6. In 6195 pints of wine, how many tuns?

Ans. 3T. Ohhds. 18gal. 1qt. 1pt.

are qts. quarts divided by are hhds. hogsheads divided by

are gals. gallons

are tuns.

Pints divided by divided by 7. Suppose you have 7 barrels of excellent cider, each con. taining 32 gallons, which you wish to draw off into bottles; the size of the bottles to be half gallons, quarts and pints, and to have an equal number of each; be so good as to find the number of bottles. Ans. 256 bottles of each kind. Reduce the barrels to pints; find now many pints will fill a bottle of each kind; then the pints in the barrel by the pints in the bottles. The barrels to be reduced to pints, because the bottles must be put down in pints, as there are pint bottles to be filled.

8. In 5 hogsheads of beer, each 54 gallons, how many 10 gallon and 5 gallon kegs, each an equal number?

Ans. 18 of each kind. Divide the gals. in the 5hhds. by the number of gals. it takes to fill a keg of each kind..

DRY MEASURE.

EXAMPLES FOR ILLUSTRATION.

1. In 26Ch. 18bu. 2pks. how many pecks?

Ch. bu. pks. 26 18 2.

36.

164

79

954 bushels.

4

3818 pecks.

Ans, 3818pks.

Here you will see, that I multiplied by 36, the bushels in a chaldron, and added in the 18 bushels; I then multiplied by 4, the pecks in a bushel, and added in the 2 pecks; this produced 3818 pecks, the answer.

EXAMPLES.

3. In 4582 pints, how many bushels? Ans. 71bu. 2pks. 3qts. Pints divided by - are quarts; quarts divided by - are pecks; pecks divided by · are bushels.

4. In 14 bushels of corn, how many quarts? Ans. 448qts. Bushels multiplied by are pecks; pecks multiplied by are qts. 5. In 6548 pecks, how many chaldron? -Ans. 45ch. 17bu. Pecks divided by are bushels; bushels divided by · are chaldrons 6. In a cask of flaxseed, that contains 224 quarts, how many bushels?

are pecks, &c.

Ans. 7bu. Quarts divided by 7. Suppose you had 12 sacks of corn, each holding 43 bushels, how many quarts do they contain? Ans. 1728qts. Find the number of bushels in the sacks; and then, bushels multiplied are pecks; pecks multiplied by are quarts.

by

8. Suppose you purchase 630 bushels of beans, how many barrels each holding 3 bushels, will it take to hold the whole? Ans. 180

Reduce both numbers of bushels into half bushels; and then by the half bushels in a barrel.

SOLID MEASURE.

EXAMPLES FOR ILLUSTRATION.

1. In 12 tons of round timber, how many solid inches? Ans. 829440in.

Tons.

12

40

480

1728

3840

960

3360

480

If you ask the reason, why I multiplied by 40, I answer: because 40 feet of round timber make a ton. Again, why I multiplied by 1728: because 1728 solid inches make a solid foot; this produced the number of inches in 12 tons.

829440

2. In 829440 solid inches, how many tons of round timber?

1728)829440(410)48(0

6912

13824
13824

Ans. 12 tons.

I divided by 1728, the solid inches 12 tons. in a foot; in the next place, by 40,

the number of feet in a ton of round timber; the last quotient was the tons required.

EXAMPLES.

3. In 8 tons of hewn timber, how many solid inches?

Tons of hewn timber multiplied by are inches.

Ans. 691200 solid in. are feet; feet multiplied by

4. In 7 cords of wood, how many solid feet and inches?
Ans. 896 feet 1548288 solid inches.

Cords multiplied by -
- are feet; feet multiplied by
5. In 896 solid inches, how many cords?
Feet divided by - are cords.

TIME.

are inches.

Ans. 7 cords.

You will find Time very useful; therefore, pay attention to it.

EXAMPLES FOR ILLUSTRATION.

1. In 21 weeks, how many days, hours, minutes and seconds? Ans. 147D. 3528hrs. 211680m. 12700800sec.

W.

21.

7

147 D.

24

588

294

3528 hrs.

I first multiplied by 7, the days in a week; then by 24, the hours in a day; then by 60, the \ minutes in an hour; and lastly, by 60, the seconds in a minute; which brought 12700800 seconds, the answer.

12700800 s. 2. In 12700800 seconds, how many weeks?

Ans. 21 weeks.

I found the answer to this question by dividing by 60, 60, 24 and 7. The reason why I divided by these figures, was, because 60 seconds make a minute; 60 minutes make an hour; 24 hours make a day; and 7 days make a week.

824692 A

EXAMPLES.

3. In 5D. 19hrs. 21m. 42sec. how many seconds?

Ans. 501702sec.

Days multiplied by are hours, &c. Examine the Table. As you multiply, add in the hours, minutes and seconds.

4. In 2834962 seconds, how many weeks?

-

Ans. 8w. Od. 19hrs. 29m. 22sec.

are minutes, &c.

Seconds divided by 5. How many days are there in 21 years, allowing a year to contain 365 days, 6 hours? Ans. 7670 days, 6 hours. As 6 hours make of a day, multiply the number of years by 3651, as taught, p. 60. If there be a remainder, when dividing by 4, bring it into hours by 24; and divide by the 4 again, to get the hours.

6. How many seconds in your age, when 14 years and 21 days old, allowing the year to contain 365 days?

When you

Ans. 443318400 seconds.

by the 365, see that you add in the 21 days. Then,

days multiplied by minutes multiplied by

are hours; hours multiplied by — are minutes;

are seconds.

7. How many days, since the birth of our Saviour to Christmas, 1831, allowing the year to contain 365 days?

Performed like the 5th example.

Ans. 668772 days 18 hours.

8. How many days, from June 6th to December 12th, (in

clusive?)

June

25 days.

July

August

September

October

November
December

Ans. 190 days. Write down the months under each other, in the order they come, from June to December, with the number of days belonging to each, except the first and last. For June, reckon how many days are gone on the 6th, and 12 days. deduct the number from the days in that month. For December, place the day of the month, the time is to be reckoned to; place the months as in the margin. As June contains 30 days, I deducted 5 from that number, for the days gone on the 6th of June. For December, I placed the number mentioned, viz. 12. Add the whole together.

190

NOTE.--When the day the time commenced, is not included, then deduct the day of the month mentioned from the days in that month. 9. How many days are there between the 21st day of August, 1820, and the 9th day of May, 1821? Ans. 262 days. reckon how many

Place the months in order, from August to May; days are yet in August, including the day mentioned, and place it at the end of that month. Then the days that belong to each month as they

10. How many years, months and days, are there between the 10th of May, 1827, and the 19th of January, 1831? Ans. 3yrs. 8mo. 9 days.

You may set down the years, months and days, last mentioned; and place the years, months, and days first mentioned, under them; the 19th of January, 1831, will stand thus: 1831y. Om. 19d.; and the other you must find yourself; the time is reckoned from January to the beginning of the year.

11. Suppose a man should begin to work with a farmer on the 21st day of April, and should work till the 29th day of October, how many days is he entitled to receive pay for?

Ans. 192 days. Performed like the 9th ex. The day he commenced is included.

CIRCULAR MOTION.

EXAMPLE FOR ILLUSTRATION.

1. In 5 signs, 16deg. 31min. 19sec, how many seconds?

In the table, I found that signs multiplied by 30, are degrees, because 30 degrees make a sign; degrees multiplied by 60, are minutes, because 60 minutes make a degree; minutes multiplied by 60, are seconds, because 60 seconds make a minute. Imultiplied by the above numbers, adding in the degrees, minutes and seconds in their proper places.

2. In 599479 seconds, how many degrees, &c.?

Seconds divided by · degrees divided by

Ans. 5s. 16deg. 31min. 19sec. are minutes; minutes divided by . are deg. are signs.

Questions for Exercise in Reduction. 1. In 37428 half pence, how many pounds?

Ans. 77£. 19s. 6d.

by the half pence in a penny; then, pence divided by

lings, &c.
2. In 12340 mills, how many half eagles?

are shil

Ans. 2 half E. 2 dolls. 34cts.

Ans. 120000 mills.

Bring the mills into dollars; and the dollars into half eagles. 3. In 120 dollars, how many mills? 4. In 6£ 4s. 3d. 3qrs. how many farthings? Ans. 5967far. See the Table. It says, pounds multiplied by 20 are shillings, &c.