus in the Example given, the 10th of April is included in the interval 25 y. 21 da., but not the 20th of March,-as is obvious from the explanation.

25. Find the interval of time between May 16th, 1834, and September 4th, 1848. Ans. 14 y. 3 m. 19 da. 26. A person was born on the 3d of April, 1807: required his age on the 15th of December, 1848.

Ans. 41 y. 8 m. 12 da. 27. How long was it from the discovery of America, October 21st, 1492, to the founding of Jamestown, May 23d, 1607? Ans. 114y. 7 m. 2 da. 28. How long was the founding of Jamestown prior to the birth of Washington, February 22d, 1732; and what was Washington's age at his death, December 14th, 1799?

Ans 124 y. 8 m. 30 da., and 67 y. 9 m. 21 da.

MULTIPLICATION OF POLYNOMIALS.

RULE XXXIX.

$197. For Polynomial or Compound Multiplication.

1. Proceeding from right to left, multiply each term of the polynomial separately, and under each set its product, if less than a unit of the next higher denomination.

2. If not less than such unit, divide the product by that number of its own denomination which makes a unit of the next higher; set the remainder, if any, under the term, and add the quotient to the product of the next term.

EXAMPLE.

To multiply 25£, 16 s. 3 d. by 3.

£, S. d.

25 16 3

3

77 8 9

Proceeding from right to left, we say 3 times 3 d. is 9 d.; 3 times 16 s. is 48 s., which, being more than 1£, we divide by 20, since 20 s. make 1£. Setting down the remainder 8 s., we add the quotient 2 to the product of the next term; 3 times 25 is 75, and 2 makes 77.

The product is thus found to be 77£, 8 s. 9 d.

This Rule depends on the same principles as the Rule for polynomial or compound addition.

EXERCISES.

1. What should be paid for 4 yards of broadcloth, at 1£, 3 s. 8 d. per yard? Ans. 4£, 14 s. 8 d.

2. Required the aggregate weight of 5 silver goblets, each weighing 1 lb. 9 oz. 13 dut.? Ans. 9 lb. 5 dut.

3 Bought 6 loads of hay, each of which weighed 19 cwt. 3 qr. 23 lb. Required their entire weight.

Ans. 119 cut. 2 qr. 26 lb. 4. An apothecary sold 7 bottles of quinine, each weighing

12 oz. 13 dr. What was the weight of the whole ?

Ans. 5 lb. 9 oz. 11. dr.

5. A farmer filled 23 sacks of corn, each containing 5 bu. 3 pk. 1 qt. What quantity did they all contain?

Ans. 132 bu. 3 pk. 7 qt. 6. A brewer sold to each one of 9 men 18 gal. 3 qt. 1 pt. of beer. What quantity did he sell in all ?

Ans. 169 gal. 3 qt. 1 pt.

7. A vintner bought of 10 persons each 3 hhd. 24 gal. 2 qt. of wine. How much did he buy from them all?

Ans. 33 hhd. 56 gal. 8. If a man travel at the rate of 33 m. 7 fur. 30 r. per day, what number of miles will he travel in 11 da.?

Ans. 373 m. 5 fur. 10 r.

9. A merchant sold 19 pieces of linen, each piece containing 16 yd. 3 qr. 2 na. How many yards did he sell?

Ans. 320 yd. 2 qr. 2 na. 10. A farmer has 13 fields, each containing 24 A. 3 R. 10 P. What quantity of land do all the fields contain?

Ans. 322 A. 2 R. 10 P.

11. If a steamboat run at the rate of 12 m. 3 fur. 19 r. per hour, what distance will it run in 14 hours? Ans. 174 m. 26 r. 12. If a ship sail at the rate of 30 L. 2 m. 4 fur. 20 r. per day, what distance will she sail in 15 da.?

Ans. 462 L. 2 m. 3 fur. 20 r. 13. A teamster hauled 16 loads of coal, averaging 2 T. 17 cwt. 1 qr. each. What was the entire weight?

Ans. 45 T. 16 cwt. 14. A manufacturer made 17 pieces of cloth, measuring 39 yd. 3 qr. each. How much cloth was there in all ? Ans. 675 yd. 3 qr. 15. An astronomical year being 365 da. 5 hr. 48 min. 51 sec., required the number of days in 20 such years.

Ans. 20 y. 4 da. 20 h. 17 min. 16. An agriculturist had 15 acres of ground in hemp, and found his crop to be at the rate of 7 cwt. 3 qr. 10 lb. per acre; what was the entire crop? Ans. 13 T. 17 cwt. 2 qr. 10 lb. 17. A brewer filled 3 hogsheads with beer, out of which he has sold to the amount of 75 gal. 3 qt. 1 pt. What quantity remains of the 3 hhd.? Ans. 1 hhd. 32 gal. O qt. 1 pt.

18. A merchant bought 7 pieces of silk containing, on an average, 47 yd. 2 qr. each. Having sold to one lady 11 yd., and to three others each 10 yd. 3 qr., how many yards of the silk remain on hand? Ans. 289 yd. 1 qr.

19. A bought of B 100 A. 2 R. 21 P. of land, of C 5 times as much as from B, wanting 10 A., and from D as much as from C, wanting 3 A. 2 R. 30 P.

his purchase?

What was the amount of

Ans. 1083 A. 1 R. 1 P.

DIVISION OF POLYNOMIALS.

RULE XL.

$198. For Polynomial or Compound Division.

1. When the divisor is an abstract number, and the dividend a polynomial.-Proceeding from left to right, divide each term of the polynomial, for the corresponding term of the quotient.

2. When a remainder occurs, reduce it to the next lower denomination, add it to the term in that denomination, if any, and divide the result for the quotient term in the same denomination.

3. When the divisor and dividend are both polynomials.-Reduce them both to monomials of the same denomination, and find the quotient in an abstract number.

EXAMPLE.

To divide 285£, 17 s. 5 d. by 3; that is to find of this polynomial.

Proceeding from left to right, we find 3 in 285, 95 times; 3 in 17, 5 times, with 2 s. over; reducing the 2 s. to pence, and adding the 5 d., we have 29 d.; then 3 in 29, 9 times, with 2d. over; reducing the 2 d. to qr., we have 8 qr.; 3 in 8, gives 23 qr. The quotient is thus found to be 95£, 5 s. 9 d. 23 qr.

The operation evidently finds of the given polynomial..

EXERCISES.

1. If 4 yards of cloth sell for 9£, 17 s. 8 d., what is the price per yard?

2. If 5 silver candlesticks weigh the average weight of each?

Ans. 2£, 9 s. 5 d. 10 lb. 7 oz. 18 dwt., what is Ans. 2 lb. 1 oz. 11 dwt.

3. If 6 barrels of pork weigh 12 cwt. 2 qr. 23 lb., what is the

average weight of each?

4. If 7 acres of ground produce what is the produce per acre?

Ans. 2 cwt. 0 qr. 131 lb.

150 bu. 2 pk. 1 qt. of wheat, Ans. 21 bu. 2 pk. 4 qt.

5. If 8 casks together contain 250 gal. 3 qt. 1 pt. of spirits,

what are the average contents of each?

Ans. 31 gal. 1 qt. 3gi.