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Metrified English unit

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A metrified Imperial system is a proposal for a metrication and unification of the English systems of measures. Usually the inch is set to 25 mm, the pint to 500 ml and the pound to 500 g and the rest accordingly.

TransitionEdit

Nowadays all Imperial units are defined in terms of their metric/SI equivalents, but mostly with quite odd factors. This choice was made to ensure largest possible continuity, but over time there have been several proposals to round off the values, which is thought to ease transition towards the metric system.

Royal System Edit

One of the earliest still known and most extensive proposals of a metrified Imperial system is from the early 1820s and is attributed to William Huskisson, but it wasn't embodied into the 1824 reformation of the Imperial system at all.

Length Edit

Metrified Imperial length units
calibre ≡ 1/100 inch = 250 µm = ¼ mm
point ≡ 1/6 line = 1/75 inch = 333 1/3 µm = 1/3 mm
line ≡ 10/125 inch ≈ 1/12 inch = 2 mm
barleycorn ≡ 1/3 inch = 8 1/3 mm
digit ≡ 1/16 foot = ¾ inch = 18¾ mm = 1.875 cm
finger ≡ 7/8 inch = 21.875 mm = 2.1875 cm
inch ≡ 25 mm = 2½ cm
stick ≡ 2 inch = 50 mm = 5 cm
nail = 3 digit ≡ ¼ span = 2¼ inch = 56¼ mm = 5.625 cm
palm ≡ 4 digit = 3 inch = 75 mm = 7.5 cm
hand ≡ 1 palm + 1 inch = 4 inch = 100 mm = 1 dm
shaftment ≡ 2 palm = 6 inch = 150 mm = 1.5 dm
link ≡ 8 inch = 200 mm = 2 dm
span ≡ 3 palm = 9 inch = 225 mm = 2.25 dm
foot = 4 palm ≡ 12 inch = 300 mm = 3 dm
cubit ≡ 1½ foot = 18 inch = 450 mm = 4.5 dm
pace ≡ 32 inch = 800 mm = 8 dm
yard ≡ 3 foot = 36 inch = 900 mm = 9 dm
ell ≡ 20 nail = 45 inch = 1.125 m
grade ≡ 2 pace = 64 inch = 1.6 m
fathom ≡ 6 foot = 72 inch = 1.8 m
rod (pole, perch) ≡ 25 link = 200 inch = 5 m
rope ≡ 20 foot = 240 inch = 6 m
chain ≡ 4 rod = 800 inch = 20 m = 2 dam
cable length ≡ 100 fathom = 7 200 inch = 180 m = 1.8 hm
furlong ≡ 10 chain = 8 000 inch = 200 m = 2 hm
mile ≡ 8 furlong = 2 000 pace = 64 000 inch = 1.6 km
nautical mile ≡ 10 cable = 2 000 yard = 72 000 inch = 1.8 km
league ≡ 3 mile = 192 000 inch = 4.8 km
sea league ≡ 3 nautical mile = 216 000 inch = 5.4 km

There is also a version with a nautical mile of 1.85 km, which is much closer to 1' of the circumference of Earth and its current value of 1.852 km. The mile is about ¼ mrad Earth, while a kilometre was at that time believed to be 0.01 grad Earth. The pace was originally 2½ foot, i.e. 30 inches or 7.5 dm, but with 32 inches or 8 dm a mile retains both its definitions: the old Roman one of being 1000 gradus and the English one of 8 furrows long. Also note, that a 1.8-km seamile is 2 000 yards or nine furlongs.

Area Edit

For area measurement of course all length units can simply be squared, e.g. 1 foot² = 9 dm². Those are not explicitly listed here.

Metrified Imperial area units
board ≡ 1 inch × 1 foot = 12 inch² = 7 500 mm² = 75 cm²
rood ≡ 1 furlong × 1 rod = 40 rod² = 1 600 000 inch² = 1 000 m² = 10 a
acre ≡ 1 furlong × 1 chain = 160 rod² = 6 400 000 inch² = 4 000 m² = 40 a
yardland, virgate ≡ ¼ hide = 25 acre = 160 000 000 inch² = 125 000 m² = 12.5 ha
hide ≡ 100 acre = 640 000 000 inch² = 400 000 m² = 40 ha
barony ≡ 40 hide = 25 600 000 000 inch² = 16 km²

Volume, capacity Edit

For volume measures of course all length units can simply be cubed, e.g. 1 foot³ = 27 dm³ = 27 l. Those are not explicitly listed here.

Metrified Imperial capacity units
perch ≡ 1 perch × 1½ foot × 1 foot = 42 768 inch³ = 675 l = 6.75 hl
freight ton ≈ 40 foot³ = 64 000 inch³ ≡ 1 m³ = 1 kl
load ≡ 50 foot³ = 86 400 inch³ = 1.35 m³
register ton ≡ 100 foot³ = 172 800 inch³ = 2.7 m³
acre-foot ≡ 1 acre × 1 foot = 19 200 000 inch³ = 12 000 m³ = 12 dam³

There are at least two gallon-based variants, one with a 4-litre gallon, the other with a 5-litre one. With 5 litre a gallon of water still weighs 10 pounds; note the correspondence between the volume and mass units which share a name.

Metrified Imperial capacity units
minim ≡ 1/20 scruple = 1/240 inch³ = 65.104 1¯6 µl
scruple ≡ 1/3 drachm = 1/12 inch³ = 1.302 08¯3 ml
dra(ch)m ≡ 1/8 ounce = ¼ inch³ = 3.906 250 ml
teaspoon ≡ 1/3 tablespoon = 1/3 inch³ = 5.208¯3 ml
tablespoon ≡ 1/16 cup = 1 inch³ = 15.625 ml = 1.562 500 cl
ounce ≡ ¼ gill = 2 inch³ = 31¼ ml = 3.125 cl
gill ≡ ¼ pint = 8 inch³ = 125 ml = 1¼ dl
cup ≡ ½ pint = 8 ounce = 16 inch³ = 250 ml = 2½ dl
pint ≡ ½ quart = 32 inch³ = 500 ml = 5 dl
≡ 4/5 quart
quart ≡ ¼ gallon = 64 inch³ = 1 l
= 80 inch³ = 1.25 l
gallon = 256 inch³ ≡ 4 l
= 320 inch³ ≡ 5 l
peck ≡ 2 gallon = 512 inch³ = 8 l
= 640 inch³ = 10 l
kenning ≡ 2 peck = 1 024 inch³ = 16 l = 1.6 dal
= 1 280 inch³ = 20 l = 2 dal
bushel ≡ 2 kenning = 2 048 inch³ = 32 l = 3.2 dal
= 2 560 inch³ = 40 l = 4 dal
firkin ≡ ½ kilderkin = 2 560 inch³ = 40 l = 4 dal
= 3 200 inch³ = 50 l = 4 dal
rundlet ≡ 1/7 pipe = 4 389 3/7 inch³ ≈ 68.57 l = 6.857 dal
= ½ tierce = 4 800 inch³ ≡ 75 l = 7½ dal
kilderkin ≡ ½ tierce = 5 120 inch³ = 80 l = 8 dal
= 6 400 inch³ = 100 l = 1 hl
barrel ≡ ½ hogshead = 7 680 inch³ = 120 l = 1.2 hl
= 8 000 inch³ = 125 l = 1¼ hl
tierce ≡ 1/3 pipe = ½ pon = 10 240 inch³ = 160 l = 1.6 hl
≡ 3 firkin = 9 600 inch³ = 150 l = 1½ hl
hogshead ≡ ½ pipe = 15 360 inch³ = 240 l = 2.4 hl
= 16 000 inch³ = 250 l = 2½ hl
quarter ≡ 8 bushel = 16 384 inch³ = 256 l = 2.56 hl
= 20 480 inch³ = 320 l = 3.2 hl
≡ ¼ tun = 1 hogshead = 16 000 inch³ = 250 l = 2½ hl
puncheon, tertian ≡ 1/3 tun = 20 480 inch³ = 320 l = 3.2 hl
≡ 3 kilderkin = 19 200 inch³ = 300 l = 3 hl
pipe ≡ ½ tun = 30 720 inch³ = 480 l = 4.8 hl
= 32 000 inch³ = 500 l
tun = 240 gallon = 61 440 inch³ ≡ 960 l = 9.6 hl
= 192 gallon
= 250 gallon = 64 000 inch³ ≡ 1000 l = 1 m³
= 200 gallon

Mass, weight Edit

The Troy pound gets replaced by the libra, the abbreviation for the real pound has to change accordingly.

Metrified Imperial mass units
grain ≡ 1/20 scruple = 1/7 680 pound = 65.104 1¯6 mg = 6.510 41¯6 cg
carat = 1/2 500 pound ≡ 200 mg = 2 dg
scruple ≡ 1/3 dram = 1/384 pound = 1.302 08¯3 g
pennyweight ≡ 1/20 ounce = 1/240 libra = 1/320 pound = 1.562 500 g
dram ≡ 1/8 ounce = 1/128 pound = 3.906 250 g
ounce = 1/12 libra ≡ 1/16 pound = 31.25 g = 3.125 dag
libra = 5760 grain ≡ ¾ pound = 375 g = 3¾ hg
pound = 7680 grain ≡ 500 g = 5 hg
clove, nail ≡ ½ stone = 6¼ pound = 3.125 kg
stone ≡ ½ tod = 12½ pound = 6.25 kg
tod, quarter ≡ ¼ hundredweight = 25 pound = 12.5 kg
hundredweight ≡ 100 pound = 50 kg
wey ≡ 1½ hundredweight = 150 pound = 75 kg
sack ≡ 2 wey = 300 pound = 150 kg
ton, tonne ≡ 20 hundredweight = 2 000 pound = 1 Mg = 1 t
last ≡ 12 sack = 3 600 pound = 1.8 Mg = 1.8 t

Derived units Edit

The knot is acknowledged as 1 nautical mile per hour.

Weight and mass are often confused and it is not surprising, that in many proposals there is no explict mention of (gravitational) force, but the pound-force is still 1 pound times Gee, see also kilopond. The poundal (1 lb.•ft./s²) equals 0.15 N with the above redefinitions of pound and foot.

Likewise you get the units of pressure, e.g. pound-force/inch² or inch mercury. For energy or heat, a British thermal unit is almost exactly 1 kJ already. The units of power are rather new, but it makes sense to round a horse power to 750 W.

Kitchen Edit

There are other metrified values for cup (240 mL or 250 mL), tablespoon (15 mL or 20 mL) and teaspoon (5 mL) in use today, independently from all the other units.

American independence Edit

[1] At the First Congress, which met in 1789 when the metric system had not yet been developed in France, the system of units to be used in the future USA was one point of discussion. The Congress would have had (and still has) the constitutional right (article I, section 8) to decide on a standard of weights and measurement, but never did so.

In the meeting Thomas Jefferson was employed to find the best system of weights and measures to be used in the USA. The decimal dollar had already been introduced at that time. In mid-1790 he proposed two systems of units, one evolutionary with a mere refinement of definitions and simplification of the existing English system, the other one revolutionary being decimal and only reusing some of the traditional names.

In coordination with scientists in France, he selected the second pendulum at 45° latitude as the basic reference. The pendulum was estimated to be 39.14912 English inches of that time long (an inch was much later defined to be 25.4 mm) or 1.5 times that for a vibrating rod (58.72368 inches), that is about 994,4 mm.

In the evolutionary approach, the foot was to be derived from that length by a simple integer factor, which would be either three or five, i.e. lengthening it from the traditional value by 1.04970¯6 inches to ca. 331.463 mm or shortening it by 0.255264 inches to ca. 298.317 mm. For practical purposes he wanted the rod to be 58¾ (new) inches long, an increase of less than 0.045%.

The revolutionary system was quite similar to the metric system, except the mentioned difference of about 5½ mm between the second rod at 45° and the 10,000th part of the distance from the northpole to the equator. Also it didn't have the concept of prefixes at all. A very similar system was a base of discussion in France after the revolution of 14 July 1789, with Jefferson observing.

Length
foot = 12 inches
yard = 3 feet
ell = 3¾ feet
fathom = 6 feet
perch, pole = 5½ yards
furlong = 40 poles
mile = 8 furlongs
league = 3 miles
Area
rood = 40 square poles
acre = 4 roods
Volume
gill = ¼ pint
pint = ½ quart
quart = ½ pottle
pottle = ½ gallon
gallon = 270 cubic inches
peck = 2 gallons
bushel, firkin = 4 pecks
strike, kilderkin = 2 bushel or firkin
coomb, barrel = 2 strikes or kilderkins
quarter, hogshead = 2 coombs or barrels
tierce = 4/3 hogshead
pipe, butt, puncheon = 2 hogsheads
ton = 2 pipes
Weight
grain = 1/24 pennyweight
pennyweight = 1/18 ounce
ounce = 1/1000 weight of 1 cubic foot of rain water at standard temperature
pound = 16 ounces
Jeffersonian decimal proposal
Length
point = 1/10 line
line = 1/10 inch
inch = 1/10 foot
foot (base) = ca. 994,4 ÷ 5 mm
decad(e) = 10 foot
rood = 10 decade
furlong = 10 rood
mile = 10 furlong ca. 2 traditional miles
Area
rood = 1 rood × 1 rood
Volume
metre = 1/10 demi-pint = 1 inch³
demi-pint = 1/10 pottle = 2 × 2 × 2½ inch³
pottle = 1/10 bushel = 5 × 5 × 4 inch³
bushel = 1 foot³ ca ¾ traditional bushel
quarter = 10 bushels
last, double ton = 10 quarters
Weight
mite = 1/10 minim
minim, demi-grain = 1/10 carat
carat = 1/10 double-scruple
double-scruple = 1/10 ounce
ounce = 1/1000 the weight of 1 bushel of water
pound = 10 ounces
stone = 10 pounds
kental = 16 stones
hogshead = 10 kentals

Isolated Edit

Besides redefinitions of the whole system, which try to keep the values close and the system immanent factors intact, there were and are simple approximations of Imperial units in metric.

Length Edit

point (352 7/9 µm) 
250 µm = ¼ mm, 350 µm, 375 µm = 3/8 mm
inch (25.4 mm) 
2.5 cm = ¼ dm, 3 cm
foot (12 inch = 0.3048 m) 
2.5 dm = ¼ m, 3 dm, 3.¯3 dm = 1/3 m
yard (3 foot = 0.9144 m) 
0.9 m, 1 m
fathom (6 foot = 1.8288 m) 
1.8 m, 1.85 m, 1.852 m, 2 m
rod, pole, perch (192 inch = 5.0292 m) 
5 m
chain (4 rod = 20.1168 m) 
20 m
cable (1/10 sea mile) 
180 m, 185 m, 185.2 m, 200 m
furlong (10 chain = 201.168 m) 
200 m
mile (8 furlong = 1.609344 km) 
1.5 km, 1.6 km, 1.609 km, 1.61 km, 2 km
nautical mile (6080 foot = 1.853184 km) 
1.8 km, 1.85 km, 1.852 km, 1.853 km, 1.9 km, 2 km; 1 equatorial minute, 1 meridian minute

Area Edit

acre (4046.8564224 m²) 
40 a, 40.5 a, 50 a = ½ ha

Volume, capacity Edit

scruple (1/3 drachm ≅ 1.184 ml) 
1 ml, 1.2 ml, 1.25 ml = 1¼ ml
drachm/dram (1/8 ounce ≅ 3.552 ml | 3.697 ml) 
3.5 ml = 3½ ml, 3.7 ml, 3.75 ml = 3¾ ml
ounce (1/5 gill ≅ 28.413 ml | ¼ gill ≅ 29.574 ml) 
25 ml, 27.5 ml, 28 ml, 28.5 ml, 30 ml
gill (¼ pint ≅ 142.065 | 118.294 ml) 
100 ml, 120 ml, 140 ml, 150 ml
pint (¼ gallon ≅ 568.26 ml | 473.176 ml | 550.61 ml) 
475 ml = 4¾ dl, 500 ml = ½ l, 550 ml = 5½ dl, 600 ml
quart (½ gallon ≅ 1.137 l | 0.946 l | 1.101 l) 
1 l, 1.1 l
gallon (≅ 4.546 l | 3.785 l | 4.405 l) 
3.8 l, 4 l, 4.4 l, 4.5 l, 5 l
(petrol) barrel (35 gallon ≅ 159,113 l | 42 gallon ≅ 158,987 l) 
159 l, 160 l
peck (2 gallon ≅ 9.092 l | 8.810 l) 
8.8 l, 9 l, 10 l
bushel (4 peck ≅ 36.368 l | 35.239 l) 
35 l, 36 l, 40 l
quarter/hogshead (8 bushel ≅ 290.9 l | 281.9 l) 
250 l ≅ volume of ¼ t water, 256 l, 280 l, 290 l, 300 l
teaspoon 
5 ml
tablespoon 
15 ml
cup 
225 ml, 240 ml, 250 ml = ¼ l

Mass, weight Edit

grain (64.79891 mg) 
50 mg
pennyweight (24 grain ≅ 1,555 g) 
1.5 g, 2 g = 10 carat
dram (1⁄16 ounce ≅ 1,772 g) 
1.5 g, 1.75 g, 2 g
ounce (1⁄16 pound ≅ 28,35 g | 20 pennyweight ≅ 31.103 g) 
25 g, 28.5 g, 30 g | 30 g, 33 1/3 g
pound (7000 grain ≅ 453,592 g | 5760 grain ≅ 373.242 g) 
450 g, 500 g | 350 g, 375 g, 400 g
stone (14 pound ≅ 6.35 kg) 
5 kg, 6.25 kg
quarter (¼ hundredweight ≅ 11.34 kg | 12.701 kg) 
12.5 kg
hundredweight (100 pound ≅ 45.359 kg | 50.802 kg) 
45 kg, 50 kg
ton (20 hundredweight ≅ 0.907 t | 1.016 t) 
0.9 t, 1 t

See also Edit

External linksEdit

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