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FRENCH SQUARE MEASURE.

274. The unit of French Superficial Measure, is the Are, whose sides are each a decametre in length; consequently, it contains 100 square metres, or 119.6648496 U. S. sq. yds.

10 ares make 1 decare

10 decares " 1 hectare
10 hectares (6
1 kilare
10 kilares
1 myriare

((

10 litres
10 decalitres
10 hectolitres

=1196.648496 U. S. sq. yds.
=11966.48496

""

(6

= 119664.8496
"C
= 1196648.496

Note. The are is divided into 10 deciares; the deciare into 10 centiares; the centiare into 10 milliares.

make 1 decalitre =

FRENCH CUBIC MEASURE.

275. The unit of French Cubic Measure, is the Stere, which is a cubic metre, and is equal to 61074.1564445 cu. in. U. S.

10 decisteres make 1 stere = 35.34384 cu. ft. U. S.
10 steres
(6 1 decastere = =353.4384

"C

"C

FRENCH LIQUID AND DRY MEASURE.

276. The unit of French Liquid and Dry Measures, is called the Litre, which is a cubic decimetre, and is equal to 61.0741564445 cu. in. U. S., or 1.05756 qts. wine measure.

10 grammes
10 decagrammes
10 hectogrammes
10 kilogrammes,

66 1 hectolitre = 26.439 (C
"1 kilolitre 264.39 ((

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2.6439 gals. wine meas.

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"L

Note. The litre is divided into 10 decilitres; the decilitre into 10 centilitres; the centilitre into 10 millilitres.

FRENCH WEIGHTS.

277. The unit of French Weights, is the weight of a cubie centimetre of distilled water, at the maximum density, and is called the Gramme. It is equal to 15.433159 grains Troy.

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make 1 decagramme
1 hectogramme 1543.3159 "L
15433.159 66
=154331.59

1 kilogramme

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1 myriagramme

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154.33159 grs. Troy.

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Note.-1. The gramme is divided into 10 decigrammes; the decigramme into 10 centigrammes; the centigramme into 10 milligrammes.

2. The denomination chiefly used in making out invoices of goods sold by weight, and in business transactions, is the kilogramme, which is equal to 1000 grammes, or 2.21 lbs. avoirdupois, very nearly.

3. In the old system of French weight, the livre-poids=2 marcs; the marc =-8 onces; the once-8 gros; the gros=72 grains. The livre is equal to onehalf the kilogramme.

FRENCH CIRCULAR MEASURE.

278. The circle is divided into 400 equal parts, called grades, and the quadrant into 100 grades. The grade is again divided into 100 equal parts, and each of these parts is subdivided into 100 other equal parts, according to the centesimal scale. Hence,

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Note. The names of the denominations larger than the unit in the French Compound Numbers, are formed by prefixing to the name of the unit, the Greek words, deca, hecto, kilo, and myria; those less than the unit, are formed by prefixing to the name of the unit, the Latin words, deci, centi, and milli.

279. Foreign Weights and Measures compared with those of the United States.*

Amsterdam.—100 lbs. (1 centner)=108.923 lbs.†; 1 last=85.25 bu.; 1 ahm= 41 gals.; 1 foot Amsterdam=114 in.; 1 foot Antwerp=114 in.; 1 ell Amsterdam=2.26 ft.; 1 ell Brabant=2.3ft.; 1 ell Hague=2.28 ft. Batavia.-1 picul=136 lbs.; 1 kann=.39 gal.; 1 ell=2.25 ft.

Bengal.—1 haut=1.5 ft.; 1 guz=3 ft.; 1 coss or mile=1.24 miles; 1 bazar

maud=82.14 lbs.; 1 factory maud=74.66 lbs.

Bencoolen.-1 bahar-560 lbs.; 1 bamboo=1 gal.; 1 coyang=8 gals.
Bombay.-1 maud=28 lbs.; 1 covid=1.5 ft.; 1 candy=25 bu.

Bremen.-1 pound=1.1 lb.; 1 centner=116 lbs.; 1 last 80.7 bu.; 1 ft. 11 in.
Canton.-1 tael=13 oz.; 1 catty=1 lbs. ; 1 picul=133 lbs. ; 1 covid=14§ in.
Denmark.-100 lbs. (1 centner)=110.25 lbs. ; 1 bbl. (toende)=3.95 bu.;

viertel 2.04 gals.; 1 foot Copenhagen, or Rhineland=12} in. Florence and Leghorn.-100 lbs. (1 cantaro)=74.86 lbs.; 1 moggio=16.59 bu.; 1 barile 12.04 gals.; 1 palmo=91 in.

* McCulloch's Commercial Dictionary; also Kelly's Universal Cambist. The pounds in this and the following comparisons are avoirdupois.

Genoa.-100 lbs. (1 peso grosso)=76§ lbs. ; 1 peso sottile=69.89 lbs.; 1 mina =3.43 bu.; 1 mezzarola=39.22 gals.; 1 palmo=91 in.

Hamburg.*-1 foot=11.3 in.; 1 ell=22.6 in. nearly; 1 ell Brabant=27.6 in.; 1 mile=4.68 miles; 1 fass=1 bu.; 1 last=89.64 bu.; 1 ahm=384 gals. Japan.-1 catti=1.3 lbs; 1 picul=130 lbs. ; 1 ichan=31 ft.; 1 inc or tetamy

6 ft.; 1 balec-16 gals.

Madras.-1 covid=1 ft.; 1 catty=1 lbs.; 1 picul=133 lbs.; 1 maud= 25 lbs.; 1 candy 500 lbs.; 1 garee 140 bu.

Malla.-1 foot-10 in.; 100 lbs. (1 cantaro)=174.5 lbs. ; 1 salma=8.22 bu.
Manilla.-1 arroba=26 lbs.; 1 picul=143 lbs. ; 1 palmo=10.38 in.
Naples.-1 cantaro grosso=196.5 lbs.; 1 cantaro piccolo=106 lbs.; 1 palmo=
10 in.; 1 tomolo=1.45 bu. ; 1 carro 52.24 bu.; 1 carro of wine=264 gals.
Netherlands.-1 ell=3.28 ft.; 1 mudde=2.84 bu.; 1 kan litre=2.11 pints;

1 vat hectolitre 26.42 gals.; 1 pond kilogramme=2.21 lbs. Portugal.-100 lbs. 101.19 lbs.; 1 arroba=22.26 lbs.; 1 quintal=89.05 lbs. ; 1 almude=4.37 gals.; 1 alquiere=4 bu. ; 1 moyo=23.03 bu.; 1 last=70 bu. ; 1 pe or foot=125 in.; 1 mile 1 mile.

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Prussia.—100 lbs=103.11 lbs.; 1 quintal (110 lbs.)=113.42 lbs. ; 1 eimar= 18.14 gal.; 1 scheffel-1.56 bu.; 1 foot=1.03 ft.; 1 ell=2.19 ft.; 1 mile= 4.68 miles.

Rome.-100 libras=74.77 lbs. ; 1 rubbio=9.36 bu.; 1 barile=15.31 gals.; 1 foot =113 in.; 1 canna=62 ft.; 1 mile=73 fur.

Russia.-100 lbs. 90.26 lbs.; 1 berquit=361.04 lbs.; 40 lbs. (1 pood)= 36 lbs. ; 1 vedro 3 gals.; 1 chetwert=5.95 bu.; 1 foot Petersburg=1.18 ft.†; 1 foot Moscow=1.1 ft.; 1 arsheen=2} ft.; 1 mile (verst)=5.3 fur. Sicily.-100 lbs. (libras)=70 lbs.; 1 cantaro grosso 192.5 lbs. ; 1 cantare sottile 175 lbs.; 1 salma generale=7.85 bu.; 1 salma grossa=9.77 bu. ; 1 salma of wine-23.06 gals.; 1 palmo=9 in.; 1 canna=6 ft. Spain.-1 arroba=25.36 lbs.; 1 quintal 101.44 lbs.; 1 arroba of wine= 44 gals.; 1 moyo=68 gals.; 1 fanega 1.6 bu.; 1 foot-11.128 in.; 1 vara= 2.78 ft.; 1 league (leagua)=4.3 m., nearly.

Sweden.-100 lbs. (victualie)=73.76 lbs.; 1 foot-11.69 in.; 1 ell=1.95 ft.; 1 mile=6.64 m.; 1 kann=7.42 bu.; 1 last=75 bu.; 1 kann of wine= 69.09 gals.

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Smyrna.—100 lbs. (1 quintal)=129.48 lbs.; 1 oke=2.83 lbs.; 1 quillot= 1.46 bu.; 1 quillot of wine=13.5 gals.; 1 pic=24 ft.

;

Trieste.-100 lbs.=123.6 lbs.; 1 stajo 2 bu.; 1 orna, or eimer=14.94 gals.; 1 ell (for silk)=2.1 ft.; 1 ell (for woollen)=2.2 ft.; 1 foot Austrian=1.037 ft. 1 mile Austrian-4.6 m.

Venice.-100 lbs. (1 peso grosso)=105.18 lbs.; 1 peso sottile=64.42 lbs.; 1 stajo =2.27 bu.; 1 mcggio=9.08 bu.; 1 anifora=137 gals.; 1 foot-1.14 ft.; 1 braccio (for silk)=24.8 in.; 1 braccio (for woollen)=26.6 in.

* New system of weights and measures adopted in 1843.

† In measuring timber English feet and inches are chiefly used throughout Russia.

REDUCTION.

280. The process of changing compound numbers from one denomination into another, without altering their value, is called REDUCTION.

Operation.
£ s. d. far.

5 2 7 3.
20s. in £1.

Ex. 1. Reduce £5, 2s. 7d. and 3 far. to farthings.

Analysis. Since in £1 there are 20s., in £5 there are 5 times as many, which is 100s., and 2, (the given shillings,) make 102s. Again, since there are 12d. in 1s., in 102s. there are 102 times as many, which is equal to 1224d., and 7 (the given pence) make 1231d. Finally, since in 1d. there are 4 far., in 1231d. there are 1231 times as many, or 4924 far., and 3, (the given far.,) make 4927 far. Ans. 4927 farthings.

102 shillings. 12d. in 1s.

1231 pence.

4 far in 1d.

4927 far. Ans.

We first reduce the given pounds to shillings, by multiplying them by 20, because 20s. make £1. (Art. 247.) We next reduce the shillings to pence, by multiplying them by 12, because 12d. make 1s. Finally, we reduce the pence to farthings by multiplying them by 4, because 4 far. make 1d.

Note.-1. In this example it is required to reduce higher denominations to lower; as pounds to shillings, shillings to pence, &c. This is done by successive multiplications.

2. In 4927 farthings, how many pounds, shillings, and pence?

Analysis. Since 4 far. make 1d., in 4927 farthings, there are as many pence as 4 is contained times in 4927, which is 1231d., and 3 far. over. Again, since 12d. make 1s., in 1231d. there are as many shillings as 12 is contained times in 1231, which is 102s., and 7d. over. Finally, since 20s. make £1, in 102s. there

QUEST.-280. What is Reduction? How are pounds reduced to shillings? Why multiply by 20? How are shillings reduced to pence? Why? How pence to farthings? Why?

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are as many pounds as 20 is contained times in 102, which is £5, Ans. £5, 2s. 7d. 3 far.

and 2s. over.

Operation. 4)4927 far.

12)1231d. 3 far. over. 20)102s. 7d. over.

We first reduce the given farthings to pence, the next higher denomination, by dividing them by 4, because 4 far. make 1d. (Art. 247.) Next we reduce the pence to shillings by diAns. £5, 2s. 7d. 3. far. viding them by 12, because 12d. make 1s. Finally, we reduce the shillings to pounds by dividing them by 20, because 20s. make £1. The last quotient and the several remainders constitute the answer.

£5, 2s. over.

Note.-2. The last example is exactly the reverse of the first; that is, lower denominations are reduced to higher, which is done by successive divisions.

281. From the preceding illustrations we derive the following

GENERAL RULE FOR REDUCTION.

I. To reduce compound numbers to lower denominations. Multiply the highest denomination given, by that number which it takes of the next lower denomination to make ONE of this higher; to the product, add the number expressed in this lower denomination in the given example. Proceed in this manner with each successive denomination, till you come to the one required.

II. To reduce compound numbers to higher denominations.

Divide the given denomination by that number which it takes of this denomination to make ONE of the next higher. Proceed in this manner with each successive denomination, till you come to the one required. The last quotient, with the several remainders, will be the answer sought.

282. PROOF.-Reverse the operation; that is, reduce back the answer to the original denominations, and if the result corresponds with the numbers given, the work is right.

QUEST.-How are farthings reduced to pence? Why divide by 4? How reduce pence to shillings? Why? How reduce shillings to pounds? Why? 281. How are compound numbers reduced to lower denominations? How to higher denominations? 282. How is Reduction proved?

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