13. Reduce 30339 gi. to T. Ans. 3 T. 3hhd. 3gal. 3gi. 14. 10125 gi. to T. Ans. 1T.1hhd. 1 gal. 1qt. 1pt. 1gi.

15. 3 puncheons to gills.

16. 5 pipes to quarts.

17. 5712 pt. to tierces.

Ans. 8064 gi.

Ans. 2520 qt.

Ans. 17 tr.

ART. 96. ALE OR BEER MEASURE

Is generally used in measuring ale, beer, and milk.

NOTE. The beer gallon contains 282 cubic inches. In most places

milk is now sold by Wine Measure.

1. Reduce 4hhd. to pints.
2. 7 hhd. 3qt. to pints.
3. 1000 pt. to barrels.
4. 443 pt. to hhd.

Ans. 1hhd. 1 gal. 1 qt. 1 pt.

ART. 97. TIME MEASURE.

Time is a measured portion of duration. The parts into which time is divided are shown in this

1 day,

da.

365 days 6 hours, (3654 da.) 1 solar year,

100 years

Also, 7 days

J See Notes on page 98.

REVIEW.-96. For what is Beer Measure used? Repeat the Table,

97. What is Time? Repeat the Table.

1 month, (nearly)

wk. mon.

1 year,

1 common year,

1 leap year,

3d Bk.

Rule for Subtraction.—1. Write the numbers, the less under the greater, placing units of the same denomination under each other.

2. Begin with the lowest order, and, if possible, take the lower number from the one above it, as in Simple Subtraction.

3. But, if the lower number of any order be greater than the upper, increase the upper number by as many units of that denomination as make one of the next higher; subtract as before, and carry one to the lower number of the next higher order. Proceed in the same manner with each denomination.

PROOF. As in Subtraction of Simple Numbers.

REM.-In Simple Subtraction, when any lower figure is greater than the upper, we borrow ten, ten units of a lower order making a unit of the next higher. In Compound Numbers, when the lower number of any order is greater than that above it, borrow the number of units in that order which makes a unit of the next higher.

12. If 2bu. 1pk. 1 qt. be taken from a bag of 4bu., what quantity will remain ? Ans. 1 bu. 2 pk. 7 qt.

13. From 100 bushels, take 24 bu. 1 pt.

Ans. 75 bu. 3 pk. 7qt. 1pt.

14. From 191b. 9oz. of silver, take 9 lb. 9oz. 10pwt. Ans. 91b. 11 oz. 9pwt. 14gr.

10 gr.

15. A silver bar of 81b. 2oz. 11 pwt., is divided into 2 parts; the less weighs 2lb. 4 oz. 7pwt. 16gr.: find the weight of the greater. Ans. 5lb. 10 oz. 3pwt. 8gr.

16. From 3b 33 13 19 12 gr., take 1b 73 29

18 gr.

17. I bought 46 lb. 9oz. 4dr., how much remained?

Ans. 1lb 83 19 14gr.

of rice after selling 191b. Ans. 27 lb. 8 oz. 12 dr.

18. A wagon loaded with hay weighs 32 cwt. 2qr. 161b.; the wagon. alone weighs 8cwt. 2qr. 171b.: what is the weight of the hay? Ans. 23 cwt. 3qr. 24lb.

19. It is about 25000 miles round the earth after a man has traveled 100 mi. 1 fur. 1 rd., what distance will remain ? Ans. 24899 mi. 6 fur. 39rd.

20. I had 146 A. 2 R. of land. 2R. 14 P.: how much was left?

I gave my son 86 A. Ans. 59 A. 3R. 26 P.

21. From 8C. 50 cu. ft. of wood, there is taken 3C.

75 cu. ft. how much is left?

22. From 25 E. Fl., take 14 E. FI.

Ans. 4C. 103 cu.ft.

1 qr. 3 na.

Ans. 10 E. Fl. 1qr. 1na.

23. From 11 yards of cloth, there is cut 3yd. 2 qr.

2na. what remains?

24. A hhd. of wine leaked; mained how much was lost?

Ans. 7yd. 1qr. 2na. only 51 gal. 1 qt. 2gi. reAns. 11 gal. 2 qt. 1 pt. 2 gi.

25. From 5 da. 10 hr. 27 min. 15 sec., take 2da. 4hr. 13 min. 29 sec. Ans. 3 da. 6 hr. 13 min. 46 sec.

REVIEW.-102. Why place units of the same denomination under each other? At which column begin to subtract? Why? How is the subtraction performed? Repeat the Rule. What is the proof?

102. REM. In subtraction of Compound Numbers when the lower number of any order is greater than the upper, what is to be done?

ART. 103. To find the Time between any Two Dates.

Subtract the first date from the last, numbering the months according to their order. See note 3, page 98.

NOTE. In finding the time between two dates, and also in Interest, consider û days 1 month, and 12 months 1 year.

26. A note, dated April 14th, 1835, was paid February 12th, 1837: find the time between these dates.

OPERATION.

yr. mon. da. 1837 2 12 1835

4 14

SOLUTION. In writing the dates, observe that February is the 2d month, and April, the 4th. In subtracting, 14 days can not be taken from 12; theref re add 30 to the 12 days, subtract, and carry 1 to the 4 months. As5 months can not be taken from 2 months, add 12 to the latter, subtract, and carry 1 to the years.

28. A certain man was born was his age Aug. 1st, 1848?

1 9 28

27. The Independence of the United States was declared. July 4th, 1776: what length of time had elapsed on the 5th of March, 1857? Ans. 80 yr. 8mon. 1 da. June 24th, 1822: what Ans. 26 yr. 1 mon. 7 da. 25th, 1807; his son was is the difference of their Ans. 24 yr. 7 mon. 3 da.

29. A man was born Nov. born June 28th, 1832: what ages?

30. The latitude of the Cape of Good Hope is 33° 55' 15" south; that of Cape Horn, 55° 58′ 30′′ south find the difference of latitude. Ans. 22° 3' 15".

31 The latitude of Gibraltar is 36° 6' 30" north; that of North Cape, in Lapland, 71° 10' north difference of latitude?

what their Ans. 35° 3' 30". 32. A ship departs from latitude 10° 25′ 48′′ north, and sails north to latitude 50° through how many degrees of latitude has she sailed? Ans. 39° 34′ 12′′. 33. Take 5 quires 11 sheets from a ream of paper, and how much will remain? Ans. 14 quires 13 sheets.

34. A man started to market with 6 doz. doz. eggs: he broke half a doz. doz.: how many were left? Ans. 792,

MULTIPLICATION OF COMPOUND NUMBERS.

ART. 104. The process of taking a number consisting of different denominations, a certain number of times, is termed Multiplication of Compound Numbers.

1. A farmer takes to mill 5 bags of wheat, each containing 2 bu. 3 pk. 4 qt.: how much in all?

Next, multiply the 3 pk. by 5, making 15 pk., to which add the 2 pk. carried, making 17 pk., which, reduced, give 4 bu. and 1 pk.; write the 1 (pk.) in the column of pk., and carry the 4 bu.

Then, multiply the 2 bu. by 5, add to the product the 4 bu. carried, and we have 14 bu. to be written in the column of bu.

In Compound, as in Simple Multiplication, multiply the lowest denomination first, so as to carry from a lower to a higher order.

2. Multiply 2 bu. 5 qt. 1 pt. by 6. 3. Multiply 2 bu. 2 pk. 2 qt. by 9.

Ans. 13 bu. 1 qt.
Ans. 23 bu. 2 qt.

Rule for Multiplication.-1. Write the multiplier under the lowest denomination of the multiplicand.

2. Multiply the lowest denomination first, and divide the product by the number of units of this denomination, which make a unit of the next higher; write the remainder under the denomination multiplied, and carry the quotient to the product of the next higher denomination.

REVIEW. 103. How find the time between any two dates ? 104. What is Multiplication of Compound Numbers? Why multiply the lowest denomination first? Repeat the Rule.