### CONTENTS

Date of first publication: 05 january 2003

Date of last modification: 19 january 2007

• Part 1: MANUAL AND EXPLANATIONS
• Part 2: TABLES; ANGLO-SAXON vs. NAPOLEON
• Part 3: TABLES; PRESSURES, BIBLE, EURO, EARTHQUAKES, others
• Part 4: TABLES; INTERNAL ANGLO-SAXON
• Part 5: REFERENCES AND INTERNET LINKS

Part 1: MANUAL AND EXPLANATIONS

Part 2: TABLES; ANGLO-SAXON vs. NAPOLEON

Part 3: TABLES; PRESSURES, BIBLE, EURO, EARTHQUAKES, others

Part 4: TABLES; INTERNAL ANGLO-SAXON

This is a separate document.

Part 5: REFERENCES AND LINKS TO INTERNET SITES

## Part 1: MANUAL AND EXPLANATIONS

#### GENERAL

This document is intended especially to convert Anglo-Saxon measures into metric (=European-continental) measures. It consists of separate tables for linear, cubic, etc. measures. Biblical, monetary and some important physical numbers have also been enlisted in this document, in separate tables. The document consists of three parts:

• Introduction and Explanation,
• Conversion tables for Anglo-Saxon versus Metric,
• Other tables

This chapter is the manual about how to read the tables. The second chapter shows the important differences between the Metric and the Anglo-Saxon measure system. The third chapter shows some conversion factors between the different Anglo-Saxon measure systems of the same class (e.g. between AVDP and Troy). This chapter is also a helpful introduction to the separate document of Part 4. The following five chapters together form the second part of the document. They contain the tables with the conversion of the measures. The last five chapters together form the third part of the document. They contain other conversion factors, even monetary ones. At the end of every section a text line can be clicked to return to the contents list.

The document is made such that it is useful for the scientists, the engineers, the merchants and the 'ordinary people'. Consequently some of the comments to the tables (especially those in the chapter about the earth sciences) may be too difficult for the non-scientists. They should not worry about this and simply skip those comments and look directly at the tables. The only consequence of this skip is that the accuracy of the figures in the tables can be interpreted wrongly and thus is lessened. Since even then enough accuracy is left for the ordinary daily life this decrease does not harm at all.

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#### JUDICIARY

Great care has been taken to make the textes and tables in this document comprehensive and reliable. Still errors and flaws may have slipped in.

Copying this document or parts of it for commercial sale of these copies is prohibited. Useage of the document is free of license.

DISCLAIMER
The author of the document can never be held responsible for damages and injuries that might have resulted from erroneous or inaccurate data in this document. He is also not responsible for misinterpretations by the reader and their consequences.

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#### PRESENTATION OF NUMBERS

!!This section is very important and should not be skipped!!

#### Display of numeric values

In this document all quantitative values are displayed with the numbers consisting of the well-known ten digits (0 to 9) and the few punctuation marks. Everyone uses this notation system daily. But nearly nobody knows that this system has its roots in the ancient Hinduistic India. One may call it the 'extended Indian number-system'.

In this document sometimes numbers are written with spaces between groups of digits. These spaces are for readability and don't have any meaning. Thus 123 45 equals 12345. In imitation of the Americans the period is used to separate the fraction from the integral part. This period is called "decimal point". The comma is not used at all.

The symbol @ in a number means exponent notation with power of ten. In fact it shifts the decimal point over the number of positions given by the exponent value. The shifting is done to the right when the exponent is positive, and to the left when the exponent is negative. Examples:
3.1 @ 2  =  310
547.8 @ -3  =  0.5478
4.1378 @ 5  =  413.78 @ 3  =  41378 @ 1  =  413780
41378 @ -5  =  413.78 @ -3  =  4.1378 @ -1  =  0.41378

The useage of the metric prefixes is given by example:
0.8 mg = 0.8 milligram = 0.8 * 1000 microgram = 800 ug
5.7 hm = 5.7 hectometer = 5.7 @ 2 meter = 570 m
This useage is also shown in the section about the basic metric units

Square and cubic measures are written in two ways: with the abbreviation of 'square' or 'cubic' before it or with the digit 2 or 3 behind its abbreviation. Example:
Area:     1 sq.inch = 1 sq.in = 1 in2     5.3 sq.meter = 5.3 sq.m = 5.3 m2
Volume:     1 cu.inch = 1 cu.in = 1 in3     5.3 cu.meter = 5.3 cu.m = 5.3 m3

When a metric prefix is used the reading of square and cubic measures must be done as shown by the examples:
1 dm3 is not 1 d(m3), but it is 1 (dm)3.      1 dm3 = 1 (dm)3 equals 1 liter. 1 d(m3) would equal 100 liters.
1 hm2 is not 1 h(m2), but it is 1 (hm)2.      1 hm2 = 1 (hm)2 equals 100 x 100 = 10000 m2 = 1 hectare. 1 h(m2) would equal 100 m2 = 0.01 hectare = 1 are.

#### Numeric accuracy

This document has two classes of numbers, the exact and the approximating ones.
A number written with a decimal point in the series of digits is always an approximating number, except when explicitly it is stated as being exact.
Exact are all numbers without decimal point and the numbers marked with the embracketed asterisk [*]. Generally they are exact because of being defined so. A number without decimal point (= integral number) is never meant to be non-exact.

An exact number is a number in which the fractional part extends at the right side with zeros only. This zero-extension is infinitely long. An approximating number has non-zero digits at the right of its fractional part, which have been omitted for the sake of readability. Then rounding off is applied.

Examples:
50 = exact 50
50. = approx. 50, i.e. somewhere between 49.5 and 50.5
50.0 = approx 50.0, i.e. somewhere between 49.95 and 50.05
50.48 = approx. 50.48, i.e. between 50.475 and 50.485
50.48[*] = exact 50.48 = 50.4800000.....000.....
1234.5@-3 = (shift point to the left over three digits) = 1.2345
12.345@+2 = (shift point to the right over two digits) = 1234.5
123.45@-6[*] = exact 0.00012345

In the actual tables the marking with the asterisk can be applied in either one of the three ways:

• Asterisk behind the number:
It applies to this number only.
• Asterisk in the header of a column:
It applies to all numbers in the column.
• Asterisk in the header of a section:
It applies to all numbers in that section.

#### Grid symbol

The grid symbol # means 'number of' or 'amount of'. This symbol is often used on top of a table column. Example:
# meters = amount in meters.

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#### HOW TO READ THE ANGLO-SAXON CONVERSION TABLES

This instruction holds for the following chapters:

• Linear measures (= Lengths)
• Square measures (= Areas)
• Cubic measures (= Volumes)
• Masses (= 'Weights')

The way of reading the conversion tables is given by an example. For this extractions of the linear surveyor+chain tables are shown. At first the interrelations amongst the non-metric measures are shown, and after this the relations with the metric measures.

#### Non-metric inter-relations

```name                  consists of       # yards
----                  -----------       -------
chain                 11  fathom            22
fathom                 2  yard               2
yard                   3  foot               1
foot                  12  inch            1/3
inch                                      1/36

chain                  4  rod               22
rod (= pole = perch)  25  link               5.5
link                   7.92 inch [*]         0.22 [*]
```

This example shows that a chain consists of 11 fathoms. A fathom on its turn consists of two yards, a yard consists of three feet, and a foot consists of 12 inches. But a chain can also be handled as a set of four rods. A rod (which is also named pole or perch) on its turn consists of 25 links. Each link contains a non-integral number of inches: 7.92 .  The bracketed asterisk shows this value is exact.

From these numbers one can calculate that a chain consists of 11 * 2 = 22 yards, or of 11 * 2 * 3 = 66 feet, or of 4 * 25 = 100 links, and that a fathom consists of 2 * 3 * 12 = 72 inches, and so on. A chain consists of 11 * 2 * 3 * 12 = 792 inches, but it also consists of 4 * 25 * 7.92 = again 792 inches. This method of multiplication in cascade allows everyone to calculate how many inches fit in a yard or how many feet in a rod, and so on.

Also forwards-backwards calculations can be performed. Example: How many links fit into one yard ?  Four answers are possible.

• Answer 1: One chain consists of 4 * 25 = 100 links. It also consists of 11 * 2 = 22 yards. Thus 100 / 22 = 4.545454 links fit into one yard.
• Answer 2: One link contains 7.92 inches. One yard contains 3 * 12 = 36 inches. Thus one yard contains 36 / 7.92 = 4.545454 links.
• Answers 3 and 4: see next section.

#### Relations with metrics

```abbrev. # meters [*]     name                  inverse
------  ------------     ----                  -------
ch      20.1168      chain                  49.7097 / km
rd       5.0292      rod (= pole = perch)  198.84 / km
fath     1.8288      fathom                  0.54681 / m
yd       0.9144      yard                    1.0936 / m
ft       0.3048      foot                    3.2808 / m
li       0.201168    link                    4.9710 / m
in       0.0254      inch                   39.370 / m
```

This table shows that the length of a chain is a little bit more than 20 meters. A little bit less than 50 chains fit into one kilometer. A foot has a length of 30.48 centimeters. Three feet plus a little bit more than a quarter foot fit into one meter. One inch has the length of 2.54 centimeters. More than 39 of them fit into one meter.

Note that in this example all the values in the left column (# meters) are exact, and those in the right column (inverse) are not. This is accidentally and not common in other tables. The values in their right column may be exact, and those in the left column may not be exact. Or in one column some values are exact and others are not.

This table can also be used for calculating the non-metric interrelations. But as the numeric values are not so accurate generally, try not to use this method.
Example: How many links fit into one yard ?  Four answers are possible:

• Answers 1 and 2: see previous section.
• Answer 3: The length of one link is 20.1168 cm, and that of one yard is 91.44 cm .  Thus 91.44 / 20.1168 = 4.545454 links fit into one yard.
• Answer 4: 4.9710 links fit into one metric meter, and 1.0936 yards fit into one meter. Thus 4.9710 / 1.0936 = 4.545538 links fit into one yard. As one can see the result is distorted by the inaccuracy of the numbers in the table.

#### Names in this document

The Anglo-Saxon measure system is a collection of factly independent measure systems. Sometimes such a self-sufficient system has an own name. Well-known are the names of the weight systems. The name 'Avoirdupois' is derived from the old French 'Avoir de pois' which means 'goods of (i.e. sold by) weight and not by volume or pieces'. The name 'Troy' references to a weight used at a fair in the central-French city of Troyes.

In the course of time a lot of measure units have been added to the set of existing units. And new units are still added. Consequently the tables cannot exhaustively mention all units.

In the whole document synonyms and abbreviations are used for some measure units. They are used intermixedly. The most important synonyms are:
British = Imperial = UK = United Kingdom
US = USA = United States of America
Fluid = Liquid
Meter = Metre
Liter = Litre
A few decades ago the metric system was also called Giorgi-system.

The singular unit name or the officially forbidden plural name of a unit are also used intermixedly, but not in the abbreviations. Example: 5 kilograms = 5 kilogram = 5 kg,   but 5 kgs is not used.

Square metric measure units are used when the sizes of areas are measured. They are displayed in two ways: with the digit 2 behind the metric unit, or with the 'word' SQ (=square) before it. Thus: m2 = sq.m,   dm2 = sq.dm,   cm2 = sq.cm .

Cubic metric measure units are used when the sizes of volumes are measured. They are displayed in two ways: with the digit 3 behind the metric unit, or with the 'word' CU (=cubic) before it. Thus: m3 = cu.m,   dm3 = cu.dm,   cm3 = cu.cm .   (cu.cm is often abbreviated to: cc) .

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#### INSTRUCTION FOR READING THE OTHER CONVERSION TABLES

This instruction holds for the following chapters:

• Metric system
• Pressures and strains
• Physical constants
• Biblical measures and money
• Euro exchange rates

The chapter about the metric measure system is the finalization of the list of conversions between the metric and Anglo-Saxon system. It shows the complete(!) set of names to be used in daily practice.
At first it gives a list of all metric prefixes with their extended names. It shows that the everyday American people use other names for them than the Europeans use, which sometimes can be quite confusing.
Secondly it shows the four basic measure units and the method of how to combine a prefix with a basic unit to construct the desired measure unit.
At third it gives some old European names whose values fit easily in the metric system.
At last it gives a proposal for new names to ease the use of the metric system for people accustomed to the Anglo-Saxon system.

A lot of systems have been invented to measure pressures of gases and liquids. All had their own definitions and units of measure. This fact results in a table of eight by eight cells with the factors for conversion between these units. The chapter itself explains how to read this table and gives some additional medical information.

The chapter with the physical constants shows the values of a lot of generally applicable constants gained by laboratory experiments in chemistry, physics and mechanics. It also contains the rules for conversion between the five temperature scales and a list of important mathematical constants.
The constants concerning pressures have their own chapter about pressures.

The tables about the measures and money types used in Biblical times show the Biblical name of every item, the number of another item it consists of, the estimated number of a present-day item, the English name given to it in translations, and the location in the Bible of one sentence (='verse') wherein it is used.

The chapter about the European currency exchange rates shows the official rates between the Euro-coin and the national coins and some easy ways to approximate these rates quickly in the head and without calculator.
For those people who also use the anglosaxon-metric tables: The table with the official rates looks like the tables for the relations with metrics. It is not, as the the second and fourth column have been interchanged. So the column '1 Euro equals' is similar to the 'inverse' column in the metrics-relation tables.

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### METRIC VERSUS ANGLO-SAXON

#### Two main 'technics cultures'

Every human society feels the need to quantify properties like time, length and mass for engineering and trade. In response to this need in early days every country or even every region had its own measure system. At present two systems are used globally: the American and the European system. Generally a country chooses to use only one of both. In reality this choice shows a greater difference in 'technics-culture' between both groups of countries than only the measure system, like the table shows:

```                            TECHNICS CULTURE
subject              American              European
-------              --------              --------
Electrical mains     110 volt, 60 Hz       230 volt, 50 Hz
Television (4:3)     EIA-525-60-NTSC       CCIR-625-50-Pal/Secam
Measures system      Anglo-Saxon           Napoleonic (=metric)
Weight,Mass       Stone, Pound, Ounce      (Kilo-)Gram
Length, Distance  Mile, Yard, Foot, Inch   (Kilo-,Centi-)Meter
Volume,Capacity   Barrel, Gallon           Liter, Cubic meter
Car-engine-power     SAE-HP                DIN-HP/PS
Cylinder-capacity    c.inch                cc
Gas-/Airpressure     psi, psf              bar, Pascal
Temperature          Fahrenheit            Celsius
Number (example)     6,789,012,345.67      6.789.012.345,67
Calendar-date-       Month + Day + Year    Day + Month + Year,
-notation                           Year + Month + Day
Hour of the day      12 hours + AM or PM   24 hours
AM = morning
PM = afternoon
```

The indicators AM and PM are derived from the Latin language:
AM = ante meridiem = in the morning,
PM = post meridiem = in the afternoon.
The number example shows the use of the punctuation marks. Both number figures represent the same value. That is elucidated in the next table:

```                       NUMERIC FIGURES NOTATION
Punctuation marks in numbers                      America   Europe
----------------------------                      -------   ------
Subdivision of the digits in groups of three:      comma    period
Separation between integer and fractional part:    period   comma
Example:                                        12,345.67 = 12.345,67
```

In this conversion document the American punctuation is used.
Scientists like to use the punctuation and measures system of Europe.
The vocal pronouncement of the numbers above one million is also different between both cultures. That pronouncement is shown in the prefixes of the metric system.

The first table shows some weird symbol sequences for the transmission of television pictures. I do not explain the meaning of these sequences, but one can see that they are not the same in both columns. In fact they tell that the two television systems are incompatible!  Consequently a videotape recorded in an 'American-type' country can not be played in an apparatus made for use in a 'European-type' country. American VHS differs from European VHS. Only the empty tapes are equal!  When a TV-network wants to broadcast pictures taken in the other system, it first has to transform them into the own system, otherwise everyone's TV-set would become confused.

#### Countries select a system

Until twenty years ago the USA, Europe and the Soviet-Union were the leading countries in the world, in economical, political and military power. Consequently the other countries felt obliged to copy one of their technical cultures. This choice was highly influenced by political and colonial relations. Consequently the global map has become a random patchwork of the two cultures, like the example shows:

```            COUNTRY WITH ... SYSTEM
American                    European
--------                    --------
United States of America    continental Europe
Japan, South Korea          former Soviet-Union states
Taiwan                      Peoples Republic of China
continent South America     Republic of South Africa
air-forces Europe (Nato!)   air-force Russia
```

Some countries have a 'mixed culture', like Great Britain.
The Soviet Union applied the European culture.

#### Road side of car traffic

The road side for the driving of motorcars is NOT related to the technics culture, as the following table shows:

```            TRAFFIC DRIVING SIDE
Left driving          Right driving
------------          -------------
Great-Britain         continental Europe
Cyprus                Turkey, Greece
Japan, South-Korea    United States of America
Hong-Kong, Taiwan     Peoples Republic of China
India, Pakistan       'Arabic' states: Maroc to Iran
Rep. South Africa     Israel, Palestina
Philippines           continent South + Meso America
Indonesia             former Soviet-Union states
Sweden until 1963     Sweden after 1963
```

Roughly one third of the countries in the world has left driving traffic, and two third has right driving traffic.

#### Pronouncement of numbers below one million

The German and the English people pronounce several numeric values below one million in a different way. The differences are for the values between 20 and 100 and for the values between 1000 and 100,000. The table shows them with examples. Herein E means English and G means German (translated into English).

```              NUMBER VOCALISATION
value     pronouncement
-----     -------------
15        E=G:  fifteen
36        E:    thirty six
G:    six and thirty
115       E=G:  hundred fifteen
436       E:    four hundred thirty six
G:    four hundred six and thirty
1500      E:    fifteen hundred
G:    thousand five hundred
3600      E:    thirty six hundred
G:    three thousand six hundred
11500     E=G:  eleven thousand five hundred
43600     E:    fourty three thousand six hundred
G:    three and fourty thousand six hundred
```

In the Netherlands a mixture of both systems is used. France uses a third system.
The numbers above one million are vocalized differently by Europe and America. That is shown by the every-day-name column in the prefixes of the metric system.

#### USA versus UK language

In this document the USA-word Meter and the UK-word Metre denoting the same quantity are used intermixedly. Similar holds for the USA-word Liter and the UK-word Litre.

The ordinary daily words are written in the British version. Examples:   Neighbour = neighbor,   Behaviour = behavior,   Useage = usage.

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#### SETTING THE POLAR HEART-RATE MONITOR

Sportsmen and sportswomen, especially those who perform endurance sports, like marathon runners, often use a heart-rate monitor in their training. Such monitor often consists of a chest belt and a wrist watch. Before the sports(wo)man can use his/her monitor (s)he has to be enter several values about the body e.g. length, weight and gender, into the wrist watch of the monitor. Also the monitor must be synchronized to the actual date and time.

A well-known brand of monitors is the Finnish company Polar. The manuals of several of these monitors have a snag: They do not tell about the hughe importance the selection of the technics culture has for a good operation of the monitor.

Before entering the present date and time and the 'fixed' body values into the Polar heart-rate monitor, the user must tell it which technics culture (s)he wants to apply. (S)he must select one of the two and cannot select a mixture of both. Alas, several Polar manuals suggest that this selection is of minor importance, as they do not state clearly its many consequences. In some monitors themselves this setting is quite cumbersome and prone to errors or even hidden deeply away in the midst of a sequence of other settings. So the user should first try to find out where in the monitor's setting system the culture is set, and perform this before all other settings. Examples of possible setting indicators are 12--24 HOURS and LB/IN--KG/CM.

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The Metric measure system has many hughe advantages above the Anglo-Saxon system. The most important advantage is that the metric system has no difficult conversion factors between the denominations of a measure type. So, once one gets accustomed to it, life becomes much easier and a little bit cheaper. Therefore nearly all scientists like to use this system even when they live and work in a country that uses the Anglo-Saxon system, e.g. the USA.

In my view life is very difficult for the factories of shoes and clothes, as they use their own measure systems that are incomprehensible to the ordinary people (who are the customers!) and even differ from country to country. Very vague are the non-numeric indicators like XXL, M, ES and so on. The apparel systems are even worse than the Anglo-Saxon system!  It is unbelievable that these factories do not switch to the metric system, but stubbornly stay at their own archaic ones. In case they would switch to the metric system, the consumers can measure their body simply at home and much easier select the right piece of clothing in the shop. This would give a boost to the mail-order and internet shops since less pieces of apparel would not fit and be returned. It also would give a boost to the ordinary shops as they can serve more customers on the same (expensive!) floor space. Also clothes can be given as a birthday present which will give an additional boost to the sales. At present nearly everyone is afraid of buying clothes for a friend or relative since "they will fit never".

History has shown that the economy and wealth increase when life is made easier for the ordinary consumers. Look at the motorcar, the tape-recorder and above all the computer: as soon as they became easier to operate their sales increased. This increase lowered the prices and enabled the manufacturers to improve the easiness of the operation, thus increasing the sales again. Difficult systems may give to the consumer the idea of skilfull craftsmanship, but in reality they create an elitarian and thus repulsing distance between the consumer and the manufacturer.

Many companies like to globalize their production and sales in order to lower the prices. So, let them first globalize the measure system. This globalization cannot trigger ethical objections except that the increase of sales may damage the natural environment more quickly. But mankind should damage the nature never at any time by any means!

We have already an example showing that globalisation of a measure system increases the wealth of most people in the world. It is the globalisation of the time measure: the creation of a standard time (Greenwich Mean Time) and the related time zones at the end of the nineteenth century. Before this moment every state and sometimes even every city or village had its own clock settings. Generally the lengthes of the time intervals like hours, minutes and seconds equalled for most locations, but the o'clock moments differed. Often these differences were only a few minutes. In the American East-coast many train passengers passed through seven local time zones, although in in general they did not travel as far away as we do. This patchwork was a waste of nerves, money and time.

Some people who like to go back in time (e.g. artisans and traditionalists) suggest that the unification of the measures may destroy the identities of the local dwellers. But the time unification shows that this is not true. The modern means of transport like bikes, trains and motorcars were already enabling people to look beyond the boundaries of their own village. So they started the deterioration of the feeling of belonging to the own small community. The unification of time made the feeling of belonging to a larger region like a state or a nation stronger as this geographical area seemed to be less fractioned.

It is easy to be romanticly nostalgic as long as one can rely on the scientific, technical and medical attainments of the modern days in case of illness, injury or emergency. The old days were often more fierceful and frightening than the present days. Only a modern war is worse than an old war. But people should be warriors never at any age!  And why should the identity of a person or community be expressed by the numeric value of a measure unit?  It is expressed by the appearance of the clothes (s)he wears, the kind of the music (s)he makes and the house (s)he dwells in!  And the construction of these things should not be hampered by such numb things like unwieldy measure units!  The human mind should be freed from them to perform its real expression.

Difficult measure systems only consume the person's identity. So let us all go metric!  This chapter will show the ease of that metric system, and the whole document is intended to help the people in switching to this transparent system.

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#### METRIC NOMENCLATURE

The method of naming the measure units in the metric system is quite different from that in the Anglo-Saxon system. In the metric system such a name is created by selecting a basic name from a very small set of names and combining it with a prefix which indicates a multiplication with an exponent-power of ten. This prefix can be empty; then its value equals 1.@0 = 1. In total less than 40 names and prefixes are required to give a name to every measure unit that is used in daily life. The Anglo-Saxon system requires much more than 40 names. Nevertheless this system has a smaller range of values in every property than the metric system has.

The same prefixes are used for all classes of measure types. Classes and their basic units are:  length -- Meter,  weight -- Gram,  time -- Second;  electricity -- Volt, and so on. All prefixes can be used with all classes. The size of the resulting measure of a prefix with a class name is always a power-of-ten times the size of a measure made by another prefix and the same class name. Mathematicians call this universal property "Orthogonality". Examples:
1 mV = 1 millivolt = 0.001 V,  1 kV = 1 kilovolt = 1000 V,
1 mg = 1 milligram = 0.001 g,  1 kg = 1 kilogram = 1000 g,
1 mm = 1 millimetre = 0.001 m,  1 km = 1 kilometre = 1000 m,
1 mA = 1 milliampere = 0.001 A,  1 kA = 1 kiloampere = 1000 A.
The universal prefixes are listed in the sub-chapter Metric prefixes.

This sub-chapter also shows the language differences between the American and continental-European people, even when both speak the same language: English. In daily life both peoples use different names for the units above the million. Example:
10@9 = one milliard in Europe = one billion in America.
Luckily both peoples use the same scientific names.

Beside the prefixes the adjectives 'square' (= sq.) and 'cubic' (= cu.) are in ubiquitous use in the metric system since they are the only official way to indicate areas and volumes. They are often notated by the suffixes 2 and 3 behind the length unit. Thus, for example:
(m1 =) m = linear meter (for length or distance)
m2 = sq.m = square meter (for area or surface)
m3 = cu.m = cubic meter (for volume or contents size)
In the Anglo-Saxon system these adjectives exist too, but they are used less often as surfaces and volumes often have their own names.

Another feature of the metric system is that it does not make a difference between the useage fields of the measure. For example: All cubic measures and volumes are expressed with the same measure units. There is no distinction between Liquids, Dry materials, Solid materials, Apothecary use and so on. The rough workers in the forest and in the harbour use the same basic units as the scientists in the laboratory do. And the shopmen join them when they sell their meat or gasoline. Even the pilots of USA's former ennemies, the Sovjets, use them in their fighting planes!  Only the prefixes may differ. But a prefix has always the same meaning, irrespective who uses it. The transparent and universal orthogonality is complete! In continental Europe the slogan by the creators of the metric system in 1795 has come to reality: "It is for all people, for all time".

Example of use: Let us take the measure-class Length with its basic unit Meter. A small unit of length can be created by adding the prefix Milli before the basic-unit name, thus giving Millimeter. This unit of length is exactly 1/1000-th of the length of the original meter.
A very small unit can be made by using the dwarf prefix Nano. Thus 1 Nanometer is 1-milliardth of a meter. A large unit is made by adding a blow-up prefix, e.g. Hecto or Kilo. Thus 1 Hectometer is 100 meters and 1 Kilometer is 1000 meters. They equal to 1.@+11 and 1.@+12 nanometers respectively.
This construction is shown in more detail in the chapter of the basic units.

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#### SOME SMALL ANOMALIES

Alas, a few anomalies make some tiny cracks in the bastion of the metric's universal orthogonality. Some of them are man-made and others arose by the physics. Some of them are shown here.

At first: Physicists made a big snag, as if they like to be terrible people. The basic unit of mass in their science of physics is not gram, but it is kilogram (1 kg = 1000 g). More about this inconsequency and its consequences is written in the chapter about the basic metric units. In daily life this snag does not give any problem.

At second: In Europe some ancient names are still in use. They are not many, and the values they stand for fit quite well in the metric system. These names are listed in the tables of the outsider units. In this document even new names for ordinary use are proposed!

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#### Smaller range

Despite the smaller amount of names in the metric system, the ratio between its smallest and its largest measure unit is much greater than in the Anglo-Saxon system. The ratio between the smallest and the largest prefix is 1.@48.   In any Anglo-Saxon measure class the maximum range between the smallest-valued name and the largest-valued name is less than 1.@15 .  Most classes have a much smaller range. Of course this is a disadvantage, but soon it will appear to be minor when compared to the one of the next section.

#### Forced cooperation of contradictory units

The above-mentioned anomalies in the metric measure system are outdwarfed by those in the Anglo-Saxon measure system which in fact is a big collection of anomalies. It has the handicap of total lack of orthogonality and universality!

The main cause of this lack is the biological basis of many of the measure units, especially our human body. This body seems to be a nice toolcase for defining measure units, especially the length units. The size of a bridge, a house, or a kitchen-table is expressed as a number of lengths of a medium-sized body part like an arm or a foot or even a foot-step. To measure small-sized objects like a dish or a candle we use a small body part like a finger. We always carry this toolkit with these coarse length units with us everywhere we go to, and we can never forget it. But this easy toolkit has one great disadvantage: Some people are tall and others are small, some people are thick and others are thin, and so are their limbs. Therefore righteous trade and commerce require standardized (= idealized) body sizes. This standardization has to be adapted when units not based on the human body must be included in the measure system.

Consequently in the early medieval times every region like a nation, township or city and every branch of industry, trade and merchandise performed the standardization in its own way, thus developing its own measure system. In later times the systems of several regions and branches were brought together. To make them 'cooperate together' several of these systems were adapted slightly. This means: the units in them were stretched or shrunk slightly. Thus the multiplication factors between the units of consecutive sizes were kept integral and not too awkward. All these processes make the history of the origination of the resulting measure system fairly muddled, and the system itself too. The Anglo-Saxon measure system is such an accumulated bunch of units.

The origins of the composing systems and their units manifest in several ways:
- selection of basic units,
- the time in history,
- by region or township,
- kind of stuff to be measured.
These four causes will be shown with examples.

First cause: Selection of basic units.
The base of the definition of the nautical mile is the length of one-sixtieth of one degree on the earth equator. A unit of around this length is useful to measure the distance of a long journey or sea voyage. The determination of that unit needs fairly complex apparatuses, although it can be done very accurately. It is based on astronomy. Only a few professionals can handle this apparatuses. In order too give their results sense to the ordinary people the idealized body must be designed such that the body based units are in concert with the earth-globe based units. Here more than one type of standard body is possible.

Second cause: Time in history.
If a new king stands up and wants to immortalize himself, he may dictate the basic measure units to be redefined to his body measures. Of course these are different from those of the previous king. Thus the same country gets another measure system.

Third cause: Dependency on region.
In past times regions like countries, counties and townships were more self-sufficient than they are now. So there was less trade between them. Consequently it was fairly easy for every region to define its own measure units. A rich region uses horses to pull the plow, but a poor region uses oxes or donkeys. These animals work slower, and so the size of the piece of land that can be plowed in one day is lower. Thus the "day's-plow-unit" differs between both regions.

Fourth cause: The kind of stuff to be measured.
This factor depends typically on the kind of trade and merchandizing. For weighing beans one cannot use a very small bucket as the inaccuracy due to the empty spaces near the wall would increase. Producers of beverages refer their volumes to the size of a typically drink glass. And coal deliverers refer to the sack they can hold firmly in their hands or on their back. A sack of wood chips cannot be much bigger, even when it is much lighter, otherwise it is too big to be grasped easily. Thus every branche of trade invents its own units of mass and weights. Another example: One branch defines the pound as the weight of one can filled with water, and the other branch defines the pound as the weight of the same can filled with oil. Of course when the latter branch uses a slightly bigger can, then the two pounds approach each other gruesome closely, which may be confusing as they are not exactly equal.

Note that the day's-plow area and the big-but-not-too-big coal-sack are also values with a biological base: muscle strength. Time keeping is a hybrid value. A coarse time unit is inside our body: the heart rate when we are in rest. Another time unit needs fairly difficult instruments for its definition, but it is much more accurate: the hour that is based on astronomy. Here we see the same as in the case of lengths: The moderate and small unit values can be based on biological properties everyone can perceive easily, but the large units are based on complex science and physics and need apparatuses to be measured. And both have to be brought into concert, i.e. the factor between the standardized heart-beat interval and the astronomy-hour must be integral and not too awkward.

#### Many Unit names and Multiplication factors

The enforcement to the unit-cooperation causes the creation of different multiplication factors between the units of the same type that are consecutive in size. Not always these differences can be washed away by introducing new units and thus making new factors, similar to the addition of the unit tenhalf and the accompanying factor 10.5 by the author. The persistent existence of these differences between multiplication factors is the undesired and cumbersome un-orthogonality of the Anglo-Saxon measure system. Example: A yard consists of two cubits, but a cubit consists of 1.5 feet and not of two feet.

Some multiplicative factors are even quite ugly. The factors 2, 3, 4 and 5 are quite nice, but 7, 11 and even 19 are awkward. In fact nearly all numbers between 1 and 20 are used as a factor. Consequently a 'difficult' conversion factor may be needed to translate one unit into another that is not in the same so-called "multiplication chain", e.g.  1 Ramden-chain = 1.515151515.... Gunter-link.   Of course the difference and sometimes-ugliness of the multiplication factors hampered the construction of a mechanical adding or subtracting machine. Only the modern electronic computers can handle them well.

#### Endless creation of new units

Another important reason for the steady proliferation of units and names is the absence of prefixes. So for every unit of measure another name must be invented, even when that unit belongs to the same class, e.g. yard and cubit in stead of half-fathom and quarter-fathom. Therefore the system must enable everyone to easily and seamlessly add new units or new names for existing units that fit better to his job. It even invites to do so.

And the people respond!  They add nearly every new contraption to the units table wherein it fits at best, of course after it has been christened with an exotic or popular name. Not surprisingly, many branches of industry and trade have often (ab)used this facility and still do. The creativity and the will to invent new and "better fitting" unit sizes appear to be endless. E.g. the name Ramden-link has been invented for the already existing and widely used foot, and a span (= linear quarter) is a kind of a small foot. This liberty for units leads to an uncontrollable proliferation of unit names. The chapter Masses: Avoirdupois - Trade+Industry is a clear result of it.

To make things worse, the newly invented Anglo-Saxon units also need not to be easily compatible with the existing ones. Consequently the 'multiplicative distances' between the units of the same class will never become equal. All these irregularities force people to invent new measure units and multiplicative factors that are more handy, thus making the problem even worse. And so the proliferation of new units and names will continue for ever. As a consequence, no document can ever display the total set of all unit names.

And still the Anglo-Saxon complexity seems not to be enough: Different application environments use different sets of names, like Troy, Avoirdupois, British-Imperial, USA-Nautical, and so on. The altitude of a tower is expressed in a naming system different from that for the altitude of a plane. Low and behold, the different naming systems often use the same set of unit names. Thus confusion may arise about the actual meaning and size of an unit. Example: A pound is 5760 grain or 7000 grain, depending on which weight measure system is used. Two different gallons and a countless number of quarts circulate in the USA. Thus the effort to save names only enhances the mess.

During the thousands of years of civilization innumerous meetings and assemblies have been held to define and redefine the basic measure units in order to keep them fit for the job and not mutually contradictory, and to avoid the quarrels about them. And these conferences are still going on.

Alltogether these points force some people to call the entire Anglo-Saxon measurement system a WOMBAT = Way Of Measuring Badly in America Today = Waste Of Money, Brains And Time.

#### The Simplicity of the Metric system

But it can be much easier: the Metric System, also called Systeme International (= S.I.) or Giorgi system. This system is not based on values determined by biology, history, trade and commerce, but only on a very few physical values determined by modern scientists. These basic units are carefully watched by the French Bureau de Poids et des Measures (= Office for Weights and Measures) at Sèvres near Paris.

Conferences are needed only to enhance the accuracy of these units as technology progresses, but not to change them significantly. There are no slightly contradictory units that are forced to 'cooperate together'. This fact enabled the metric-system designers to prohibit all multiplicative factors except one, and favorize that single one. This makes the system total orthogonal and universal. The choosen factor is a nice one: 10 = 2 * 5.  Thus a kilometer consists of 1000 meters, and a meter consists of 1000 millimeter and not of e.g. 800 millimeters.

This rigidity in the metric system makes its use easy, eases the construction of mechanical adding and subtracting machines, and enables the protection from the infinite proliferation of unit names and multiplicative factors. It firmly discourages personal creativity in the making of a new unit. It forces everyone to combine a prefix and a basic unit name to make a unit that fits better to the job. Both the prefix (like milli and kilo) and the basic name (like meter and gram) must be taken from predefined sets. These sets are fairly small, so they can be listed all together on two sheets of paper. In fact the chapter about the metric system covers the whole part of the system for daily use.

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#### METRIC PITFALLS: SQUARE AND CUBIC

Has the metric system advantages only?  Alas not!   Unnecessarily and perhaps unwittingly the designers have built in one great (and in my eyes) quite severe disadvantage. It has a tricky pitfall in the notation of a square or cubic measure. An examples shows this.
dm3 does not mean d(m3) = 1/10-th of a cubic meter,
but it means (dm)3 = 1/1000-th of a cubic meter.
Similar holds for the square measure:  dm2 equals 1/100-th of a square meter and not 1/10-th.

This notation makes the range of values between two consecutive prefixes rather large, as the multiplication factor between the two prefixes becomes very large. For example: Between the consecutive prefixes Kilo and Mega this factor is one million (= 1.@6) for square measures and one milliard (= 1.@9) for cubic measures. The latter value is approximates fairly the total range of any Anglo-Saxon system.

Here the Anglo-Saxon notation system has great advantage. The average of the multiplication factors between two names with consecutive unit values is roughly the same for linear, square and cubic measures. For example, a fathom is two yards and a peck is two gallons. Perhaps this advantage has motivated the American and some British people to stick to their measure system.

So it seems reasonable that in the daily talks of the ordinary British everyman who has to get accustomed to the metric system, names will be given to intermediately sized values which fit well inside this metric system. Therefore the people may create new names, but also borrow existing ones from the continental-European and the Anglo-Saxon system. In the latter case the name may be given a metric value in the neighbourhood of its original Anglo-Saxon value. Perhaps the proposed set of names may emerge. It is not surprising that in this set the number of volumes is high. It is to split up the hughe range of one 'official' volume step.

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### RELATIONS: INTERNAL ANGLO-SAXON AND WITH METRICS

#### PREDEFINED BASIC UNITS

The old Imperial (now UK) measure system was originally defined by three standard measures which were held in London: the yard, the pound and the gallon. For example, the gallon was the volume of ten AVDP-pounds of water at 62 degrees Fahrenheit and a pressure of 30 inch mercury. The USA had their own system that also was defined originally by physical standard measures: the yard, the pound, the gallon and the bushel. Similarily herein the gallon was roughly the volume of ten Troy-pounds of water.

At present all these basic standard measures are redefined by referencing them to the standard measures of the S-I-system that have been developed in 1795, introduced by Napoleone Buonaparte in his empire, and are nowadays widely used in continental Europe: the metre, the kilogram and the litre. These equivalence figures are exact. Hence the bracketed asterisk [*] on top of the values column.

```Anglo-Saxon               Metric               Where used
name          value [*]         type         USA   UK
-----------      --------------------------    ----------
yard             0.9144            metre        USA + UK
pound (avdp)     0.453 592 37      kilogram     USA + UK
gallon           4.546 09          litre              UK
gallon (fluid)   3.785 411 784     litre        USA
bushel (dry)    35.239 070 166 88  litre        USA
```

[*] = All values in this column are defined as being exact.

Note particularly that the UK gallon is a different size to the US-fluid gallon so that NO liquid measures of the same name are the same size in the UK and US systems. The US-fluid gallon equals 231 cubic inches.

The table also means that the accuracy of the Anglo-Saxon measures depends on the accuracy of the underlying measures in the Napoleonic system. The Anglo-Saxon measure system is not autarkic ('self-sufficient') anymore.

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#### DERIVATION OF TROY-POUND

The defined pound is the Avoirdupois-pound. The pound of the Troy+Apothecary system is derived from this pound by the formula:

```       pound(tr/ap) = pound(avdp) * 5760 / 7000
= pound(avdp) * 144 / 175
= pound(avdp) * 0.822857142857....
= 0.3732417216[*] kilogram
```

Its reverse is:

```       pound(avdp) = pound(tr/ap) * 7000 / 5760
= pound(tr/ap) * 175 / 144
= pound(tr/ap) * 1.215277777777....
= 0.45359237[*] kilogram
```

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#### THREE SIZES OF GALLON

The following table shows the conversion factors between the three sizes of gallons. Herein:   dry-gallon = dry-bushel / 8.   This table should be read as follows:
One unit written alongside the vertical axis ('row name')   equals   one unit written alongside the horizontal axis ('column name')   times   the numeric value in the table cell.
Example:   1 Imperial-gallon = 1.20095 * 1 USA-fluid-gallon

```   GALLON   |   USA-fluid   |    USA-dry     |    Imperial    |
------------+---------------+----------------+----------------+
USA-fluid  |        1      |  0.8593670074  |  0.8326741846  |
------------+---------------+----------------+----------------+
USA-dry    |  1.163647186  |        1       |  0.9689389719  |
------------+---------------+----------------+----------------+
Imperial   |  1.200949926  |  1.032056743   |        1       |
------------+---------------+----------------+----------------+
```

From the actual volume tables it can be derived that 1 UK-gill = 5 UK-ounce, and that 1 US-fluid-gill = 4 US-fluid-ounce.
When some inaccuracy is allowed, the following approximations can be applied:

```approximation                          accuracy better than
-------------                          --------------------
6 USA-fluid gill  = 5 Imperial gill       0.08 percent
7 USA-fluid gill  = 6 USA-dry gill        0.26 percent
1 Imperial gill   = 1 USA-dry gill        3.3  percent
1 USA-fluid ounce = 1 Imperial ounce      4.1  percent
```

This approximation table holds for the three gills and most of the equally named units 'above' them (e.g. gallon, kilderkin, bushel). And it holds for the two ounces and most of the equally named units 'below' them (e.g. dram, minim).

The the number of gallons in the following units have been defined such that the units differ less than 0.08 percent in actual size:
USA-tierce = 84 gallon   and   Imperial-puncheon = 70 gallon

In fact a fourth measure system for volumes exists, having its own size of the gallon. It is the old British-beer system. It is is described in the section below this one.

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#### OLD-BRITISH UNITS AND BEER

The volume systems used in the USA are based on old British systems that are nearly out of use and unknown to most people. Units in these old systems that are out of use, are nevertheless added to the American systems in this document. If such unit has the same name as an USA-unit but has a different size, then the unit is marked with "OB" = Old-British. The USA-unit does not get a mark. Example with unit name 'Tierce' in the USA-fluid system:
Tierce = 84 gallon     (used in USA)
OB-Tierce = 42 gallon     (Old-British, out of use)

The old British-beer system is a fourth measure system for fluid volumes. It has its own size of the gallon. At present this system is put aside as being 'unofficial'. So it is not used much anymore and even unknown at all to most people. For the sake of completeness its volume tables are listed also in this document. The following table shows the old British base of all four volume systems.

```Present-day volumes      Old-British base
-------------------      ----------------
USA-Fluid                Wine (by Queen-Anne)
USA-Dry                  Dry before 1824
Imperial                 Dry+Fluid since 1824
old-British beer         old-British beer+ale+porter
```

The following table lists the number of cubic inches in a gallon for each system. In two systems this size has been changed slightly during the history. The size of the gallon in the old British-Dry-before-1824 system was 268.75 cubic inches. Nowadays it is 268.8025 cubic inches in the USA-Dry system. Similarly the size of the old British wine-gallon has once been 231.18 cu.inch = 3.7884 liters, whilst it is now exact 231 cu.inches in the USA-liquid system. The size of the Imperial gallon has only been made more accurate as the measurement apparatuses have become more accurate.

In this document the latter is assumed also for the old British-beer system. For its conversion-to-metrics table the size of the cubic present-day-inch is taken and not that of of an cubic old-inch.

```Volume system       # cubic inches / gallon
-------------       -----------------------
USA-Fluid             231      (was 231.18)
USA-Dry               268.8025 (was 268.75)
Imperial              277.42
old-British beer      282
```

The actual tables of the old British-beer system show the simplicity the other three volume systems also had in early days. In the run of the last two centuries the latter have increased in size nearly uncontrollably. Thus the beer-system confirms the disadvantages of the Anglo-Saxon system.

During the same period the small Napoleonic system did increase nearly not at all. Only a few prefixes and a few complete new types of units were added. These types were unknown at the time this system was created, e.g. Ampère for electric current. The Anglo-Saxon system never adopted these new types.

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#### THE UNIT "TENHALF"

The unit Tenhalf (= ten and a half gallons) means ten gallons plus five percent to compensate spillage. It accidentally happens to be equal to 1.5 * 7.  It is a virtual unit as it is introduced by the author to make a better fit for other units. These units are:

```name            # tenhalf   # gallon[*]
----            ---------   -----------
wine-tun            24        252
butt                12        126
wine-puncheon        8         84
(old) tierce         4         42
wine-barrel          3         31.5
tenhalf              1         10.5
```

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#### SUMMARY OF IMPORTANT VALUES

```Anglo-Saxon        r e l a t e s   t o
measure       Anglo-Saxon         Metrics
unit             [*]               [*]

Length          # inch          # decimeter
------          ------          -----------
inch               1               0.254
foot              12               3.048
yard              36               9.144

Surface        # sq.inch        # sq.decimeter
-------        ---------        --------------
sq.inch             1             0.064 516
sq.foot           144             9.290 304
sq.yard          1296            83.612 736

Volume         # cu.inch            # cu.decimeter
------         ---------            --------------
cu.inch             1                0.016 387 064
cu.foot          1728               28.316 846 592
cu.yard         46656              764.554 857 984
Gallon:
USA-dry         268.8025           4.404 883 770 86
USA-fluid       231                3.785 411 784
Brit.Imp.       277.4194327916[~]  4.54 609
Old.Brit.Beer   282                4.621 152 048

Weight           # grain          #  g r a m
------           -------          ----------
grain                1             0.064 798 91
Troy-pound        5760           373.241 7216
AVDP-pound        7000           453.592 37
```

In this table all values are exact, except the one indicated by [~].
sq. means square;   cu. means cubic

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## Part 2: TABLES; ANGLO-SAXON vs. NAPOLEON

### LINEAR MEASURES = LENGTHS

#### Length units by names

For the sake of clarity the length units of yarn and textiles are not presented here, but they are in a separate chapter about the measures for Yarn and Textiles.

```     name               consists of [*]      # feet [*]
----               ---------------      ----------
++++++++ British nautical ++++++++

+++  geograph. league  291840  inch            24320  +++
geograph. league       4  nautical mile   24320

+++  marine league     218880  inch            18240  +++
marine league          3  admiralty mile  18240
admiralty mile         1  nautical mile    6080
(nautical) mile       10  old-cable-length 6080
old-cable-length    32 * 19  foot           608

+++  radar-data-mile    72000  inch             6000  +++
sea-mile            1000  fathom           6000

++++++++ Ordinary standard +++++++

+++  (land) league     190080  inch            15840  +++
>> (land) league          3  statute mile    15840
old land-league        1.5  statute mile   7420
(statute, land) mile   4  quarter          5280
quarter                2  furlong          1320
furlong               10  (Gunter-)chain    660
(Gunter-) chain                              66
>> old-Brit.land-mile    50  Ramden-chain     5000
USA-cable-length       6  Ramden-chain      600
Ramden-chain         100  foot              100

+++  Gunter and Ram(s)den    ...                   - +++

+++  chain         11 * 9 * 8 = 792  inch         66  +++
Gunter-chain           1  chain              66
>> CHAIN                 11  fathom             66
fathom                 2  yard = verge        6
yard = verge           3  foot                3
foot                  12  inch                1
>> CHAIN                  4  pole (perch,lug)   66
pole (= perch = lug)   1  rod                16.5
rod                   11  cubit              16.5
cubit                 18  inch                1.5
>> CHAIN                  4  rod                66

+++  human run/walk/length    ...                  -      +++
MARATHON-distance    26 mile + 385 yard  138435
USA-football-field  120 or 100 yard     360 or 300
with end-zone      1  (cotton-)skein     360
without end-zone   3  Ramden-chain       300
USA-military-step    30 or 36 inch       2.5[*] or 3
moderate speed     1  step                 2.5[*]
quick speed        1  yard                 3
CRICKET-pitch         1  Gunter-chain        66
smoot          5 feet + 7 inch            5.58333[~]
UK-rail.gauge  4 feet + 8.5[*] inch       4.70833[~]

+++  navy-cable-length   8640  inch              720  +++
navy-cable-length      1  (new)cable-length 720
(new) cable-length     2  (cotton-) skein   720
(cotton-) skein        4  shackle, shot     360
shackle = shot         7.5  mark-twain       90
mark-twain             2  fathom             12
fathom                 2  yard, verge         6
yard = verge           2  cubit               3
old-cable-length    32 * 19  foot           608
USA-cable-length     100  fathom            600

+++  diverses             ...  rope                -  +++
(cotton) skein        18  rope              360
(wool) wrap           12  rope              240

+++  Ramden-chain        1200  inch              100  +++
Ramden-chain           1  engineer's chain  100
engineer's chain       5  rope              100
rope                   2  US-electric-stick  20
US-electric-stick      2  stride             10
stride                 1  geometrical pace    5
geometrical pace       1  (great) pace        5
(great) pace           2  step                5

+++  fall                 270  inch               22.5  +++
FALL                   6  (English) ell      22.5
ell = English ell      5  span                3.75
Flemish ell            3  span                2.25

+++  cubit          18 inch = 2 span = 1.5 foot    1.5  +++
yard                   2  cubit               3
yard                   3  foot                3
yard                  36  inch                3
cubit                  1.5  foot              1.5
cubit                  2  span                1.5
cubit                 18  inch                1.5
foot                  12  inch                1

# inch [*]
++++++++ Small lengths ++++++++       ----------

+++  diverses             ...  hand                -  +++
great-lug = long-rod   7  yard  = 21 foot   252
great-lug = long-rod   9  arm's-length      252
arm's length           7  hand               28
billet                 5  small palm-length  40
small palm-length      2  hand                8
hand                   4  inch                4

+++  diverses             ...  foot                -  +++
yard = verge           3    foot             36
step                   2.5  foot             30
home-el.equip.stand.U  1.75 foot             21
diamond-mark unit      1.6  foot             19.2
cubit                  1.5  foot             18

+++  electronic equipment  ... inch                -  +++
home-standard U       21  inch               21
laboratory CAMA       19  inch               19

+++  span                 360  button-line         9  +++
linear-quarter         1  span                9
palm-length            1  span                9
>> SPAN                   2  finger-length       9
finger-length          2  nail                4.5
nail                   3  finger-width        2.25
finger-width           1  digit               0.75
digit                 30  button-line         0.75
button-line                                   0.025
>> SPAN                   3  palm, ounce         9
palm = ounce           4  digit               3
digit                 30  button-line         0.75
button-line                                   0.025
finger breadth        35  button line     7/8=0.875
>> SPAN                   3  palm, ounce         9
palm = ounce           3  thumb-width         3
thumb-width            1  inch                1
inch                  40  button-line         1
button-line                                   0.025

+++  foot                  12  inch               12  +++
>> FOOT                   2  shaftment          12
shaftment              2  palm, ounce         6
palm = ounce           3  inch                3
inch                                          1
>> FOOT                   3  hand, fist         12
hand = fist            4  inch                4
inch                                          1

+++  inch                 ...  diverses            1  +++
thumb-width            1  inch                1
>> INCH                  40  button-line         1
button-line            2.5  calibre         1/40
calibre                1  centinch          1/100
centinch              10  mil, millinch       0.01
mil = millinch         1  thou, point         0.001
thou = point           4  silversmithpoint  1/1000
silversmithpoint                            1/4000
>> INCH                  14  print.agate-line    1
printing-agate-line                         1/14
>> INCH                   3  barley-corn-len.    1
barley-corn-length     4  line              1/3
line                                        1/12
>> INCH                  16  pin-length          1
pin-length             4  shoe-ounce        1/16
shoe-ounce                                  1/64

+++  line                1440  twip              1/12
poppy-seed             1  line              1/12
second                 1  line              1/12
>> LINE                   4  shoe-iron         1/12
twip                                        1/1440
twip                                        1/1440
>> LINE                  10  gry               1/12
gry                   12  twip              1/120
twip                                        1/1440
```

[*] All numeric values in this table are exact !,
except those indicated with [~].
The table can be seen as a set of sub-tables which are interconnected by some of the measure names. These names are seen in two or more sub-tables. The beginning of each sub-table is indicated by the line with the +++ symbols.

##### Metric equivalents

```abbrev. # meters [*]     name                  inverse
------  ------------     ----                  -------
42194.988       marathon-distance      0.02369950 / km
7412.736       geographical league     0.1349030 / km
5559.552       nautical league         0.1798706 / km
4828.032       (land) league           0.2071237 / km
2414.016       old land-league         0.4142475 / km
mi      1853.184       nautical mile           0.5396118 / km
mi      1609.344       (statute) mile          0.6213712 / km
1524           old-British-land-mile   0.6561680 / km
Q,qtr    402.336       quarter                 2.4854848 / km
219.456     (new, navy-)cable-length  4.5567221 / km
fur      201.168       furlong                 4.9709695 / km
185.3184     (old, sea) cable-length  5.3961182 / km
182.88        USA-cable-length        5.4680665 / km
109.728       skein (cotton)          9.1134442 / km
109.728    US-football-f.-plus-ends   9.1134442 / km
91.44     US-football-f.-no-ends    10.936133 / km
ch        30.48        Ramden/engineer-chain  32.808399 / km
27.432       shackle = shot         36.453777 / km
ch        20.1168      chain (of Gunter)      49.709695 / km
20.1168      cricket-pitch          49.709695 / km
6.858       fall                  145.81511 / km
6.4008      long-rod = great-lug  156.23047 / km
6.096       rope                  164.04199 / km
5.0292      pole = perch = lug    198.83878 / km
rd         5.0292      rod                   198.83878 / km
3.6576      mark-twain            273.40332 / km
3.048       USA-electric-stick    328.08399 / km
fath/fth   1.8288      fathom                546.80665 / km
1.7018      smoot (of MIT-Boston) 587.61312 / km
1.524       stride                656.16798 / km
1.524       geometrical-pace      656.16798 / km
1.524       (great) pace          656.16798 / km
1.4351      UK+EUR railway-gauge  696.81555 / km
Eng.e      1.143       (English) ell         874.89064 / km
1.016       billet                984.25197 / km
yd         0.9144      yard                    1.093613 / m
0.9144      verge                   1.093613 / m
0.9144      US-milit.quick pace     1.093613 / m
0.762       US-milit.modest pace    1.312336 / m
0.762       step                    1.312336 / m
0.7112      arm's length            1.406074 / m
0.6858      Flemish ell             1.458151 / m
0.5334      home-elec.-standard-U   1.874766 / m
0.4826      laborat.-elec.-CAMAC    2.072109 / m
0.48768     diamond-mark unit       2.050525 / m
0.4572      cubit                   2.187227 / m
ft         0.3048      foot                    3.280840 / m
0.2286      span = palm-length      4.374453 / m
Q,qr       0.2286      linear-quarter          4.374453 / m
0.2032      small palm-length       4.921260 / m
li         0.201168    link (of Gunter)        4.970970 / m
0.1524      shaftment               6.461680 / m
0.1143      finger-length           8.748906 / m
0.1016      hand = fist             9.842520 / m
0.0762      ounce                  13.12336 / m
0.0762      palm (-width)          13.12336 / m
nl         0.05715     nail                   17.49781 / m
0.0254      thumb-width            39.37008 / m
in         0.0254      inch                   39.37008 / m
0.022225    finger breadth         44.99438 / m
0.01905     finger-width = digit   52.49344 / m

abbrev. #millimeters     name                  inverse
------  ------------     ----                  -------
8.46666667    barley-corn-length     1.181102 / cm
li       2.11666667    line                   4.724409 / cm
2.11666667    poppy-seed = second    4.724409 / cm
1.81428571    agate-line for print   5.511811 / cm
li       0.635  [*]    button-line           15.74803 / cm
0.52916667    shoe-iron             18.89764 / cm
0.396875 [*]  shoe-ounce            25.19685 / cm
0.254  [*]    calibre = centinch    39.37008 / cm
0.21166667    gry                   47.24409 / cm
0.17638889    hair breadth          56.69291 / cm
0.0254 [*]    thou = point         393.70079 / cm
0.0254 [*]    mil = millinch       393.70079 / cm
0.01763889    twip                 566.92913 / cm
0.00635 [*]   silversmithpoint    1574.80315 / cm
```

Sometimes a pace is falsely called a step.
Foot = International foot = Ordinary foot.
Yard = International yard = Ordinary yard.
Ordinary chain (792 inch) = Gunter chain = Imperial chain.
Mil (with one L) = milli-inch; Mill (with two L's) = milli-metre.
Thou = one thousandth of an inch.
Twip = one twentieth of an (Adobe-) point.
Button-line = button-thickness-line.
Ounce = old name for 1/12 yard.
Poll = pollex = thumb-witdh.
Palm = palmus = palm-width.
Smoot = length of a scientist at MIT-Boston.

The values in the lower left column of #millimeters are not exact, except those marked with [*].
[*] = All values in the upper left column (# meters) are exact, as:

!!!! The value of  2.54  cm per inch is exact !!!!

#### Splitting of Feet and Inches

In the Napoleonic system the ordinary decimals are used always to notate the fractions of a meter, decimeter or a centimeter. The above Anglo-Saxon tables show that the feet and inches are split often into non-decimal parts. Some of these are:

```                                   metric length
Name              part of foot    in centimeters [*]
----              ------------    ------------------

span = palm-length   3 / 4             22.86
shaftment            1 / 2             15.24
finger-length        3 / 8             11.43
palm = ounce         1 / 4              7.62
nail                 3 / 16             5.715
fing.width = digit   1 / 16             1.905

hand = fist          1 / 3             10.16
inch = thumb-width   1 / 12             2.54

metric length
Name              part of inch     in millimetres
----              ------------     --------------

inch                   1          25.4 [*]
barley-corn length   1 / 3         8.46666666...
line = poppy-seed    1 / 12        2.11666666...
(shoe-) iron         1 / 48        0.5291666666...
hair breadth         1 / 144       0.1763888888...

button-line          1 / 40        0.635 [*]
gry                  1 / 120       0.2116666666...
twip                 1 / 1440      0.017638888888...

pin-length           1 / 16        1.5875[*]
shoe-ounce           1 / 64        0.396875 [*]
```

In the Anglo-Saxon system even a non-decimal system without names is used to notate the fractions of an inch: the BINARY-SPLIT system. This binary inch-splitting means: Break the inch into two equal parts. Each part has the length of a half inch. Then break each half into two equal parts. Each such part has the length of a quarter of an each. Then break each quarter into to equal parts. Each such part has the length of an eighth of an inch. Then break ..., and so on. The table shows the results of this binary splitting until one-sixteenth.

```  P a r t s   o f   I n c h      Length in        Inverse
Binary split   Decimal digits    Millimeters      # / dm.
------------   ---[*]--------    ---[*]-----      -------

1            1.0              25.4          3.93700787
15 / 16         0.9375           23.8125       4.19947507
7 / 8          0.875            22.225        4.49943757
13 / 16         0.8125           20.6375       5.72655691
3 / 4          0.75             19.05         5.24934383
11 / 16         0.6875           17.4625       5.72655691
5 / 8          0.625            15.875        6.29921260
9 / 16         0.5625           14.2875       6.99912511
1 / 2          0.5              12.7          7.87401575
7 / 16         0.4375           11.1125      8.998875141
3 / 8          0.375             9.525       10.49868766
5 / 16         0.3125            7.9375      12.59842520
1 / 4          0.25              6.35        15.74803150
3 / 16         0.1875            4.7625      20.99737533
1 / 8          0.125             3.175       31.49606299
pin-length:
1 / 16         0.0625            1.5875      62.99212598

shoe-ounce:
1 / 64         0.015625         0.396875      0.251968504
```

Back to Index

#### US-Survey = Old-USA

NOTE: the name 'US-Survey' does NOT mean 'Surveyor'!

The old measure system of the USA is still in use for the geodetic surveying, thus for cartography, land measurements and land surveillance. Hence it has been renamed to 'US-Survey'. It uses the same measure names as those in the Surveyor+Chain system. But the corresponding sizes are slightly bigger. It is based on the old value the foot had in the United States. This value had been defined as exactly 1200/3937 metric meters. Thus one meter is exactly 39.37 survey inches long. The number 3937 is a combination of two weird prime numbers: 3937 = 31 * 127

The old British foot was 1200000/3937014 meters long. This value is out of use nowadays. So no references are made to it.

A multiplication factor exists between both measure systems in the USA. This factor is exactly: (3937*254)/1000000 = 0.999998   herein 254/10000 being the length in meters of the Survey+Chain inch. So it holds exactly:

Surveyor+Chain-length = 0.999998 * US-Survey-length

Thus the most important linear US-Survey measures are:

```# centimeters      name            inverse
-------------      ----            -------
185318.7706375     naut.mile    0.5396107456140/km
160934.7218694     stat.mile    0.6213699494949/km
91.44018288037     yard         1.0936111111111/m
30.48006096012     foot         3.2808333333333/m
2.540005080010     inch            39.37[*] / m

999998  =  3937 * 254  =  31 * 127  *  127 * 2
```

The inverse of the multiplication factor is 1.000002000004000.   A very good approximation is 1.00000200. Thus the ratio US-Survey-measure / Surveyor+Chain-measure becomes:
1.000002 = 1+2.0@-6 for linear measures;
1.000004 = 1+4.0@-6 for square measures;
1.000006 = 1+6.0@-6 for cubic measures.

This leads to the very good approximations in the following table with examples wherein 'ordinary' means: Surveyor+Chain:

``` name              consists of                # metric
----              -----------                --------
US-Survey mile   1.000 00200 ordinary mile    1609.347 218 688 m
US-Survey-foot   1.000 00200 ordinary foot    0.3048 00 6096 m
US-Survey-inch   1.000 00200 ordinary inch    0.0254 000 508 m

US-Survey acre   1.000 00400 ordinary acre    4046.8726 09826 m2
square USur.mile 1.000 00400 square ord.mile  2.58 9998 47029 km2
square USur.yard 1.000 00400 square ord.yard  0.8361 3070 451 m2
square USur.foot 1.000 00400 square ord.foot  929.03411 61216 cm2

cubic int.mile   1.000 00600 cubic ord.mile   4 168 206 834.5 m3
```

##### The intended values were designed as:

```   name                      consists of
----                      -----------
circumference of          40227  kilometer
earth equator
-- idem --          360  degrees of earth equator
degree on earth equator      15  geographical leagues
-- idem --           20  marine leagues
geographical league           4  international miles
marine league                 3  international miles
international mile            1  minute of earth equator
-- idem --           10  ordinary cable-lengthes
internat. cable-length      608  ordinary feet
```

This table is not actually used, as some measure values rising from these intentions are slightly contradictory. Besides this one wants the translation of the measures into the metric system not to result into too awkward numbers. So the measure sizes have been adapted slightly. The international nautical mile is defined such that it consists of an integral number of metric meters. Since the same holds for the Canadian landmile this mile is added to the tables. Consequently:

##### The actual values have become:

```                                      metric equivalents:
name              consists of          # meters    inverse
----              -----------          --------    -------
geograph.league    4  nautical mile    7408        0.13498920 / km
marine league      3  nautical mile    5556        0.17998560 / km
old-Fr.mar.lieue   2.4 [*] naut.mile   4444.8[*]   0.22498200 / km
nautical mile     10  int.cable-len.   1852        0.53995680 / km
int.cable-length                        185.2[*]   5.39956803 / km
Canadian mile                          1609        0.62150404 / km
metric kilometer                       1000        1          / km
ordinary foot     12  ordinary inch    0.3048[*]   3280.839895 / km
US-Survey foot    12  USSurvey inch  0.3048006096  3280.833333 / km

Brit.naut. mile    1.000 6393   nautical mile     = 1853.184[*] m
nautical mile      0.999 3611   Brit.naut. mile   = 1852 meters
statute mile       1.000 2138   Canadian mile     = 1609.344[*] m
Canadian mile      0.999 78625  statute mile      = 1609 meters
```

[*] = This non-integral value is exact.

##### Number of feet

```name                 # US-Survey feet      # ordinary feet
----                 ----------------      ---------------
geograph.league      24304.4133333...      24304.4619423
marine league        18228.31 [*]          18228.3464567
old-Fr.mar.lieue     14582.648 [*]         14582.6771654
nautical mile         6076.1033333...       6076.1154856
int.cable-length       607.6103333...        607.6115486
metric kilometer      3280.8333333...       3280.8398950
Brit.naut. mile       6079.98784 [*]        6080
old-Brit.cable-len     607.998784 [*]        608
statute mile          5279.98944 [*]        5280
US-Survey foot           1                     1.00000200
ordinary foot            0.999998 [*]          1
metric meter            39.37 [*] USS-inch   39.37007874 inch
```

Meanings of symbols and abbreviations in this table:
[*] = this value is exact
333... = infinite sequence of the digit 3
ordinary = Surveyor+Chain+British-nautical
marine league = international nautical league
nautical mile = international nautical mile
old-Brit.cable-len = old British nautical cable-length
old-Fr.mar.lieue = old French lieue-maritime (=sea-league)

Other synonyms:
mi = abbreviation for any mile
admiralty mile = British nautical mile
geographical mile = air-mile = sea-mile = international nautical mile
short cable-length = international cable length
international foot = ordinary foot = Surveyor+Chain foot
international yard = ordinary yard = Surveyor+Chain yard
international-foot and -yard are the official names for the ordinary-foot and -yard.

Back to Index

#### COLLECTION OF MILES

There are several miles that are intended to be one sixtieth of the length of one degree on the earth equator. But many of them are approximations only. All have a length between 1852 and 1856 metric meters. So the earth degree is between 59.7 and 60.3 actual miles long. There are also several leagues that are intended to be one fifteenth or one twentieth of one earth degree, and thus contain three or four of such miles. Some of the miles and leagues are listed in the table below. Many of them are called "geographical". In formulas the abbreviation for a mile of any type is often 'mi'.

```name             consists of          # meters    inverse
----             -----------          --------    -------
---  values from above  ---
statute league    3  statute mile     4828.032    0.20712373 / km
statute mile     5280 ordinary foot   1609.344    0.62137119 / km
US-survey mile   5280 / 0.999998 foot 1609.34722  0.62136995 / km
old-UK-land-mile  5000 ordinary foot  1524        0.6561680 / km

geograph.league   4  Brit.naut.mile   7412.736    0.13490296 / km
Brit.naut.league  3  Brit.naut.mile   5559.552    0.17987061 / km
Brit.naut.mile   6080 ordinary foot   1853.184    0.53961182 / km

radar-data mile  6000 ordinary foot   1828.8      0.54680665 / km

Canadian mile                         1609        0.62150404 / km

int.geogr.league  4  int.naut. mile   7408        0.13498920 / km
int.naut.league   3  int.naut. mile   5556        0.17998560 / km
int.naut. mile                        1852        0.53995680 / km

old-Fr.sealeague  2.4 int.naut.mile   4444.8      0.22498200 / km

---  other modern values  ---
geograph.league   4  geograph. mile   7421.5912   0.13474199 / km
geograph. mile                        1855.3978   0.53896798 / km

geograph. mile   6087.2 ordin.foot    1855.37856  0.53897357 / km
geograph. mile                        1855.32572  0.53898892 / km
USA-nautic.mile  6080.2 ordin.foot    1853.245    0.53959407 / km
= earth-equator's minute

int.statute mile                      1609.347    0.62137003 / km
int.Survey mile  1852 x 1.000002 m.   1852.03704  0.53995572 / km
Telegraph mile                        1855.3176   0.53899128 / km

Irish mile       6720  ordinary foot  2048.256    0.4882202 / km

French post-league  2  French mile    3898.0872   0.2565361 / km
French mile      6000  French foot    1949.0436   0.5130715 / km

---  metrical  ---
Spanish league      5  kilometre      5000        0.2 / km
ordinary league     4  kilometre      4000        0.25 / km
USA-mile            1.6  kilometre    1600        0.625 / km
European mile       1.5  kilometre    1500        0.6666667 / km
kilometre                             1000        1 / km

---  old Roman values  ---      (metric approximation)
day's march      12.5[*] Roman mile   18500      0.054054054 / km
Roman mile       5000  Roman foot      1480       0.67567568 / km
```

Back to Index

#### Old British

The old British inch has the length of 2.53998 cm. So the multiplication factor for the linear old-UK measures is: 0.999 99213.    This factor has to be used in the same way as the factor in the old US-Survey system.

#### Canadian (Quebec) and Old French (Paris)

```  name             consists of       meaning of name
----             -----------       ---------------
lieue-de-poste      2  mille         post-league
mille            1000  toise         mile
arpent (linear)    10  perche        <- arepennis = ?
perche (linear)     3  toise         perch, log, beam
toise (='fathom')   4  coudee        <- tendre = stretch
passe de Haiti      3.5[*] pied      Haitian pace
coudee              1.5[*] pied      ell, ellbow
pied (de roi)      12  pouce         foot
pouce              12  ligne         thumb, inch
ligne              12  douzieme      line
douzieme                             one-twelfth
```

##### Metric equivalents

```abbr. #meters[*]        name                inverse
----- ----------        ----                -------
3898.0872         lieue-de-poste     0.2565361 / km
1949.0436         mille              0.5130715 / km
58.471308         (linear) arpent    0.01710238 / m
5.8471308         (linear) perche    0.1710238 / m
1.9490436         toise              0.5130715 / m
1.1369421         passe de Haiti     0.8795523 / m
0.4872609         coudee             2.052286 / m
0.3248406         pied (de roi)      3.078429 / m
0.02707005        pouce             36.94115 / m
2.2558375@-3      ligne            443.29380 / m
1.87986458333@-4  douzieme        5319.53210 / m
```

##### Anglo-Saxon equivalents

At present the exact definition of the arpent is 191.835 foot = 58.471308 meter. This leads to the following table:

```                        equals Anglo-Saxon:
name               foot [*]         yard [*]
----               -------------------------
lieue-de-poste       12789            4263
mille                 6394.5          2131.5
arpent (linear)        191.835         661+1/6
perche (linear)         19.1835
toise (='fathom')        6.3945
passe de Haiti           3.730125
coudee                   1.598625
pied (de roi)        12.789 inch
pouce                 1.06575 inch
ligne                 0.0888125 inch
```

#### Ireland and Wales

```name               consists of [*]        # feet
----               ---------------        ------
Ireland mile        8  Irish furlong       6720
Ireland furlong    10  Irish chain          840
Ireland chain       4  Irish perch           84
Ireland perch      21  ordinary foot         21
any Irish length = 14/11 (= 1.27272727...) English length

Welsh ridge         3  Welsh leap     81/4 = 20.25
Welsh leap       6 foot + 9 inch      27/4  = 6.75[*]
Jersey foot        11 inch            11/12 = 0.916667
Jersey foot        12 Jersey inch         11/12
Jersey inch                          11/144 = 0.0763889
```

##### Metric equivalents

```# meters[*]       name                 inverse
-----------       ----                 -------
2048.256          Irish mile           0.4882202 / km
256.032          Irish furlong        3.905762 / km
25.6032         Irish chain         39.05762 / km
6.4008         Irish perch          0.1562305 / m
6.1722         Welsh ridge          0.1620168 / m
2.0574         Welsh leap           0.4860504 / m
0.3048         ordinary foot        3.280840 / m
0.2794         Jersey-foot          3.579098 / m
0.02328333[~]  Jersey-inch         42.949177 / m
```

#### Russia

```name               consists of [*]        # feet
----               ---------------        ------
sadzhen = sagene    3  arshin                 7
arshin             28  inch                  7/3
arshin             16  vershok, verchok      7/3
vershok = verchok                             1.75[*] inch
```

##### Metric equivalents

```# meters[*]       name                 inverse
-----------       ----                 -------
1066.8        versta                 0.9373828 / km
2.1336        sadzhen, sagene        0.4686914 / m
0.7112        arshin                 1.406074 / m
0.04445       vershok = verchok      22.49719 / m
```

virsta = vehrsta = versta = verst = werst

#### Old Netherlands

```   name                   consists of
----                   -----------
amsterdam cable-length    120  amst. fathoms
amsterdam fathom            6  amst. feet
```

##### Metric equivalents and other values

```abbrev. # meters      name                 inverse
------  --------      ----                 -------
203.9     amsterdam cable-length   4.905 / km
1.699     amsterdam fathom         0.589 / m
0.283     amsterdam foot           3.534 / m
0.6858    old Dutch ell            1.458 / m
0.750     old Dutch step           1.333 / m
0.314858  old S.African Cape-foot  3.176035 / m
```

#### Metric meter

```        --- scientists' definition: ---
abbrev.  name     consists of
------   ----     -----------
m     meter    1 / 299 792 458 -th  part of
the length travelled by
the light in one second.
```

Back to Index

#### YARN AND TEXTILES

The lenght measures of yarn and textiles presented here fit into the the general length system. But for the sake of clarity they are not listed in the general lengths table, but they are in the separate tables of this chapter.

The general length units in these tables refer to the length units defined in the chapter Surveyor + Chain + British-nautical.

```name               consists of [*]     # yard [*]
----               ---------------     ----------
+++++  general for linen, cotton and wool  +++++
any linen-length  = 2.5 cotton-length with same name
any cotton-length = 1.5 wool-length with same name

bundle              20  hank
hank                 6  heer
heer                 2  cut
cut                wool:  46+2/3 yard       46.667[~]

hank                 7  skein
skein                1  lea, rap
lea = rap          wool:  80  yard          80

+++++  linen  +++++
bundle              20  hank             42000
hank                 6  heer              2100
heer                 2  cut                350
cut                175  yard               175

hank                 7  skein             2100
skein                1  lea, rap           300
lea = rap          200  French ell         300
French ell           3  cubit                1.5

+++++  cotton, silk, worsted  +++++
bundle              20  hank             16800
spindle             18  hank             15120
hank                 6  heer               840
heer                 2  cut                140
cut                 70  yard                70

hank                 7  skein              840
skein                1  lea, rap           120
lea = rap           80  cotton-thread      120
French ell           3  cubit                1.5

+++++  wool  +++++
bundle              20  hank             11200
hank                 6  heer               560
heer                 2  cut                 93.333[~]
cut                 46+2/3 yard             46.667[~]

US-hank             20  skein             1600
hank                 7  skein              560
skein                1  lea, rap, wrap      80
lea = rap = wrap    80  yard                80
yard                 2  cubit                1

+++++  lint, jute  +++++
spindle              4  hasp, hank       14400
hasp = hank          6  heer              3600
heer                 2  cut                600

+++++  general  +++++
gener.bolt-of-cloth  2.5[*] cotton-bolt    100
landcable-length     6  cotton-bolt        240
landcable-length     8  hank-of-cloth      240
cotton-bolt         20  fathom              40
hank-of-cloth       15  fathom              30
wool-, lint-bolt    35  fathom              70
yard                 2  cubit                1

# inch [*]
+++++  clothings  +++++           ----------
wool-bolt-width     20  palm-width          60
cotton-bolt-width   14  palm-width          42
palm-width           3  inch                 3

Scottish ell         4 + 1/9  span          37
French ell           6  span                54
English ell          5  span                45
yard                 4  span                36
Flemish ell          3  span                27

French ell           3  cubit               54
yard                 2  cubit               36
linear-quarter       1  span                 9
span                 2  finger-length        9
finger-length        2  nail                 4.5
nail                 2.25  inch              2.25
```

[~] = These few values are NOT exact !!
In earlier times the Scottish ell was 37.2[*] or 37.0598 inch long. At present it is redefined to exactly 37 inches.

##### Metric equivalents

```abbrev. # meters [*]     name                  inverse
------  ------------     ----                  -------
bdl    38404.8         linen-bundle          0.02603841 / km
bdl    15361.92        cotton-bundle         0.06509603 / km
13825.728       cotton-spindle        0.07232892 / km
13167.36        lint-spindle          0.07594537 / km
bdl    10241.28        wool-bundle           0.09764404 / km
3291.84        hasp                  0.30378147 / km
1920.24        linen-hank            0.52076824 / km
1463.04        US-wool-hank          0.68350831 / km
768.096       cotton-hank             1.301921 / km
548.64        lint-heer               1.822689 / km
512.064       wool-hank               1.952881 / km
320.04        linen-heer              3.124609 / km
274.32        lint-cut                3.645378 / km
274.32        linen-skein             3.645378 / km
274.32        linen-lea, -rap         3.645378 / km
219.456       (land) cable-length     4.556722 / km
160.02        linen-cut               6.249219 / km
128.016       cotton-heer             7.811524 / km
109.728       cotton-skein            9.113444 / km
109.728       cotton-lea, -rap        9.113444 / km
91.44        general-bolt-of-cloth  10.936133 / km
85.344       wool-heer              11.717285 / km
73.152       wool-skein             13.670166 / km
73.152       wool-lea,-rap,-wrap    13.670166 / km
64.008       cotton-cut             15.623047 / km
64.008       lint-bolt              15.623047 / km
42.672       wool-cut               23.434571 / km
36.576       cotton-bolt            27.340332 / km
27.432       hank-of-cloth          36.453777 / km
fath       1.8288      fathom                546.80665 / km
1.524       wool-bolt-width       656.16798 / km
Fr.e       1.3716      French ell            729.07553 / km
Eng.e      1.143       (English) ell         874.89064 / km
1.0668      cotton-bolt-width     937.38283 / km
Sc.e       0.9398      Scottish ell            1.064056 / m
yd         0.9144      yard                    1.093613 / m
Fl.e       0.6858      Flemish ell             1.458151 / m
0.4572      cubit                   2.187227 / m
ft         0.3048      foot                    3.280840 / m
qr         0.2286      span = linear-quarter   4.374453 / m
0.1143      finger-length           8.748906 / m
0.1016      hand                    9.842520 / m
0.0762      palm-width             13.123360 / m
nl         0.05715     nail                   17.497813 / m
in         0.0254      inch                   39.370079 / m
```

Back to Index

#### Yarn mass units

```abbr.  name     consists of            mass/meter
----   ----     -----------            ----------
tex       9  denier             1 mg/m = 1 g/km
tex      10  drex               1 mg/m = 1 g/km
drex      1  dtex               0.1 [*] mg/m
dtex (= deci-tex)               0.1 [*] mg/m
den   denier (= 1 g / 9 km)           0.11111 mg/m
poumar  1@-6 (avdp)pound/yard   0.49605465 mg/m

typp    1000 yard/(avdp)pound   2.01590693 m/g
US-run  1600 yard/(avdp)pound   3.22545108 m/g
```

#### Speed units

```abbrev.  unit                  meters/hour[*]    meters/sec
------   ----                  --------------    ----------
kph     kilometers per hour         1000        0.27777778
fps     feet per second             1097.28     0.3048 [*]
mph     statute miles per hour      1609.344    0.44704[*]
knot    internat. miles per hour    1852        0.51444444
(knot)   UK-nautic. miles per hour   1853.184    0.51477333
mps     meters per second           3600        1
Mach    speed of sound (typical) 1193760      331.6
```

[*] = This value is exact.
The speed of sound and so the Mach speed depends on the temperature and the pressure of the air. Here the value at 0 degree Celsius and 1 atmosphere is shown. Generally values from 1060 up to 1230 kph can occur in the air.
In Germany the abbreviation 'kph' is written 'kmh'.
Note that exactly holds:
1 kph = 5/18 mps
and     mph = 22/15 fps
and     knot = 463/900 mps,
and that roughly holds:
1 mps = 2 knots = 9/4 mph = 10/3 fps = 18/5 kph
and     1 mph = 1.5 fps
and     1 fps = 1.1 kph

Back to Index

### SQUARE MEASURES = AREAS

#### SURVEYOR + CHAIN + BRITISH-NAUTICAL

```  name               consists of [*]      # sq. yard [*]
----               ---------------      --------------
sq. geograf.league   16  sq. naut.mile    591462400/9
sq. naut.league       9  sq. naut.mile     36966400
sq. naut.mile       100  sq. cable-len.    36966400/9
sq. cable-length   369664  sq. foot          369664/9

hundred             100      hide          58080000
hide = carucate       4   virgate, yardland  580800
virgate = yardland    2     oxgang, bovate   145200
oxgang = bovate      15      acre             72600

hide = carucate       6      nook            580800
hundred               3      barony        58080000
barony               40      USA-hide      19360000
USA-hide              5      nook            484000

township          4  sq. land-league  111513600
sq. land-league       9  sq. (stat)mile    27878400
sq. (stat)mile        1      USA-section    3097600
USA-section       4    quarter-section  3097600
USA-lot           4      nook            387200
nook              2  sq. furlong          96800
sq. furlong          10      acre             48400
acre             10  sq. chain             4840
sq. chain            16  sq. pole, sq.perch     484
sq. perch = sq. pole  1  sq. rod              30.25
sq. rod             625  sq. link             30.25
sq. link             62.7264  sq. inch       0.0484

sq. (stat)mile      640      acre           3097600
Welsh-cover      2/3     acre             29040/9
acre              4      farthingdale      4840
farthingdale      1      rood              1210
rood             40  sq. rod, perch, pole  1210
sq. rod (sq.perch,
sq.pole)   121  sq. cubit            30.25

sq. fall            225  sq. cubit            56.25
sq. cubit             2.25  sq. foot     1/4 = 0.25

US-football-area  1600  sq. fathom            6400
commerc.acre   1000  sq. fathom            4000

sq. Ramden-chain    100      timber-square    10000/9
timber-square     1      square             100/9
square          100  sq. foot               100/9
(wallpaper-)roll   30  sq. foot                10/3

basebox    128*5*49=31360  sq.inch        1960/81

sq. chain           121  sq. fathom             484
sq. fathom            4  sq. yard                 4
sq. yard              9  sq. Ramden-link          1
sq. Ramden-link       1  sq. foot                 1/9
super(-ficial) foot  1  sq. foot                 1/9

sq. foot            144  sq. inch                 1/9
sq. inch                                       1/1296
```

[*] = All numeric values in this table are exact!
US-football-area = area of USA football field with end zones

##### Metric equivalents

```abbrev. # sq.meters          name                inverse
------- -----------          ----                -------
twp     93.2395720 @+6         township        0.01072506 / sq.km
54.9486550 @+6     sq. geograf.league  0.01819881 / sq.km
30.9086184 @+6     sq. nautic.league   0.03235344 / sq.km
23.3098930 @+6     sq. (land-)league   0.04290024 / sq.km
4.85622771 @+6         hundred          0.2059212 / sq.km
3.43429094 @+6     sq. nautic.mile      0.2911809 / sq.km
mi2     2.58998811 @+6     sq. (statute-)mile   0.3861022 / sq.km
2.58998811 @+6         USA-section      0.3861022 / sq.km
1.61874257 @+6         barony           0.6177635 / sq.km
647497.03             quarter-section  1.5444086 / sq.km
485622.77             hide = carucate  2.0592115 / sq.km
404685.64             USA-hide         2.4710538 / sq.km
323748.51             USA-lot          3.0888173 / sq.km
121405.69             virgate          8.2368460 / sq.km
121405.69             yardland         8.2368460 / sq.km
80937.13             nook             12.355269 / sq.km
60702.85             bovate = oxgang  16.473692 / sq.km
40468.56         sq. furlong          24.710538 / sq.km
5351.215         US-football-area     1.868734 / ha
ac,A       4046.856            acre              2.471054 / ha
3344.50944 [*]      commercial-acre   2.989975 / ha
2697.904            Welsh-cover       3.706581 / ha
1011.714            rood              9.884215 / ha
929.0304  [*]  sq. Ramden-chain     10.76391 / ha
404.6856       sq. chain            24.71054 / ha
47.032164     sq. fall            212.6205 / ha
25.29285      sq. pole, sq.perch  395.3686 / ha
rd2          25.29285      sq. rod             395.3686 / ha
20.2322176 [*]      basebox         494.2612 / ha
9.29 0304    [*]      timber-square     0.1076391 / sq.m
9.29 0304    [*]      square            0.1076391 / sq.m
3.3445 0944  [*]  sq. fathom            0.2989975 / sq.m
2.7870 912   [*]      (wallpaper-)roll  0.3587970 / sq.m
yd2      0.8361 2736  [*]  sq. yard              1.195990 / sq.m
0.2090 3184  [*]  sq. cubit             4.783960 / sq.m
super.ft 0.0929 0304  [*]      superficial-foot 10.76391 / sq.m
SF/ft2   0.0929 0304  [*]  sq. foot             10.76391 / sq.m
li2      0.0404 6856       sq. link             24.71054 / sq.m
in2      6.4516 sq.cm [*]  sq. inch              0.15500 / sq.cm

```

[*] = This value is exact.
The foot is the ordinary foot.
The ordinary link and chain are the Imperial ones by Gunter.

Back to Index

#### US-Survey

For the US-Survey square measures, read the section Linear measures: US-Survey + Int.Nautical.

#### Circular and international-nautical

A circular measure gives the area of the largest circle that fits completely inside the square with the corresponding name. Its value is pi/4 times the value of the square. Herein:
pi/4 = 0.7853981633975
Examples are the two circular units in the table below.

```    # sq.meters       name                 inverse
-----------       ----                 -------
54878464      sq. int.geograph.league  0.01822208 / km2
30869136      sq. int.nautical league  0.03239482 / km2
3429904      sq. int.nautical  mile   0.29155335 / km2
2693840.30   circular int.naut.mile   0.37121725 / km2
2034171.91   circular statute-mile    0.49160054 / km2
```

#### Old square values

```name               consists of [*]        # sq. feet
----               ---------------        ----------
Ireland acre       160  sq. Irish-perch    70560
Guernsey-vergee    6/7  Jersey-vergee      16594.286
Jersey-vergee   44 * 44 * 10  sq. foot   19360
Haitian carreau  10000  sq. Haitian-pace  139138.325
sq. Russ.arshin   49/9  sq. foot           5.4444444
South-Africa morgen  1 * 47 * 109 sq.yard  10246 yd2
Welsh stang          5 * 8 * 81 sq.yard     3240 yd2
```

##### Metric equivalents

```# sq. meters      name                 inverse
------------      ----                 -------
12926.373         Haitian carreau     0.7736122 / ha
8566.961          South-Africa morgen  1.167275 / ha
6555.2385024[*]   Irish acre           1.525498 / ha
2709.053          Welsh stang          3.691327 / ha
1798.603          Jersey-vergee        5.559871 / ha
1541.660          Guernsey-vergee      6.486516 / ha
5.0580544[*]  sq. arshin              0.1977045 / m2

5188.277465       Cunningham-acre    192.742198 / km2
5188.277465       plantation-acre    192.742198 / km2
4935.190759       Scotland-acre      202.626413 / km2
3418.89386    sq. Paris-arpent       292.492262 / km2
34.18894      sq. Paris-perch        292.492262 / hm2
4.088963      sq. Paris-toise        0.244560783 / m2
```

Back to Index

### CUBIC MEASURES = VOLUMES

#### SURVEYOR + CHAIN + BIG-CARGO

```   name                   consists of             # cu. foot
----                   -----------             ----------
++++  nautical & geodetic  ++++

cu. Br.naut.-mile      1000  cu. cable-length  224755712@+3
cu. cable-length      224755712 cu.foot        224755712

cu. (statute) mile      512  cu. furlong       147197952@+3
cu. furlong            1000  cu. chain            287496@+3
cu. chain              1331  cu. fathom           287496
cu. fathom                8  cu. yard                216
cu. yard                 27  cu. foot                 27

++++  transport  ++++

(volume-) rod         1      cunit              1000
cunit                 1      register-ton        100
register-ton          2.5[*] freight-ton         100
freight-ton           1      USA-shipping-ton     40
USA-shipping-ton      1      marine-ton           40
marine-ton            8      bulk-barrel          40
displacement-ton      7      bulk-barrel          35

forty-ft-e.u.         2      twenty-ft-e.u.     2560
twenty-ft-e.u.      256      sugar-barrel       1280
sugar-barrel          1      bulk-barrel           5
bulk-barrel           5  cu. foot                  5

UK-shipping-ton      14      garden-straw-bale    42

++++  wood and timber  ++++

London-standard      10  cu. yard                270
cu. fathom                2      stack               216
stack (coal,firewood) 4  cu. yard                108
cu. yard                 27  cu. foot                 27

freight-ton           2.5[*] cord-foot            40

twenty-ft-e.u.       10      cord               1280
cord                  2      face-cord           128
face-cord             4      cord-foot            64
cord-foot            16  cu. foot                 16

cord                  3      small face-cord    128
small face-cord       1      house-cord           42.66667
house-cord            1      rick, tier           42.66667
rick = tier         512      board-foot           42+2/3

cu. foot                 12      super(-ficial)-foot   1
super(-ficial) foot   1      board-foot            0.083333
board-foot          144 cu.inch = 1/12 cu.foot     1/12

London-standard      54      bulk-barrel         270
Riga-last-sq.sawn    16      bulk-barrel          80
Riga-last-round      13      bulk-barrel          65
bulk-barrel           5  cu. foot                  5

NorthAmerican-deal    2      whole-deal       2.2916666667
whole-deal            2      split-deal       1.1458333333
split-deal          990  cu. inch             0.5729166667

++++  others & general  ++++

masonry-perch   16.5 * 1.5 [*]  cu. foot          24.75[*]

mega-acre-foot     1000  kilo-acre-foot        4356 @ 7
kilo-acre-foot     1000      acre-foot         4356 @ 4
acre-foot            12      acre-inch         43560
acre-inch          3630  cu. foot               3630

garden-straw-bale     3  cu. foot                  3

bulk-barrel          60      board-foot            5
USA-dry-barrel       49      board-foot            4.083333
board-foot          144  cu. inch           1/12 = 0.083333

cu. foot               1728  cu. inch                  1
cu. inch                                         5.787037037@-4

note: 3630 = 11 * 11 * 10 * 3
1331 = 11 * 11 * 11
1728 = 12 * 12 * 12
```

[*] = This value is exact !
Forty-ft-e.u. = forty feet equivalent unit = long freight container. One such container fits on a lorry.
Twenty-ft-e.u. = twenty feet equivalent unit = short freight container. Two of these in series fit on a lorry.
Riga-last-sq.sawn = Riga last square-sawn.
Br.naut.-mile = British nautical mile.
Cable-length = land cable length.
Board-foot = feet-board measure.
The foot is the ordinary foot.
Displacement-ton approximates well the volume of the mass of one long ton of sea water. The volume of one long ton of fresh water is 35.84 cu.feet.
The bulk-barrel (= 8640 cu.in) and the USA-dry-barrel (= 7056 cu.in) are also mentioned in the section about the USA-dry volumes.

##### Metric equivalents

```abbrev.   # cubic meters     name              inverse
------    --------------     ----              -------
6.364373017380 km3  cu. Br.naut.mile    0.1571247 / cu.km
4.168181825441 km3  cu.(statute)mile    0.2399128 / cu.km
Maf       1.2334818 km3       mega-acre-foot    0.8107132 / cu.km
8140980.1        cu. furlong        122.83533 / cu.km
6364373.0        cu. cable-length   157.12467 / cu.km
kaf       1233481.8         kilo-acre-foot    810.7132 / cu.km
af,ac.ft  1233.4818            acre-foot      810.7132 / cu.hm
8140.9801        cu. chain          122.8353 / cu.hm
102.79015            acre-inch     9728.5583 / cu.hm
FEU       72.491127            forty-ft-e.u     0.01379479 / cu.m
TEU       36.245564            twenty-ft-e.u    0.02758958 / cu.m
28.316847            volume-rod       0.03531467 / cu.m
7.645549          London-standard    0.13079506 / cu.m
6.116439        cu. fathom           0.1634938 / cu.m
3.624556            cord             0.2758958 / cu.m
3.058219            stack            0.3269877 / cu.m
RT         2.831685            register-ton     0.3531467 / cu.m
2.831685            cunit            0.3531467 / cu.m
2.265348         Riga-last-sq.sawn   0.4414333 / cu.m
1.840595         Riga-last-round     0.5433026 / cu.m
1.812278            face-cord        0.5517917 / cu.m
1.208185         small face-cord     0.8276875 / cu.m
1.208185            house-cord       0.8276875 / cu.m
1.208185            rick = tier      0.8276875 / cu.m
1.189308          UK-shipping-ton    0.8408254 / cu.m
1.132674         USA-shipping-ton    0.8828666 / cu.m
FT         1.132674            freight-ton      0.8828666 / cu.m
1.132674            marine-ton       0.8828666 / cu.m
DT         0.9910896        displacement-ton    1.0089905 / cu.m
cy         0.7645549       cu. yard             1.3079506 / cu.m
0.7008420           masonry-perch    1.4268552 / cu.m
0.4530695           cord-foot        2.2071666 / cu.m
0.1415842           bulk-barrel      7.0629333 / cu.m
0.1415842           sugar-barrel     7.0629333 / cu.m
bbl        0.1156271         USA-dry-barrel     8.6484898 / cu.m
84.950540 cu.dm   garden-straw-bale  11.7715556 / cu.m
64.892773 cu.dm   NorthAmerican-deal 15.4100364 / cu.m
32.446387 cu.dm      whole-deal      30.8200728 / cu.m
ft3       28.316847 cu.dm  cu. foot            35.3146667 / cu.m
16.223193 cu.dm      split-deal      61.6401456 / cu.m
super.ft   2.359737 cu.dm      super-foot       0.4237760 / cu.dm
BF/fbm     2.359737 cu.dm      board-foot       0.4237760 / cu.dm
in3       16.387064 cu.cm [*]  cu. inch        61.0237441 / cu.dm
```

[*] = This value is exact !

Back to Index

#### USA DRY (fruit, wheat, etc.)

The USA-dry-volumes system has been derived from the old British dry-system. Therefore some old British striked (= not-heaped) dry-units are included in the tables. If such unit has the same name as an American unit, but a different size, then it is marked with the prefix OB = old-British.

```name            consists of         # cu.inch[*]    # gallon
----            -----------         ------------    --------
bulk-barrel    128.57 quart           8640             32.14
barrel         105.00 quart           7056             26.25

wey              5  quarter          86016.8         320

chaldron         4  fatt             77415.12         288
fatt             2  OB-barrel        19353.78          72
OB-barrel        9  bucket            9676.89          36

big sack         5  bushel           10752.1           40
fatt             3  bag              19353.78          72
bag = sack       3  bushel            6451.26          24

berries-tray     3  quartern           403.20375        3/2
trug-of-grain    2/3 bushel           1433.613333[~]   16/3

US-citrus:
field-box   10  US-c-box         34406.72         128
box          2  US-c-carton       3440.672         12.8[*]
carton       0.1 [*] quarter      1720.336          6.4[*]

tun = ton        2  Scott.quarter    68813.44         256
Scott.quarter    2  quarter, seam    34406.72         128
quarter = seam   2  coomb(e)         17203.36          64
coomb(e)         2  strike            8601.68          32
strike           2  bushel            4300.84          16
bushel           2  bucket            2150.42           8
bucket           2  peck              1075.21           4
peck             2  gallon             537.605          2
gallon           2  pottle, quartern   268.802 5        1
pottle=quartern  2  quart              134.401 25       1/2
quart            2  pint, chopine       67.200 625      1/4
pint = chopine   2  cup, demiard        33.600 3125     1/8
cup = demiard    2  gill, roquille      16.800 15625    1/16
gill = roquille                          8.400 078125   1/32
```

7056 = 144 * 49 .
[*] = All values in the cu.inch-column are exact, except the one indicated with [~].
The barrel and the bulk-barrel (= sugar barrel) belong to the cubic-measure system of Surveyor+Chain+Big-cargo. Therefore they are also mentioned in that section. Consequently their values 105.00 and 128.57 in the left column and their values 26.25 and 32.14 in the right column are not exact.

Gallon = Queen-Elisabeth-1 gallon = old-British corn-gallon = old-British grain-gallon.
Bushel = Winchester bushel of 1696. In spite of its name it has no relation to the Winchester quart. In early days the size of this bushel was exactly 2150 cubic inch. At present the size is 2150.42 cubic inch. The corresponding sizes of the gallon are: old = 268.75 in3, nowadays = 268.8025 in3.

Note the difference in the meanings of the very similarily spelled words Quart and Quarter.
Chalder = chaldron = chauldron = cauldron = large kettle.
Scott.quarter = Scottish quarter.
OB = old-British dry-system.

##### Metric equivalents

```abbrev.  # cu.dm     name              inverse
------   -------     ----              -------
2819.1256   last               0.3547199 / m3
1409.5628   wey                0.7094398 / m3
chal/chd 1268.6065   chaldron           0.7882665 / m3
1127.6502   tun = ton          0.8867998 / m3
563.82512   Scott.quarter      1.7735996 / m3
563.82512   US-citr.field-box  1.7735996 / m3
317.15163   fatt               3.153066 / m3
qtr/qr   281.91256   quarter = seam     3.547199 / m3
176.19535   big-sack           5.675519 / m3
158.57582   OB-barrel          6.306132 / m3
141.58423   bulk-barrel        7.062933 / m3
140.95628   coomb(e)           7.094398 / m3
bbl      115.62712   barrel             8.648490 / m3
sk       105.71721   bag = sack         9.459198 / m3
70.478140   strike            14.18880 / m3
56.382512   US-citrus-box     17.735996 / m3
bu(sh)   35.239070   bushel            28.37759 / m3
28.191256   US-citrus-carton  35.47199 / m3
23.492713   trug-of-grain     42.56639 / m3
17.619535   bucket            56.75519 / m3
pk       8.8097675   peck               0.1135104 / dm3
6.6073257   berries-tray       0.1513472 / dm3
gal      4.4048838   gallon             0.2270207 / dm3
2.2024419   pottle = quartern  0.4540415 / dm3
qt       1.1012209   quart              0.9080830 / dm3
pt       0.5506105   pint = chopine     1.816166 / dm3
0.2753052   cup = demiard      3.632332 / dm3
gi       0.1376526   gill = roquille    7.264664 / dm3
```

The exact value of the bushel is 35.239 070 166 88 litre.
OB = Old-British unit with same name as an USA-unit.

Back to Index

#### USA LIQUIDS-FLUIDS + APOTHECARY

The USA-liquids-volumes system has been derived from the old British wine-system. Therefore some old British wine-units are included in the tables. If such unit has the same name as an American unit, but a different size, then it is marked with the prefix OB = old-British.

```name                consists of       # gal/in3
----                -----------       ---------

+++++  trade and industry  +++++  # gallon
--------
oil-drum           55  gallon            55
oil-tanker  2 000 000 petroleum-barrel   84 @ 6
oil-barge      25 000 petroleum-barrel  105 @ 4
wine-puncheon       2 petroleum-barrel   84
petroleum-barrel    1  wine-tierce       42
wine-tierce         4  tenhalf           42
tenhalf            10.5 [*] gallon       10.5[*]

tun = ton           2  butt, pipe       252
butt = pipe         1  puncheon         126
wine-barrel         3  tenhalf           31.5[*]
tenhalf            10.5 [*] gallon       10.5[*]

beer-barrel         2  beer-keg          31
beer-keg            2  ponykeg           15.5[*]
ponykeg             7.75 [*] gallon       7.25[*]

tun = ton           3  tierce, tertian  252
tierce = tertian    1  thirdendel        84
thirdendel          1  wine-puncheon     84
wine-puncheon       2  wine-tierce       84
wine-puncheon       7  wine-keg          84
wine-keg           12  gallon            12

runlet = rundlet    1  kilderkin         18
kilderkin           2  firkin            18
firkin              2  pin                9
pin                 2  beer-case          4.5[*]
beer-case           9  quarts             2.25[*]
unit-case           6  quarts             1.5[*]

proof-spirit-barrel 4  anker             40
anker               2  sales-bucket      10
sales-bucket        5  flagon             5
flagon              1  gallon             1

++++++ domestic  +++++          # cu. inch
----------
gallon        3 * 7 * 11  cu.inch       231

gallon            160  OB-ounce         231

gallon              5  (wine-)fifth     231
(wine-) fifth       1  whiskey-bottle    46.2[*]
whiskey-bottle      2  can, (wine)tenth  46.2[*]
can = (wine-)tenth 16  OB-ounce          23.1[*]

gallon             32  gill, roquille   231
gill = roquille     5  OB-ounce           7.21875[*]
OB-ounce                                  1.44375[*]

gallon            128  ounce            231

gallon              6 champagne-bottle  231
champagne-bottle  64/3 = 21+1/3 ounce    38.5[*]

champagne-bottle   2/3 quart             38.5[*]
champagne-quart     1  wine-bottle       46.921875[*]
wine-bottle        26  ounce             46.921875[*]
soda-bottle        12  ounce             21.65625[*]

gallon              2  pottle           231
pottle              2  milk-bottle      115.5[*]
milk-bottle         1  quart             57.75[*]
quart               2  pint, chopine     57.75 [*]
pint = chopine      2  OB-chopin         28.875 [*]
OB-chopin           1  cup, demiard      14.4375[*]
cup = demiard       1  tumbler, glass    14.4375[*]
tumbler = glass     2  quartern          14.4375[*]
quartern            1  wine-glass         7.21875[*]
wine-glass          1  butter-stick       7.21875[*]
butter-stick        1  gill, roquille     7.21875[*]
gill = roquille     2  double             7.21875[*]
double              2  ounce              3.609375[*]
ounce                                     1.8046875[*]

+++++  cans  +++++

number-10-can     105  ounce            189.4921875[*]
number-5-can        7  cup = 56 oz      101.0625[*]
number-3-can        4  cup = 32 oz       57.75[*]
number-2.5-can      3.5[*] cup = 28 oz   50.53125[*]
number-2-can       19  ounce             34.2890625[*]
number-1-can       10  ounce             18.046875[*]
cup                 8  ounce  = 2 gill   14.4375[*]

+++++  apothecary and cooking  +++++

ounce               1  shot, pony         1.8046875[*]
shot = pony         1  coffeemeasure      1.8046875[*]
coffeemeasure       2  bartender-count    1.8046875[*]
bartender-count     1  tablespoon         0.90234375[*]
tablespoon          2  papspoon           0.90234375[*]
papspoon            2  bart.teaspoon      0.451171875[*]
bart.teaspoon       1  dram               0.22558594
dram                3  scruple            0.22558594
scruple             1  saltspoon          0.075195313
saltspoon           2  pinch, smite       0.075195313
pinch = smite       2  dash               0.037597656
dash                5  drop               0.018798828
drop                1  minim              0.003759766
minim                                     0.003759766

dash                6  old-kitchen-drop   0.018798828
old-kitchen-drop                          0.003133138

ounce               3  dessertspoon       1.8046875[*]
tablespoon          3  teaspoon           0.90234375[*]
dessertspoon        2  teaspoon           0.6015625[*]
teaspoon            2  coffeespoon        0.30078125[*]
coffeespoon         2  saltspoon          0.150390625[*]
saltspoon           1  scruple            0.075195313
scruple            20  drop               0.075195313
drop                                      0.003759766

+++++  bartender (= bart. = b.)  +++++

soda-bottle        12  ounce  = 3 gill   21.65625[*]

soda-bottle         2  soda-split        21.65625[*]
soda-split          2  b.snit            10.828125[*]
b.snit              2  b.jigger           5.4140625[*]
b.jigger            4  b.tablespoon       2.70703125[*]
b.tablespoon        3  b.teaspoon         0.67675781

b.jigger            1.5[*]  shot, pony    2.70703125[*]
b.shot              1.25[*] shot, pony    2.255859375[*]
shot, pony          1  ounce              1.8046875[*]
ounce               2  b.count            1.8046875[*]
b.count             4  b.teaspoon         0.90234375[*]
b.teaspoon          1  dram (drachm)      0.22558594
dram (drachm)       4  b.dash, b.splash   0.22558594
b.dash = b.splash                         0.05639648
```

[*] = This value is exact.
Note: 1 gill = 4 ounce (not 5 as in UK-Imperial and Old-British-Beer).
A Minim is roughly the size of one droplet of water.
Gallon = 1707 Queen-Anne's wine gallon.
OB = old-British wine-system.
Tenhalf = unit invented by the author.
Oil-tanker = roughly the size of most crude-oil super-tank-ships.
Petroleum-barrel = oil-barrel = the famous volume-unit used by the oil producing and exporting countries (OPEC) when determinating the price of crude oil.

##### Metric equivalents

```abbrev. # cu.dm           name            inverse
------  -------           ----            -------
317974600  crude-oil super-tanker 3.144905 / hm3
3974682.4       petr.oil-barge    251.5924 / hm3
953.9238        tun = ton         1.048302 / m3
476.9619        butt = pipe       2.096604 / m3
pun(ch) 476.9619        puncheon          2.096604 / m3
317.9746        tierce, tertian   3.144905 / m3
317.9746        thinderdel        3.144905 / m3
317.9746        wine-puncheon     3.144905 / m3
hhd/hka 238.4809        hogshead          4.193207 / m3
208.1976        oil-drum          4.803128 / m3
158.9873        wine-tierce       6.289811 / m3
bo/bbl  158.9873        petrol.-barrel    6.289811 / m3
151.4165     proof-spirit-barrel  6.604301 / m3
bbl     119.2405        wine-barrel       8.386414 / m3
bbl     117.3478        beer-barrel       8.521679 / m3
68.13741        run(d)let        14.67623 / m3
68.13741        kilderkin        14.67623 / m3
58.67388        beer-keg         17.04336 / m3
45.42494        wine-keg         22.01434 / m3
39.746824       tenhalf          25.15924 / m3
ank     37.854118       anker            26.41721 / m3
fir     34.068706       firkin           29.35245 / m3
29.33694133     ponykeg          34.08672 / m3
18.92705892[*]  sales-bucket     52.83441 / m3
17.03435303     pin              58.70490 / m3
8.517176514[*]  beer-case         0.11740980 / dm3
5.678117676[*]  unit-case         0.17611470 / dm3
3.785411784[*]  flagon            0.26417205 / dm3
gal     3.785411784[*]  gallon            0.26417205 / dm3
3.105220604     number-10-can     0.32203831 / dm3
1.892705892[*]  pottle            0.52834410 / dm3
1.656117656     number-5-can      0.60382183 / dm3
0.946352946[*]  number-3-can      1.05668821 / dm3
0.946352946[*]  milk-bottle       1.05668821 / dm3
qt      0.946352946[*]  quart             1.05668821 / dm3
0.828058828     number-2.5-can    1.2076437 / dm3
0.768911769     wine-bottle       1.300539 / dm3
0.768911769     champagne-quart   1.300539 / dm3
0.7570823568[*] fifth             1.320860 / dm3
0.7570823568[*] whiskey-bottle    1.320860 / dm3
0.630901964     champagne-bottle  1.585032 / dm3
0.561897062     number-2-can      1.779685 / dm3
pt      0.473176473[*]  pint = chopine    2.113376 / dm3
can     0.378541178     can               2.641721 / dm3
0.354882355     soda-bottle       2.817835 / dm3
0.295735296     number-1-can      3.381402 / dm3
0.236588237     OB-chopin         4.226753 / dm3
0.236588237     cup = demiard     4.226753 / dm3
0.236588237     tumbler = glass   4.226753 / dm3
0.177441177     soda-split        5.635670 / dm3
gi      0.118294118     gill = roquille   8.453506 / dm3
0.118294118     wine-glass        8.453506 / dm3
0.118294118     butter-stick      8.453506 / dm3
0.118294118     quartern          8.453506 / dm3
0.088720589     bartender-snit   11.27134 / dm3
0.059147059     double           16.90701 / dm3
0.044360294     bartender-jigger 22.54268 / dm3
0.036966912     bartender-shot   27.05122 / dm3
0.029573530     shot = pony      33.81402 / dm3
0.029573530     coffeemeasure    33.81402 / dm3
fl.oz   0.029573530     ounce            33.81402 / dm3
0.023658824     OB-ounce         42.26753 / dm3
14.78676 cu.cm  bart.-count      67.62805 / dm3
tblsp   14.78676 cu.cm  tablespoon       67.62805 / dm3
11.09007 cu.cm  bart.-tablespoon 90.17073 / dm3
dssp    9.857843 cu.cm  dessertspoon    101.44207 / dm3
7.393382 cu.cm  papspoon        135.25609 / dm3
tsp     4.928922 cu.cm  teaspoon        202.88414 / dm3
fl.dr   3.696691 cu.cm  dram            270.51218 / dm3
3.696691 cu.cm  bart.-teaspoon  270.51218 / dm3
2.464461 cu.cm  coffeespoon     405.76827 / dm3
ssp     1.232230 cu.cm  saltspoon       811.53654 / dm3
1.232230 cu.cm  scruple         811.53654 / dm3
0.92417280 cm3  bartender-dash    1.082049 / cm3
0.92417280 cm3  bart.-splash      1.082049 / cm3
0.61611520 cm3  pinch = smite     1.623073 / cm3
0.30805760 cm3  dash              3.246146 / cm3
gt/ggt  0.061611520 cc  drop             16.23073 / cm3
min     0.061611520 cc  minim            16.23073 / cm3
0.051342933 cc  old-kitchen-drop 19.47688 / cm3
```

bo = barrel of oil.
bbl = brl = bl = barrel (general).
tblsp = tbsp = Tsp = tablespoon.
gt = ggt = gutta = Latin word for drop.
hm3 = cu.hm = cubic hectometer = 1 000 000 000 litre.
cc = cm3 = cu.cm = cubic centimeter = 0.001[*] litre.
OB = Old-British-wine unit with same name as an USA-unit.
In early British times the gallon was ca. 0.18 cu.inch bigger: 3.7884 liters.

#### Water, the ultimate fluid

The volume of the transparent water can on top of the water coolers in offices and convenience shops is one sales-bucket. Everyday people should drink at least half a gallon = 8 glasses of water or 'thin' non-alcoholic beverages (e.g. lemon-juice, not thick lentil-soup); when sporting much much more, maybe one or even two gallons a day!    The best and cheapest sports-drink is the humble water.

Back to Index

#### BRITISH IMPERIAL (FLUID and DRY)

```name             consists of      # gallon
----             -----------      --------

wine-bottle      80/3  ounce       1/6 = 0.16666...
reputed-quart     2 reputed-pint   1/6 = 0.16666...
reputed-pint      1/3  quart      1/12 = 0.083333..

herrings-cran    37.5 [*]  gallon     37.5[*]

wine-butt        12  tenhalf         126
tierce            4  tenhalf          42
wine-barrel       3  tenhalf          31.5[*]
tenhalf          10.5 [*] gallon      10.5[*]

butt = pipe       2  hogshead        108

chaldron          4  fatt            288
fatt              2  barrel           72
barrel            2  runlet, rundlet  36
runlet=rundlet    1  kilderkin        18
kilderkin         2  firkin           18
firkin            2  pin               9
pin               4.5 [*] gallon       4.5[*]

last              2  wey             640

puncheon          7  anker            70
alcohol-barrel    5  anker            50
big sack          4  anker            40
anker             5  peck             10

chaldron          9  coomb(e)        288
water-ton         7  coomb(e)        224
coomb(e)          4  bushel           32
fatt              3  bag, sack        72
boll              2  bag, sack        48
bag = sack        2  firlot           24
firlot            1.5 [*] bushel      12
big sack          5  bushel           40

heaped bushel     1.278 bushel        10.224

Scott.chalder     2  tun, ton        512
tun = ton         2  Scott.quarter   256
Scott.quarter     2  seam            128
seam              1  (dry) quarter    64
(dry) quarter     2  amber            64
amber             1  coomb(e)         32
coomb(e)          2  strike           32
strike            2  bushel           16
bushel            2  bucket            8
bucket            2  peck              4
peck              2  gallon            2
gallon          277.42 cu. inch        1

+++++  domestic  +++++        # cu. inch
----------
gallon            1  congius         277.4194327916
congius           2  pottle          277.4194327916
pottle            1  dry-quartern    138.7097
dry-quartern      2  quart           138.7097
quart             2  pint, chopine    69.35486

pint = chopine    1  octarius         34.67743
octarius          2  old-chopin       34.67743
old-chopin        1  breakfast-cup    17.33871
breakfast-cup     1  tumblerful       17.33871
tumblerful        1  Australian middy 17.33871
Austral. middy    2  gill, roquille   17.33871
gill = roquille   1  noggin, teacup    8.669357
noggin = teacup   1  fluid-quartern    8.669357
fluid-quartern    2  wineglass         8.669357
wineglass         2.5[*] ounce         4.334679
small-teacup      3  ounce             5.201614
small-wineglass   2  ounce             3.467743

pint              3  large-teacup     34.67743
large-teacup                          11.559143

ounce             2  tablespoon        1.733871
tablespoon        2  dessertspoon      0.8669357
dessertspoon      2  teaspoon          0.4334679
teaspoon          1  drachm (dram)     0.2167339
drachm (dram)     3  scruple           0.2167339
scruple           1  coffeespoon       0.07224464
coffeespoon      20  drop              0.07224464
drop              1  minim             0.003612232
minim                                  0.003612232

scruple          24  old-kitchen-drop  0.07224464
old-kitchen-drop                       0.0030101935

wineglass         3  nip, pub-tot      4.334679
nip = pub-tot                          1.444893
wineglass         4  medic.tablespoon  4.334679
med.-tablespoon   4  medical-teaspoon  1.083670
medical-teaspoon                       0.2709174
```

[*] = This value is exact.
Note: 1 gill = 5 ounce (not 4 as in USA-fluid).
A Minim is roughly the size of one droplet of water.
Dry-quartern = Winchester-quart. In spite of its name it has no relation to the Winchester-bushel.
Note the difference in the meanings of the very similarly spelled words Quart, Quarter and Quartern.
Med. = medi. = medic. = medical .
Chalder = chaldron = chauldron = cauldron = large kettle.
Tenhalf = unit invented by the author.
The Scottish volumes are dry-general.

##### Metric equivalents

```abbrev.    # cu.dm        name             inverse
------     -------        ----             -------
2909.4976[*]     last             0.34370195 / m3
2327.59808[*]    Scottish-chalder 0.42962744 / m3
1454.7488[*]     wey              0.6874039 / m3
chal/chd 1309.27392[*]    chaldron         0.7637821 / m3
1163.79904[*]    tun              0.8592549 / m3
1163.79904[*]    ton              0.8592549 / m3
1018.32416[*]    water-ton        0.9820056 / m3
581.89952[*]    Scottish-quarter 1.718510 / m3
572.80734[*]    wine-butt        1.745788 / m3
490.97772[*]    butt             2.036753 / m3
490.97772[*]    pipe             2.036753 / m3
327.31848[*]    fatt             3.055128 / m3
pun(ch)   318.2263[*]     puncheon         3.142418 / m3
qtr/qr    290.94976[*]    (dry) quarter    3.437020 / m3
290.94976[*]    seam             3.437020 / m3
hhd       245.48886[*]    hogshead         4.073505 / m3
hhd       238.669725[*]   wine-hogshead    4.189890 / m3
227.3045[*]     alcohol-barrel   4.399385 / m3
218.21232[*]    boll             4.582693 / m3
190.93578[*]    tierce           5.237363 / m3
181.8436[*]     big sack         5.499231 / m3
170.478375[*]   herrings-cran    5.865847 / m3
bbl/bl    163.65924[*]    barrel           6.110257 / m3
145.47488[*]    amber            6.874039 / m3
145.47488[*]    coomb(e)         6.874039 / m3
143.201835[*]   wine-barrel      6.983151 / m3
sk        109.10616[*]    sack             9.165385 / m3
109.10616[*]    bag              9.165385 / m3
run       81.82962[*]     run(d)let       12.22051 / m3
81.82962[*]     kilderkin       12.22051 / m3
72.73744[*]     strike          13.74808 / m3
54.55308[*]     firlot          18.33077 / m3
47.733945[*]    tenhalf         20.94945 / m3
46.479224       heaped bushel   21.51499 / m3
ank       45.4609[*]      anker           21.99692 / m3
fir       40.91481[*]     firkin          24.44103 / m3
bu(sh)    36.36872[*]     bushel          27.49616 / m3
20.457405[*]    pin             48.88206 / m3
18.18436[*]     bucket          54.99231 / m3
pk        9.09218[*]      peck           109.98462 / m3
gal       4.54609[*]      gallon           0.21996925 / dm3
4.54609[*]      congius          0.21996925 / dm3
2.273045[*]     pottle           0.4399385 / dm3
2.273045[*]     dry-quartern     0.4399385 / dm3
qt        1.1365225[*]    quart            0.8798770 / dm3
0.75768167      reputed-quart    1.3198155 / dm3
0.75768167      wine-bottle      1.3198155 / dm3
pt        0.56826125[*]   pint             1.759754 / dm3
0.56826125[*]   chopine          1.759754 / dm3
0.56826125[*]   octarius         1.759754 / dm3
0.37884083      reputed-pint     2.639631 / dm3
0.2841306       old-chopin       3.519508 / dm3
0.2841306       breakfast-cup    3.519508 / dm3
0.2841306       tumblerful       3.519508 / dm3
0.2841306       Austral. middy   3.519508 / dm3
0.1894204       large-teacup     5.279262 / dm3
gi        0.1420653       gill             7.039016 / dm3
0.1420653       noggin           7.039016 / dm3
0.1420653       roquille         7.039016 / dm3
0.1420653       fluid-quartern   7.039016 / dm3
0.1420653       teacup           7.039016 / dm3
0.08523919      small-teacup    11.731693 / dm3
0.07103266      wineglass       14.07803 / dm3
0.056826125[*]  small-wineglass 17.59754 / dm3
fl.oz     0.02841306      ounce           35.19508 / dm3
0.02367755      nip             42.23410 /dm3
0.02367755      pub-tot         42.23410 /dm3
0.01775816      med.tablespoon  56.31213 / dm3
tbsp/Tsp  0.01420653      tablespoon      70.39016 / dm3
dssp/dsp  7.103266 cu.cm  dessertspoon   140.7803 / dm3
4.439541 cu.cm  medi.teaspoon  225.2485 / dm3
tsp       3.551633 cu.cm  teaspoon       281.5606 / dm3
fl.dr     3.551633 cu.cm  drachm (dram)  281.5606 / dm3
1.183878 cu.cm  scruple        844.6819 / dm3
gt/ggt  0.05919388 cu.cm  drop            16.89364 / cu.cm
min     0.05919388 cu.cm  minim           16.89364 / cu.cm
0.04932823 cu.cm old-kitchen-drop 20.27237 / cu.cm
```

Back to Index

#### OLD BRITISH-BEER

```name                consists of      # gallon
----                -----------      --------
tun = ton           2  pipe, butt     216
pipe = butt         2  beer-hogshead  108
puncheon = tertian  2  beer-barrel     72
beer-barrel         2  kilderkin       36
kilderkin           2  firkin          18
firkin              9  gallon           9

ale-barrel         34  gallon          34

strike              2  bushel          16
bushel              8  gallon           8

# cu.inch[*]
------------
gallon        2 * 3 * 47  cu.inch     282
gallon              2  pottle         282
pottle              2  quart          141
quart               2  pint            70.5
pint                2  (old)-chopin    35.25
(old)-chopin        2  gill            17.625
gill                5  ounce            8.8125
ounce                                   1.7625
```

[*] = These values are exact.
Note: 1 gill = 5 ounce (not 4 as in USA-fluid).

##### Metric equivalents

```abbrev.   # cu.dm    name          inverse
------    -------    ----          -------
998.1688    tun = ton     1.001835 / m3
499.0844    pipe = butt   2.003669 / m3
pun(ch)  332.7229    puncheon      3.005504 / m3
332.7229    tertian       3.005504 / m3
hhd      249.5422    beer-hogshead 4.007338 / m3
bbl      166.3615    beer-barrel   6.011007 / m3
157.1192    ale-barrel    6.364596 / m3
83.18074    kilderkin     12.02201 / m3
fir      41.59037    firkin        24.04403 / m3
73.93843    strike        13.52477 / m3
bu(sh)   36.96922    bushel        27.04953 / m3
gal      4.621152    gallon        216.3963 / m3
2.310576    pottle        432.7925 / m3
qt       1.155288    quart         865.5850 / m3
pt      0.5776440    pint          1.731170 / dm3
0.2888220    (old)-chopin  3.462340 / dm3
gi      0.1444110    gill          6.924680 / dm3
fl.oz  0.02888220    ounce         34.62340 / dm3
```

To construct the conversion-to-metrics table the size of the cubic present-day-inch is taken and not that of an cubic old-inch.
Thus the exact value of the gallon is 4.621 152 048 litre.
The official name for this gallon is Queen-Elizabeth-1 gallon.

Back to Index

#### Large wine-bottles

Large wine-bottles often have been christened with the names of old-testamentical priests and kings. These are:

```               # wine-         #  m i l l i l i t e r s
name           bottles    USA-fluid     UK-Imperial    Metric
----           -------    ---------     -----------    ------
picolo, split     1/4      192.22794      189.42042    187.5[*]
quarter-bottle    1/4      192.22794      189.42042    187.5[*]
chopine           1/3      256.30392      252.56056      250
demi              1/2      384.45588      378.84083      375
UK-reputed-pint   1/2         --          378.84083       --
metric tenth      1/2         --             --          375

metric fifth       1          --             --          750
UK-reputed-quart   1          --          757.68167       --
US-champag.quart   1       768.91177         --           --
standard           1       768.91177      757.68167      750
magnum             2      1537.8235      1515.3633      1500
marie-jeannne      3      2306.7353      2273.045[*]    2250
UK-half-gallon     3          --         2273.045[*]      --
UK-pottle          3          --         2273.045[*]      --
double-magnum      4      3075.6471      3030.7267      3000
jeroboam           4      3075.6471      3030.7267      3000
'metric one-th'    5          --             --         3750
bordeaux-jeroboam  6      4613.4706      4546.09[*]     4500
rehabeam,rehoboam  6      4613.4706      4546.09[*]     4500
UK-gallon          6          --         4546.09[*]       --
imperial           8      6151.2941      6061.4533      6000
methusalah         8      6151.2941      6061.4533      6000
salmanazar        12      9226.9412      9092.18[*]     9000
UK-peck           12          --         9092.18[*]       --
balthasar         16     12302.588      12122.907      12000
melchior          24     18453.882      18184.36[*]    18000
UK-bucket         24          --        18184.36[*]       --
solomon           28     21529.530      21215.087      21000
sovereign       100/3    25630.392      25256.056      25000
primat            36     27680.824      27276.54[*]    27000
melchizedek       40     30756.471      30307.267      30000

--BASIC UNITS--
gallon             -   3785.411784[*]    4546.09[*]       --
ounce              -     29.573530      28.4130625[*]     30
gallon             -     128 ounce       160 ounce        --
stand.wine-bottle  1      26 ounce    26+2/3 ounce    25 ounce
```

Note:
The metric one-th bottle does not exist actually.
UK-imperial bottle is about 1% larger than Metric bottle.
USA-fluid bottle is about 2.5% larger than Metric bottle.

#### US-Survey

For the US-Survey cubic measures, read the section Linear measures: US-Survey + Int.Nautical.

#### International-nautical

```abbrev. #cu.kilometer[*]    name                inverse
------  ----------------    ----                -------
406.539661312    cu. geograph. league   0.0024597846 / km3
171.508919616    cu. marine league      0.0058306005 / km3
cubim     6.352182208    cu. int.naut. mile     0.1574262147 / km3
```

#### Quebecois and Old-Parisian

```# liters    name                           inverse
--------    ----                           -------
1439.661    volume tonneau = 42 cu.pied    0.6946080 / m3
34.27764    cubic pied                     29.17354 / m3
```

Back to Index

#### GASOLINE CONSUMPTION BY A CAR

The distance a motorcar can travel on one volume unit of gasoline is expressed in Miles per Gallon or in Kilometers per liter. The table lists the conversion factors between these consumption rates.

```                              E  Q  U  A  L  S
| kilometers | miles per  | miles per  |
| per liter  | USA-gallon | UK-gallon  |
-----------------+------------+------------+------------+
D   kilometres  |            |            |            |
I   per litre   |      1     |  2.352146  |  2.824809  |
S  -------------+------------+------------+------------+
T   miles per   |            |            |            |
A   USA-gallon  | 0.4251437  |      1     |  1.200950  |
N  -------------+------------+------------+------------+
C   miles per   |            |            |            |
E   UK-gallon   | 0.3540062  | 0.8326742  |      1     |
-----------------+------------+------------+------------+
```

1 kilometre per litre = 2.352146 mile per USA-gallon.
1 mile per UK-gallon = 0.3540062 kilometre per liter.
Examples:
24 mile per USA-fluid-gallon = 24 * 0.4251437 kilometre per litre = 10.20 kilometer per liter
30 miles / UK-gallon = 10.62 kilometre / litre

Herein is:
UK-gallon = Imperial gallon
USA-gallon = USA-liquid gallon
1 mile = 1 land-mile = 1 statute-mile = 1.609344[*] kilometer

Back to Index

### MASSES = "WEIGHTS"

#### AVOIRDUPOIS - GENERAL

The tables in this section only list the Avoirdupois weight units that are generally used. Several units used in specific branches of trade and industry are listed in the specials section.

##### Long and Short weights

```abbrev.       British name    USA-name            # pounds
------        ------------    --------            --------
++++++++ long weights ++++++++
ton             long ton              2240
U-L-quarter    -              long quarter           560
hundredweight   long hundredweight     112
B-L-quarter   long quarter     -                      28
st            stone            -                      14
long assay-ton   -                   0.07202

++++++++ short weights +++++++
short ton       ton                   2000
U-S-quarter    -              short quarter          500
cental          short hundredweight    100
B-S-quarter   short quarter    -                      25
st             -              wool-stone              12.5[*]
-              short assay-ton      0.06430

++++++++ small weights +++++++
lb.avdp       pound           pound           7000 troy grain
gr         troy grain      troy grain    0.064 798 91 [*] gram

-  = no name
```

Single-letter abbreviations:
U-L = USA-long; U-S = USA-short;
B-L = British-long; B-S = British-short.
Example: B-L-quarter = British-long-quarter.
Quarter, another word is Quartermass.

NOTE: In ancient times 'hundred' meant every number between 100 and 120.    Great-hundred = 120.

##### Inter-dependencies

```     name              consists of            # pounds
----              -----------            --------
+++++++ long + Brit. weights +++++++
U-L-quarter        7776  long assay-ton        560
long assay-ton      112  assay-element       0.07202

long ton              4  U-L-quarter          2240
U-L-quarter           5  coal-sack             560
coal-sack             1  long hundredweight    112
long hundredweight    2  (general) truss       112
(general) truss       1  firkin                 56
firkin                2  B-L-quarter            56
B-L-quarter           1  (wool-) tod            28
(wool-) tod           2  stone                  28
stone                 2  (wool-) clove          14

bushel                9  (wool-) clove          63
(wool-) clove         1  brick                   7
brick                 2  quartern                7
quartern              3.5  pound                 3.5[*]

wey                   9  B-L-quarter           252
B-L-quarter           7  loaf-quartern          28
Scottish stone        4  loaf-quartern          16
loaf-quartern         4  pound                   4

box                   9  gallon                 90
frail (-of-raisins)   5  gallon                 50
score                 2  (Imp.) gallon          20
(Imp.) gallon         2  block                  10
block                 5  pound                   5

head                 6+3/4 = 27/4 pound          6.75[*]

+++++++ short + USA. weights +++++++
U-S-quarter        7776  short assay-ton       500
short assay-ton     100  assay-element       0.06430

short ton             2  kip (= kilopound)    2000
kip (= kilopound)     2  U-S-quarter          1000
U-S-quarter           5  cental                500
cental                1  quintal               100
quintal               1  short hundredweight   100
short hundredweight   4  B-S-quarter           100
B-S-quarter           2  USA-wool-stone         25
USA-wool-stone        2.5 [*] block             12.5[*]
block                 5  pound                   5

elvis                51  block                 255

# troy grains
-------------
++++++++++ physics weights +++++++++
slinch = snail       12  slug              2702620.08
slug                  1  geepound           225218.34
geepound             32.174049  pound       225218.34

+++++++++++ small weights ++++++++++
pound                 2  marc, marco          7000
marc = marco          2  US-butter-stick      3500
US-butter-stick       4  ounce                1750

ounce                16  dram (drachm)         437.5 [*]
dram (drachm)        27.34 375 [*]  troy grain

ounce                18  scruple               437.5 [*]
dram (drachm)       9/8 = 1.125[*]  scruple
scruple              24.30 555 556  troy grain

assay-element       4.501 0288 066  troy grain

(Avdp-)pound       7000  troy grain           7000
troy grain      64.798 91 [*] milligram          1
```

Factorial: 7776 = 6 * 6 * 6 * 6 * 6
The name 'assay-element' is invented by the author.

##### Metric equivalents

```abbrev. # kilograms             name           inverse
------  -----------        --------------      -------
dwt     1016.04690         deadweight-ton      0.9842065 / t
tn/t    1016.04690         (long,Brit.) ton    0.9842065 / t
sh.tn/t  907.18474[*]      (short,US) ton      1.102311 / t
kip      453.59237[*]      kilopound           2.204623 / t
qtr/qr   254.0117          U-L-quarter         3.936826 / t
qtr/qr   226.7962          U-S-quarter         4.409245 / t
175.12683525      slinch = snail      5.710147 / t
115.6661          elvis               8.645579 / t
wey      114.3053          wey                 8.748502 / t
50.80235         coal-sack          19.68413 / t
cwt       50.80235      long-hundredweight    19.68413 / t
cwt/ctl   45.359237[*] short-hundredweight    22.04623 / t
ctl       45.359237[*]     cental             22.04623 / t
ctl       45.359237[*]     quintal            22.04623 / t
40.8233133[*]    box                24.49581 / t
28.576319        bushel             34.99401 / t
25.401173        truss (general)    39.36826 / t
25.401173        firkin             39.36826 / t
14.59390294      geepound = slug    68.52177 / t
12.70059         (wool-) tod        78.73652 / t
qtr/qr    12.70059         B-L-quarter        78.73652 / t
qtr/qr    11.33981         B-S-quarter        88.18490 / t
9.0718474[*]    score             110.2311 / t
7.257478        Scottish-stone    137.7889 / t
st         6.350293        stone             157.4730 / t
5.669905        USA-wool-stone    176.3698 / t
4.5359237[*]    (Imper.) gallon   220.4623 / t
3.175147        (wool-)clove      314.9461 / t
3.175147        brick             314.9461 / t
2.26796185 [*]  block             440.9245 / t
1.81436948 [*]  loaf-quartern     551.1557 / t
1.587573        quartern          629.8922 / t
lb.avdp  453.59237 g [*]   pound               2.204623 / kg
226.7962 g        marc, marco, mark   4.409245 / kg
113.39809 g       US-butter-stick     8.818490 / kg
32.66612 g       long assay-ton     30.61276 / kg
29.16618 g       short assay-ton    34.28629 / kg
oz.avdp   28.349523 g      ounce              35.27396 / kg
dr.avdp    1.771845 g      dram = drachm     564.3834 / kg
s.avdp     1.574974 g      scruple           634.9313 / kg
0.2916618 g     assay-element       3.428629 / g
gr       64.798 91 mg [*]  troy grain         15.43236 / g
```

Grain = 0.064 798 91 gram [*]
Pound = 0.453 592 37 kilogram [*]
[*] = This value is exact !
Letter g means metrical gram (=0.001[*] kg)
Letter t in inverse-column means metrical ton (=1000 kg).
The name 'assay-element' is invented by the author.
U-L = USA-long; U-S = USA-short; B-L = British-long; B-S = British-short.
quintal = kintal = kantal = cental.
slinch = slug-inch = mug = many-slug.
elvis = the weight of Elvis Presley at the time of his death.
The assay units are jewellers units.
An (Imperial-) gallon is the weight of around one Imperial gallon of water.
The background of the geepound is described in the section 'other weights'.

Back to Index

#### Several pounds and ounces

The basis of the Anglo-Saxon weight-system is the Troy-system Herein during the last millennium many pounds and ounces have been applied. And most of them have already been abolished. The following table shows some of them. This table also shows that the present-day Avoirdupois-system is a direct descendant of the Troy-system.

Remarkably enough, the weight of the grain did not change during this long time. Its definition only got more accurate. In earlier days it equalled the average weight of the barley-corn grain which equals to 4/3 of that of the wheat-grain. At present it is tightly connected to the metric system, so its relative accuracy is determined by the definition of the metric kilogram.

```pound-              #grains     #grains     #ounces
type              per pound   per ounce   per pound
------             ---------   ---------   ---------
'French'-merchant    7680       480           16
old-Avoirdupois      7200         450         16
old-London  =^       7200         450         16
English-merchant     6750         450         15
Apothecary           5760       480           12
Troy  =^             5760       480           12
old-Saxon            5400         450         12
old-Tower =^         5400         450         12

Scottish-tron        9520        476          20
(new) Avoirdupois    7000        437.5[*]     16
old-wool             6992         -            -
```

=^ means this pound-type equals the pound type above it.
Factorial: 6992 = 16 * 19 * 23

##### Relations between the pounds or ounces

```name                 equals   [*]
----                 ------------
old-London-pound    15/16  = 0.9375     'French'-merchant-pound
Engl.merch-pound   225/256 = 0.87890625 'French'-merchant-pound
Troy-pound           3/4   = 0.75       'French'-merchant-pound
old-Tower-pound     45/64  = 0.703125   'French'-merchant-pound
Engl.merch-pound    15/16  = 0.9375     old-London-pound
Troy-pound           4/5   = 0.8        old-London-pound
old-Tower-pound      3/4   = 0.75       old-London-pound
Engl.merch-pound    75/64  = 1.171875   Troy-pound
old-Tower-pound      4/5   = 0.8        English-merchant-pound
old-Tower-pound     15/16  = 0.9375     Troy-pound

old-London-ounce    15/16  = 0.9375    'French'-merchant-ounce
Troy-ounce                 1           'French'-merchant-ounce
Engl.merch-ounce           1           old-London-ounce
old-Tower-ounce            1           old-London-ounce

wheat-grain            3/4  = 0.75      Troy-grain
(barley-) grain             1           Troy-grain
```

##### Metric equivalents

```abbrev.  # grams [*]      name               inverse (# /kg)
------   -----------      ----               ---------------
--- pounds ---
616.8856232      Scottish-tron         1.621046
497.6556288      'French'-merchant     2.009422
466.552152       old-London            2.143383
466.552152       old-Avoirdupois       2.143383
lb.avdp  453.59237        (new) Avoirdupois     2.204623
453.07398        old-wool              2.207145
lb.merc  437.3926425      English-merchant      2.286275
lb.ap    373.2417216      Apothecary            2.679229
lb.tr    373.2417216      Troy                  2.679229
349.914114       old-Tower             2.857844
349.914114       old-Saxon             2.857844
--- ounces ---
31.1034768      'French'-merchant    32.15075
oz.ap     31.1034768      Apothecary           32.15075
oz.tr     31.1034768      Troy                 32.15075
30.84428116     Scottish-tron        32.42092
oz.merc   29.1595095      English-merchant     34.29413
29.1595095      old-London           34.29413
29.1595095      old-Avoirdupois      34.29413
29.1595095      old-Saxon            34.29413
29.1595095      old-Tower            34.29413
oz.avdp   28.349523125    (new) Avoirdupois    35.27396
--- grains ---
gr         0.06479891     barley               15432.36
gr         0.06479891     Troy                 15432.36
0.0485991825   wheat                20576.48
```

Note: The 'French'-merchant pound and ounce differ only 1.7 percent from the pound and ounce of old-Paris and Quebec. See the Other-Weights section. The grains are more different.

#### Relations with the other units

For the Assay weights: see the above section Avoirdupois-General.
In the table below, 'pound' and 'ounce' without preceding name mean 'Troy-pound' and 'Troy-ounce'.

```name               consists of             # grains[*]
----               -----------             -----------
-------  O L D   W E I G H T S   -------
old London-stone    12.5 [*] old-Lond.pound  90 000
mast                 2   old-London-pound    14 400
old London-pound    15   ounce                7 200
old London-pound    16   old-Tower-ounce      7 200

Engl.merch.pound    14.0625 [*]  ounce        6 750
Engl.merch.pound    15   old-Tower-ounce      6 750

old Tower-pound     11.25 [*] ounce           5 400
old Tower-pound     12   old-Tower-ounce      5 400
old Tower-ounce     20   old-silver-penny       450
old silv.penny       1   English-merch.-penny    22.5
Engl.merch.penny    22.5 [*] grain               22.5
old silv.penny      30   wheat-grain             22.5

Scot.tron-stone     16   Scot.tron-pound     152320
Scot.tron-pound     20   Scot.tron-ounce       9520
Scot.tron-ounce     16   Scot.tron-drop         476
Scot.tron-drop      29.75 [*]  grain             29.75

-----   P R E S E N T - D A Y   W E I G H T S   -----
ton                 20   hundredweight    11520 000
hundredweight        4   quarter            576 000
quarter             10   mast               144 000
mast                 2.5 [*] pound           14 400
pound                6   mancus               5 760
mancus               2   ounce                  960

hundredweight        3   gold-bar           576 000
gold-bar           400   ounce              192 000

ounce                8   drachm (dram)          480
dram (drachm)        3   scruple                 60
scruple             20   grain                   20

dram (drachm)        2.5 [*] pennyweight         60
pennyweight         24   grain                   24
pennyweight         32   wheat-grain             24
wheat-grain          0.75[*] grain               3/4

ounce               30   AngloSaxon-gram        480
pennyweight          1.5 [*] AngloSaxon-gram     24
AngloSaxon-gram     16   grain                   16

grain                1   barleycorn-weight        1
barleycorn-weight    1   minim                    1
minim               20   mite                     1
mite                24   doite                    0.05
doite                                            1/480

(Troy-)pound      5760   grain                5 760
grain             64.798 91 [*] milligram         1
```

##### Metric equivalents

```abbrev.  # grams [*]      name               inverse
------   -----------      ----               -------
746.4834432 kg   ton                 0.13396 / t
cwt       37.32417216 kg  hundredweight      26.79229 / t
12.44139072 kg  gold-bar           80.37687 / t
9.8701699712 kg Scot.tron-stone  101.3154 / t
qr         9.33104304 kg  quarter           107.1692 / t
5.8319019 kg   old-London-stone  171.4706 / t
933.104304       mast                1.071692 / kg
616.8856232      Scott.tron-pound    1.621046 / kg
466.552152       old-London-pound    2.143383 / kg
lb.merc  437.3926425      Engl.merch.pound    2.286275 / kg
lb.tr/ap 373.2417216      pound               2.679229 / kg
349.914114       old-Tower-pound     2.857844 / kg
62.2069536      mancus             16.07537 / kg
oz.tr/ap  31.1034768      ounce (=toz =ozt)  32.15075 / kg
30.84428116     Scott.tron-ounce   32.42092 / kg
29.1595095      old-Tower-ounce    34.29413 / kg
dr.tr/ap   3.8879346      dram (drachm)     257.2060 / kg
1.9277675725   Scot.tron-drop    518.7347 / kg
dwt        1.55517384     pennyweight       643.0149 / kg
1.457975475    Engl.merch.penny  685.8826 / kg
1.457975475    old-silver-penny  685.8826 / kg
s.tr/ap    1.2959782      scruple           771.6179 / kg
1.03678256     AngloSaxon-gram   964.5224 / kg
gr        64.79891  mg    grain              15.43236 / g
64.79891  mg    minim              15.43236 / g
64.79891  mg    barleycorn-weight  15.43236 / g
48.5991825 mg   wheat-grain        20.57648 / g
3.2399455 mg   mite               30.86472 / g
0.13499773[~]mg  doite            740.75320 / g
```

Grain = 0.064 798 91 gram [*]
Pound = 0.373 241 721 6 kilogram [*]
[*] = All values in the left column are exact, except the doite which is indicated with [~].
Letter t in inverse-column means metrical ton (=1000 kg).
dwt = denier weight. Denier is a very old French word for penny.

#### Old English money

The subdivision of the old-Tower-pound and Troy-pound was the basis of the English monetary structure until 1970:

```name               consists of       # pence
----               -----------       --------
Sterling-pound     20  shilling        240
shilling           12  penny            12
penny                                    1
```

Back to Index

#### Carats and Karats

There are two types of Carat (= ct) for indicating the weight of diamonds and gem stones. And there is one Karat (= kt) for indicating the part of gold in an alloy.
NOTE: Do not exchange the words Carat and Karat!  Some people do this falsely.

#### Carat (ct) [weight]

The Carat indicates the weight (but not the economical value) of a diamond or another gem stone. In previous times its definition was based on the weight of the carob seed. These seeds are astonishingly equal in weight, and this weight is scarcely influenced by the local soil and weather conditions the carob tree lives in. It is around 0.2 grams.

Later on the carat was redefined to be more accurate. Alas, every country created its own definition, that in general differed slightly from those of its neighbouring countries (e.g. in USA: 1 carat = 0.2056 grams).   Consequently several slightly different values of the carat arose, all around 0.2 grams. In 1907 one started to define it as an exact value in the metric weight-system. At present since 1914 this definition is in use everywhere.

The two most important carat-weights are:

```measure system        # grams     # troy-grains
--------------        -------     -------------
Imperial-1877         0.20530       3.168263
Metric                0.2 [*]       3.086472
```

The carat is subdivided into smaller units, and some pearl-units have been related to it.

```name            consists of             # points
----            -----------             --------
carat            4  carat-quarter         100
carat-quarter    1  carat-grain            25
carat-grain     25  carat-points           25
carat-point                                 1
****  pearl units  ****
momme           18.75[*] metric-carat    1875
pearl-grain      1 Imp-1877-carat-grain    25
```

##### Troy equivalents:

```abbr  # Troy-grain     name          inverse
----  ------------     ----          -------
****  Imp-1877 carat  ****
ct    3.168263        carat        0.3156303 / gr
0.7920658       quarter      1.262521 / gr
0.7920658       grain        1.262521 / gr
0.7920658     pearl-grain    1.262521 / gr
0.03168263      point       31.56303 / gr

****  metric carat  ****
57.871344        momme        0.017279709 / gr
ct    3.0864717       carat        0.32399455 [*] / gr
0.77161792      quarter      1.2959782 [*] / gr
0.77161792      grain        1.2959782 [*] / gr
0.030864717     point       32.399455 [*] / gr
```

##### Metric equivalents:

```abbr   #milligram     name           inverse
----   ----------     ----           -------
****  Imp-1877 carat  ****
ct    205.30         carat           4.870921 / g
51.325        quarter        19.48368 / g
51.325        grain          19.48368 / g
51.325      pearl-grain      19.48368 / g
2.0530       point         487.0921 / g

****  metric carat  ****
3750           momme            0.266667 / g
ct    200           carat            5 / g
50           quarter         20 / g
50           grain           20 / g
2           point          500 / g
```

[*] = These non-integral values are exact.
Momme = Japanese pearls weight unit. The metricalized version mentioned here equals 75 carat-grain = 15/4 gram.
--- Synonyms: ---
Old-London carat = Imperial-1877 carat
Metric-1914 carat = Metric carat
jeweller's grain = carat grain

#### Karat (kt) [fineness]

The Karat is a ratio for indicating the fineness (= purity) of gold or another precious metal in an alloy:

```                    1 gram of gold
kt  =  Karat  =  --------------------  =  4.1666667 %
24 gram of mixture
```

This Karat can be used easily in conjunction with the Troy+Apothecary weight system. As one Troy pennyweight consists of 24 Troy grains, the number of karats equals the number of grains of pure gold in the pennyweight of alloy. Thus for example, one pennyweight of a 9 Karat alloy contains 9 grains of pure gold.

A modern measure for the fineness of gold or another precious metal in an alloy is simply called: Fineness. Its definition is:

```                          1 gram of gold
(metric) Fineness  =   --------------------   =   0.1 %
1000 gram of mixture
```

Back to Index

#### AVOIRDUPOIS - TRADE AND INDUSTRY

The tables in this section list several Avoirdupois weight units that are or were used in only one or a very few branches of trade and industry. Most of them are British. The units for general use are listed in the general-units section. A few of those general units are also listed in the present section to establish the connections between the tables in both.

In the following table many weight units are prefixed, what they in reality are not. The prefix indicates the type of the product:
w = wool
c = coal
f = flour
b = butter + cheese
h = hay + straw
Example: c-sack = coal sack; f-sack = flour sack; w-sack = wool sack.

```name                  consists of            # pounds
----                  -----------            --------
+++  multiplication chains based on seven-pounder +++
c-barge = c-keel      8  c-chalder           47488
c-chalder            53  hundredweight        5936

c-barge = c-keel     21.2 [*] long-ton       47488
c-barge = c-keel    3 c-room + 4 c-sack      47488
c-room                7  long ton            15680
long ton             10  b-barrel             2240
b-barrel              1  c-large-sack          224
c-large-sack          2  long hundredweight    224
long hundredweight    1  c-sack                112
f-bushel              1  b-firkin               56
b-firkin              1  pig                    56
pig                   1  h-truss-old-hay        56
h-truss-old-hay       1  (general) truss        56
(general) truss       2  B-L-quarter            56

cotton-candy          7  long hundredweight    784
long ton              4  U-L-quarter          2240
U-L-quarter           5  long hundredweight    560
b-Essex-wey(?)        3  long hundredweight    336
long hundredweight    2  B-L-quarter           112

w-sack               13  B-L-quarter           364
f-barrel              7  B-L-quarter           196

U-L-quarter           2  salt-barrel           560
salt-barrel           1  f-sack                280
f-sack                2  f-bag                 280
f-bag                 1  USA-cotton-sack       140
USA-cotton-sack       5  B-L-quarter           140

wey                   3  b-tub                 252
potatoes-sack         2  b-tub                 168
b-tub                 3  B-L-quarter            84

w-last                6  w-sarpler            4368
w-sarpler             2  w-sack                728
w-sack                2  w-wey                 364
w-wey                13  stone                 182

B-L-quarter           1  w-tod, tod             28
w-tod = tod           2  stone                  28
stone                 2  w-clove                14
w-clove               7  pounds                  7

++++++++  other multiplication chains  ++++++
USA-Short-quarter    10  frail-of-raisins      500
beef,fish,pork-barrel 2  nails-keg             200
nails-keg             1  USA-f-sack            100
USA-f-sack            2  frail-of-raisins      100
frail-of-raisins      4  USA-w-stone            50
USA-w-stone          12.5[*]  pound             12.5[*]

fotmal                9  butcher-stone          72

beef,fish,pork-barrel 5  f-poll                200
f-poll                5  butcher-stone          40
w-pack                2  iron-fagot            240
iron-fagot            1  glass-seam            120
glass-seam            5  UK-old-w-stone        120
UK-old-w-stone        3  butcher-stone          24

Scottish stone        2  butcher-stone          16
b-clove               1  butcher-stone           8
sugar-stone           1  butcher-stone           8
butcher-stone         8  pound                   8

h-truss-new-hay      10  sixpounder             60
wey                   7  h-truss-of-straw      252
h-truss-of-straw      6  sixpounder             36
sixpounder            6  pound                   6

+++++++  small and no chains  +++++++
USA   75  pound                  75
general   76.5 [*] pound             76.5[*]

bone-dry-unit         1.2[*] bone-dry ton     2400
bone-dry-ton          1  short ton            2000

stone                14  pound                  14
USA-cement-barrel     4  USA-cement-bag        376
USA-cement-bag      2 * 47  pound               94

b-Suffolk-wey       4 * 89  pound              356
USA-salt-sack       5 * 43  pound              215
soap-firkin         2 * 31  pound               62
USA-b-stick          1/4    pound                0.25[*]

cotton-bale-of:
Egypt (old)         1.5 USA-cott.bale old   750
Egypt (present)     1.5 USA-cott.bale new   720
Egypt (average)     719  pound              719
USA (old)           1 USA-Short-quarter     500
USA (at present)    480  pound              480
USA (average)       477  pound              477
India (old)         400  pound              400
East-India (avg)    396  pound              396
Brazil + Peru (old) 250  pound              250
Brazil (new)        220  pound              220

pound                 7000  troy grain           1
old wool-pound   6992=16*19*23 troy-grain   0.9988571
```

The factorials (e.g. 2*47) are given by the author.
The name 'sixpounder' is an invention of the author.
Chalder = chaldron = chauldron = cauldron = large kettle.
U-L = USA-long; B-L = British-long.
Concrete-sack = cement-bag.
Mercury = quicksilver.

##### Metric equivalents

```abbrev. # kilograms          name               inverse
------  -----------     --------------          -------
430 803.889        coal-ship-load         0.002321242 / t
21 540.194        coal-barge              0.04642484 / t
21 540.194        coal-keel               0.04642484 / t
7112.328        coal-room               0.1406009 / t
2692.524        coal-chalder            0.3713987 / t
1981.291        wool-last               0.5047213 / t
1088.622        bone-dry-unit (wood)    0.9185928 / t
1016.04690      long-ton                0.9842065 / t
90.718474[*]   bone-dry-ton (wood)     1.102311 / t
90.718474[*]   short ton               1.102311 / t
355.6164       cotton-candy            2.812019 / t
340.1943   old cotton-bale-Egypt       2.939497 / t
330.2152       wool-sarpler            3.028328 / t
326.5865   new cotton-bale-Egypt       3.061976 / t
326.1329   avg cotton-bale-Egupt       3.066235 / t
254.0117       USA-Long-quarter        3.936826 / t
226.7962       USA-Short-quarter       4.409245 / t
226.7962   old cotton-bale-USA         4.409245 / t
217.7243   new cotton-bale-USA         4.592964 / t
216.3636   avg cotton-bale-USA         4.621850 / t
181.4369   old cotton-bale-India       5.511557 / t
179.6226   avg cotton-bale-East-India  5.567229 / t
170.5507       USA-cement-barrel       5.863358 / t
165.1076       wool-sack               6.056656 / t
161.4789       Suffolk-butter-wey      6.192760 / t
152.4070       Essex-butter-wey(?)     6.561377 / t
127.0059       flour-sack              7.873652 / t
127.0059       salt-barrel             7.873652 / t
wey      114.3053       wey                     8.748502 / t
113.3981   old cotton-bale-Brazil+Peru 8.818490 / t
108.8622       wool-pack               9.185928 / t
101.6047       large-coal-sack         9.842065 / t
101.6047       butter-barrel           9.842065 / t
99.79032  new cotton-bale-Brazil     10.02101 / t
97.52236      USA-salt-sack          10.25406 / t
95.2543977[*] fothers                10.49820 / t
90.718474[*]  beef,fish,pork-barrel  11.02311 / t
88.90410      flour-barrel           11.24807 / t
82.55381      wool-wey               12.11331 / t
76.20352      potatoes-sack          13.12275 / t
63.50293      flour-bag              15.74730 / t
63.50293      USA-cotton-sack        15.74730 / t
54.43108      iron-fagot             18.37186 / t
54.43108      glass-seam             18.37186 / t
cwt       50.80235      long-hundredweight     19.68413 / t
50.80235      coal-sack              19.68413 / t
45.359237[*]  nails-keg              22.04623 / t
45.359237[*]  USA-flour-sack         22.04623 / t
42.63768      USA-cement-bag         23.45343 / t
38.10176      butter-tub             26.24551 / t
32.65865      fotmal                 30.61976 / t
28.12273      soap-firkin            35.55843 / t
27.21554      truss-new-hay          36.74371 / t
25.40117      truss-old-hay          39.36826 / t
25.40117      truss (general)        39.36826 / t
25.40117      flour-bushel           39.36826 / t
25.40117      butter-firkin          39.36826 / t
25.40117      pig                    39.36826 / t
22.67962      frail-of-raisins       44.09245 / t
18.14369      flour-poll             55.11557 / t
16.32933      truss-of-straw         61.23952 / t
12.70059      tod = wool-tod         78.73652 / t
qr        12.70059      British-Long-quarter   78.73652 / t
10.88622      UK-old-wool-stone      91.85928 / t
7.257478     Scottish-stone        137.7889 / t
st         6.350293     stone                 157.4730 / t
5.669905     USA-wool-stone        176.3698 / t
3.628739     sugar-stone           275.5778 / t
3.628739     butcher-stone         275.5778 / t
3.628739     butter-clove          275.5778 / t
3.175147     wool-clove            314.9461 / t
2.721554     sixpounder            367.4371 / t
lb.avdp  453.59237 g[*] pound                   2.204623 / kg
453.07398 g    old-wool-pound          2.207145 / kg
113.39809 g    USA-b-stick             8.818490 / kg
```

Grain = 0.064 798 91 gram [*]
Pound = 0.453 592 37 kilogram [*]
[*] = This value is exact !
Letter g means metrical gram (=0.001[*] kg)
Letter t in inverse-column means metrical ton (=1000 kg).

Back to Index

#### BUSHEL-WEIGHTS IN USA-AGRICULTURE

One dry bushel (= 2150.42 cu.inch) of alfalfa weights approximately 60 pounds. Therefore the alfalfa-bushel is fixed to exactly 60 pounds. This is 27.22 kilograms. So 36.74 of these bushels fit into one metric ton. Now the bushel is not any more a volume measure, but it has become a weight measure.

Similar has been done to the bushels of more food stuffs. Their appointed weight values are listed in the table below. This table also shows that (for example:) cowpeas, flax and the different kinds of clover have got the same weight values as alfalfa has.

```stuff                #pound   #kilograms[*]  #bushels/ton
-----                ------   -------------  ------------
general                63      28.57631931   34.9940099

Grass: blue            14       6.35029318   157.473044
brome (smooth)
fescue (tall)
orchard
redtop

Turnip-greens, dry     16       7.25747792   137.788914

Turnip-greens, wet     18       8.16466266   122.479035
Mustard-greens

Spinach                20       9.07184740   110.231131

Field-peas             25      11.33980925    88.184905

Ocra                   26      11.79340162    84.793178

Grass, sudan           28      12.70058636    78.736522
Pole-beans

Snap-beans             30      13.60777110    73.487421
Lima-beans, unshelled
English-peas, in hull

Cotton                 32      14.51495584    68.894457

Egg-plant              33      14.96854821    66.806746

Grass, timothy         45      20.41165665    48.991614
Rice

Barley                 48      21.77243376    45.929638
Apples
Cucumbers

Millet                 50      22.67961850    44.092452
Peaches
Sorghum, forage
Sweet-potatoes, dry

Tomatoes               53      24.04039561    41.596653

Turnips, without tops  54      24.49398798    40.826345

Sweet-potatoes, green  55      24.94758035    40.084048

Corn, shelled          56      25.40117272    39.368261
Sorghum, grain
Rye

Onions                 57      25.85476509    38.677590

Alfalfa                60      27.21554220    36.743710
Clover: alsike
crimson
sweet
white
red
Cowpeas
Flax
Rape
Soybeans
Trefoil, birdsfoot
Vetch
Wheat

Corn, in ear           70      31.75146590    31.494609

Sunflower, oil-type    24 to   10.88621688    91.859276
32      14.51495584    68.894457

Lespedeza              40 to   18.14369480    55.115566
50      22.67961850    44.092452

volume          #cu.inch[*]     #liters      #bushels/m3
------          -----------    ----------    -----------
USA-dry-bushel    2150.42      35.2390702     28.3775933
```

Back to Index

#### Quebecois and Old French (Paris)

```  name          consists of       meaning of name
----          -----------       ---------------
tonneau         20  quintal       tun, ton, tonne
quintal        100  livre         cental
livre            2  marc          pound
marc             2  quatreron
quatreron        4  once          four-ounces
once             2  lot           ounce
lot              4  gros
gros             1  drachme
drachme          3  denier        drachme
denier           1  scrupule      from: denarius
scrupule        24  grain         small itchy pebble
grain            1  grain         e.g. wheat granule
grain   0.053 115 234 375 [*] metric gram
```

##### Metric equivalents

```abbr.  # grams [*]         name              inverse
-----  -----------         ----              -------
979020             tonneau         1.0214296 / t
48951              quintal        20.42859 / t
489.51             livre          2.042859 / kg
244.755            marc           4.085718 / kg
122.377 5          quarteron      8.171437 / kg
30.5943 75         once          32.68575 / kg
15.2971 875        lot           65.37149 / kg
3.82429 6875       gros         261.4860 / kg
3.82429 6875       drachme      261.4860 / kg
1.27476 5625       denier       784.4579 / kg
1.27476 5625       scrupule     784.4579 / kg
53.1152 34375 mg   grain         18.82699 / gram
```

[*] = The values in the left column are exact.

#### International units

The biological effect (= activity) of many vitamins and drugs depends on the way they have been prepared. So there is no direct relation between the weight of a quantity of such stuff and its effect. Therefore this effect is compared to the effect of a quantity-unit of the stuff prepared in the standardized way. If both effects are equal, then the dose of 'unknown' stuff is said to be 1 IU (= international unit).

For some stuffs the weight of one IU of the standard specimen is:

```stuff:             1 IU weights:
------             -------------
Penicilline         0.6  micro-gram
Insuline           45.5  micro-gram
Vitamin A           0.3  micro-gram
Vitamin C          50    micro-gram
Vitamin D          25    nano-gram
Vitamin E      2/3 = 0.66667 milli-gram
```

Example: The theoretical biological activity of a beta-carotene molecule equals twice that of a vitamin-A molecule. However in the reality it is only one-third!  Thus six grams of beta-carotene perform the same biological effect in the human body as one gram of vitamin-A. So 1 IU of beta-carotene weights 1.8 micrograms.

All mammals must consume twelve vitamins. A few of them, cavia, primate apes and human, even one more: vitamin C = ascorbic acid. Four vitamins are fat soluble: A, D, E and K. Three vitamins are anti-oxydants: A, C and E.

#### Geepound, Mug and Poundal

```abbrev. # kilograms     name               inverse
------  -----------     ----               -------
175.12683525     slinch = snail      5.710147 / t
14.59390294     geepound = slug    68.52177 / t
9.80665        mug = hyl         101.97162 / t
```

Several masses have been devised for simulating the force of earth gravity in horizontal equipment. Three of them are:
Geepound (= G-pound) = Slug = the mass of a body which, when acted upon by a force of one poundforce, acquires an acceleration of one foot per second per second.
Slinch (= Slug-inch) = Snail = the mass such that a force of one poundforce accelerates this mass by one inch per second per second.
Mug (= Metric slug) = the mass accelerated at one meter per second per second by a force of one kilogramforce. Other names for it are: Techma = Technische Masse-Einheit = TME = Unite de Masse = UdM = Par = Hyl.

-- Herein is:
Poundforce = the force given by the earth gravity to a body with a mass of one pound.
-- Do not confuse this with:
Poundal = the force required to impart an acceleration of one foot per second per second to a body with a mass of one pound.
Poundfoot = the torque caused by one poundforce on a lever with a length of one foot (in Newton-meter).
Footpound = the enery delivered by one poundforce over a displacement of one foot (in Joule).
-- Densities for textile-yarn are:
Poumar = pound per million yard = a density of textile-yarn.
Typp = thousand yard per pound = in fact the inverse of poumar.
US-run = # 1600-yard wool-hanks per pound.

When we look at the values only, and not at the types of the units (e.g. time or length or mass), then the following equations hold, some of them ONLY in the METRIC system:

```mug = hyl = kilogramforce = kgf = earth-gravity
poundforce = pound(avdp) * earth-gravity
footpound = poundfoot = poundforce * foot
geepound = poundforce / foot
slinch = poundforce / inch = 12 * geepound
poundal = poundfoot / earth-gravity = pound(avdp) * foot
poumar = pound(avdp) / ( foot * 3@+6 )
typp = 3000 * foot / pound(avdp) = 0.001 / poumar
US-run for wool-yarn = 1.6 * typp
pound-per-square-inch = psi = poundforce / square-inch
pound-per-square-foot = psf = geepound / foot = psi / 144
water-atmosphere = watm = water-density * earth-gravity * 10
technical-atmosphere = at = kgf/cm2 = 10000 * earth-gravity
```

In the metric system their values are:

```mug = 9.80665
poundforce = 4.4482216
poundfoot = 1.35581795
footpound = 1.35581795
geepound = 14.593903
slinch = 175.12684
poundal = 0.13825495
poumar = 0.49605465 @-6
typp = 2.01590693 @+3
US-run = 3.22545108 @+3
psf = 47.880259
psi = 6894.7573
watm = 98063.754
at = 98066.5
```

See also the sub-section "Inter-measure coefficients" in Pressures: Basic units and Coefficients.

Back to Index

### THE METRIC SYSTEM

#### METRIC PREFIXES

The user has to write one of these prefixes before the basic measure unit of the right class to form the desired measure unit.

```        sci.                      every-day name
abbrev. name  10 to power of  cont.Europe      USA
------  ----  --------------  -----------   -----------
Z     zeta        +21       trilliard     sextillion
E     exa         +18       trillion      quintillion
T     tera        +12       billion       trillion
G     giga        + 9       milliard      billion
M     mega        + 6       million       million
myria       + 4       tenthousand   tenthousand
k     kilo        + 3       thousand      thousand
h     hecto       + 2       hundred       hundred
da    deca,deka   + 1       ten           ten
[none]        0       one           one
d     deci        - 1
c     centi       - 2
m     milli       - 3
u,mc   micro       - 6
n     nano        - 9
p     pico        -12
f     femto       -15
a     atto        -18
y     yocto       -21
z     zepto       -24

Myria has no symbol.
dk    This symbol is obsolete for deka.
```

Back to Index

#### METRIC BASIC UNITS

The classes and the basic units on which the metric measure system is based, and which are used by the everyday man, are:

```                                      abbreviation of
class                basic unit       basic-unit name
-----                ----------       ---------------
mass                 kilogram               kg
length               meter (or: metre)       m
time                 second                  s
electric current     Ampere                  A
```

Yes indeed folks, that is all!

At present these units themselves are defined by using the physical properties of atoms and light waves. Some results of this 'higher science' are described in the section Physical constants: Definition of Meter and Second.

By combining a prefix with a basic name, every user can make the name for every measure unit he likes. He/she is never urged to search for an (unprefixed) name. No hyphen or space should be written between the prefix and the basic name. Examples:
ms = millisecond = 1/1000-th of a second
dm = decimeter = 1/10-th of a meter
km = kilometer = 1000 meters
ns = nanosecond = 1 milliardth of a second
Ms = megasecond = 1 million seconds
uA = micro-ampere = 1 millionth of an Ampere

Areas are always derived from the length class by using the adjective 'square' (= sq.) or the suffix 2. Thus: sq.km = km2
Volumes are always derived from the length class by using the adjective 'cubic' (= cu.) or the suffix 3. Thus: cu.dm = dm3
The electric tension (in Volt) is derived from all four classes together.

The combination of the area- or volume-adjective together with a prefix leads to a snag that is dealt with extensively in the chapter Metric pitfalls: Square and Cubic.

The name of the unit of mass, kilogram, has a snag too. It is made up from the prefix 'kilo' and an old mass-unit called 'gram' abbreviated as 'g'. When it is prefixed, the prefix merges itself with the built-in prefix 'kilo', thus making a new prefix in front of the old unit 'gram'. Examples:
kg = kilogram = 1@3 gram = 1000 g
g = gram = 1/1000 kilogram
kkg = kilo-kilogram = 1@(3+3) gram ==> 1@+6 gram = megagram = Mg
mkg = milli-kilogram = 1@(3-3) gram ==> gram = g [without any prefix]
ukg = micro-kilogram = 1@(3-6) gram ==> 1@-3 gram = milligram = mg
dkg = deci-kilogram = 1@(3-1) gram ==> 1@+2 gram = hectogram = hg
dakg = deka-kilogram = 1@(3+1) gram ==> 1@+4 gram = myriagram
nkg = nano-kilogram = 1@(3-9) gram ==> 1@-6 gram = microgram = ug

Why not simply saying: the basic unit of mass is the gram? The reason is that in calculations of force and energy the kilogram is the basic unit. The names of the other three basic units do not have this illogical snag.

Back to Index

#### OUTSIDER UNITS

In Europe some ancient names are still in use. They are not many, and the values they stand for fit quite well in the metric system. Several of these names are listed here.

##### Linear [*]

```abbrev. name         value
------  ----         -----
spat         1 @ +12  m
myriameter  10000 m
league       4000 m
mile         2000 m
cable         220 m
Dutch-rood     10 m
toise           2 m
pace            1.5 m
step           75 cm
foot         1/3 m = 33.333... cm
thumb, inch  27.5  mm
line         2.3  mm
Q,kyu   quarter      0.25 mm  (= metric-point)
pm      perm         0.1  mm
u,um    micron       1 @ -6   m
A       Angstrom     1 @ -10  m
uu,pm   bicron       1 @ -12  m  (micronmicron = bi-micron)
F       Fermi        1 @ -15  m
```

##### Square [*]

```abbrev. name              consists of          # sq.m
------  ----              -----------          ------
Dutch-bannier (bunder) 1  hectare          10 000
Dutch-morgen       0.85 hectare         8 500
ha      hectare            2  soccer-fields    10 000
soccer-field       5  dekare            5 000
da      dekare            10  Dutch (sq.-)rood  1 000
Du.(sq.)rood       1  are                 100
a      are              100  centiare            100
ca      centiare                                    1
barn = Fermi (F)   1 @ -24  sq.cm       1@-28

soccer = European-style football
```

##### Cubic + Volume [*]

```name              # liters
----              --------
dekastere         10000
stere (s,st)       1000
raummeter (Rm)     1000
festmeter (Fm)     1000
drum                200 or 205 or 208
decistere           100
Dutch sack          100

name                  # cu.cm
----                  -------
Winchester-quart       2500
milk-bottle            1000
liter (ltr, lt, L)     1000
wine-quart             1000
wine-fifth              750
wine-bottle (btl)       750
pint                    500
demipint, large cup     250
cup, glass, butcher     200
seven (= ca. 7 fl.oz)   200
French champaign-split  200
wine-split (= 1/4 btl)  187.5[*]
fluid ounce              30
shot                     25
big tablespoon           20
(small) tablespoon       15
thimble                  10
pap-spoon                 8 or 7.5[*]
(big) tea-spoon (tsp)     5
small tea-spoon           3
coffee-spoon              1.25[*]
cc                        1
drop                      0.05
lambda                    0.001

Note:
1 m3 = 1 cu.m = 1000 cu.dm = 1000 dm3
1 liter = 1 cu.dm = 1 dm3 = 1000 cm3 = 1000 cu.cm
1 cc = 1 cu.dm = 1 cu.cm = 1000 cu.mm = 1000 mm3
1 lambda = 1 cu.mm = 1 mm3 = 1 uL

```

##### Weight [*]

```name                     consists of           metrical
----                     -----------           --------
commercial-load          3  ton, tonne         3000  kg
German-load              2  ton, tonne         2000  kg
deadweight-ton (dwt)     1  ton, tonne         1000  kg
bone-dry metr.ton (bdmt) 1  ton, tonne         1000  kg
ton = tonne (t)         10  quintal            1000  kg
quintal = Russ.centner   2  hundredweight       100  kg
hundredweight = centner  1  sack, bag            50  kg
sack = bag               5  myriagram            50  kg
myriagram               10  kilogram             10  kg
kilogram                 2  pound              1000  g
pound                    5  Dutch-ounce         500  g
Dutch-ounce            100  glug                100  g
glug                     1  gram                  1  g
gram                     5  carat              1000  mg
carat                    4  (wheat-)grain       200  mg
German-grain             1  drugs-grain          60  mg
drugs-grain             30  point                60  mg
(wheat-) grain          25  point                50  mg
point                    2  milligram             2  mg
milligram             1000  gamma              1000  ug
gamma                    1  microgram             1  ug

kg = kilogram  = 1 @ +3 g
mg = milligram = 1 @ -3 g
ug = microgram = 1 @ -6 g
g = gram
```

[*] = All values in these tables are exact.
Note, the metric quintal is not 100 pound, but it is 100 kg.

##### Liter (Litre)

In early days the litre was defined as the volume of one kilogram of water at four degrees Celsius. This value approximates very well the size of one cubic decimeter, but does not match it exactly. It is a very little bit more. This very small difference does not make any sense in the ordinary daily life. Nowadays since 1964 one litre is defined as one cubic decimeter. So one litre of water weighs slightly less than one kilogram. The old liter has also been fixed by definition and thus also been detached from the actual water density. Thus:
1 old-litre = 1.000028 [*] dm3
1 litre = 1 dm3
Ton is (approx.) the weight of 1 m3 filled with water.

Back to Index

#### PROPOSAL FOR NAMES

This is a proposal of a set of new and existing names that may ease the daily use of the metric system. The values given to the originally Anglo-Saxon names are in the neighbourhood of the values these names represent actually.

```      VOLUME [*]                           AREA [*]
Name             dm3               Name              m2
----             ---               ----              --
dekastere     10 000               hectare       10 000
stere          1 000               soccer-field   5 000
barrel=oil-drum  200               acre           4 000
oil-barrel       160               rood = dekare  1 000
decistere = bag  100               are              100
bushel            40               roomfloor         20
big-bucket        20               kitchen-floor     10
peck              10
house-bucket      10
half-bucket        5                    WEIGHT [*]
gallon             4               Name             kg
triple-liter       3               ----             --
pottle = oil-can   2               ton            1000
liter=milk-bottle  1               double-cental   100
wine-bottle        0.75            cental           50
pint               0.5             house-bucket     10
soda-bottle        3.75            stone             5
mug = big-cup      0.25            brick             2.5
cup = glass        0.2             kilogram          1
gill               0.125           pound             0.5
deciliter          0.1             Dutch-ounce       0.1

APOTHECARY, VOLUME AND/OR WEIGHT [*]
Name               cm3 or gram
----               -----------
deciliter, Du.ounce   100
ounce                  30
big-tablespoon         20
small-tablespoon       15
dessertspoon           10
papspoon                7.5
big-teaspoon            5
drachme, dram           3.75
small-teaspoon          3
coffee-spoon            2.5
pennyweight             1.5
salt-spoon, scruple     1.25
cc, gram                1
pinch                   0.625
dash                    0.3125
carat                   0.2    = 1/5
minim, grain            0.0625 = 1/16
drop, small-grain       0.05   = 1/20
```

[*] = All values in these tables are intended to be exact.

Back to Index

## Part 3: TABLES; PRESSURES, BIBLE, EURO, EARTHQUAKES, others

### PRESSURES AND STRAINS

#### Four unit systems

A unit of pressure (stress) or strain is expressed in force per unit of surface. Several units of pressure and strain are used as a consequence of different methods of measuring a pressure or strain. The units can be translated into each other by multiplications with constant values. Strain can be seen as the opposite of pressure. The four main methods of measuring the pressure and their corresponding units are:

• Physical (or Ordinary) Atmosphere: indicated by the height of a column of mercury at a temperature of 0 centigrades. The unit name is 'atm' and the scale is divided in 'mmHg'.
• Water Atmosphere: indicated by the height of a column of water at a temperature of 4 centigrades. The unit name is named by me 'watm' and the scale is divided in 'mH2O'.
• Force by Gravity: indicated by the weight of a mass in the earth-gravity field. The two unit names are 'psi' and 'kgf/cm2'. The latter is called: 'Technical Atmosphere'.
• Scientific formula: based on a unit theoretically derived from the metric system. The unit name is 'Bar' and the scale is divided in 'Pascal'. One-tenth of a Pascal is called a 'Barye' (= 'Heavy' in Greek language)

The relations between a pressure unit and its scale division units are defined as:

```abbrev.    name                         consists of
-------    ----                         -----------
atm,atmos  physical/ordinary atmosphere  760 torr
torr      Torricelli                      1 mmHg
mmHg      millimeter mercury-column

watm      water atmosphere               10 mH2O
mH2O      meter water-column

at        technical atmosphere            1 kgf/cm2
kgf/cm2   kilogramforce per square cm.  9.80665 N/cm2

psi       poundforce per square inch    144 psf
psf       poundforce per square foot

Bar       Bar                           100 pieze
pieze                          10 mBar
mBar      millibar                        1 hPa
hPa       hecto-pascal                  100 Pa
Pa        Pascal                         10 Barye
uBar,ba   Barye = microbar              0.1 N / sq.m

Bar       Bar                         10 N / sq.cm
Pa        Pascal                       1 N / sq.m
N         Newton                       1 kg.m/s2
```

#### Inter-measures coefficients

The numeric notation of a pressure value in one system can be easily translated into the corresponding notation of another system. The coefficients that connect the four systems and are used in these translations are:

```    torricelli      =  0.001 333 2237   Bar
earth gravity   =  9.806 65 [*]     m/s2
water density   =  0.999 972        kg/dm3
pound (avdp)    =  0.453 592 37 [*] kg
square inch     =  6.451 6 [*]      cm2
```

[*] = This value is exact by definition. The other values in this table are measured values.
The formulas to derive the different types of pressure from these basic coefficients are:

```psi  = pound * earth-gravity / square-inch
psf  = pound * earth-gravity / square-foot
watm = 10 * water-density * earth-gravity
bar  = 100000 * Newton / square-meter
at   = 10000 * earth-gravity * kg/m2
```

On 18 may 2003 the NIST published the redefinition of the ordinary atmosphere. Its value has become 1.01325 bar exactly. In the construction of the inter-unit-coefficients table in the section below the definitions of the above tables are used, not this redefinition of the atmosphere. Nevertheless no contradiction will occur since this 'new' value lies within the accuracy of six to eight digits used in making the inter-unit-coefficients table. Therefore none of the values in that table need to be recalculated. They remain correct.

Back to Index

#### INTER-UNIT COEFFICIENTS TABLE

Now we have all tools to calculate every coefficient between the one unit or scale division and any other unit or scale division. Put together all coefficients form a table. The most important ones are listed below. The table thus created consists of eight by eight cells.

For the ease of the user the table has got additional organisation. That is written in the following paragraphs up to the 'Note'.

The rows and columns have been ordered in such a way that the number in a cell is greater when the cell is located in a higher row and/or a more right column.

The numeric values below the 1-1-1 diagonal are the inverses of those above this diagonal. Example: The inverse of 51.714932 is 0.019336775

For the sake of easy reading and printing on small computer peripherals the table is split into four two-column tables.

NOTE: Many of the listed numbers are written with an accuracy of eight or nine digits. This is done to avoid cumulative calculation errors in complex and cascade-like calculations. The actual accuracy of the most of the numbers is only six digits, since the accuracy of the water-density and that of the gravity are six digits !!

The table should be read as follows:
One unit written alongside the vertical axis ('row name')  equals  one unit written alongside the horizontal axis ('column name')  times  the numeric value in the table cell.
Example:  1 psi = 51.714932 torr

```            |        atm        |        bar        |
--------+-------------------+-------------------+
atm     |         1         |  1.01325001       |
--------+-------------------+-------------------+
bar     |  0.986 923 26     |         1         |
--------+-------------------+-------------------+
at      |  0.967 841 09     |  0.980 665 [*]    |
--------+-------------------+-------------------+
watm    |  0.967 813 99     |  0.980 637 54     |
--------+-------------------+-------------------+
psi     |  0.068 045 963    |  0.068 947 573    |
--------+-------------------+-------------------+
torr    |  0.001 315 789 5  |  0.001 333 223 7  |
--------+-------------------+-------------------+
hPa     |  0.000 986 923 26 |  0.001 [*]        |
--------+-------------------+-------------------+
psf     |  0.000 472 541 41 |  0.000 478 802 59 |
--------+-------------------+-------------------+

|        at         |       watm        |
--------+-------------------+-------------------+
atm     |  1.033 227 47     |  1.033 256 40     |
--------+-------------------+-------------------+
bar     |  1.019 716 2      |  1.019 744 77     |
--------+-------------------+-------------------+
at      |         1         |  1.000 028 0      |
--------+-------------------+-------------------+
watm    |  0.999 972        |         1         |
--------+-------------------+-------------------+
psi     |  0.070 306 958    |  0.070 308 927    |
--------+-------------------+-------------------+
torr    |  0.001 359 509 8  |  0.001 359 547 9  |
--------+-------------------+-------------------+
hPa     |  0.001 019 716 2  |  0.001 019 744 77 |
--------+-------------------+-------------------+
psf     |  0.000 488 242 76 |  0.000 488 256 43 |
--------+-------------------+-------------------+

|        psi        |        torr       |
--------+-------------------+-------------------+
atm     |  14.695 949       |        760        |
--------+-------------------+-------------------+
bar     |  14.503 774       |  750.061 67       |
--------+-------------------+-------------------+
at      |  14.223 343       |  735.559 23       |
--------+-------------------+-------------------+
watm    |  14.222 945       |  735.538 64       |
--------+-------------------+-------------------+
psi     |         1         |   51.714 932      |
--------+-------------------+-------------------+
torr    |   0.019 336 775   |         1         |
--------+-------------------+-------------------+
hPa     |   0.014 503 774   |    0.750 061 67   |
--------+-------------------+-------------------+
psf     |   0.006 944 444 4 |    0.359 131 47   |
--------+-------------------+-------------------+

|        hPa        |        psf        |
--------+-------------------+-------------------+
atm     | 1 013.250 01      |  2 116.216 6      |
--------+-------------------+-------------------+
bar     |      1000         |  2 088.543 4      |
--------+-------------------+-------------------+
at      |   980.665 [*]     |  2 048.1614       |
--------+-------------------+-------------------+
watm    |   980.637 54      |  2 048.104 1      |
--------+-------------------+-------------------+
psi     |    68.947 573     |        144        |
--------+-------------------+-------------------+
torr    |     1.333 223 7   |      2.784 495 6  |
--------+-------------------+-------------------+
hPa     |          1        |      2.088 543 4  |
--------+-------------------+-------------------+
psf     |     0.478 802 59  |          1        |
--------+-------------------+-------------------+
```

Back to Index

#### APPROXIMATING COEFFICIENTS TABLE

One can conclude from the above table that the units atm, bar, at and watm can be supposed to be equal when an inaccuracy of 3.5% or more is allowed. Then the table shrinks into the following very small layout:

```       |    bar   |   psi  |  torr  |   hPa  |   psf  |
-----+----------+--------+--------+--------+--------+
bar  |     1    |  14.5  |  750   |  1000  |  2000  |
-----+----------+--------+--------+--------+--------+
psi  |   0.07   |    1   |  52.5  |   70   |   144  |
-----+----------+--------+--------+--------+--------+
torr | 0.001333 | 0.019  |    1   | 1.3333 | 2.6667 |
-----+----------+--------+--------+--------+--------+
hPa  |  0.001   | 0.0145 |  0.750 |    1   |    2   |
-----+----------+--------+--------+--------+--------+
psf  |  0.0005  | 0.007  |  0.375 |   0.5  |    1   |
-----+----------+--------+--------+--------+--------+
```

Herein:  atm = bar = at = watm

Back to Index

#### FLUID-COLUMN PRESSURES TABLE

The inter-unit-coefficients table would become too big when all fluid-column pressures were added to it. Therefore in the following table they are compared to the bar only. This table must be read as follows: One foot of mercury equals 0.406 bar.

```                 BAR-pressure in case of:
|      water        |     mercury       |
---------+-------------------+-------------------+
inch  | 0.00 249 081 936  |  0.033 863 882 0  |
---------+-------------------+-------------------+
foot  | 0.02 988 983 23   |  0.406 366 584    |
---------+-------------------+-------------------+
yard  | 0.08 966 949 69   |  1.219 099 751    |
---------+-------------------+-------------------+
meter  | 0.09 806 375 42   |  1.333 223 7      |
---------+-------------------+-------------------+
```

ft-hd = foot-of-head = foot of water-column.
in-WC = in-wg = inch of water-column = inch of water-gauge.

Back to Index

#### HUMAN CARDIAC BLOOD PRESSURE

The blood pressure in a human body (except in the lungs) is measured in the the neighbourhood of the heart, e.g. on an upper arm. It is expressed in mmHg or Torr. Two values that can be obtained easily by every physician are very important:
Systolic pressure: This is the maximum pressure value during the heartbeat. A healthy value is 125 mmHg.
Diastolic pressure: This is the minimum pressure that occurs during the resting phase of the heart between two beats. A healthy value is 75 mmHg.
Thus in a healthy person the value of the blood pressure moves constantly back and forth between one sixth and one tenth of an atmosphere, i.e. between 1.6 and 1 mH2O.

Higher pressures make that the heart has to work harder thus causing more wear and tear, and that the bloodvessels are more strained which in the long time may lead to tiny cracks in their walls. These cracks cause bloodclots and thrombosis which on their turn may cause strike attacks in the heart and the head with irreversible damage.

Some scientists suggest that the intense use of salt makes the blood pressure to increase slowly during the aging of a person. This increase can be stopped, but not made undone by stopping the excessive salt consumption.
Too much fat tissue also increases the blood pressure as it pinches several blood vessels in the belly. This is similar to pinching a garden hose to increase the water pressure. Then in case of physical strain the head feels to explode. This over pressure can be made undone simply by slimming.

Back to Index

### EARTH SCIENCES

#### COOPER-TEST: DISTANCES BY RUNNERS

The table below gives the distances in metric hecto-meters covered by a recreational runner at his maximum effort during twelve minutes. This is called the Cooper-test. The table shows the dependence on the gender and the age of the person.

NOTE: This table is not applicable for people who perform very few body exercise or none at all.

```                   C O O P E R T E S T
Form   Gender  Distance in hectometers in 12 minutes run

Age --->        0-29   30-39   40-49   50-59   60-...

Very poor F     0-15    0-14    0-12    0-11    0-10
M     0-16    0-15    0-14    0-13    0-12

Poor      F    15-18   14-17   12-15   11-14   10-13
M    16-20   15-19   14-17   13-16   12-15

Mediocre  F    18-22   17-20   15-19   14-17   13-16
M    20-24   19-23   17-21   16-20   15-19

Good      F    22-27   20-25   19-23   17-22   16-21
M    24-28   23-27   21-25   20-24   19-23

Very good F    27-31   25-29   23-27   22-26   21-25
M    28-32   27-31   25-29   24-28   23-27

Excellent F    31-35   29-33   27-31   26-30   25-29
M    32-36   31-35   29-33   28-32   27-31
```

Distances have been rounded to integral hectometer-units.
Hectometer equals hundred meters.
Age is given in years.
Gender: M = Male; F = Female.

Example: A 34 years old woman runs 1830 meters (= 18.3 hm) during twelve minutes. The Coopertest table says that her sports form is mediocre.

Back to Index

#### BEAUFORT: WIND-FORCE AND -SPEED

Three tables are given in relation to the windforce as defined by Francis Beaufort (1774-1857) and later on refined by others. The abbreviations in these three tables are:
index = Beaufort number
psi = pounds per square inch
mps = meters per second
kph = kilometers per hour
mph = statute miles per hour
knot = internat. miles per hour
23-> = 23->> = 23 and more

At present the Beaufort index is determined by averaging the wind speed over a period of ten minutes. So the incidental gusts are ruled out and thus unable to lift up the index to a higher number. The measurements are done on an open water or open land area at the height of ten meters.

#### Pressure

The primary base of the Beaufort scale is not the speed of the wind, but the force it exerts on objects like ships and buildings. Therefore the first table shows the pressure by the wind and the resulting wave size in giant open waters. The pressure is measured with a disk of one square foot in area.

```                     average
index  pressure   sea wave height     description
(psi)    (m,cm)   (ft,in)
-----  --------  -------   -------    -----------
0     0.0       0 cm     0 in      calm, no wind
1     0.01      7 cm     3 in      light air
2     0.08     13 cm     5 in      light breeze
3     0.28     60 cm     2.0 ft    gentle breeze
4     0.67      1  m     3.5 ft    moderate breeze
5     1.31      2  m     6.5 ft    fresh breeze
6     2.3       3  m     9.5 ft    strong breeze
7     3.6       4  m    13.5 ft    near gale / moderate gale
8     5.4       5.5 m   18 ft      gale / fresh gale
9     7.7       7  m    23 ft      strong gale
10    10.5       9  m    29 ft      storm / whole gale
11    14.0      11  m    37 ft      violent storm / storm
12    17->      14-> m   45-> ft    hurricane, tyfoon, cyclone
```

In case of a double description with '/' the right part is the description used by Francis Beaufort himself. The left part is the one used in the modern days.

The wave heights are the typical heights at open seas or giant lakes. The "freak waves" are left out of sight. At the stormy windforces of ten or more such unpredictable rogue waves may suddenly occur. Such a wave rises out of the water as a 25 to 30 meters high wall, breaks like a surf wave and then falls down on the ship. Thus it can swallow the largest freight or passenger ship entirely. Often the ship disappears without any sign left.

#### Inland effects

Beaufort made a table that describes the effect of the wind on a ship and how the sailors must handle to keep the ship safe at sea. In 1926 meteorologists added a list of the effects by the wind at the inland.

```index  effects on land
-----  ---------------
0    smoke rises vertically
1    smoke drift shows direction of wind
2    wind felt on face; leaves rustle;
ordinary vane moves
3    leaves and small twigs in constant motion;
wind extends light flag
4    raises dust and loose paper; small branches move;
hair is disordered
5    small trees in leaf begin to sway;
crested wavelets form on inland waters
6    large branches in motion; difficult to use
umbrellas; whistling heard in telegraph wires
7    whole trees in motion; inconvenience felt when
walking against wind
8    breaks twigs off trees; generally impedes walking
9    small structural damage (chimney post, roof tiles
and slates removed)
10    trees uprooted; considerable structural damage;
11    widespread damage in forests and buildings
12    widespread damage, apocalyptic like in the hell.
```

Windforce 10 is seldomly experienced inland; windforce 11 and 12 very rarely. When the windforce index is 12 or more, the storm is named a hurricane or tyfoon or cyclone (all three words are the same). The intensity of such storms is listed by the Scale of Saffir-Simpson.

#### Speed intervals

```index   speed(mps)  speed(kph)  speed(mph)  speed(knot)
-----   ----------  ----------  ----------  -----------
0     0.0 -  0.3     0 -   1     0 -  1     0 -  1
1     0.3 -  1.5     1 -   5     1 -  3     1 -  3
2     1.6 -  3.3     6 -  11     4 -  7     4 -  6
3     3.4 -  5.4    12 -  19     8 - 12     7 - 10
4     5.5 -  7.9    20 -  28    13 - 18    11 - 16
5     8.0 - 10.7    29 -  38    19 - 24    17 - 21
6    10.8 - 13.8    39 -  49    25 - 31    22 - 27
7    13.9 - 17.1    50 -  61    32 - 38    28 - 33
8    17.2 - 20.7    62 -  74    39 - 46    34 - 40
9    20.8 - 24.4    75 -  88    47 - 54    41 - 47
10    24.5 - 28.4    89 - 102    55 - 63    48 - 55
11    28.5 - 32.6   103 - 117    64 - 75    56 - 63
12    32.7 ->>      117 ->>      75 ->>     64 ->>
```

The four definitions of the wind speeds that border the zone of one Beaufort index do not match exactly, although they are the definitions used by the official weather institutes. The wind pressure and the wave heights in the first table are those in the midst of the zone.

Back to Index

#### Science of making the Richter scale

The scale made in 1935 by Charles Richter (1900 - 1985) is not based on the effects by the earthquakes, but on the amplitudes of the ground motions. The amplitude selected for this measure is not simply the maximum sway of the ground. The determination of the right amplitude size is much more complicated because of the following reasons:

• The ground motions vary in size during the quake. At the beginning of the quake they do not always start with full strength and at the end they fade out.
• A quake is composed of two perpendicular horizontal wave-like movements: the longitudinal (= push-pull = 'pumping') P-waves and the horizontal transversal (= sideways = shear) S-waves. Together they can make a rotation in the resulting movement. Vertical waves are very rare.
• The S-waves are generally bigger and thus cause more damage than the P-waves. They are Stronger and thus more Severe.
• The propagation speeds of both wave types through the earth's crust differ. The P-waves travel faster than the S-waves, so they arrive earlier at a seismometer. (Therefore also: P = primary; S = secondary = slower). This time difference increases when the seismometer is put further away. Consequently the quake has another appearance for each of the seismometers that are spread in a vast area.
• The source of the quake can be very deep under the earth surface or very superficial. This deepness influences the mutual ratio between the deflections of the seismometers in the wide area.

Therefore the seismologists have the difficult task to calculate an 'average sway' having the 'average amplitude' in the epicenter. The epicenter is the location on the earth surface right above the source (= center) of the quake. The total duration of the quake is not taken into account, and also not the noisy vibrations that feel like a giant lorry near the house.

For easiness not the average amplitude itself, but its logarithm is published to the news press. This value is called the "Richter magnitude". Its value is:
RichterMagnitude = log ( AverageAmplitude )
This formula shows that the amplitude is ten times bigger when the magnitude increases by one.

A few days after the quake the seismic data are evaluated more meticulously. Often this leads to a correction of the average amplitude. Then the Richter magnitude may change with a value of up to 0.3

In a woodland a quake does not harm. In mountain areas it can break rocks. When under the see it can create hughe tidal waves called "tsunami"s. These can be dangerous when trapped in a harbor or impeded by a long coast line. The table below lists the earthquake damages in populated areas on land.

#### Effects by earth quakes

```Richter
magnitude   effects on land
---------   ---------------
under 2.0   micro-earthquake; not felt.
under 3.5   generally not felt, but recorded only;
sometimes felt as a small vibration.
3.5 - 5.4   moderate earthquake; often felt, rarely damage,
some chimneys may topple off.
under 6.0   at most slight damage to well-designed buildings,
major damage to poorly constructed buildings
over small regions.
6.1 - 6.9   strong earthquake; destructive in populated
areas up to about 100 kilometers.
7.0 - 7.9   major earthquake; serious damage in larger areas.
8 or more   great earthquake; serious damage in areas several
hundred kilometers across.
```

Back to Index

#### Astronomical time versus Calendar time

The time the earth needs to circle around the sun is called the "solar year" or "tropical year". This solar year has not always the same length. In the course of time it gets shorter slightly. Therefore the scientists, like astronomers and physicists, use the solar year of 1900 as the reference year for their definitions of date and time. That year had the duration of 365.242198781 days = 31556925.9747 seconds. This is 365 days, 5 hours, 48 minutes and (approx.) 46 seconds.

At present the solar year lasts shorter for over half a second. The duration of the solar year of 2000 is 31556925.444 seconds = 365.24219264 (1900-)days. This is 365 (1900-)days, 5 hours, 48 minutes and 45.444 seconds. The scientifically determined length of a day in 2000 is 86400.002 seconds. So the 'solar day' does not match exactly the 'calendar day' too!. And a lunar month also does not match an ordinary month:
lunar month = 29.53059 days = 2551442.976 seconds.

The solar year is very important for our civilization as it dictates the seasons and thus the periodicity of the weather types. By this way it dictates the human food production by the agriculture and cattle raising. For a good grow one must know when (and how) to plow, sow, mow and stow and cover the cow. These activities must be performed months in advance of harvesting and collecting the resulting food.

Alas, the solar year has not an integral number of days. Therefore humans introduced the approximating "calendar year" or "civil year" which has an integral number of days. This 'integralization' makes its duration slightly different from that of the solar year. Consequently, due course of time the calendar year would loose totally its relation with the solar year and thus render itself useless. In order to avoid this slip we must use two types of calendar years, each having its own integral number of days, and place them in an intermixed sequence.

The two types of calendar year are the "normal year" (with 365 days) and the "leap year" (with 366 days). The eternal time is divided into sets of four calendar years, each set consisting of three normal years and one leap year. This results into the well-known rule that each year with a number dividable by four is a leap year, e.g. 1904, 1908, 1912, and so on. The others are normal years.

In a very few sets the leap year is replaced by a normal year. This is done only once in a period of 100 or 200 years. It is not done within the 199 years period from 1901 to 2099. The years 1900 and 2100 are normal years that replace leap years. But the year 2000 stays a leap year. By these ways we can keep the difference between the solar year and the current calendar year always less than one day.

In old medieval times efforts had already been made to determine the length of the solar year. At first this lead to the Julian and later to the more accurate Gregorian year.

Note that the year 0 does not exist. So the year -1 = 1 BC is followed immediately by the year +1 = 1 AD. The reason is that until the year 700 the number 'zero' was not known in Europe. The Hindus have invented it.

#### The units of calendar time

The following table shows the relations between the man-made calendar-units of time, except months.

```abbrev    name            consists of      # seconds
------    ----            -----------      ---------
+++  present-day calendar  +++
Gregorian year  365.2425[*] day   31556952
Julian year     365.25[*] day     31557600
a, y, yr  leap year       366  day          31622400
a, y, yr  normal year     365  day          31536000

fortnight         2  sennight      1209600
se(ve)nnight      1  week           604800
w      week              7  day            604800
d      day               6  ship-watch      86400
ship-watch        2  ship-dog-watch  14400
ship-dog-watch    2  hour             7200
h      hour              2  ship-bell        3600
ship-bell         2  quarter          1800
quarter          15  minute            900
m      minute (= ')     60  second             60
s      second (= ")     60  third               1
third (= "')                       0.0166667

+++  medieval  +++
h      hour              5  point            3600
point             8  moment            720
moment           12  ounce              90
ounce            47  atom                7.5[*]
atom           1/376  minute       0.1595745

+++  old-Roman  +++
hour             24  scrupulus        3600
scrupulus     [*] 2.5 (modern) minute  150

+++  metric  +++
day              10  m.hour          86400
m.hour          100  m.minute, beat   8640
m.minute = beat 100  m.second, blink   86.4[*]

+++ scientists' definition: +++
s    second = 9 192 631 770 wave periods of
the light emitted by an
excited Cesium-133 atom
```

When put together the facts described above make a large table. The part of it with the most-commonly used time-units forms the following table, that for the ease of printing on paper has been split into two parts. This table must be read as follows: One column item consists of cell-number row items. Example: one day consists of 1440 minutes.

```                       solar year
leap year       1900       normal year
+-----------+---------------+-----------+
second  | 31622400  | 31556925.9747 | 31536000  |
+-----------+---------------+-----------+
minute  |  527040   | 525948.766245 |  525600   |
+-----------+---------------+-----------+
hour    |   8784    | 8765.81277075 |   8760    |
+-----------+---------------+-----------+
day     |    366    | 365.242198781 |    365    |
+-----------+---------------+-----------+
week    | 52.285714 | 52.1774569688 | 52.142857 |
+-----------+---------------+-----------+
normal  | 1.0027397 |  1.0006635583 |     1     |
year  +-----------+---------------+-----------+
solar   | 1.0020748 |       1       |
year  +-----------+---------------+
leap    |     1     |
year  +-----------+

week     day    hour   min.  sec.
+--------+-------+------+-----+-----+
second  | 604800 | 86400 | 3600 | 60  |  1  |
+--------+-------+------+-----+-----+
minute  | 10080  | 1440  |  60  |  1  |
+--------+-------+------+-----+
hour    |   168  |  24   |   1  |
+--------+-------+------+
day     |    7   |   1   |
+--------+-------+
week    |    1   |
+--------+
```

#### Months

The several man-made periods of time in a calendar are supposed to have a constant duration. There is one type of period that has not: the month. Every of the twelve months in a year has its own length. That is an integral number from 28 to 31 days. The following table shows the length in days of every month and the day-in-the-year-number of the day immediately before the first day of the month.

```               normal year          leap year
month name  length  day before  length  day before
----------  ------  ----------  ------  ----------
january       31         0        31         0
february      28        31        29        31
march         31        59        31        60

april         30        90        30        91
may           31       120        31       121
june          30       151        30       152

july          31       181        31       182
august        31       212        31       213
september     30       243        30       244

october       31       273        31       274
november      30       304        30       305
december      31       334        31       335

next-year's
january   31       365        31       366
```

The way of calculating the daynumber in the year is given by an example.
5 MAY in a normal year:   120 + 5 = 125
5 MAY in a leap year:      121 + 5 = 126
1 JANUARY:   0 + 1 = 1

Back to Index

### PHYSICAL CONSTANTS

#### TEMPERATURE

```initial-degree-type     calculation     degree-type-target
-----------             -----------             ----------
Kelvin        K - 273.15  =  C                  Celsius
Kelvin       (K - 273.15) * 9/5 + 32.0  =  F    Fahrenheit
Kelvin       (K - 273.15) * 4/5  =  R           Reaumur
Kelvin             K * 9/5   =  A               Rankine
Celsius            C + 273.15  =  K             Kelvin
Celsius            C * 9/5 + 32.0  =  F         Fahrenheit
Celsius            C * 9/5 + 491.67  =  A       Rankine
Celsius            C * 4/5  =  R                Reaumur
Rankine            A * 5/9  =  K                Kelvin
Rankine       A - 459.67  =  F                  Fahrenheit
Rankine      (A - 491.67) * 5/9  =  C           Celsius
Rankine      (A - 491.67) * 4/9  =  R           Reaumur
Fahrenheit   (F - 32.0) * 5/9 + 273.15  =  K    Kelvin
Fahrenheit   (F - 32.0) * 5/9  =  C             Celcius
Fahrenheit   (F - 32.0) * 4/9  =  R             Reaumur
Fahrenheit         F + 459.67  =  A             Rankine
Reaumur            R * 5/4 + 273.15  =  K       Kelvin
Reaumur            R * 5/4  =  C                Celsius
Reaumur            R * 9/4 + 32.0  =  F         Fahrenheit
Reaumur            R * 9/4 + 491.67  =  A       Rankine
```

In this table:
A = Rankine
R = Reaumur
C = Celcius
F = Fahrenheit
K = Kelvin
273.15 * 9/5 = 491.67 = 459.67 + 32.0
One degree difference in Kelvin = one degree difference in Celsius

Example with some equivalents of Celsius and Fahrenheit:

```    Celsius   Fahrenheit           Celsius   Fahrenheit
-------   ----------           -------   ----------
100          212                 22         71.6
93.33       200                 20         68
60          140                 10         50
50          122                  4         39.2
40          104                  0         32
39          102.2              -10         14
37.78       100                -17.78       0
37           98.6              -20         -4
30           86                -40        -40
```

The temperature of the indicator fluid in the process of measuring a volume or a pressure is very important for an accurate result. The temperatures of the indicators in our tables are:

• mH2O = Pressure created by a 1 meter high water column at 4 centigrades.
• mmHg = Pressure created by a 1 millimater high column of mercury at 0 centigrades.
• Litre = Volume of 1 kg of water at 4 degrees Celsius.
• Brit.Imp.Gallon = Volume of 10 pounds-avdp of water at 22 centigrades.
• US.fluid.Gallon = 231 cu.inch.  This approximates the volume of 10 pounds-troy of water at 55 centigrades.

Back to Index

#### DEFINITION OF METER AND SECOND

Meter, by Napoleon Bonaparte and his geodetical engineers:

```(metric) meter =
Circumference of earth   minus   measurement error of 8 km
----------------------------------------------------------
40 million
```

Meter, in 1963 by the physics scientists:

```(metric) meter =  1 650 763.73 wave lengths of
the light emitted by an
excited Krypton-86 atom.
```

Meter, at present, since 1983 by the physics scientists:

```(metric) meter =  1 / 299 792 458 -th  part of
the length travelled by
the light in one second,
in an absolute vacuum.
```

Second, as defined by astronomists in earlier days:

```     second =
1/86400-th part of the average length
of the days in a year.
```

Second, at present by the physics scientists:

```       second =  9 192 631 770 wave periods of
the light emitted by an
excited Cesium-133 atom.
```

Second, proposed in may 2005 by scientists in Tokyo:

```       second =  429 228 004 952 wave periods of
the light emitted by an
excited Strontium atom
emprisoned by laser beams.
```

Kilogram is the mass of a platinum-iridium cylinder stored in the French Bureau-International-des-Poids-et-Mesures at Sevres near Paris.

Back to Index

#### ASTRONOMY

```speed of light  = c         2.99792458 @ 8 [*] m/s
9.83571056 @ 8    ft/s
1.86282397 @ 5  mile/s

astronomical unit (1996)    1.49597870691 @ 11  m
= au = ua               9.29558072674 @ 8   mile

spat                        1 @ +12  m
6.68458712267 astronom.unit

light year                  9.460528405 @ 15   m
5.878499814 @ 12   mile
6323.972635  astronom.unit

parallax second = parsec    3.08567758 @ 16   m
1.91735116 @ 13   mile
206264.80625      astronom.unit
3.2616334409      light year

Hubble                      1 @ +9  lightyear
9.460528405 @ 24   m
```

Back to Index

#### MECHANICS

##### Mass and Density

```specific density of water (at 4`C)  0.999 9724  kg / cu.dm
thus:   1 old litre               1.000 028  cu.dm
norm volume of idealized gas       22.4129  ltr / mol
-- idem --                 22.414 cu.dm / mol
number of particles
in one mol  = Avogadro's-nr.     6.022142 @ 23
amu = unit of atomic mas  = Dalton
=  1/ Avogadro's-number          1.660539 @ -27  kg
bes = hyle                       1000.29  kg
crith (1L H2 at 0.01'C & 1 atm)    89.2295583  mg
density of seawater (at 4`C)        1.026493 * density of normal
```

##### Speed

```nautical speed:           1 knot =   1852 m/h  =  0.5144 m/s
airplane speed:           1 mach = (approximated)
typical                       1193.4 km/h = 331.5 m/s
at sea-level                  1223.1 km/h = 760 miles/h
at high altitude              1062.2 km/h = 660 miles/h
speed of sound of 0 Hz at 0 deg.C    1193.4 km/h
speed of light:               c  =   299 792 458  m/s
```

##### Acceleration and Force

```G = grav = standard acceleration
by earth gravity      9.80665 [*]  m/s2 = 32.174 ft/s2
kilogram-force (kgf)             9.80665 [*]  N
poundforce (lbf)                 4.4482216  N
poundal                          0.13825495  N
Newton (N)                       0.2248089 poundforce  =
0.1019716 kilogramforce =
7.2330139 poundal
sthene                           1  kN  =  1000  N
dyne (dyn)                      10  uN  =  1 @ -5  N [*]
```

##### Energy and Power

```erg                             1 @ -7 J  =  0.1 uJ  [*]
footpound                       1.35581795  J
British thermal unit (Btu)   1055.05585262  J [*]
calory (cal; chemical)          4.1840  J
calory (cal; IT-steam)          4.1868  J [*]
food-Calorie (=1000 IT-st.cal)  4186.8  J [*]
joule (J)                       0.239  cal
watt-hour                       3600   J    (= 0.859845228 Cal)
kilowatt-hour (kWh)             3.6   MJ [*] (= 859.845228 Cal)
gas-constant R (in PV=RT)       8.31432 J / mol / Kelvin
horsepower:
Euro-continent (pk/ps)     735.5  W  =   75 kgf.m/s
USA  (hp)                  745.7  W  =  550 lbf.ft/s
waterpump                  746.043 W = 550.253 lbf.ft/s
donkey-power                  250  W  (= ca. 1/3 horsepower)
USA-man-power                  74.57  W  (= 1/10 horsepower)
```

[*] = This value is exact.

Back to Index

#### MATHEMATICAL CONSTANTS

##### General constants

```square-root of 2               1.41421 35623 73095
square-root of 3               1.73205 08075 68877
square-root of 5               2.23606 79774 99790
square-root of 7               2.64575 13110 64591
square-root of 10              3.16227 76601 68379
pi (of circle circumference)   3.14159 26535 89793
e (the natural number)         2.71828 18284 59045
e-log 10  = ln 10              2.30258 50929 94046
10-log e  = 1 / e-log 10       0.43429 44819 03252
gamma (of factorial calcul's)  0.57721 56649 01533
golden ratio of beauty = (1+sqrt(5))/2  = 1.618034

Pythagoras-constant = sqrt(2)
Archimedes-constant = pi
Euler-constant = Euler-Mascheroni constant = gamma
base of Napier-logarithm = e
```

##### Approximations easily to remember

```Rough approximation         Deviation in %
-------------------         --------------

pi = 3,1415926535897932384626433832795
10-log( pi ) =~= 1/2 = 0.5       +0.6
sqrt( pi ) =~= 1 + 3/4 = 1.75    -1.3
pi^2 =~= 10                      +1.4
pi^3 =~= 31                      -0.02

e = 2,7182818284590452353602874713527
10-log( e )  =~= 4/9 = 0.4444    +2.25
sqrt( e ) =~= 1 + 2/3 = 1.667    +1.25
e^2 =~= 7.5                      +1.667
e^3 =~= 20                       -0.5

10-log(2) = 0,30102999566398119521373889472449
10-log( 2 )  =~= 0.30103000      +15@-7
10-log( 2 )  =~= 0.30            -0.35

Some physical constants:

gravity      =~= 10              +2.2
calory       =~= 4.2             +0.4
horsepower   =~= 750             +2
light-speed  =~= 3 @ 8           +0.07
```

##### History of PI

The name PI stands for the first letter of the Greek word Perimeter, which means Circumference.

For thousands of years the mathematicians tried to find the exact value of PI. Until the Renaissance era they believed that it can be expressed as the ratio of two integral numbers. Some of them (e.g. Ahmes) even thought each of these numbers itself is the square value of another integral number. This is the so-called quadrature of the circle. Therefore they zealously tried to find this rational quotient. They could approach the actual value of PI very closely, but never found it exactly.

Of course they never found this value by that way because PI is an irrational and even transcendental number. This has been proven by Lambert (1728-1777) in 1766, by Legendre (1752-1833) in 1794, and by F.Lindeman in 1882. Therefore the value of PI should be calculated by an infinite polynomial. For this several polynomials are available. In the actual calculation some of these converge very quickly, whilst other ones converge very slowly like the one of Leibniz in 1673.

Some of the old rational approximations are listed here, in the order of increasing accuracy. The factorial subdivisions of the Indian and the Ptolemaian values into prime numbers are made by the author of this history, not by the discoverers of those values. Nowadays in some cases the simple approximation 22/7 by Archimedes is still in use.

```Old-Babylon and Biblical Old-Testament (1-Kings 7:23):
pi = 3
A rough modern-day approximation might be:
pi =        sqrt (10)        =  3.162277660168379332
Ahmes (ca. 2000-1600 BC):
pi = (16/9)^2  =  256 / 81   =  3.160493827160
Archimedes (287-212 BC):
pi lies between    22 / 7    =  3.142857142857
and   223 / 71   =  3.140845070423
pi = 29*13/120 =  377 / 120  =  3.141666666....
in India (ca. 0 - 700 AD), e.g. Aryabhata in 476 A.D.:
pi = (2^3)*3*7*11*17 / 10000 =  3.1416  ['exact']
Actual value (see above):
pi = 3.14159 26535 89793 23846 26433 83279 50288
```

##### Useage of PI

```circle with radius R:
circumference = perimeter length =  2 * PI * R
disc area =  PI * R*R  =  PI * R^2

surface area =  4 * PI * R*R  =  4 * PI * R^2
volume =  (4/3) * PI * R*R*R  =  (4/3) * PI * R^3
```

Back to Index

#### Scales

At first a list of the used names and abbreviations:

```abbreviation     meaning
------------     -------
deg              arcdegree = circular degree
min = '          arcminute = circular minute
sec = "          arcsecond = circular second
[no abbrev.]     centesimal second
mil              NATO-artillery mil
rhumb            nautical rhumb = compass point
```

The mathematical relations between the deg, gon, mil and rhumb are quite easy. Read the table as by this example: 1 rhumb = 25/2 gon = 12.5 gon.

```unit      deg        gon         mil         rhumb
----      ---        ---         ---         -----
deg        1        10/9        160/9        4/45
gon       9/10        1          16          2/25
mil       9/160     1/16          1          1/200
rhumb     45/4      25/2         200           1
```

##### Relations between the scale elements

The following numerical relations hold beteen the rad, deg, gon, mil and rhumb. Read the table as by this example: 1 gon = 16 mil.

```unit              rad            deg
----              ---            ---
full circle     6.28318531       360
deg           0.01745329252       1
gon           0.01570796327      0.9[*]
mil          0.000981747704    0.05625[*]
rhumb          0.196349541      11.25[*]

unit              gon            mil           rhumb
----              ---            ---           -----
full circle       400            6400            32
deg            1.11111111     17.7777778     0.08888889
gon               1              16             0.08
mil             0.0625[*]         1            0.005
rhumb            12.5[*]         200             1
```

Some relations with the other units are:

```circular degree               60 min
circular degree             3600 sec
circular minute               60 sec
centesimal minute            100 centesimal-seconds

circular degree                0.01745 32925 19943 rad
circular minute                0.00029 08882 08666 rad
circular second                0.00000 48481 36811 rad
```

The circular degree and its derivatives the minute and the second are the types of angular units most often used in the technical applications of the goniometry.

##### Larger parts of the circle

A circle is often divided into parts, e.g. quadrants. The table below lists the names and numerical sizes of these parts. Read the table as by this example: An octant is one-eight part of a circle and contains 45 degrees.

```name          part of circle      rad            deg
----          --------------      ---            ---
revolution,cycle   1/1          6.28318531       360
half circle        1/2          3.14159265       180
third circle       1/3          2.09439510       120
sextant            1/6          1.04719755        60
octant             1/8         0.7853981634       45
sign               1/12        0.5235987756       30
hour               1/24        0.2617993878       15

name               gon            mil           rhumb
----               ---            ---           -----
revolution,cycle   400            6400            32
half circle        200            3200            16
third circle     133.33...      2133.33...     10.666...
sextant           66.66...      1066.66...      5.333...
octant              50             800             4
sign              33.33...       533.33...      2.666...
hour              16.66...       266.66...      1.333...
```

#### Goniometrics

In this chapter the circular degrees are used, of which 360 units make a full circle.

##### Easy operations

The following table is a contraption for easy remembrance of some very important sinus-values.

```sin ( 0 )   =  sqrt(0) / 2  =  0
sin ( 30 )  =  sqrt(1) / 2  =  0.5 [*]
sin ( 45 )  =  sqrt(2) / 2  =  0.7071067811865
sin ( 60 )  =  sqrt(3) / 2  =  0.8660254037844
sin ( 90 )  =  sqrt(4) / 2  =  1

[*] means this value is exact.
```

The following table gives the derivatives of the sinus values for every value of x in the range from 0 to 90 degrees.

```cos ( x ) = sin ( 90-x )
tan ( x ) = sin(x) / cos(x)
cot ( x ) = cos(x) / sin(x) = 1 / tan(x)
secans ( x ) = 1 / sin(x)
cosec ( x )  = 1 / cos(x)
```

The goniometric function values of the angles other than those mentioned in the contraption table and in the range from 0 en 90 degrees can roughly be gained by linear interpolation. Example for 50 degrees:

```50 = 45 * 2/3 + 60 * 1/3
sin(50)  =(approx.)=  sin(45) * 2/3 + sin(60) * 1/3
=  0.70711 * 2/3 + 0.86603 * 1/3
=  0.76008
The actual value is 0.76604444

40 = 30 * 1/3 + 45 * 2/3
cos(50) = sin(90-50) = sin(40)
sin(40)  =(approx.)=  sin(45) * 2/3 + sin(30) * 1/3
=  0.70711 * 2/3 + 0.50000 * 1/3
=  0.63807
The actual value is 0.64278761

tan(50) = sin(50) / cos(50) = 0.76008/0.63807 = 1.19122
The actual value is  0.76604444 / 64278671 = 1.1917536
```

Similarily the values of the cotangens, the secans and the cosecans can be calculated.

##### Better accuracy

For better accuracy between sin(60) and sin(90) and thus between cos(30) and cos(0) and the derivative functions in these areas, use quadratic approximation in stead of linear approximation. The formulas for this approximation are:

```for sinus between 60 and 90 degrees:
sin(x) = 1 - 0.0001488606624618 * (90-x) * (90-x)

for cosinus between 0 and 30 degrees:
cos(x) = 1 - 0.0001488606624618 * x * x
```

Example:

```sin(75) = cos(15)  =(approx.)=
=  1 - 0.000148861 * 15 * 15
=  1 - 0.000148861 * 225
=  1 - 0.033494
=  0.966506

The actual value is:  0.9659258262891
```

When x is near zero, the value of the sinus can be calculated by a very simple formula. The value of the tangens will be equal to it. Similar holds for the value of the cosinus and that of the cotangens for x near 90 degrees. In that area the value of the tangens is also very simple. The value of the cotangens is simple for x near zero degrees. These formulas are:

```For x near 0 degrees:
sin(x) = tan(x)  =(approx.)=  0.01745329252 * x
cot(x) = 1 / ( 0.01745329252 * x )

For x near 90 degrees:
cos(x) = cot(x)  =(approx.)=  0.01745329252 * (90-x)
tan(x) = 1 / ( 0.01745329252 * (90-x) )
```

The more x approximates the 0 or 90 degrees, the more accurate the formulas will become. At x = 13 resp. 77 degrees the inaccuracy of the formulae for the sinus or cosinus is only just 1 percent. And then the tangens and cotangens formulae are 2 percent inaccurate.

##### Final remarks

Of course, when the other scale-units are used, they must be converted into degrees before they are used in the goniometric formulae given here. Example:  sin(800 mil) = sin(50 gon)= sin(4 rhumb) = sin(1 octant) = sin(45 degree) = 0.7071068

Now everyone can calculate the goniometric-function values with an inaccuracy of only a few percents by using a simple office calculator, even an ancient mechanical one!

Back to Index

### GREEK, ROMAN AND BIBLICAL MEASURES AND MONEY

The sections with the measure-unit tables are split into two parts: The Old-Testamentical part and the (Greco-)Roman part which embraces the New-Testamentical measure units. For many units the tables mention the Biblical location of only one verse wherein the unit is used.

It was very difficult to collect the right and consistent values. So the tables may have errors very likely. These can be reported to the author.

#### ROMAN AND INDIAN NUMBERS

A "number" is the sequence of symbols (letters or digits) representing a numeric value. There are several ways of making numbers. At present the extended Indian system is the system most common in use. Today the clumsy Roman numbers are in use for romantic purposes only.

##### Roman numbers

Up to medieval times the Europeans used the Greek, the Jewish and above all the Roman system for the notation of numeric values. These systems have two disadvantages compared with the today's notation system.

The first although minor disadvantage of these systems was that the digits were not represented by graphical symbols put apart for the digits only, but by some letters of the alphabet. This may hamper the readability of a text wherein numeric values are used. In the Indian system the symbols of the digits differ from those for the letters. The letters and their numeric values used by the ancient Romans are:

```        M = 1000           (mille)
D =  500           (demi-mille)
C =  100           (centum)
L =   50           (lira)
X =   10           (easy notation of two V's?)
W = VV = 10
U =  V =  5        (unknown; abstraction of spreaded hand?)
Y = IJ = II = 2
I =  J =  1        (bare bar, see text far below)
```

In this Roman system an upperscore (= line above the letter) means that the value of the letter is multiplied by 1000. So an X with an upperscore has the value of 10000. Here the value of the letter is changed by adding a line to it. This worsens even readability. Note that I with upperscore equals M, and Y with upperscore equals MM.

The second and major disadvantage of the Roman, Greek and Hebrew notation systems is the cumbersome way of representing a numeric value. The value is difficult to read. This makes this notation inept for writing down intermediate results in long calculations. Therefore an abacus is often needed. The final result of the abacus calculation must be 'translated' before it is written down on paper.

In general the value of a number is calculated by adding together the values of all digits in that number. But, the value of a digit is subtracted in stead of added when this digit has a right neighbour with a greater value. A digit between two of greater value is subtracted from the right one. Then the left one is added to this result (or when smaller subtracted from it). These rules imply that a numeric value can be notated in different ways. Example:       MDCCCCLXXXYY = MCMXXCIV = 1984.

##### Indian numbers

At around 700 A.D. the Muslim Arabs copied from Hinduistic India a system for writing numbers quite different from the Roman system. It is much easier in use, and so they tried to export it to Europe, in which they succeeded a few centuries later. Therefore often it is unjustly called the Arabic number system. In the past five centuries the European colonialism spread it over the entire world.

Around the year 500 A.D. the Indians invented the digit for the notation of 'nothing': the zero. Also all values between zero and ten got their own digit. So there were ten digits for the ten values from zero up to nine. The values of ten and more did not get a digit at all. These inventions enabled the invention of the main characteristic of the Indian system:

The value of the digit is determined by the position of its symbol in the number. One position to the left means multiplying with the factor ten. One position to the right means dividing by ten. Never additional lines or serifs are added to the symbol to mark its actual value. Simply its position suffices. The total value of the number is always the addition of the values represented by the individual digits. No subtraction is in use. Example:       1984 = 1*thousand + 9*hundred + 8*ten + 4*one

This notation system has great advantages. First a numeric value can be represented in only one way. There never are two notations for the same numeric value. Second enormously big values can be displayed without the creation of new symbols. The ten digit-symbols suffice always. (Remarkably the Arabs use other symbols for these 'Arabic' digits than the Europeans and the rest of the world do). When the value increases the number becomes longer. Thus the length of the number already gives a rough indication of the bigness of the value. Example:       The value of 2000 is displayed with more digits than the smaller value of 37. In the Roman system it is with less digits: MM and XXXVII (= XXCIIIX).

Also the numbers are very well readable. So this notation can be used both for the final result and for the intermediate values in a long calculation. Also the final result can be used directly as input for an other calculation. The abacus becomes superfluous. Therefore the invention of position dependency is invaluably great. It has enabled the steep rise of the modern mathematics and science.

The German baron Gottfried Wilhelm von Leibniz (or: Leibnitz) (1646-1716) invented a similar system with only two digits, 0 and 1: the binary system. Herein the numbers become roughly three times as long as in the Indian decimal system. They are less readable for humans, but they are more apt for the use in mechanical calculators like the modern electronic computers. Example:       BIN-11111000000 = DEC-1984

By the Indian way only integral values could be displayed. Two extensions were added in later times. To show the broken numbers the notation of the fractional part was added. Its length shows the accuracy with which the number approximates the actual value. The exponent notation was added to ease the display of extremely large or small values. Both are applied in the binary system too.

In all number systems the bare bar indicates the digit one. It is derived from a single stroke in the sand or a straight finger (called 'dik' by modern etymologists). A finger bent in the fist is not to be counted. Perhaps this was the basis of the notation for the zero: a circle.
In different languages the Indian word SIFR (=> cipher) has got different meanings: Encryption code, Digit (one out of 0 to 9), Digit zero or Value zero.

Back to Index

#### LENGTHES

For several lengths only one verse is mentioned wherein they are used.

#### Old-Testament lengths

```                              metrical
Hebrew name  consists of   meters   English name  where
-----------  -----------  --------  ------------  -----
amma         2  zeret      48  cm   cubit       Deut  3:11
zeret        3  tofach     24  cm   hand-span     Ex 28:16
tofach       4  esba        8  cm   hand-breadth  Ex 25:25
esba                        2  cm   finger       Jer 52:21
```

#### Greco-Roman lengths

```                               metrical
Greco-Roman name  consists of   meters   English name  where
----------------  -----------  --------  ------------  -----
---- in the Bible ----
pechys                           48  cm   Greek ell   John 21: 8
sabbat.journey  2000  Grk ell   960  m                Acts  1:12
milion,miliarium   8  stadia   1480  m    Roman mile  Matt  5:41
stadion(-um)     100  orguia    185  m    furlong     Luke 24:13
orguia             5  palmipes  185  cm   fathom      Acts 27:28

---- in general ----
milestones-distance             1520   m
schoenus          4   milion    5920   m
leuga, leuca    1.5[*] milion   2220   m     Gaulish/Celtic mile
milion, -arium  1000  passus    1480   m     from: mille = 1000
milion, -arium     8  stadion   1480   m     Roman mile
stathmos         100  stadion     18.5 km    day's march
actum(circumfer.)  4 actum(len.) 142   m
actum (length)     6 actum-minor  35.5 m
actum-minor        2  decimpeda  592   cm
decimpeda          2  passus     296   cm    perch, ten-feeter
passus             5  pes        148   cm    foot step
cubitus-maior      7  palmus      51.8 cm    long cubit
cubitum(cubitus)   6  palmus      44.4 cm    cubit, ellbow
palmipes           5  palmus      37   cm    big foot
pes                4  palmus      29.6 cm    foot
palmus-major       3  palmus      22.2 cm    stretched-hand length
palmus (-minor)    3  uncia        7.4 cm    width of hand-palm
palmus (-minor)    4  digitus      7.4 cm    palm-width
pes, pedes         3  manus       29.6 cm    foot
manus              4  uncia        9.867 cm  hand
pes-naturalis     10  uncia       24.67 cm   natural foot
uncia (='1/12-th')                 2.467 cm  inch, ounce, thumb-width
digitus                            1.85 cm   finger-width

```

At present the sabbatical journey is 2000 meters.
Other distances for the Roman foot have been: 29.42 cm, 29.73 cm, 33.3 cm, 33.35 cm

#### Twelve-knots rope

Many people think that in medieval times in Europa only a very few and rudimentary measurement devices did exist. So the medieval craftsmen would perform every measure by their expert eyes, even when building a hughe cathedral or castle. This is not true. Those people were clever enough to make and use sophisticated and accurate masurement devices.

At building sites they used the so-called Twelve-Knots-rope. This is a circular rope with twelve knots distributed equally over its full length. The rope must be very flexible and the knots must not shift over it.

With this rope several geometric figures can be made with always a knot on every corner point. These figures are parallograms (= slanted rectangles) and triangles. Between the corners the rope is pulled straight, so the intervals between the knots all have the same length, e.g. one ell.

Important shapes are:

• Right-angled triangle: The side of three intervals lies on the floor, the side of four intervals stands upright, and the slanted side (hypotenusa) has five intervals, according to the famous theorem of Pythagoras. Thus one of the three angles is perpendicular.
• Isosceles triangle: Two intervals lie on the floor. The two other sides that stand slanted upright, contain five intervals each. The top-knot hovers exactly above the knot in the middle of the floor side.
• Equilateral triangle: This is an isosceles triangle wherein each side consists of four intervals.
• Slanted rectangle: Two opposite sides both consist of two or one interval. The other two sides have four or five intervals. To keep the angles perpendicular a second device is required.
• Slanted square: This is a slanted rectangle wherein each side consists of three intervals.

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#### Areas in Roman times

```                                      metrical
Roman name          consists of      sq. meters
----------          -----------      ----------
saltus              8  centuria      201.87 hectare
centuria           50  geredium       25.23 hectare
geredium,heredium   2  iugerum          5047.
iugerum             2  acnua            2523.  (day's-work of oxes)
acnua               1  sq. actum        1262.  (120^2 ft2)
sq. actum           4  clima            1262.
clima               9  sq.act.minor     315.4
sq. actum-minor     4  sq.decimpeda     35.05
sq. decimpeda     100  sq. pes           8.7616  (when foot exactly
sq. pes           36/25 sq.pes.natur.    0.087616   equals 29.6 cm)
sq. pes-natur.                           0.058411
```

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#### VOLUMES

For several volumes only one verse is mentioned wherein they are used.

#### Old-Testament volumes

```                            metrical
Hebrew name    consists of   liters    English name  where
-----------    -----------  --------   ------------  -----
---  dry  ---
homer            1  kor       365.                  Levi 27:16
kor              2  lethek    365.      cor         Ez   45:14
lethek           5  ephah     182.5
ephah           10  (g)omer    36.5     epha        Judge 6:19
gomer = omer                    3.65                Exod 16:16
ephah            3  seah       36.5     epha
seah             6  cab        12.17
cab                             2.03
---  liquid  ---
homer           10  bath      365.
bath             3  seah       36.5                 Ez   45:10
seah             2  hin        12.17
hin             12  log         6.1                 Exod 29:40
log                             0.5
```

#### Greco-Roman volumes

```                            metrical
Gr.Roman name  consists of   liters    English name  where
-------------  -----------  --------   ------------  -----
---- in Bible: fluid + dry ----
metretes = Greek-amphora       38.8     measure     John  2: 6
koros (grain)   10  bath      345.8     cor         Luke 16: 7
batos = bath     4  modios     34.58    bath        Luke 16: 6
modios (grain)   8  choinix     8.64    bushel      Matth 5:15
choinix (grain)                 1.08    measure     Revel 6: 6

---- Greco-Roman volumes in general ----
-- connection to foot --
cubic-foot       1  quadrantes     25.934336 (when foot exactly
quadrantes       3  modius/-os     25.934336      equals 29.6 cm)
-- fluid --
dolium          20  amphora       518.7
amphora          1  quadrantes     25.93    Roman amphora
urna             4  congius        12.97
congius          6  sextarius       3.24
sextarius        2  h/gemina        0.540   flu+dry
g/hemina         2  quartarius      0.270
quartarius       2  acetabulus      0.135   flu+dry
acetabulus       6  ligula          0.0675
ligula                              0.0113
congius          8  octarius        3.24
octarius         3  quartarius      0.405
quartarius                          0.135
-- dry --
koros           10  batos         345.8
batos            4  modios         34.58
modios/-us       2  semodius        8.64
semodius         4  choinix         4.32
choinix          2  sextarius       1.08
sextarius        3  ciate           0.540   flu+dry
ciate            4  dry-hemina      0.180   flu
dry-hemina       4  ligula          0.0450
ligula                              0.0113  flu
```

Ltr = Litre = cu.dm = dm3 .

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#### Old-Testament Hebrew weights

```                                 metrical
Hebrew name     consists of       grams     English name
-----------     -----------      --------   ------------
talent          50  early-mina   30. kg
talent          60  later-mina   30. kg
mina (early)    60  shekel        600.       pound
mina (later)    50  shekel        500.       pound
shekel          3/2 = 1.5  pim     10.
pim             4/3 = 1.33 beka     6.67
shekel           2  beka           10.
beka             2  rebah           5.
rebah            5  gerah           2.5      quarter
gerah                               0.5      gram
```

During the exile in Babylon the weight units were twice as heavy. Then a talent weighted around 60 kilograms.

#### Old-Greek weights

```                                   metrical
Greek name      consists of          grams     English name
----------      -----------         --------   ------------
talanton          60  mina           25.86 kg
mina, mna, mnea   25  tetradrachme  431.        pound
drachme            3  diobolos        4.31
diobolos           2  obolos          1.437
obolos             8  halk            0.718
halk                                  0.0898
```

#### Roman weights

For one weight the verse is mentioned wherein it is used.

```                                   metrical
Roman name      consists of          grams     comments
----------      -----------         --------   --------
centenarius       100  libra        32749.
centumpondus      100  libra        32749.
pondus = litra =                    327.5  'pound', see John 12:3
= libbra = libra  12  uncia              equals 0.722 avdp-pound

uncia               2  semiuncia     27.29
semiuncia           2  sicilicus     13.65
sicilicus           2  denarius       6.823
denarius            3  scrupulus      3.411

uncia               3  duella        27.29
duella              2  solidus        9.097
solidus             4  scrupulus      4.549

mina (=Greek-lb.) 5/3  libra        545.8
mina (=Greek-lb.)  20  uncia        545.8
uncia               5  milliaresium  27.29
milliaresium       24/5 scrupulus     5.458

uncia               8  drachma       27.29
drachma             3  scrupulus      3.411

scrupulus           2  obolus         1.137
obolus                                0.569
```

The name Centenarius came to us, westerners, by the Arab way.    Roman centenarius -> Arabic cantar -> Arabic qintar -> European quintal -> European cental.

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#### 'Money' in the Old Testament

The money in the way we know it has been invented by the state of Lydia (in present-day Turkey) at around 700 B.C.   The richest king of this state was Croesus who lived at around 500 B.C.  So before the exile in Babylonia the Israelites did not have coins. They paid with rods and rings of silver of which the values were determined by their weight. One talent is approximately 30 to 60 metric kilograms of silver. It contains: 1 talent = 60 pounds = 3000 shekels. See the table of Old-Testamentical weights in the weights-section.

#### Money denominations in Greek and Roman empire

In this section the money denominations mentioned in the New Testament of the Christian Bible are tabulated, which are the Greco-Roman ones. In the section following the table the explanations and additional notes are written.

In the money table one Denarion is supposed to be equal to 50 Euro. This estimation is valid for the years around 2000. See the elucidation after the table.
For every denomination only one Biblical verse is mentioned wherein it is used.

```Biblical name  #Denar  English name  (est.)# Euro  where
-------------  ------  ------------  ------------  -----
Denarion           1   penny                  50   Matth 20: 4
Drachme            1   drachma                50
Didrachme          2   didrachma             100   Matth 17:24
2   tribute money         100
Stater (silver)    4   stater                200   Matth 17:27
Argurion           4   piece of silver       200   Matth 27: 3
4   silver shekel         200
Stater (gold)     20                       1 000
Mna, mnea        100   minas, pound        5 000   Luke  19:13
Sestertium       250   sestertium         12 500
Talanton        6000   talent            300 000   Matth 18:24

Sestertius       1/4   sesterce               12.5
As, Assarion    1/16   farthing                3.1  Luke 12: 6
Kodrantes       1/64   quadrans                0.8  Matth 5:26
Lepton         1/128   mite                    0.4  Marc 12:42
```

Sestertium is shorthand of mille sestertium = 1000 sesterces.

During the years around 2000 one US-Dollar equalled one Euro very roughly. And also very roughly one British-Pound equalled one and a half Euro. So the values in the table can be translated into the USA- and British currency by the formulas:
Amount of Dollars = Amount of Euros,
Amount of Pounds = Amount of Euros * 2 / 3.

#### Elucidation of the money table

Estimations of the present-day values of the different money denominations are given. These are based on the exact multiplication factors between the different denominations and the words of Jesus in Matt.20:1-16 about the value of one of them. In that paragraph Jesus told about a 'right wage for a day's work'. He means the buying power of the wage of one day's work. This value is one Roman coin called Denarion, which has been translated into the English word Penny. At present (around the year 2000), a (not big, but still) right wage for a day's work is 50 Euro. So in the table the Denarion is put on a par with 50 Euro.

Inflation was unknown in the Greek and Roman empire before Christ. So the Denarion-Euro ratio holds for several hundreds of years, and the table can be applied to the Greek period of 500 years earlier.

#### Big money in the Bible

In many books (even new ones) one can see figures for the conversion between Roman and present-day currencies that are unrealistic small. These figures are derived from a very old table. This table can be found easily by dividing the number of Euros in the upper table by 250.  See the next table:

```                             estimated number of Euros
Biblical name      #Denar    upper table    old tables
-------------      ------    -----------    ----------
Talanton            6000      300 000       1200
(mille) Sestertium   250       12 500         50
Mna, mnea            100        5 000         20
Stater (gold)         20        1 000          4
Argurion               4          200          0.8
Stater (silver)        4          200          0.8
Didrachme              2          100          0.4
Drachme                1           50          0.2
Denarion               1           50          0.2
Sestertius           1/4           12.5        0.05
As, Assarion        1/16            3.1        0.0125
Kodrantes           1/64            0.8        0.0031
Lepton             1/128            0.4        0.0016
```

The values of the upper table give a much better insight in the meaning of the amounts of money mentioned in the several locations in the Bible. They show that similarly to us the people in those times sometimes liked to think big and at other moments they thought too small. Here are some Biblical and non-biblical examples:

Betrayal by Judas = 30 silverpieces = 120 denarii = 6000 Euro (Matthew 26:15). This is in fact a very small amount of money for such an important deal.

Pouring of 325 grams of nard balm = 300 denarii = 15000 Euro! (Mark 14:5). One can buy a rather nice car for it, e.g. a simple BMW. At present only famous fashion houses like Dior, Chanel, Gucci, etc. may sell such expensive perfume bottles.

A very big value is mentioned in the parable of the merciless slave (Matthew 18:23-35). The debt of the second slave was 5000 Euro. The debt of the merciless slave was 3@9 (= 3 milliard-billion) Euro!  Perhaps this slave had wrongly invested in a giant Manhattan-like real-estate project. Only Bill Gates can remit a debt of this size without getting much pain.

The yearly salary of an Athenian citizen in 450 B.C. was on average 500 drachmes. The building of the Acropolis then costed 'several thousands of talents' with a today's value of 10@9 (= one EUR-milliard = one USA-billion) Euros. At that time Athens became a rich state as the silver mines of Laurion delivered 3000 tons of pure silver in total during their hundred years of existence.

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### EXCHANGE RATES in the EMU

#### OFFICIAL EXCHANGE-RATES

On 1-jan-1999 the European Central Bank at Frankfurt connected the value of the Euro-currency to the national currencies according to the following EXACT six-digit values:

```abbrev.  1 Euro eqls  currency type             #Euros (*1000)
-------  --- [*] ---  -------------             --------------
IEP     0.787564  Irish pound                 1269.7381
DEM     1.95583   German mark                  511.29188
NLG     2.20371   Netherlands gulden           453.78022
FIM     5.94573   Finnish markka               168.18793
FRF     6.55957   French franc                 152.44902
ATS    13.7603    Austrian schilling            72.672834
BEF/LUF    40.3399    Belgian + Luxemburg franc     24.789353
ESP   166.386     Spanish peseta                 6.010121
PTE   200.482     Portuguese escudo              4.987979
SIT   239.640     Slovenijan tolar (1-jan-2007)  4.172926
GDR   340.750     Greek drachme (1-jan-2001)     2.9347029
ITL  1936.27      Italian lire                   0.5164569
GBP    --.--      British pound did not join the EMU  -.--
```

[*] = All values in the column '1-Euro-equals' are exact.
The values in the column '#Euros' are approximations. This column is the inverse of the other column.
Example on how to read the table: One Euro equals (exactly) 40.3399 Belgian francs. Thousand Belgian francs together equal (approximately) 24.789353 Euro.
Confusing are the three names for a small country in Nothwestern Europe: Netherlands = Holland = Dutch country. Its currency also had two names: Gulden and Florijn. From the latter comes the old abbreviation DFL = Dutch florine. To enhance the confusion: One of its neighbouring countries calls itself Deutschland.

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#### EASY EXCHANGE-RATES

Numbers of six digits are not easy for use in daily life. Here simple approximations are often satisfactory, like the following rules of thumb:

#### How to compute from local currency to value in euros

```currency  country      actions to be performed
--------  -------      -------------------------------------
IEP   Ireland      multiply with 10, then divide by 8
DEM   Germany      divide by 2
NLG   Netherlands  divide by 2, then subtract 10 %
FIM   Finland      divide by 6
FRF   France       multiply with 3, then divide by 20
ATS   Austria      multiply with 3, then divide by 40
BEF/LUF   Belgium+Lux  divide by 40
ESP   Spain        multiply with 6, then divide by 1000
PTE   Portugal     divide by 200
SIT   Slovenija    divide by 240
GDR   Greece       multiply with 3, then divide by 1000
ITL   Italy        divide by 2000

rough: SIT Slovenija   multiply with 4, then divide by 1000
```

#### How to compute from euros to value in local currency

```currency  country     actions to be performed
--------  -------     -------------------------------------
IEP   Ireland     multiply with 8, then divide by 10
DEM   Germany     multiply with 2
NLG   Netherlands multiply with 2, then add 10 %
FIM   Finland     multiply with 6
FRF   France      multiply with 20, then divide by 3
ATS   Austria     multiply with 40, then divide by 3
BEF/LUF   Belgium+Lux multiply with 40
ESP   Spain       multiply with 1000, then divide by 6
PTE   Portugal    multiply with 200
SIT   Slovenija   multiply with 240
GDR   Greece      multiply with 1000, then divide by 3
ITL   Italy       multiply with 2000

rough: SIT Slovenija  multiply with 1000, then divide by 4
```

#### Other use of the Euro-calculators

During the years around 2000 one US-Dollar equalled one Euro very roughly. And also very roughly one British-Pound equalled one and a half Euro.

The Dutch people should not throw away their Euro-calculators as they can use them for a rough calculation of the avdp-pounds and the brit.imp.gallons. The following table shows the conversion numbers and between parentheses the percentage of the inaccuracy that will occur when the NLG-Euro-calculator is used.

```1 Euro   =   2.20371 NLG
1 kilogram = 2.20462 avdp-pounds  (inacc. = 0.05 %)
10 litres =  2.1997  brit.imp.gallon  (inacc. = 0.2 %)

1 NLG = 0.45378 Euro
1 avdp-pound = 0.45359 kilogram    (inacc. = 0.05 %)
1 brit.imp.gallon = 4.5461 litres  (inacc. = 0.2 %)

Note:  0.1% = 1 gram per kilogram
```

Perhaps the Euro-calculators of other countries can be used for similar conversions between the metric and the Anglo-Saxon measure systems.

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