The gallon for liquors and corn contains 277 274 cub. in., and holds 10 lbs. Avoird. of distilled water.

A solar year = 365 dys. 5 hrs. 48′ 47′′ nearly.

The common year is divided into 12 calendar months, whose lengths may be remembered by the following lines:

Thirty days has September
April, June, and November;
February has twenty-eight alone,
And all the rest have thirty-one.
But leap-year, coming once in four,
Gives to February one day more.

The Centuries are not leap-years, except when their numbers are divisible by 4: thus 1800, 1900, 2100, &c., are not leap-years.

QUARTERLY TERMS.

Lady-Day, March 25th; Midsummer, June 24th; Michaelmas, Sept. 29th; Christmas, Dec. 25th.

In Scotland:

Candlemas, Feb. 2nd; Whitsuntide, May 15th; Lammas, Aug. 1st; Martinmas, Nov. 11th.

CHAPTER II.

REDUCTION AND COMPOUND RULES.

9.-REDUCTION is the method of changing the denomination in which a quantity is expressed, without altering its value: or, as it may be expressed more shortly, of changing one denomination to another.

RULES.

To reduce a higher denomination to a lower :-Multiply by so many of the lower as make one of the higher.

If there are intermediate denominations, reduce step by step, adding in successively the numbers of the denominations given.

To reduce a lower denomination to a higher :-Divide by so many of the lower as make one of the higher.

If there are intermediate denominations, reduce step by step, the successive remainders being numbers of those denominations.

Ex. (1). Reduce £34 into shillings.

£34

20

680s. Ans.

For since each pound contains 20 shillings, 34 pounds will contain 34 times 20 shillings, i. e. 34 X 20 = 680. The same kind of explanation may easily be applied to the following examples.

Ex. (2) Reduce £71 138. 6d. into pence.

Ex. (3) Reduce 17 tons 3 cwt. 2 qrs. 22 lbs. into pounds.

tons cwt. qrs. lbs.

17. 3. 2 22

20

343 cwt.

4

1374 qrs.

28

10992
2748

22

38494 lbs. Ans.

Ex. (4) Reduce 37845 pence into shillings.

12 | 37845d.

31538.. 9d. Ans.

For since every shilling contains 12 pence, as many 12d.'s as there are in 37845 d. so many shillings will there be, and the remainder 9 will be 9d. additional.

Ex. (5) In 372845 farthings how many guineas are there?

Ex. (6) How many lbs. Troy are there in 219078 grains?

In some cases both the above rules must be applied.
Ex. (7) Reduce 3697 crowns into guineas.

There is not an exact number of crowns in a guinea, so that the crowns must be reduced into shillings, and these shillings into guineas.

To this class belong such questions as the following:

Ex. (8) Reduce 37597 feet into poles.

Five-and-a-half yds. are a pole, i. e. eleven half-yds.; so the 12532 yds. are reduced into half-yds., and these into poles. The remainder 6 represents 6 half-yds., i. e. 3 yds.

Reduce:

Exercise 6.

(1) £3724 into pence; £48613 into farthings.

(2) £583 6s. 8d. into pence; 23791 guineas into farthings.

(3) £79 188. 11d. into farthings; 4812 crowns 3s. 6d. into pence.

(4) 72837 shillings into halfpence; 238901 half-sovereigns into farthings.

(5) 834216 fourpenny pieces into farthings; 98657 guineas into halfpence.

(6) £287 98. 10ld. into halfpence; 896302 florins into farthings.