Measuring Systems and Time Keeping (Cromwell the Great)

Illustration of metric units.

Observe due measure, for right timing is in all things the most important factor.
Hesiod, Works and Days (c. 700 BC) line 694.

A system of measurement is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. In modern times, after the French Revolution and European Revolutionary Wars, there are two major systems in use: the metric system and the British system.

Metric System

Metric prefixes in everyday use
Text	Symbol	Factor	Power
exa	E	1000000000000000000	1018
peta	P	1000000000000000	1015
tera	T	1000000000000	1012
giga	G	1000000000	109
hebdo-	H	10000000	107
mega	M	1000000	106
myria	my	100000	104
kilo	k	1000	103
hecto	h	100	102
deca	da	10	101
(none)	(none)	1	100
deci	d	0.1	10−1
centi	c	0.01	10−2
milli	m	0.001	10−3
dimi-		0.0001	10−4
micro	μ	0.000001	10−6
nano	n	0.000000001	10−9
pico	p	0.000000000001	10−12
femto	f	0.000000000000001	10−15
atto	a	0.000000000000000001	10−18

The metric system is decimal system of measurement. The new system of measures has a rational mathematical basis and ideally with reference to natural phenomena rather than unique artifacts. the metric system is part of the radical effort to sweep away old traditions and conventions and replace them with something new and better.

During the Enlightenment there were proposals to use more rational measuring systems. The French revolution enable to advance in this direction. In 1790, a panel of scientists and deputies recommended the adoption of system of measurements based on natural and universal phenomena. The National Convention accepted the recommendation and mandated the Academy of Sciences to work out a proposal. The Academy of Sciences based on the report of the working groups proposed the new system to the National Convention that approved its proposals in 1791. In 1794. after preliminary work on the units. the National Convention approved the new metric system by law. The law defined the metric, declared mandatory its use in trade, commerce and government, mandated the construction of provisional and definitive standards and established the Committee for Weights and Measures to carry out the study, construction and archive of physical prototypes, improvement, establishment of new units based on the metric system or natural phenomena and divulgation of the metric system.

Initially develop and implemented in France, later it became the official system of measurement of Helvetia, German and Italian states, Louisiana, Spain, Portugal, Scandinavia, South American Republics, Russia, Ottoman Empire and Austria.

It consists of a basic set of units of measurement, known as base units. Derived units are built up from the base units using logical rather than empirical relationships while multiples and submultiples of both base and derived units were decimal-based and identified by a standard set of prefixes.

The base units are:

• The mètre (symbol: m) the unit of length, defined as one ten-millionth of the distance between the North Pole and the Equator on the Meridian passing through Paris.
• The are (are) for land area, defined as the area of a square with sides of length ten metres.
• The stère (st) for volume (particularly of stacked firewood, grains or coal), defined as one cubic metre.
• The litre (l) for dry and liquid volume, defined as the volume of a cube with sides of one-tenth of a metre.
• The gramme (g) for weight, defined as the weight of a cube of pure water with sides of one-hundredth of a metre and at the temperature of melting ice.

The derived units are:

• Centigrade scale (°C) a unit of measurement for temperature. Were 0 °C is the temperature of freezing water, 100 °C the temperature of boiling water.
• The gradian a unit of measurement of an angle. Later replace by the radian. A full rotation of a circle is 400 gradians.
• The radian (rad) a unit for measuring angles. Though the degree of arc is more commonly used.
• The pascal (Pa) a unit of pressure used to quantify internal pressure, stress.
• The poncelet (p) a unit of power. One poncelet is defined as the power required to raise a hundred-kilogram mass (quintal) at a velocity of one metre per second (100 kilogram-force·m/s).

British system

The British system (also called Exchequer Standards or customary units) is the system of units used by the British Commonwealth and its territories. The customary units are based on the historical units of measurement used in England.

The Act for ascertaining and establishing Uniformity of Weights and Measure of 1730 standardized the customary units creating the British Exchequer Standards and redefined units, simplified the association of measurements. It was predated by the Standard Weights and Measures Act of 1706 that abolished obsolete, not widely used or arcane measuring units and repealed local customary units used in Scotland and Ireland. The Act of 1706 also withdrew from circulation and established as nonlegal tender all minted coins not conforming to the Coinage Act (or Coinage Union) of 1701 and its secondary legislation within a four-year period.

The Exchequer Standards of 1730 takes in account more or less the ideas of the Society for Promoting and Improving Knowledge (SPIK), promoted since 1670s, in the need to specify a basic unit and subunits formalized according to a basic unit (inch, pound and gallon). However the base units were defined to certain physical constants or to easily built physical standards. For example the units of length are based on the seconds pendulum.

Besides the British Exchequer Standards, that only consider length, volume and weight, there also exist the maritime units or Greenwich Standards that are used by the British Navy and naval merchants. The SPIK is also defined other units such as temperature and specific scientific ones (electricity, power, etc.). In land survey and plot for legal and commercial purposes Gunter’s measurement or surveyor’s measurement (1620) is used.

There are two temperature scales:
a) The Joint Regulations of the Mints of the Commonwealth of 1706 that created and defined the Newton degrees for metals (°N). This temperature scale is a calibrated to measure the melting points of metals. The thermometer uses linseed oil as thermometric material and measured its change of volume against his reference points, that are the temperature of melting metals. The scale became widely used in pottery, ceramic and glass making. Briefly used in steam engines until the Roemer-Fahrenheit became the standard unit.
b) The Roemer-Fahrenheit degrees (°RF), a usual unit of temperature as defined by the SPIK in 1735. The Roemer-Fahrenheit is a calibrated scale combined the proposals of Ole Christensen Rømer (1701), in calibrating the scale on the freezing and boiling points of pure water, and Daniel Gabriel Fahrenheit (1724) that increased the number of division in order to eliminate fractions and increase the granularity of the scale. The °RF discarded the freezing and boiling points of Fahrenheit and used pure water at normal air pressure as the most easily available and reproducible method of calibration with the freezing point been 0 °RF and 120 °RF its boiling point.

The physical standards of weight, length and volume are keep at the Greenwich Observatory that also has the Maritime units (Greenwich Standards) and Gunter's survey units.

Length

Inch (in), foot (ft) = 12 inches, 1 yard (y )= 3 feet, 1 rod, pole or perch (rd) = 12 feet, 1 mile (mi) = 5280 feet or 1760 yards.

Maritime units (Greenwich Standards)

Nautical mile (M, NM), knot (kn) =o ne nautical mile per hour, used as unit of speed, fathom (ft) used as measure of water depth and cable (1/10 of a nautical mile).

Gunter's survey units

rod/perch or pole, and link

Area

acre =4 rods, 1 square mile = 640 acres

Dry volumes

ounce (oz) = 1 cubic inch, 1 pound = 16 ounces, 1 ton = 2240 pounds. Bushel

Liquid volumes

1 Gallon =2 pottle = 4 quarts = 8 pints

Mass and weight

grain (gr), dram (dr), ounce (oz), pound (lb), stone (st), quarter (qr) and, ton (t).

Pressure

Pounds per square inch (psi)

Temperature (liquids and usual unit)

As defined in The Philosophical Transactions of the SPIK of July 1735. Roemer-Fahrenheit (°RF) Where 0 °RF is the freezing point of water and 120 °RF the point of boiling water.

Temperature of metals (melting points of metals)

Defined by the Joint Regulations of the Mints of the Commonwealth of 1706. Newton (°N), where 0 °N ice melts, 33 °N water boils, 40 °N melting point of an alloy of one part lead, four parts tin and five parts bismuth, 48 °N melting point of an alloy of equal parts of bismuth and tin, 76 °N melting point of tin, 81 °N melting point of bismuth, 96 °N melting point of lead.

Power

Horsepower (HP) and its various versions

Time keeping

Time keeping embodies date (calendars) and time (hour).

Calendars

The main calendars are the following:

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A) The Gregorian calendar, or civil calendar, is a solar calendar. A regular Gregorian year consists of 365 days, in certain years, called a leap year (366 days), a leap day is added to February. A leap year occurs every four years, but the Gregorian calendar omits a leap day in three of every 400 years. The calendar year is from 1 January to 31 December. Each month consists of 28, 30 and 31 days. The week is of seven days.
Its epoch marking retrospectively established are anno Domini[a] (AD) and before Christ (BC) that are used to label or number years in the Gregorian calendars. Though some countries also use the regnal years of the monarchs or an historical event such as Commonwealth Year or the founding of Rome (AUC).

The Gregorian or civil calendar is the most widely used system in the western world, that is to say Europe and America.

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B) The French Republican Calendar is a solar calendar. Its 365 days are divided in 12 months, each of 30 days. The calendar year starts in northern autumnal equinox (22 of September) and the years is from 1 of Vendémiaire to fourth or fifth complementary day. The week consists of ten days called décades. The names of weekdays are primidi (first day), duodi (second day), tridi (third day), quartidi (fourth day), quintidi (fifth day), sextidi (sixth day), septidi (seventh day), octidi (eighth day), nonidi (ninth day) and décadi (tenth year). The tenth day, décadi, replaced Sunday as the day of rest and festivity. Later the quintidi was also declared of rest. The five or six extra days needed to approximate the solar or tropical year were placed after the months at the end of each year and called complementary days.
The leap year is called Sextile, an allusion to the "bissextile" leap years of the Gregorian calendar, because it contains a sixth complementary day.

The Republican Calendar is officially use in France and its colonies and Louisiana. It is co-official in Haiti, Rhenania and Switzerland were the official one is the Gregorian, It also used in the Indian states of Mysore, Hyderabad, Travancore and Coorg were its the main civil calendar along the Gregorian, Islamic and Hindu calendars. It was also used by the Northern Italian republics until its replacement with the Italo-Iberian Civil Calendar.

In 24 October 1792 the French Republican Calendar is adopted and also extended proleptically to its epoch of 22 September 1790. The epoch marking is the Year I of the Republic (22 September 1790).

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C) The Italo-Iberian Civil Calendar is a solar perennial calendar. Its 365 days are divided in 8 months of 28 days and 4 months of 35 days. The one or two extra days are called intercalendary days. The week is of seven days. The week starts on Monday and the names of the weekdays are the same as in Italian, Spanish, Portuguese, Latin, Greek, Tagalog, and Cebuano. The calendar year starts in the March equinox (20 of March) and the years is from 1st of Primio to the first or second intercalendary day. The leap year is the same as in the Gregorian calendar.

This calendar was made has a compromise between the Gregorian and Republican calendars by the Commission on Calendar Reform of the Italian Republic being also its early users the Spanish and Portuguese republics. Its epoch marking is the same of the Gregorian Calendar. The official year notations are Before Common Era (BCE) and Common Era (CE) as replacements of BC/AC. An alternative notation is Era Vulgaris (EV) instead of CE. However, in common usage BCE/CE and BC/AD are used interchangeably. In Italy some dates and calendars are given out the year in the epoch era AUC for the founding of Rome. AUC being the abbreviation of: Ab urbe condita (from the founding of the City) or Anno urbis conditæ (in the year since the City's founding). For example the year 1848 AD is rendered as 2601 AUC.

The 20 March 1815 the Italo-Iberian Civil Calendar came in official use in the Italian Republic, Liguria, Etruria and Piedmont. is the official civil calendar in Iberia since 1826. It is co-official in some South American republics and the Philippines.

D) Islamic Calendars

D1) The Islamic, Muslim, or Hijri calendar (Arabic: التقويم الهجري‎ at-taqwīm al-hijrī) is a lunar calendar consisting of twelve months in a year of 354 or 355 days. It is used to date events in Muslim countries. It is also used by Muslims to determine the proper days of Islamic holidays and rituals, such as the annual period of fasting and the proper time for the pilgrimage to Mecca.
The Hijri calendar is the official one in all Islamic countries. In Iran, Afghanistan and Ottoman Empire it is used along the respective Solar Hijri and Rumi calendars.

D2) The Solar Hijri calendar (Persian: گاه‌شماری هجری خورشیدی, Pashto: لمريز لېږدیز کلیز) is a solar calendar that begins on the March equinox as determined by astronomical calculation for the Iran Standard Time meridian (52.5°E) and has years of 365 or 366 days divided in twelve months. Its epoch dates from the Hijrah (633, but as it is a solar calendar, its year numbering does not coincide with the Lunar Hijri calendar. It is used in Iran, Afghanistan and Central Asia.

D3) The Rumi calendar (Turkish: Rumi takvim, "Roman calendar") is a specific calendar based on the Julian calendar but starting with the year of Muhammad's emigration (Hijra) in 622 AD, officially used by the Ottoman Empire after Tanzimat. Adopted for civic matters and is a solar based calendar, assigning a date to each solar day.

All Islamic calendars (Hiir, Solar HHihir and Rumi) employ the Hijri era whose epoch was retrospectively established as the Islamic New Year of AD 622. During that year, Muhammad and his followers migrated from Mecca to Yathrib (now Medina) and established the first Muslim community (ummah), an event commemorated as the Hijra.

Months in major western calendars

Calendars, ordered according to respective first to last month of year

No. of month	Gregorian (length in days)	French Republican (each month as 30 days)	Italo-Iberian Civil (length in days)
1	January (31 days)	Vendémiaire	Primio (28 days)
2	February (28 days, 29 in leap years)	Brumaire	Secondorio (35 days)
3	March (31 days)	Frimaire	Tertio (28 days)
4	April (30 days)	Nivôse	Quartil (28 days)
5	May (31 days)	Pluviôse	Quintil (35 days)
6	June (30 days)	Ventôse	Sextil (28 days)
7	July (31 days)	Germinal	Septembero (28 days)
8	August (31 days)	Floréal	Octobero (35 days)
9	September (30 days)	Prairial	Novembero (28 days)
10	October (31 days)	Messidor	Dicembre (28 days)
11	November (30 days)	Thermidor	Undicembre (35 days)
12	December (31 days)	Fructidor	Duodicembre (28 days)
Intercalation	none	Complementary days (5 days, 6 days in leap years)	Intercalendary days (1 day, 2 days in leap years)

Hours

Clock with 12 hour clockface

The two main standard time units used worldwide are the following:
The Clock time or sexagesimal time divides the day into or 24 hours, each hour into 60 minutes and each minute into 60 seconds.

1 day=24 hours,
1 hour=60 minutes,
1 minute = 60 seconds

The basic 24 hour format of time is [hh]:[mm] and the long format is [hh]:[mm]:[ss], were:
[hh] refers to a zero-padded hour between 00 and 24 (where 24 is only used to denote midnight at the end of a calendar day).
[mm] refers to a zero-padded minute between 00 and 59.
[ss] refers to a zero-padded second between 00 and 60 (where 60 is only used to denote an added leap second).
The 12 hour format is divided into two periods:a) 00:00 to 12:00 that is AM (from Latin ante meridiem, translates to, before midday) and b) 12:01 to 23:59 that is PM (from Latin post meridiem translates to, past midday).

Clock time is used in the Commonwealth and mostly standard worldwide and is used by the GMT (Greenwich Mean Time) as part of its time zones. The International Meridian Conference established that sexagesimal time is one of its two time units to be used in the Coordinated Meridian Time.

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Public 10-hour clock

The Decimal time or French Time is defined as the division of the day into 10 decimal hours, each decimal hour into 100 decimal minutes and each decimal minute into 100 decimal seconds.

1 day=10 decimal hours,
1 hour=100 decimal minutes,
1 minute = 100 decimal seconds

The basic 10 hour format of time is [hh]h.[mm]m. (08h.32m) or [hh].[mm]h (8.32h)

The decrees of 1792 and 1794 established the basis of the decimal hour and the Hour of Paris (Heure de Paris) as the standard time of reference. In 1810 under the Consulate it was established the national time for France and the Hour of Paris was renamed the Normal Hour of France (Heure normale de France, HNF).

The 10-hour standard is used in France, Rhenania, Louisiana, Dakota, Haiti, and in part by sister republics. The decimal time was used in the temps universel coordonné (TUC) that was the 10-hour alternative to the GMT time zones, using the HNF.. The International Meridian Conference established that decimal time is one of its two time units to be used in the Coordinated Meridian Time.

Geographic Coordinate Systems and Time Zones

The Two Prime Meridians before the Rhenania Conference.

A geographic coordinate system is a coordinate system that enables every location on Earth to be specified by a set of numbers, letters or symbols. A common choice of coordinates is latitude, longitude and elevation.

With the advancement of railroads, steamboats and radio communications that it became convenient to take in account due to their differences in their geographical longitudes the variations in time, which varied by four minutes of time for every degree of longitude, and a form to have a common local time across large areas and in countries themselves. Various methods were tried and the creation of time zones was the most convenient. The first one was the use of GMT, that was already used in sea navigation to determine the longitude. Later France created a metric based system, the TUC. Due to differences in the prime meridian they used it became troublesome to make conversions between the two rival time zones.

An International Meridian Conference was called by Rhenania in order to choose a meridian to be employed as a common zero of longitude and standard of time reckoning throughout the world. The conference, besides choosing the Greenwich Meridian, it established the CMT as the basis for a common time zone standard

Prime Meridian

A prime meridian is a meridian (a line of longitude) in a geographic coordinate system at which longitude is defined to be 0°. There were two competing prime meridians until the International Meridian Conference recommended the Greenwich Meridian as the prime meridian and the Coordinated Meridian Time as its time zone standard.

Prime Meridian	Greenwich (degrees)	Paris (degrees)	Greenwich (gradians)	Paris (gradians)
The Greenwich Meridian, based at the National Observatory, Greenwich, in London, Commonwealth. It is the most used reference meridian on charts and maps. Became the prime meridian on recommendation of the International Meridian Conference.	0°	2° 20´ 15" E	0	-2.5954g
The Paris Meridian (French: méridien de Paris) is the meridian line running through the Paris Observatory in Paris, France. It was a long-standing rival to the Greenwich Meridian as the prime meridian of the world.	2° 20´ 15" W	0°	+2.5954g	0

Previous commonly used prime meridians were:

• Ferro Meridian (18° 03′ W, later redefined as 17° 39′ 46″ W)
• The Cadiz meridian (6° 17' 35.4" W) used by the Spanish and later the Iberian Navy until switched to Greenwich meridian
• The meridian of Antwerp (4° 24′ E) used for geographic referencing in Flanders.
• The Amsterdam meridian (4° 53′ E)
• the Pulkovo meridian (30° 19′ 42.09″ E) that passed on the center of the Pulkovo Observatory of Saint Peterborough. Used in Russia before changing to Greenwich.

Time Zones

Before the use of time zones and before clocks were invented, it was common practice to mark the time of day with apparent solar time (also called "true" solar time) – for example, the time on a sundial – which was typically different for every location and dependent on longitude. With well-regulated mechanical clocks it became widespread in each city began to use some local mean solar time.

The advancement of steamboats and railroads aroused the need of a more convenient form of time zone covering larger areas became necessary. Though the Commonwealth and France by law established national standard times: Commonwealth Standard Time (CST) and Heure normale de France (HNF, former Heure de Paris).

Early examples of time zones were:

A) the Atlantic Time (or Boston Time) used by the British colonies in north-west America,

B) Louisianian Time (or Mississippi Hour),

C) the Australian time zones of New Arcadia and Cygnia

D) the three time zones of India - West (Bombay), Central (Madras) and East Indian (Calcutta)

E) the five South American Time Regions promoted by the League of American Republics (Atlantic, East Central Austral, West Central and Pacific).

The time zones of Australia and India were used by common agreement between France, Commonwealth, Dutch Republic and other European countries. By the late 18th century all existing regional times zones were replaced either by the GMT or the UTC.

There were two worldwide time zones used before the Coordinated Meridian Time (CMT). These were:

Greenwich Mean Time (GMT) that divides Earth in 24 equal time zones of 15 degrees each, where each zone as a common local time that is an offset of one hour from the GMT.

GMT	Degress (Greenwich Meridian)	GMT (time)	Gradian equivalent	HNF equivalent
-12	-180	-12	200.00	-5.00.00
-11	-165	-11	216.67	-4.58.33
-10	-150	-10	233.33	-4.16.66
-9	-135	-9	250.00	-3.75.0
-8	-120	-8	266.67	-3.33.33
-7	-105	-7	283.33	-2.91.66
-6	-90	-6	300.00	-2.50.00
-5	-75	-5	316.67	-2.08.33
-4	-60	-4	333.33	-1.66.66
-3	-45	-3	350.00	-1.25.0
-2	-30	-2	366.67	-0.48.33
-1	-15	-1	383.33	-0.41.66
0	0	0	0.00	0.00.00
1	15	1	16.67	0.41.66
2	30	2	33.33	0.83.33
3	45	3	50.00	1.25.0
4	60	4	66.67	1.66.66
5	75	5	53.33	2.08.33
6	90	6	100.00	2.50.00
7	105	7	116.67	2.91.66
8	120	8	133.33	3.33.33
9	135	9	150.00	3.75.0
10	150	10	166.67	4.16.66
11	165	11	183.33	4.58.33
12	180	12	200.00	5.00.00

Temps universel coordonné (TUC) that divides Earth in 10 equal time zones of 40 gradians each, where each zone as a common local time that is an offset of one decimal hour from the Heure normale de France (HNF, former Heure de Paris).

Time zones TUC

Degrees (Paris Meridian)	Gradians	HNF	GMT equivalent
180 W	200	-5	-12:00
144 W	240	-4	-9:36
108 W	280	-3	-7:12
72 W	320	-2	-4:48
36 W	360	-1	-2:24
0	0	0	0:00
36 E	40	1	2:24
72 E	80	2	4:48
108 E	120	3	7:12
144 E	160	4	9:36
180 E	200	5	12:00

The international standard for time zones is:

the Coordinated Meridian Time (CMT) that divides Earth in 20 equal time zones of 18 degrees/20 gradians each, where each zone as a common local time that is an offset of 72 sexagesimal/50 decimal minutes from the GMT and HNF respectively. Both GMT and HNF refer to midnight as zero hour (00:00:00, 0.0h). The Conference also gave room that national or territorial hours could deviate if they are inside one of the CMT zones, for example add or subtract minutes from the CMT common local time, usually half-hours or quarter-hours. Some CMT times were locally rounded to the nearest quarter half until the invention of electro-mechanical clocks and radio time signals.

Time zones CMT

CMT	Degrees (Greenwich Meridian)	Gradians (Greenwich Meridian)	GMT	HNF
-10	180 W	200	-12:00	-5.00
-9	162 W	220	-10:48 (local -10:45)	-4.50
-8	144 W	240	-9:36 (local -9:45)	-4.00
-7	126 W	260	-8:24 (local -8:30)	-3.50
-6	108 W	280	-7:12 (local -7:15)	-3.00
-5	90 W	300	-6:00	-2.50
-4	72 W	320	-4:48 (local -4:45)	-2.00
-3	54 W	340	-3:36 (local -3:30)	-1.50
-2	36 W	360	-2:24 (local 2:30)	-1.00
-1	18 W	380	-1:12 (local -1:15)	-0.50
0	0	0	0:00	0.00
1	18 E	20	1:12 (local 1:15)	0.50
2	36 E	40	2:24 (local 2:30)	1.00
3	54 E	60	3:36 (local 3:30)	1.50
4	72 E	80	4:48 (local 4:45)	2.00
5	90 E	100	6:00	2.50
6	108 E	120	7:12 (local 7:15)	3.00
7	126 E	140	8:24 (local 8:30)	3.50
8	144 E	160	9:36 (local 9:45)	4.00
9	162 E	180	10:48 (local 10:45)	4.50
10	180 E	200	12:00	5.00

Summmary

	British norms	Metric norms	Other commonly used norms
Weights and measures	British system (Exchequer Standards or customary units)	Metric system	Customary systems
Units of currency	Non-decimal	Decimal	Non-decimal
Calendar system (solar)	Gregorian calendar, or civil calendar	French Republican Calendar	Italo-Iberian Civil Calendar, Julian calendar, and Rumi calendar
Calendar system (lunar)	n/a	n/a	Islamic, Muslim, or Hijri calendar
Calendar system (lunisolar)	n/a	n/a	Chinese calendar and variants, Imdic/Hindu calendars, Buddhist calendars and Hebrew calendar
Time format	Clock time or sexagesimal time	Decimal time	Local solar time
Prime Meridian	Greenwich Meridian (Degrees)	Paris Meridian (Gradian)
Time zones	Greenwich Mean Time (GMT) and Coordinated Meridian Time (CMT)	Temps universel coordonné (TUC) and Coordinated Meridian Time (CMT)

See also

Currencies.

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