Metrology

The English of Weights and Measures

Topic status automatically displays here - do not remove.

Bookmark me!Bookmark this topic  Print me!Print this topic

The imperial measuring system and much of its terminology was introduced to ancient Briton by the Romans (of the Roman Empire) who conquered, occupied, and ruled over ancient Briton for over 500 years during the period 54BC to 476AD.

Note Note

The Julian Calendar using 365 days per year was introduced in 45BC. See [topic to be defined].

You will observe in the topic below that the use of Roman measurement terms are prefixed with 'Roman' as in "the Roman foot", and are used to qualify which measurement scale is being referred to. Please be aware that standard measurements have been redefined and changed over millennia. For example, the standard 'foot' length has stretched over time from the 'Roman' foot at an accepted modern 296mm, to the current 'English' foot of 304.8mm length. That's a variation of nearly 3%. Consider the possible effects of this variance when multiplied over a larger distance. For example, a length of only 100ft could result in a variation of 3 foot between these different scales! When referring to a measurement value, please remain aware of the scale being used.

[Introductory text goes here with links to the topic sections.]

See linear below.

See planar below.

See cubic below.

Back to Top

First dimension—linear

Linear meaning 'related to a straight line' and 'having only one dimension', is derived from the Latin 'linearus' meaning 'created by lines'; from the root 'linea' meaning 'line'. 

Length

"Length" is the noun form of the adjective "long" from the Latin "longus" meaning "long" as we now know it.

"Distance" is the noun form of the adjective "distant" from the Latin "distans" as used by the Romans to mean "being apart".  Presumably 'tans' means together?

Imperial

The base measurement of distance at the time of the Roman Empire was the Roman foot called in Latin "pes" (plural "pedes"), an actual measure of the physical length of the Roman Emporer's foot (equivalent to a modern 296mm). There were three Roman Emporers which are known to have their name associated with a foot:

Note Note

The modern standard length of a foot was sanctioned by British Royal authority in 1824 to be 304.8mm. See [topic to be defined].

To measure longer distances, the Romans averaged the marching double stride of a Roman soldier (left step right step) called in Latin "passus" anglicised as "pace", and which measured 5 static Roman feet (equivalent to a modern 1.48m).

Two paces (left-right – left-right) called in Latin "pertica" anglicised as "perch", measured 10 static Roman feet (equivalent to a modern 2.96m).

[Col: There's a whole lotta stuff about perch lengths, ranging from this Roman 10ft version to the now standard 16.5 foot version. Check it out.]

Accordingly, by counting their paces during a long distance march, Roman soldiers could measure longer distances with some consistency. 1000 paces (5000 Roman feet) they called in Latin "milia passuum" anglicised and shortened to "mile" (equivalent to a modern 1.48km). The distance of 1500 paces (7500 Roman feet) they called in Latin "leuga" anglicised as "league" (equivalent to a modern 2.22km).

To measure lengths smaller than a foot, the Romans used the width of their palm called in Latin "palmus" anglicised as "palm", and which measured one-quarter of a Roman foot (equivalent to a modern 74mm).

For even smaller units, the Romans used the end digit of their thumb called in Latin "uncia" anglicised as "inch", and which measured one-twelfth of a Roman foot (equivalent to a modern 24.6mm).

The smallest Roman unit of measure was the middle digit of their little finger called in Latin "digitus" anglicised to "digit", and which measured one-sixteenth of a Roman foot (equivalent to a modern 18.5mm).

Thus the Romans gave us the Latin source and meaning for the English words "line" and its derivatives, as well as "long", "distant", "digit", "inch", "palm", "pace", "perch",  "mile", and "league". The derivations from the Latin "pede" meaning "related or associated with the foot" provide us with the source and meaning of many English words like "pedal", "pedestal", "pedestrian", "pedate", "pedicure", "centipede" and "millipede".

Metric

As is generally known, the devisers of the metric system originally calculated the length of a metre as one ten-millionth of the length of a quadrant of the circumference of the Earth measured from the equator to the pole. With the instruments and techniques of the day, they didn't quite get it right, but the metre was formalised as the length of a metal rod kept in Paris and was later redefined as 1,650,763.73 wavelengths of the orange-red line in the krypton-86 spectrum.

Back to Top

Second dimension—planar

Area

Area is a measure of two distances in the same plane as each other, and is sourced from the Latin "area" meaning "piece of level ground" or "open space". The Romans measured area using the same methods as they used to measure length and distance—by foot.

A furrow (grooved row) is the old Briton name given to a line of ploughed land from the Latin "strio" meaning "striped" or "grooved".

[Speculation:] The area of land that a single (Roman era) ox could furrow (pulling a single bladed plough) in one day of work (sunrise to sunset) was equivalent to 120 Roman feet square.

This was measured using the ploughman's Roman sized "perch" of the period, which consisted of a 10 foot long wooden pole used to control the beast of burden during the ploughing from behind the hand-guided plough. Using the Roman perch (stick) as a handy measuring stick, and laying it out along the ground, the ploughman could count the number of perches (distance) required to accurately layout and measure the area of his field. This method (of repeatedly laying a stick of known length end to end in a straight line on the ground) for (relatively short) distance measurement was practiced until quite recent times (last century).

Thus, 12-perch-long formed the length of a furrow called in Latin "actus" meaning "potential (before)" or "action (after)", and measured 120 linear Roman feet (equivalent to a modern 35.52m). The Latin "actus quadratus" meaning "action squared", consisted of a field 120 Roman feet long by 120 Roman feet wide, totaling 14,440 Roman square feet; (equivalent to slightly less than a modern …“ acre1260m).

The word "acre" was a general term derived from the Latin "ager", meaning "a field", and was never a definitively measured area, as fields tended to be irregular in shape and followed the landscape, so were also not commonly flat and level. Fields were rarely square, but land measurement in Roman times was in units of Roman square feet. The area of an 'acre' has evolved over time since then.

In Roman terms, Latin "jugerum" meaning "yoke" was an area of two 'actus quadratus', measuring 240 Roman feet long by 120 Roman feet wide. The jugerum was the common measure of land among the Romans; (equivalent to slightly less than a modern …” acre2520m).

[Speculation:] This was referred to as a 'yoke', because it was the area of land which could be ploughed in a day by two oxen yoked together—double the area that could be ploughed by a single ox in the same time.

According to William Smith 'A Dictionary of Greek and Roman Antiquities' (John Murray, London, 1875):

"It seems probable that, as the word was evidently originally the same as jugus or jugum, a yoke, and as actus, in its original use, meant a path wide enough to drive a single beast along, that jugerum originally meant a path wide enough for a yoke of oxen, namely, the double of the actus in width; and that when actus quadratos was used for a square measure of surface, the jugerum, by a natural analogy, became the double of the actus quadratus; and that this new meaning of it superseded its old use as the double of the single actus."

To complete the subject of Roman area definitions, two "jugera" represented a "heredium" meaning "lordship" (heredium, from herus—lord), and 100 "heredia" represented one "centuria". Land under Roman occupation was assigned in parcels of "jugerum", and two jugera were given to each citizen as Latin "heredium" meaning heritable property, in the belief that this amount of land would support a citizen and their family for garden farming purposes—not grazing; (equivalent to the about the area of 1 modern acres—5040m).

Thus the Romans gave us the Latin source and meaning for the English words "area", "acre", "action" and "yoke". The derivations from the Latin "herus" meaning "lord" provide us with the source and meaning of many English words like "herald" and its variants, as well as "heir", "heredity", "hierarchy", and "inheritance".

Lets speculate a little about the differences between the ancient (Roman) and the modern (English) measurements. It was the Romans which were the first in ancient Briton to consistently use a common measurement, and that was based upon the foot. The jugerum, which measured 240 Roman feet long (by 120 Roman feet wide), was the standard unit of area measurement; and equally the heredium, which measured 240 Roman feet square, was their common size of land assignment. So it would seem most likely that all land definition (boundaries) would be in measures of 240 Roman feet.

[Postulation] As the Roman foot measured a modern 296mm, the distance of 240 Roman feet is equivalent to a modern 71.04m. When it came time to reassess these ancient boundaries using a different scale of a modern 304.8mm per foot, the calculation resulted in the Roman 240 foot being equivalent to a modern 233 feet, a difference in count of 7 feet for the same actual distance.

[Col: Lookup Yardstick. Perhaps it can play a role in this logic?
And also lookup the turning circle space of the oxe and plow. 1 actus or jugerum?]

Yard: a unit of length equal to 3 feet; defined as 91.44 centimeters; originally taken to be the average length of a stride

The furlong (furrow long) is the old Briton name given to the length of a furrow which could be made by two pair of yoked oxen before they required a rest, and measured a modern 660 feet, which is exactly 40 rods, or 10 chains, or 220 yards, or 1/8 mile (and is equivalent to a modern 201.168m).

The acre was originally defined as the area that could be ploughed in a day by a yoke of oxen. By the end of the ninth century it was generally understood to be the area of a field one furlong (40 rods or 10 chains) long by 4 rods (or 1 chain) wide. Thus an acre is 10 square chains, 160 square rods, 43 560 square feet or 4840 square yards. There are exactly 640 acres in a square mile.

The pole, also known as a rod, is a traditional unit of distance equal to 5.5 yards. The rod and the furlong were the basic distance units used by the Anglo-Saxon residents of England before the Norman conquest of 1066. The Saxons generally called this unit the gyrd, a word which comes down to us as the name of a different unit, the yard. "Rod" is another Saxon word which meant just what it means today: a straight stick. The Normans preferred to call the gyrd a pole or a perch . The length of the rod was well established at least as early as the eighth century. It may have originated as the length of an ox-goad, a pole used to control a team of 8 oxen (4 yokes). Scholars are not sure how the rod was related to shorter units. It may have been considered equal to 20 "natural" feet. In any case, when the modern foot became established in the twelfth century, the royal government did not want to change the length of the rod, since that length was the basis of land measurement, land records, and taxes. Therefore the rod was redefined to equal 16.5 of the new feet. This length was called the "king's perch" at least as early as the time of King Richard the Lionheart (1198). Although rods and perches of other lengths were used locally in Britain, the king's perch eventually prevailed. The relationship between the rod and the other English distance units was confirmed again by the Parliamentary statute of 1592, which defined the statue mile to be either 320 rods or 1760 yards, thus forcing the rod to equal exactly 5.5 yards or 16.5 feet.

standards were not fixed with precision and changed from period to period

Henry I (1100–1135) introduced as unit the yard (3 feet), to replace the cubit (1 feet), and fixed its length by a bar of iron, this length must have been substantially the same as that of the bars constructed during the Renaissance and used to determine the English foot of 1824 A.D.

Back to Top

Third dimension—cubic

 

Back to Top

Modern Dimensions

Linear measurements

Linear measurements table
Term Inches Feet Yards Rods Chains Metres
Inches 1 1/12 1/36 1/198 1/792

0.0254

Feet

12

1 1/3 2/33 1/66 0.3048
Yards 36

3

1 2/11 1/22 0.9144
Rods 198 16.5

5.5

1 1/4 5.0292
Chains 792 66 22

4

1 20.1168
Furlong 7920 660 220 40

10

201.168
Mile 63360 5280 1760 320 80 1609.344

 

Back to Top

Planar measurements

Planar measurements table
Term Sq.Inches Sq.Feet Sq.Yards Sq.Rods Sq.Chains Sq.Metres
Sq.Foot

144

1 1/9 4/1089 1/4356 0.09290304
Sq.Yard 1,296

9

1 4/121 1/484 0.83612736
Sq.Rod 39,204 272.25

30.25

1 1/16 25.2928526
Sq.Chain 627,264 4,356 484

16

1 404.685642
Acre 6,272,640 43,560 4,840 160

10

4046.85642
Sq.Mile 4014 million 27,878,400 3,097,600 102,400 6,400 2.59 million

The only term representing an area which is not the square of a linear term is the 'acre', which is 1 furlong long by 1 chain wide = 4046.8564224 sq.m.

 

Back to Top

Circle calculations:

area = PI * (radius) * (radius) or
area = PI * (diameter / 2) * (diameter / 2)
radius = (diameter / 2) or
radius = sqrt(area / PI)
diameter = 2 * radius or
diameter = circumference / PI
circumference = PI * diameter or
circumference = PI * (radius * 2)
sphere surface area = 4 * PI * (radius * radius)
sphere volume = 4/3 * PI * (radius * radius * radius)
 

http://www.unc.edu/~rowlett/units/

 

Back to Top

See Also

xyz Lotech Solutions' Tips, Tricks, and Procedures

Back to Top