- 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
- Linear measures = Lengths
- Square measures = Areas
- Cubic measures = Volumes
- Masses = 'Weights'
- Metric system
- Pressures
- Earth sciences
- Physical constants
- Greek, Roman and Biblical measures and money
- European currency exchange rates
- Writer's Home-page and E-mail:
- Books used:
- CRC Handbook of Chemistry and Physics,

ed. 1974/75 = nr. 55 (yes, that old) - Webster's Comprehensive Dictionary, ed. 1996
- Frithiof Dahlby: Bibel-ABC, Stockholm Svenska

Kyrkans Diakonistyrelses Bokforlag - Terry Jones: The Story of One, TV-documentary

BBC-TV-one, autumn 2005

- CRC Handbook of Chemistry and Physics,
- Internet sites:
- Frank Tapson
- Russ Rowlett
- Jack Proot
- the Foot Rule, for old-english measures
- Internet-French-Property real estate agents
- UK Metrication Association
- US Metrication Association
- Brian P(...)
- Sergey & Anna Gershteins
- Chemistry Dept. of Free Univ. at Berlin
- The constants and equations page
- Jacobs astronomical data
- US Geological Survey
- USGS (2)
- USGS (3)
- J. Louie
- North-American atmosphere research institute
- Jim Croft
- South-Korean writer Jinsuk
- Robert Fogt (old version was used)
- Alan Eliasen for the Frink calculating tool
- Italian writer 'TheMeter' which cannot be retraced.
- Some other sites which I cannot retrace anymore.

- Sites about karats and carob trees:
- Introduction and Explanation,
- Conversion tables for Anglo-Saxon versus Metric,
- Other tables
- 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. - Linear measures (= Lengths)
- Square measures (= Areas)
- Cubic measures (= Volumes)
- Masses (= 'Weights')

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-SAXONThis is a separate document.

Part 5: REFERENCES AND LINKS TO INTERNET SITESBack to Top of Index

## Part 1: MANUAL AND EXPLANATIONS

READ ME FIRST #### 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:

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.

Back to Index

#### 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.Back to Index

#### 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 = 0.41378The 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 unitsSquare 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 m3When 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.

See also the section about metric pitfalls.#### 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 0.00012345In the actual tables the marking with the asterisk can be applied in either one of the three ways:

#### 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.Back to Index

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

This instruction holds for the following chapters:

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) .

Back to Index

#### 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.Back to Index

METRIC VERSUS ANGLO-SAXON #### DIFFERENCE IN CULTURE OF TECHNICS

#### 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 Australia Canada 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.

Back to Index

#### GLOBAL ADVANTAGES

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.

Back to Index

#### 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.Back to Index

#### 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!

Back to Index

#### ORTHOGONALITY AND ANGLO-SAXON DISADVANTAGES

#### 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.

Back to Index

#### 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.

Back to Index

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.

Back to Index

#### 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`Back to Index

#### 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

USA-hogshead = 63 gallon and Imperial-wine-hogshead = 52.5 gallonIn 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.

Back to Index

#### 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.

Back to Index

#### 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 hogshead 6 63 wine-hogshead 5 52.5 (old) tierce 4 42 wine-barrel 3 31.5 tenhalf 1 10.5`Back to Index

#### 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 cubicBack to Index

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

LINEAR MEASURES = LENGTHS #### SURVEYOR + CHAIN + BRITISH-NAUTICAL

#### 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 +++ radar-data-mile 1 sea-mile 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 ... - +++ Gunter-chain 100 Gunter-link 66 Gunter-link 7.92 inch 0.66 Ramsden-chain 100 Ramsden-link 100 Ramsden-link 12 inch 1 engineer's-chain 100 engineer's-link 100 engineer's-link 12 inch 1 +++ 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 rod (pole,perch,lug) 25 (Gunther-)link 16.5 link = Gunther-link 7.92 inch 0.66 +++ 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 step 2.5 Ramden-link 2.5 Ramden-link 1 engineer's link 1 engineer's link 1 foot 1 +++ fall 270 inch 22.5 +++ FALL 6 (English) ell 22.5 ell = English ell 5 span 3.75 FALL 5 goad 22.5 goad 2 Flemish ell 4.5 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 Ram(s)den-link 1 foot 12 engineer's link 1 foot 12 +++ 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 +++ Ram(s)den-link 1 foot 12 engineer's link 1 foot 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 shoe-iron 3 hair breadth 1/48 hair-breadth 10 twip 1/144 twip 1/1440 >> LINE 6 Adobe-point 1/12 Adobe-point 2 hair-breadth 1/72 hair-breadth 10 twip 1/144 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 1828.8 radar-data-mile 0.5468066 / 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 1.3716 goad 729.07553 / 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 0.3048 Ramden/engineer-link 3.280840 / 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 0.35277778 Adobe-point 28.34646 / 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 link (7.92 inch) = Gunter link = Imperial link.

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 [*] ---- ------------ ------------------ foot = Ramden-link 1 30.48 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... Adobe-point 1 / 72 0.3527777777... 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

#### USA-SURVEY + INTERNATIONAL-NAUTICAL

#### 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:

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

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.`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`#### International-Nautical and Canadian

##### 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 league 3 Canadian mile 4827 0.20716801 / 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 Canadian league 15836.5825 [*] 15836.6141732 Canadian mile 5278.8608333... 5278.8713911 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 league 3 Canadian mile 4827 0.20716801 / 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

#### OTHER MEASURES

#### 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 ---- --------------- ------ versta 500 sadzhen, sagene 3500 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 cotton-thread 1 French ell 1.5 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 cut 120 lint-thread 300 lint-thread 5 cubit 2.5 +++++ 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 fathom 2 ounce-thread 2 ounce-thread 1 yard 1 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 goad 1 French ell 54 French ell 3 cubit 54 yard 2 cubit 36 cubit 2 breadth-of-flags 18 breadth-of-flags 1 linear-quarter 9 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 2.2860 lint-thread 437.44532 / km fath 1.8288 fathom 546.80665 / km 1.524 wool-bolt-width 656.16798 / km 1.3716 goad 729.07553 / km 1.3716 cotton-thread 729.07553 / 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 0.9144 ounce-thread 1.093613 / 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 0.2286 breadth-of-flags 4.374453 / 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 AND VEHICLE SPEED

#### 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 kphBack 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 quarter-section 1 homestead 774400 homestead 2 USA-lot 774400 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 647497.03 homestead 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

#### OTHER AREAS

#### 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 register-ton 2 squared-load 100 squared-load 1.25[*] unhewn-load 50 Riga-last-sq.sawn 2 unhewn-load 80 unhewn-load 1 freight-ton 40 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 Petrograd-standard 33 bulk-barrel 165 Riga-last-sq.sawn 16 bulk-barrel 80 Riga-last-round 13 bulk-barrel 65 squared-load 10 bulk-barrel 50 unhewn-load 8 bulk-barrel 40 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 cu. yard 1 USA-general-load 27 USA-general-load 9 garden-straw-bale 27 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.

Petrograd-standard = st.Petersburg-standard = Pittsburg-standard.

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 4.672280 Petrograd-standard 0.2140283 / 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 1.415842 squared-load 0.7062933 / 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 1.132674 unhewn-load 0.8828666 / cu.m DT 0.9910896 displacement-ton 1.0089905 / cu.m 0.7645549 USA-general-load 1.3079506 / 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 last 2 horse-load 172033.6 640 horse-load 1 wey 86016.8 320 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 horse-load 0.7094398 / 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 puncheon 2 hogshead 126 hogshead 2 wine-barrel 63 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 hogshead 7 firkin 63 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 ---- ----------- -------- +++++ trade and industry +++++ 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 wine-hogshead 5 tenhalf 52.5[*] tierce 4 tenhalf 42 wine-barrel 3 tenhalf 31.5[*] tenhalf 10.5 [*] gallon 10.5[*] claret-hogshead 46 gallon 46 butt = pipe 2 hogshead 108 hogshead 3 runlet, rundlet 54 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 wey 1 horse-load 320 horse-load 5 seam 320 horse-load 8 big-sack 320 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 1454.7488[*] horse-load 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 209.12014[*] claret-hogshead 4.781940 / 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-hogshead 3 kilderkin 54 beer-barrel 2 kilderkin 36 kilderkin 2 firkin 18 firkin 9 gallon 9 ale-hogshead 1.5[*] ale-barrel 51 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 235.6788 ale-hogshead 4.243064 / 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

#### WINE BOTTLES AND OTHER VOLUMES

#### 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 nebuchadnezzar 20 15378.235 15153.633 15000 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 | -----------------+------------+------------+------------+`Reading of the table:

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 / litreHerein is:

UK-gallon = Imperial gallon

USA-gallon = USA-liquid gallon

1 mile = 1 land-mile = 1 statute-mile = 1.609344[*] kilometerBack 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 deadweight-ton 1 long ton 2240 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 3.0617485 head 326.6108 / 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

#### TROY + APOTHECARY + OLD ONES

#### 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

#### JEWELRY

#### 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-ship-load 20 c-keel, c-barge 949760 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 h-load-old-hay 9 b-barrel 2016 b-barrel 1 c-large-sack 224 c-large-sack 2 long hundredweight 224 long hundredweight 1 c-sack 112 c-sack 1 b-dutch-cask 112 b-Dutch-cask 2 f-bushel 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 h-load-old-hay 6 b-Essex-wey(?) 2016 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[*] new lead-fother 19.5[*] long-hundredw. 2184 old lead-fother 1 h-load-new-hay 2160 h-load-new-hay 30 fotmal 2160 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-load-new-hay 36 h-truss-new-hay 2160 h-truss-new-hay 10 sixpounder 60 h-load-of-straw 36 h-truss-of-straw 1296 wey 7 h-truss-of-straw 252 h-truss-of-straw 6 sixpounder 36 sixpounder 6 pound 6 +++++++ small and no chains +++++++ mercury-flask: UK 76 pound 76 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 fothers 6 Canada-cement-barrel 2100 Canada-cement-barrel 2 lead-wey 350 lead-wey 2.5 [*] lead-fotmal 175 lead-fotmal 5 stone 70 stone 14 pound 14 lead-wey 2 Canada-cement-bag 175 Canada-cement-bag 7 USA-wool-stone 87.5[*] USA-wool-stone 1 lead-stone 12.5[*] lead-stone 12.5[*] pound 12.5[*] 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 990.6457 new-lead-fother 1.009443 / t 979.7595 old-lead-fother 1.020659 / t 979.7595 load-new-hay 1.020659 / t 914.4422 load-old-hay 1.093563 / t 90.718474[*] bone-dry-ton (wood) 1.102311 / t 90.718474[*] short ton 1.102311 / t 587.8557 load-of-straw 1.701098 / 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 158.7573 Canadian-cement-barrel 6.298922 / 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 79.37866 lead-wey 12.59784 / 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 Dutch-butter-cask 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 39.68933 Canadian-cement-bag 25.19569 / t 38.10176 butter-tub 26.24551 / t 34.69982 general-mercury-flask 28.81860 / t 34.47302 UK-mercury-flask 29.00819 / t 34.01943 USA-mercury-flask 29.39497 / t 32.65865 fotmal 30.61976 / t 31.75147 lead-fotmal 31.49461 / 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 lead-stone 176.3698 / 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 Oats (not in Canada) Egg-plant 33 14.96854821 66.806746 Canada-oats 34 15.42214058 64.841842 Grass, timothy 45 20.41165665 48.991614 Rice Barley 48 21.77243376 45.929638 Apples Cucumbers Millet 50 22.67961850 44.092452 Muscadines 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 ladino 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

#### OTHER WEIGHTS

#### 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 ------ ---- -------------- ----------- ----------- Y yotta +24 quadrillion septillion Z zeta +21 trilliard sextillion E exa +18 trillion quintillion P peta +15 billiard quadrillion 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 AmpereAreas 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 = ugWhy 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 Dutch-load 3000 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 #### BASIC UNITS AND COEFFICIENTS

#### 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 moreAt 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; adult people are overthrown 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

#### RICHTER: EARTHQUAKES

#### 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

#### CALENDAR: DATE AND TIME

#### 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[*] m.second = blink 0.864[*] +++ 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 = 1Back 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

Synonym: Centigrade = degree CelciusExample 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 water at 4 centigrades`##### 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.

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#### 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 Ptolemaios (ca. 125-150 AD): 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 globe, ball with radius R: 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

#### CIRCLES: SCALES AND GONIOMETRICS

#### Scales

##### Elements: radians, degrees, grades, etc.

At first a list of the used names and abbreviations:

`abbreviation meaning ------------ ------- rad radian deg arcdegree = circular degree min = ' arcminute = circular minute sec = " arcsecond = circular second gon centesimal grade angular-mil centesimal deci-grade centigon centesimal minute = centigrade [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 rad 1 57.2957795 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 rad 63.6619772 1018.59164 5.09295818 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 grade 54 min centesimal grade 3240 sec centesimal grade 10 angular-mil centesimal deci-grade 10 centigon centesimal minute 100 centesimal-seconds radian 57deg 17' 44.80625" radian 57.29577 95131 deg radian 3437.74677 07849 min radian 2 06264.80625 sec 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 quadrant 1/4 1.57079633 90 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... quadrant 100 1600 8 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 stadion(stadium) 125 passus 185 m 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 400-BC.Greek Olympia stadion 192.28 m`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.

Back to Index

#### AREAS

#### 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`sq = square = quadratus. Example sq.actus = actus quadratus

Back to Index

#### 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 quadrantes 2 urna 25.93 flu+dry 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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#### WEIGHTS

#### 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 tetradrachme 4 drachme 17.24 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

#### '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 Tetradrachme 4 tetradrachma 200 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 Tetradrachme 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.Back to Index

#### 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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