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4. What is the latitude of Washington, if it be 61° 46' 20' north of Rio Janeiro, and the latter place be 21° 54' south latitude?

5. When it is 20 minutes after noon at Washington, it is 21 min. 26 sec. before noon at Chicago, 87° 30' west. What is the longtitude of Washington ?

MISCELLANEOUS EXAMPLES.

366. 1. A messenger leaves the Greenwich Observatory, westward bound, at noon, Dec. 31, and by a uniform rate of speed encircles the globe in 24 hours. Where is he at the end of the old year?

2. Suppose the messenger be eastward bound, at what point will he meet the new year?

3. When it is 20 minutes past 10 A. M. at Cape Horn, 68° west, what is the time at Cape of Good Hope, 18° 19' east?

4. When it is noon at London, what is the time at St. Augustine, 81° 35' west? At Berlin, 13° 30' east? At New Orleans, 90° west? At Sidney, 152° 20 east? At Paris, 20° 20' 22' east? At New York, 74° 3' west?

ENGLISH MONEY.

367. English or Sterling Money is the legal currency of Great Britain.

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Scale, ascending, 4, 12, 20; descending, 20, 12, 4. 368. The standard unit is the pound sterling, the value of which, in United States money, is shown, together with the other coins, in the following

Comparative Table.
The farthing = $f cent. The shilling = 24} cents.
= 29 cents.

The pound

= $4.8665. REMARK. — The farthing is but little used, except as a fractional part of the penny.

The penny

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COINS OF GREAT BRITAIN. 369. The gold coins are the sovereign and the half-sovereign.

The silver coins are the crown (equal to 5 shillings), the half-crown, the florin (equal to 2 shillings), the shilling, the six-penny and three-penny pieces.

The copper coins are the penny, the half-penny, and the farthing.

The guinca (equal to 21 shillings) and the half-guinea are in use, but are no longer coined.

REDUCTION OF ENGLISH MONEY.
370. To Reduce English Money from Lower to Higher Denominations.
EXAMPLE.—Reduce 13206 farthings to units of higher denominations.
OPERATION

EXPLANATION.—Since 4 farthings equal one penny, 13206 far

things equal as many pence as 4 is contained times in 13206, or 4 ) 13206 far.

3301, plus 2 remainder, equal 3301 pence, 2 farthings; since 12 12 ) 3301 d. + 2 far. pence equal 1 shilling, 3301 pence equal 275 shillings, plus 1

penny; since 20 shillings equal 1 pound, 275 shillings equal 13 20 ) 275 8. + 1 d.

pounds, plus 15 shillings. Therefore, 13206 farthings equal £13, £13 + 15 s. 15 s. 1 d. 2 far, 13206 far. = £13, 15 s. 1 d. 2 far.

Rule.-Divide by the units in the scale from the given to the required denomination.

EXAMPLES FOR PRACTICE.

371. Reduce 1. 5124 s. to pounds. 2. 11916 far. to shillings.

3. 13042 d. to pounds.
4. 187409 far. to higher denominations.

4 s.

372. To Reduce English Money from Higher to Lower Denominations. EXAMPLE.—How many farthings in £9, 4 s. 3 d. 2 far. ?

OPERATION. £9, 4 s. 3 d. 2 far. 20

EXPLANATION.-Since 1 pound equals 20 shillings, 9 pounds OPERATION 180 s.

equal 180 shillings, and 180 shillings, plus 4 shillings, equal 184 CONTINUED.

shillings; since 1 shilling equals 12 pence, 184 shillings equal 2208 2211 d.

pence, and 2208 pence, plus 3 pence, equal 2211 pence; since 1 184 s.

4

penny equals 4 farthings, 2211 pence equal 8844 farthings, and 12

8844 far. 8844 farthings, plus 2 farthings, equal 8846 farthings. Therefore, 2208 d.

2 far.

£9, 4 s, 3 d. 2 far, -8846 far. 3 d.

8846. 2211 d.

Rule.-Multiply by the units in the scale from the given to the required denomination.

EXAMPLES FOR PRACTICE.

3.

373. 1. How many pence in £27?
2. How many farthings in 19 s. 11 d. ?

How many pence in £161, 17 s. 9 d.? 4. Reduce £41, 1 s. 10 d. 2 far. to farthings. 5. How many farthings in £13, 15 s. 1 d. 2 far.? 374. To Reduce English Money to Equivalents in United States Currency. EXAMPLE.- Reduce £15, 3 s. 7 d. 2 far. to dollars and cents.

FIRST EXPLANATION.-Since £1 equals $4.8665, £15 equal $72.9975; since 1 shilling equals 24} cents, 3 shillings equal $.73; since 1 penny equals 235 cents, 7 pence equal $.1414; since 1 farthing equals 5cent, 2 farthings equal $.0101. Therefore, £15, 3 s. 7 d. 2 far. = $73.8789, or $73.88,

SECOND EXPLANATION.-Call each 2 shillings 1o of a pound, then 3 shillings equal £.15; call the pence and farthings, reduced to farthings, so many too of a pound, then 7 pence, plus. 2 fartbings, equal 30 farthings, equal £.030; to these add the £15, and the result is £15.18. And, since £1 equals $4.8665, £15.18 equal 15.18 times $4.8665, or $73.88, as before found.

Rules.—1. Multiply each of the orders of Sterling money by its equivalent in United States currency, and add the results. Or,

2. Reduce the Sterling expression to pounds and decimals of a pound by calling each 2 shillings is of a pound, and the pence and farthings, reduced to farthings, so many tuvo of a pound; multiply the pounds and decimals of a pound thus obtained by 4.8665, and the product will be the answer in dollars and cents.

REMARK.—This is exact to within nio of the part represented by the pence and farthings.

EXAMPLES FOR PRACTICE.

375. Reduce to equivalents in United States money
1. £71, 19 s. 5 d. and 3 far.
2. £108, 11 d. and 1 far.
3. £13057, 10 s. and 4 d.
4. £3, 1 s. 9 d. and 2 far.
5. £11, 3 s. 1 d. 1 far.

376. To Reduce United States Money to Sterling equivalents. EXAMPLE.—Reduce $5164.28 to equivalents in English inoney.

OPERATION. 4.8665 ) 5164.28 £1061 + £.189 rem.

EXPLANATION.-Since $4.8665 equal £1, $5164.28 20

equal £1061.189; multiply the decimal by the units 3 s. +.78 s. rem. in the scale, 20, 12, 4, in order, pointing off as in 12

decimals, and obtain 3 s. 9 d. 1 far., which, added to 9 d. + 36 d. rem.

the £1061, equals £1061, 3 s. 9 d. 4 far. 4

1 far. +.44 far.

Rule.-Divide the expression of decimal currency by 4.8665, and the integers of the quotient will be pounds Sterling; reduce the decimal of the quotient, if any, by multiplying by the lower units in the scale.

EXAMPLES FOR PRACTICE.

377. 1. Reduce $185 to equivalents in English money. 2. Reduce $308.50 to equivalents in English money.

Reduce $2500 to equivalents in English money. 4. Reduce $3658.21 to equivalents in English money. 5. Reduce $110085.75 to equivalents in English money.

MEASURES OF WEIGHT.

378. Weight is the measure of gravity, and is of three kinds, distinguished from each other by their uses, viz :

Troy weight, with units of pounds, ounces, pennyweights, and grains, used for weighing precious metals.

Avoirdupois weight, with units of tons, hundred weights, pounds, ounces, and drams, used for weighing products and general merchandise.

Apothecaries' weight, with units of pounds, ounces, drams, scruples, and grains, used by druggists.

TROY WEIGHT. 379. The Troy pound is the standard of weight, and is equal to 22.7944 cubic inches of pure water, at its greatest density. The grains of the other weights are the same as the Troy grains.

Table.

OZ.

24 grains (gr.) = 1 pennyweight.... pwt.
20 pennyweights = 1 ounce
12 ounces = 1 pound...

lb.
descending, 12, 20, 24.

1 lb. = 5760 grains. ascending, 24, 20, 12.

1 oz. = 480 grains.

Scale

REDUCTION OF DENOMINATE NUMBERS.

172 oz. 11 oz.

380. To Reduce Denominate Numbers from Higher to Lower Denominations. EXAMPLE_Reduce 6 lb. 11 oz. 15 pwt. 21 gr., Troy, to grains. OPERATION.

FIRST EXPLANATION. Since 1 pound equals 18 6 lb. 11 oz. 15 pwt. 21 gr. ounces, 6 pounds equal 72 ounces, and 72 ounces plus 12

11 ounces equal 83 ounces; since 1 ounce equals 20 pennyweights, 83 ounces equal 1660 pennyweights, and 1660 pennyweights plus 15 pennyweights equal 1675 pennyweights; since 1 pennyweight equals 24 grains,

1675 pennyweights equal 40200 grains, plus 21 grains 20

equal 40221 grains. Therefore, 6 lb. 11 oz. 15 pwt. 1660 pwt.

21 gr. Troy, = 40221 gr. 15 pwt.

SECOND EXPLANATION.-Since 1 pound equals 5760 1675 pwt.

grains, 6 pounds equal 34560 grains; siuce 1 ounce equals 24

480 grains, 11 ounces equal 5280 grains ; since 1 pen

nyweight equals 24 grains, 15 pennyweights equal 360 21 gr.

grains; to these add the 21 grains, and the entire sum is 40221 grains.

83 02.

40200 gr.

40221 gr.

REMARK. -A thorough knowledge of the unit equivalents, together with readiness in the use of the multiplication table, renders the second form much the shorter of the two methods.

Rules.-1. Multiply the units of the highest denomination given by that number in the scale which will reduce it to the denomination next lower, and add the units of that louer denomination; continue in this manner until the required denomination is reached. Or,

2. Multiply the units of cach denomination by the number of units of the desired equivalent which it takes to make one of that denomination, and add the products thus obtained.

381. To Reduce Denominate Numbers from Lower to Higher Denominations. EXAMPLE.-Reduce 40221 gr., Troy, to higher denominations. FIRST OPERATION.

EXPLANATION.—Since 24 grains equal 1 pennyweight, 24 ) 40221 gr.

40221 grains equal 1675 pennyweights, plus 21 grains; since 20 ) 1675 pwt. + 21 gr.

20 pennyweights equal 1 ounce, 1675 pennyweights equal

83 ounces, plus 15 pennyweights; since 12 ounces equal 12 ) 83 oz. + 15 pwt. 1 pound, 83 ounces equal 6 pounds, plus 11 ounces. There

fore, 40221 gr., Troy, 6 lb. 11 oz. 15 pwt. 21 gr. 6 lb. + 11 oz. 40221 gr., Troy, = 6 lb. 11 oz. 15 pwt. 21 gr.

SECOND OPERATION. 5760 ) 40221 gr. ( 6 lb. EXPLANATION.-Since 5760 grains equal 1 pound, 40221 34560

grains equal 6 pounds, plus 5661 grains; since 480 grains 480 ) 5661 gr. ( 11 oz.

equal 1 ounce, 5661 grains equal 11 ounces, plus 381 grains; 5280

since 24 grains eqnal 1 pennyweight 381 grains equal 15

pennyweights, plus 21 grains. Therefore, 40221 gr. = 6 lb. 24 ) 381 gr. ( 15 pwt. 11 oz. 15 pwt. 21 gr., as before found.

360

21 gr.

40221 gr., Troy, = 6 lb. 11 oz. 15 pwt. 21 gr. REMARK.—The first form is advised for practice, as the operations may usually be performed by short division.

EXAMPLE 2.-Reduce 11426 gr., Troy, to higher denominations. EXPLANATION.—Divide the given number by 24, the integers of the quotient by 20, the integers of the new quotient by 12.

Rules.-1. Divide by the successive units in the scale. Or, 2. Divide by the unit equivalents of each of the higher denominations.

382. To Reduce Denominate Fractions from a Higher to a Lower Denomination, EXAMPLE.—Reduce 1860 lb., Troy, to the fraction of a pennyweight.

FIRST OPERATION. 1560 X 1 X 4 = 1888 = 1 EXPLANATION.—1867 of a pound equals 1880 of the 12

ounces in 1 pound, or 1840 ounces; 1840 of an ounce SECOND OPERATION.

equals 1$ty of the 20 pennyweights in 1 ounce, or 1988,

which equals ji pennyweights. Therefore, 18780 lb., taka x x P = fi pwt. Troy, = fi pwt.

.

33
31

Rule.- Multiply the fraction by the units in the scale, from the given to the required denomination.

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