The metric system is now in use in the greater part of the civilized world, but some of the measures retain the names of old disused measures. In Germany, for instance, the Pfund is ½ kilogramme, and is approximately equal to 11⁄10 ℔ English.

119. British Systems.—The British systems have various origins, and are still subject to variations caused by local usage or by the usage of particular businesses. The following tables are given as illustrations of the arrangement adopted elsewhere in this article; the entries in any column denote multiples or submultiples of the unit stated at the head of the column, and the entries in any row give the expression of one unit in term of the other units.

Length

Inch.Foot.Yard.Chain.Furlong.Mile.
11⁄121⁄361⁄7921⁄79201⁄63360
1211⁄31⁄661⁄6601⁄5280
36311⁄221⁄2201⁄1760
792662211⁄101⁄80
79206602201011⁄8
63360528017608081

Weight (Avoirdupois)

Ounce.Pound.Stone.Quarter.Hundred-
weight.
Ton.
11⁄161⁄2241⁄4481⁄17921⁄33840
1611⁄141⁄281⁄1121⁄2240
224141½1⁄81⁄160
4482821¼1⁄80
17921128411⁄20
33840224016080201

(Also 7000 grains = 1 ℔ avoirdupois.)

120. Change of System.—It is sometimes necessary, when a quantity is expressed in one system, to express it in another, The following are the ratios of some of the units; each unit is expressed approximately as a decimal of the other, and their ratio is shown as a continued product (§ 116), a few of the corresponding convergents to the continued fraction (§ 117) being added in brackets. It must be remembered that the number expressing any quantity in terms of a unit is inversely proportional to the magnitude of the unit, i.e. the number of new units is to be found by multiplying the number of old units by the ratio of the old unit to the new unit.

Yard= 9144⁄10000= 10000⁄10935= 22⁄12· 884⁄385· 8225⁄8224 ... (11⁄32, 32⁄35 = 8⁄7· 4⁄5, 235⁄257).
Metre
Inch= 25400⁄10000= 10000⁄3937= 2⁄5· 66⁄65· 1651⁄1650 ... (5⁄2, 33⁄13, 127⁄50).
Centimetre
Mile= 16093⁄10000= 10000⁄6214= 8⁄5· 185⁄184· 2369⁄2368 ... (8⁄5, 37⁄23, 103⁄64).
Kilometre
Square Yard= 8361⁄10000= 10000⁄11960= 5⁄6· 306⁄305· 15250⁄15249 ... (5⁄6, 51⁄61, 250⁄299).
Square Metre
Acre= 4047⁄10000= 10000⁄24711= 2⁄5· 85⁄84· 5320⁄5321 ... (2⁄5, 17⁄42, 380⁄939).
Hectare
Quart= 11365⁄10000= 10000⁄8799= 8⁄7· 175⁄176· 8976⁄8975 ... (8⁄7, 25⁄22, 408⁄359).
Litre
Pound= 4536⁄10000= 10000⁄22046= 1⁄2· 10⁄11· 484⁄485· 29391⁄29392 ... (1⁄2, 5⁄11, 44⁄97, 303⁄668).
Kilogramme

(ii.) Special Applications.