For Librarians

Mathematical data for bibliographic descriptions of cartographic materials and spatial data

Jan Smits, Koninklijke Bibliotheek

Original release: 1996
Last update: February 15, 2013

Recovered by Joel Kovalsky, October 23, 2015

Diacritical signs recovered by Miljenko Lapaine, November 2, 2015

Online again by Dražen Tutić, November 2, 2015

Map projections
Map projection is “the process of systematically transforming positions on the Earth’s spherical surface to a flat map while maintaining spatial relationships. This process is accomplished by the use of geometry or, more commonly, by mathematical formulas. Map projection can be best visualized by imagining a light bulb placed at the centre of a transparent globe and having its lines of longitude and latitude cast upon either a flat sheet of paper or a sheet of paper rolled into a cylinder or cone placed over the globe.” (from Atlas of Canada: map projection).

A good text for beginners to consult the text concerning scale and map projection from Arthur H. Robinson’s et al. book Elements of cartography (6th ed., New York, 1995).
For a more sophisticated approach one can use the unit on , which is part of Brian Klinkenberg’s GIS and Cartography Online Resources with the University of California at Santa Barbara.

For those converting analogue to digital the following publications are available:

Map projections used by the U.S. Geological Survey / by John P. Snyder. – 2nd ed. – Washington : United States Government Printing Office, 1984. – 313 p. : ill. ; 23 cm + map. – (Geological Survey bulletin ; 1532)

A more recent online edition of this publication with a zipped file which contains the entire text of USGS Bulletin 1856, Bibliography of Map Projections, edited by John P. Snyder with Harry Steward and published in 1988. John Snyder has since corrected, supplemented, and renumbered the text in 1994 and 1996. It is also converted from a coded file, which can be printed with all the diacritical marks in the various languages on an Epson printer using a homemade word processor, to HTML codes to permit reading of all diacriticals allowed on the Internet. The exceptions are diacriticals used only in Eastern European languages, which are removed and the letter shown without a diacritical, except that the Hungarian double accent acute is made an umlaut. He also has the Bibliography in a Microsoft Word file, so that all Eastern- and Western-European diacriticals, as well as new insertions of Russian Cyrillic following the transliterations already included, may be displayed in the printed form or on the screen.
The USGS upkeeps the site Map projections, which contains a description and visualisation of 17 main projections, a summary of projection properties, and a summary of areas suitable of mapping with projections.
Some of these projections are also illustrated on Zbigniew Zwolinski’s ‘The Great Globe Gallery’.

The most recent publication in this field is:
Map projection transformation : principles and applications / Qihe Yang, John P. Snyder, Waldo R. Tobler. – London : Taylor & Francis, 2000. – xv, 367 p. : ill. ; 21 cm. – ISBN 0-7484-0667-0 (Hard cover); ISBN 0-7484-0668-9 (pbk.).

A more sophisticated site with actual mapprojection and their algebraic formulae can be found on the Map projection-page of Wolfram Research.

Somewhat older, simpler and less extensive publications are:

  • Map projections are easy / by D.G. Watts. – 2nd ed. – Milford haven : D.G. Watts, 1972. – 63 p. : ill. ; 22 cm.
  • An introduction to the study of map projections / J.A. Steers. – [14th ed.]. – London : University of London Press, 1965.

Still older and more specialized is the Dutch publication with projections concerning charts:

  • Kaartprojecties beschouwd uit een hydrografisch oogpunt / Hydrografisch Bureau. – ‘s-Gravenhage : Staatsdrukkerij, 1951. – 167 p. : ill. ; 25 cm.

And in English

  • Elements of map projection with applications to map and chart construction / by Charles H. Deetz and Oscar S. Adams. – 4th ed.revised. – Washington : Government Printing Office, 1934. – 200 p., IX bl. pl. : ill. ; 29 cm. – (Special publication / Department of Commerce, U.S. Coast and Geodetic Survey ; no. 68) Met index.
  • A little book on map projection / by William Garnett. – 3d ed. – London : George Philip, 1924. – viii, 112 p. : illus., diagrs. ; 22 cm

Going back in time I have found a German booklet as number 30 in the series Bibliothek zur Erd-, Länder- u[nd] Völkerkunde aus der Sammlung Göschen:

  • Kartenkunde / von M. Groll: I: Die Projectionen. – 2. Aufl. / neubearbeitet von Otto Graf. – Berlin ; Leipzig : Walter de Gruyter & Co, 1931. – 116 p. : 56 ill. ; 16 cm.

Even older in time are the following publications:

  • Leitfaden der Kartenentwurfslehre fuer Studierende der Erdkunde und deren Lehrer / bearb. von Karl Zoeppritz. – 2. neubearb. und erw. Aufl. / hrsg. von Alois Bludau. – Leipzig : Teubner, 1899. – X, 178 p. : ill. ; 25 cm.
  • Ueber die geographischen wichtigsten Kartenprojektionen, insbesondere die zenitalen Entwuerfe, nebst Tafeln zur Verwandlung von geographischen Koordinaten in azimutale / von E. Hammer. – Stuttgart : Metzler, 1889. – X, 148 p. : ill. ; 24 cm.
  • Traite des projections des cartes geographiques : representation plane de la sphere et du spheroide / A[drien Adolphe Charles] Germain. – Paris, [1866]. – XVI, 383 p. : ill. ; 24 cm.

With the computerization of cartography the amount of projections proliferated and fortunately also the Internet-resources available. The following sources are multiple sources with many hyperlinks to other documents or web-sites.

At this map projection homepage you will find a collection of information relating to map projections. This Home Page was inspired by a seminar in map projections in the Geography Department, Hunter College, City University of New York, led by Dr. Keith C. Clarke , Geography Department, UCSB.

Other extensive home pages are the Map Projection Overview by Peter H. Dana of the Department of Geography, University of Texas at Austin, and the European Map Projections by Stefan A. Voser of the Institut für Geodäsie, Universität der Bundeswehr München.

Bar scale values
Scale is “A ratio representing the relationship between a specified distance on a map and the actual distance on the ground. For example, at the scale of 1:50 000, 1 unit of measurement on the map equals 50 000 units of the same measurement on the ground. Map scale is frequently expressed as a representative fraction and graphically as a bar scale” (from : Scale).

Herman Wagner (1840-1929) gives a large historical expose concerning scales in “The mapscale” (Der Kartenmaßstab. In: Zeitschrift der Gesellschaft für Erdkunde zu Berlin. 1914. pp. 1-34, 81-117), where he connects the use of the scale with the projection used. Knowing this one must always be aware that a certain scale (being it a scale bar or a representative fraction) only gives true values on but a small part of a map. Depending on the kind of projection the deviation will be larger or smaller, also keeping in mind whether it is a large scale or small scale map one is viewing.

To calculate the distance between two cities using the great circle method (as the crow flies) one needs to know latitude and longitude of the two places. Bali and Indonesia on the net provides a distance calculator using geographic placenames. It does the arithmetics based on the ‘PROJ’ system available from the U.S. Geological Survey, when necessary supported by a locational map, and a travel map with driving directions. It also shows the compass headings between the two cities.
Another easy to use programme is the Great Circle Calculator. Here one should, however, fill in the right geographical co-ordinates for latitude and longitude. The result will be a distance in miles or kilometres. There are no auxiliary services. For those interested in these calculations a query on distance “great circle” on the search-engine Google will result in 21,600 hits.

Trying to give scales for pre-1800 maps implies always 3 to 4 measurements and should result in phrases as ‘Scale varying from [ca. 1:7,400] to [ca. 1:8,400]’ when derived from measurements on modern maps. Or ‘Scale [ca. 1:7,900], measurement derived from scale bar (900 rods = 33 mm)’. When the scale bar is not used in this way its mention should be relegated to the notes.
I advise curators and editors of facsimiles to be careful with scales and never to use one scale denominator when the map does not have a geometrical basis based on triangulation. When the cataloguer is not sure it is better to state ‘Scale unknown’ and give a scale-bar note than giving a quizzing approximation with which nothing can be proved or which creates confusion.

When the calculation of a scale is dependent on a grid of geographic co-ordinates one should measure the distance between two succesive parallels (1º = 111.11 km or 60 nautical miles, 1′ = 1.85 km or 1 nautical mile) using a meridian, when possible in the middle of the map.

For those not used to calculating scales Terry Reese has created the site Scale calculator, which allows for American standard, metric, and miscellaneous conversions.

In Petermanns geographische Mitteilungen (1855-2004), a famous German geographical journal, almost every map contains a scale denominator as well as a scale bar. The scale bar denominates a certain value per 1° longitude at the equator. The longitudinal measurement of 1° longitude at the equator is 111,324 kilometres or 60 nautical miles.
As there are some very exotic local scale bars which might be unknown the following table gives the values (in order of precision, as used in Petermann) ordered by the English name of the country in which the value is used. It may be that a bar scale is wrongly attributed to a certain country or area as they have to be interpreted from the German or do not have any explication of their origin.
Some values are only related to specific maps [i.e. 4,000 pied = 20 mm] and thus do not give any objective measure. They are included, however, to show their existence. Numbers in Bold under the heading ‘1 degree’ are most used on the maps.
Only verbatim statements from Petermann are used and in no way are measures recalculated.

The table is updated till and including annual 1945.

PETERMANN’S BAR SCALE VALUES

CountryName1 degreeRemarks
    
    
GENERALGeographical mile151 = 7,420.44 m
 Kilometre111; 111.11; 111.3; 111.301; 111.3066**; 111.307; 111.31
111.324 with an equator of 40,076.60 km
 
 Nautical mile60In 1874 ‘geographical miles’ are used in Stieler’s Schulatlas
1,000 geometrical paces****
 Nautic league, Sea league****20 
AFRICAPack-camel hours30; 31; 331 = 3.7 km
1 = 3.6 km
1 = 4.415 km, 69-74 camel paces per minute (1 metre = 1.022 pace)
 Travel-camel hours171 = 6.5 km
 (Caravan) hours25 
 travel hours (on land)22.6; 301 = 5 km = 1 hour on horse
1 = 4.8 km
1 daytrip of 10 hours of 4 km = 80 mm
 travel hours (by boat) 1 = 6 km
ARABIAGreat miles****50 
ARGENTINALegua21.42; 21.5 
ASIAParasang 1 = ca. 5.2 km
AUSTRIAPost (or Polizey) Meile14.671 = 4,000 Wiener Klaften = 24,000 Wiener Fusse
 Wiener Klafte58,683 
 Wiener Zoll 1 = 500 Wiener Klaften
BELGIUMmijl20 
BRAZILLegua181 = 6,000 m
CHILELegua20.0; 24.6 
CHINALi193; 193.4**; 199.9; 200; 250 
 Great li or Chinese furlongs****200 
COLOMBIALegua Granadinas22.151 = 6,280 Varas = 5.024 km
By Law of May 25, 1836
CUBALegua regular antigua 20 = 60 mm
DANMARKMile*14.77; 14.79*** 
 League****13.5 
FRANCEHeure25 
 Lieue25 
 Lieue marine20 
 Lieue metrique28 
 Pied 4,000 = 20 mm
GERMANY(Geographische) Meile151 = 1[0],000 Schritt
1 = 4 nautische Meilen
1 = 1,972.25 Rheinl. Ruthen
1 = 7.42 km
 Baierische Chaussée Meile***15.009 
 Kleine Böhmische Meile***16.12; 17.3**** 
 Jewish mile**100.80 
 Norddeutsche Meile**14.84 
 Nürnberger Meile**13.10 
 Preussische Meile14.77; 14.776***1 = 2,000 Rh. Ruthen = 10,000 Schritt
 (Reise)Stunde251 = 1,1182.15 Rheinl. Ruthen
GREECEMiles employed in the Archipelago****95.5 
 Miles employed in Turkey****87 
 Olympic stadi *6001 = 184.7 m
1 = 184.18 m /1 pletron = 100 feet /1 foot = 0.3 m
 Strabonic stadi6251 = 180 m
 Royal stadi111,3071 = 1 km
HUNGARYMile**13.30 
ICELANDPingmannaleidir2.9951 = 5 danish miles = 60,000 el
INDIACosses of Hindoostan****42 
 Carnatic cosses****37.5 
INDONESIAJavaanse palen59.09; 60; 73.8; 73.86 
IRANAdschmi17.4 
 Farsak 10 = 78 mm
 Mile**22.50 
IRAQAdschmi17.4 
IRELANDMile****54.4.34.2 
ITALYCommon miles of Piemonte****50 
 Great miles of Piemonte****45 
 Miles of Milan and Tuscany****67.2 
 Roman mile*75600 = 49 mm [= 872 km]; 1=7,000 nAPOLITAN PALMS****
JAPANRi28.3; 28.321 = 36 Tcho
LITHUANIAMile****20 
MEXICOLegua26.56; 26.6 
 Millas79.7 
NETHERLANDSuren**19.67 
 mijl111.307 
NORWAY[pace] 3,000 = 21 mm
 Miles*9.85 
OTTOMAN EMPIRE
see also: Turkey
hours25 
PERSIACommon pasarangs****17 
 Legua or Great pasarangs****50 
POLANDMile**20 
PORTUGALLegoa18; 22.26; 17.5****1=7.572 varas****
 Legua maritima20 
RUSSIAWerst104; 104.16; 104.2; 104.3; 104.33; 104.34; 105*6.96 = 1 geographical mile
20 = 1 Zoll; 1=500 sazen****
 Werst fixed by Peter The Great****90 
SPAINLegua nueva16.6; 16.64; 16.65; 17.66; 17.5****1 = 8,000/7.572**** varas
 Castilian legal league****26.51 = 5,000 varas
SPANISH AMERICALegua (maritima)20Probably a Spanish measure; 1 = 5,000 m, 1 = 5,770 m
SWEDENMiles*10.41 (12; 10.5****) 
 League****12.5 
 League used in Lapland****21 
SWITZERLANDRuthe 2.000 = 88 mm
 Stunde23.15; 23.18; 20.67***1 = 16,000 Swiss feet = 4,800 metres
TURKEYAgat22.26; 22****1 = 3 Berri
 Berri**66.67 
 [feet] 200 = 63 mm
 [hour]25 
UNITED KINGDOMStatute mile69.1; 69.12; 69.13; 69.15; 69.16; 69.164Also called English, British or American miles
 Geographical mile60 
    

*

From: Brockhaus’ Conversations-Lexikon, 13. Aufl., 1882-1887.
** From: Mass und Gewicht / Hans-Joachim v. Alberti, 1957 (see below).
*** From: Stieler’s Karte von Deutschland in 25 Blätter **** From: An untitled English atlas, published 1790-1798

MILE

Miglio (Italian), mijl (Dutch), mile (English), milha (Portuguese), milla (Spanish), mille (French), all deriving from the Latin mille = thousand. Measure in ancient Rome as milia passuum, later miliarum = 1,000 steps (paces) of 5 Roman feet = 1,478.7 m or 8 stadia (the latter according to classical authors).
In general 1 sea mile = 1 nautical mile = 1 geographical mile = 1 minute latitude or 1 minute longitude at the equator. (info: Maura O’Connor)
A closely related measure derived from the mile is the old Gaulish measure leig, in Latin leuca or leuga, later league (English), lega (Italian), legua (Spanish and Provencal), legoa (Portuguese), lieue (French), which usually was equivalent to 3 miles.
Both denominations seem to have been rather common in western Asia and Europe.

The following measures derive from: Lexikon der Münzen, Maße, Gewichte, Zählarten und Zeitgrößen aller Länder der Erde / be arbeitet und herausgegeben von Richard Klimpert. – 2. Vielfach verb. Und verm. A ufl. – Berlin : Regenhardt, 1896. [metres Lex.] or
Grand dictionnaire universel du XIXe siècle / par Pierre Larousse. – Paris : Administration du Grand Dictionnaire Universel, 1874. [metres Dict.].
Though the mile and league seem to be common names sources do not totally agree as to their value!

MILE measurements

CountryArea/namemetres Lex.metres Dict.1 degreeRemarks
AUSTRIABohemia 6,910  
 Malachia7,848.5  4,000 klafter
 Postal mile7,585.937 14.654,000 klafter = 24,000 feet
DANMARK 7,532.485 14.77Prussian mile
FRANCELieue vieil4,451.94,44425Picardie, Normandie, Champagne
 Lieue moyenne5,008.4   
 Lieue marine5,564.95,55520 
 Lieue d’Artois / Maine / Perche / Poitou 3,96428 
 Lieue de Beauce/ Gâtinais 3,26834 
 Lieue du Bourbonnais 4,82623 
 Lieue de Bourgogne 5,12121.5 
 Lieue de Bretagne / d’Anjou 4,58124.25 
 Lieue de Paris / Sologne / Touraine 3,93328.25 
 Lieue de Provence / Gascogne 5,84919 
GERMANYBaden8,889 12.50 
 Baltic provinces7,467.5 14.879 
 Bayern7,420,4387,42615 
 Böhmen7,498.5 14.82112,600 el
 Braunschweig7,419.42   
 Bremen 1,852  
 Geographic mile7,420.438 15 
 Gotha7,421.125   
 Hamburg7,532.4857,500 Prussian mile
 Hannover7,4197,53215.00224,000 Rheinland feet
 Hessen-Darmstadt7,500   
 Kurhessen9,206.37 12.07 
 Lippe-Detmold9,264.42   
 North German Bund7,5007,40714.84 
 Nürnberg  13.10 
 Oldenburg, police mile8,876.37  1,500 ruthe
 Oldenburg, geographic mile7,419.86   
 Prussia7,532.4857,407.40714.75424,000 feet
 Rhine 7,783  
 Saxonian mile7,500 14.84 
 Saxonian police mile 9,064 32,000 feet
 Schleswig-Holstein8,803.48   
 Tirol = Innsbruck10,691.111   
 Weimar7,363.0266,798  
 Württemberg7,448.748 14.67 
GREAT BRITAINLeague 5,569.339  
 sea-league   3 nautical miles or 5.556 km (info Victor Prescott)
 London mile1,523.986 73.03085,000 feet or 8 furlongs
 Statute mile1,609.3295 69.16Since the change of the statute in 1593 this is 5,280 feet
 Nautical/geographic mile1,854.965 606,085.898 feet
HUNGARY 8,353.6 13.30 
IRELANDIrish mile   2,240 yards or 6,720 feet (Gazetteer of the British Isles, J. Bartholomew Sons, 1966)
IRAN  4,946  
ITALYLombardia1,784.808   
 Napels1,855.110 60 
 Piemonte2,466.0768   
 Rome1,487.934 74.675 
 Toscane1,635.67   
 Venice1,738.6751,834  
 Venice nautical mile 1.852  
LITHUANIA  8,954 28,530 Rheinland feet
NETHERLANDSMijl5,5655,85720.2020,629 Rheinland feet (Dict.)
 Nautical mile 5,55620 
NORWAY 11,295.4811,1399.8536,000 feet
PERSIA. see: IRAN     
POLAND 7,420.438 20 [!] 
PORTUGALLegoa 6,179.740  
 Legoa nova5,000 22.26 
 Milha2,065.653   
RUSSIAWerst1,067 104.3 
SPAINCommon league 5,606.569  
 Legua maritima = Legua legal5,565.3296,365  
 Legua nueva6,687.24 16.64 
 Legua regular antigua5,572.7   
 Royal league 7,066.375  
 Milla 1,413 1,000 paces
SWEDENMil10,688.436 10.4136,000 feet
SWITZERLAND 4,8084,48023.15hour
TUNESIALand mileappr. 1,500   
 Nautical mile1,806.7 56.673,700 Draa
TURKEYMile 1,607  
 Nautical mile 1,479  

Geoff Armitage’s Conversion table of measurements
Geoff Armitage of the British Library Map Library in the past years has created a conversion table into millimetres of measures appearing in the British Library map catalogues. I am greatly indebted to him to be able to enrich this document with his table.

GEOFF ARMITAGE’S CONVERSION TABLE OF MEASUREMENTS

Name of MeasureApprox. Equivalent in millimetres
Antwerp ruthen5,736
Aunes1,143
Baras castellanes835
Bolognese foot380
Brabant foot281
Bracas2,200
Braccia600
Brasse595
Brazos castellanas1,683
Brazza595
British fathom1,828
Cable219,456
Calemberger foot292
Calemberger ruthen4,672
Canne2,000
Canne anconitane2,000
Canne napolitane2,096
Canne romane2,112
Canne siciliane2,028
Carmi2,000
Castilian league6,350,500
Castilian varas835
Chain20,117
Cleffter2,000
Common league7,408,900
Dutch league5,969,990
Dutch mile1,000,000
English league4,828,032
Faden1,629
Fathom1,828
Florentine braccia583
Florentine mile1,778,000
Foot305
French foot330
French league4,448,200
French marine league5,556,700
French pace812
French toise1,949 (post-1812: 2,000)
Genevese toise2,599
Geometrical foot337
Geometrical pace1,524
German mile7,649,000
Irish perch6,400
Italian mile1,852,200
Italian pace1,500
Kilometre1,000,000
Klaffter2,000
Lachter2,036
League4,828,032
Leucarum Hispanicarum [= Spanish league???]6,300,000
Lieue [= league]4,828,032
Lieue commune de France4,445,400
Lieue japonaise???
Lieue marine5,556,700
Marine league5,556,700
Marine mile1,852,200
Metre1,000
Mexican league4,190,000
Mexican varas848
Milanese mile1,652,600
Mile1,609,344
Miliarium/milliaria [= English mile]1,609,344
Mille (itineraire)1,949,000
Mille marin1,852,200
Milliaria anglica [= English mile]1,609,344
Milliaria germanica [=German mile]7,649,000
Milliaria Italica [= Italian mile]1,852,200
Milliaria thietm. [= Thietmarsh mile ???]???
Modenese perch3,180
Nautic[al] mile1,852,200
Pace762
Palmi250
Palmi genovese249
Palmi romani228
Paraguay league4,190,000
Paris foot330
Pas [= French pace]812
Passi1,500
Pedum [= Foot???]305
Perch5,029
Perticarum [= Perch]5,029
Pertiche ferrarese4,038
Pertiche modenese3,180
Pertiche versonese2,057
Piedmontese mile1,778,000
Pole5,029
Rhenish/Rheinland/Rynland – rod/ruthen/roeden3,766
Rhenish foot314
Rhenish verge/yard3,766
Rhine see Rhenish 
Rod5,029
Roden/Danish perches??? (La Rode)3,138
Roman palmi228
Russian faden/fathom1,629
Russian toise1,604
Rynland see Rhenish 
Scala [ignore; note the next word] 
Schrit[te]1,710
Schuh [= German foot???]290
Scots chain22,676
Sea league = marine league???5,556,700
Sea mile = nautic[al] mile???1,852,200
Spanish league6,300,000
Spanish maritime league5,566,700
T. [= Toise]2,000
T[h]oise2,000
Trabocci/Trabucchi3,000
Trabocchi of Piacenza2,819
Varas [Castellanas/Castille/Espanolas/Spanish]858
Venetian mile1,738,700
Venetian pasa/pace1,739
Verge de Rhin[land]3,766
Veronese mile1,778,000
Werst1,066,780
Yard914

As an aid to research and cataloguing the following table contains publications which concern measures etc. Should there be more than one significant publication in a country they are, when possible, organized from the general to the specif ic.

PUBLICATIONS CONCERNING BAR SCALE VALUES AND OTHER MEASURES

CountryPublicationRemarks (LANGUAGE)
   
UNIVERSALDictionnaire des poids et mesures anciens et modernes, contenant des tables des monnais de tous les pays / par Horace Doursther. – 3e éd. – Amsterdam : Meridian, 1976. – IV, 603 p. – ISBN 90-6041-111-0
Original ed.: Bruxelles : M. Hayez, 1840
Reprint: Amsterdam : Meridian, 1965
Based on published works between 1830-1840. All measures are converted to the decimal system and, where necessary, to other universal measures. Measures are usually regionally subdivided to area of origin. Also locally used designations are included with reference to the french designation (FRENCH)
 Elsevier’s encyclopedic dictionary of measures / Donald Fenna. – Amsterdam (etc.) : Elsevier, 1998. – XXIII, 582 p. ; 25 cm. – ISBN 0-444-50046-4Some 4,000 terms are identified in familiar English alphabetic order and related to their fellow units within their culture and to corresponding terms of adjacent and other interacting peoples. With index by country. (ENGLISH)
 Geographical conversion tables = Tables de conversion géographique = Geographischen Umrechnungstafeln = Geograficeskie tablicy perevoda = Tablas de conversion geográficas / comp. and ed. by D.H.K. Amiran and A.P. Schick. – Chicago : UGI ; Zürich : International Geographical Institute. – XXXVI, 315 p. : tab., maps ; 25 cm.(ENGLISH, FRENCH, GERMAN, RUSSIAN, SPANISH)
 Mass und Gewicht : geschichtliche und tabellarische Darstellungen von den Anfängen biz zur Gegenwart [Measures and weights : history and tables from the beginning till the present] / Hans-Joachim v. Alberti. Berlin : Akademie Verlag, 1957. – XX, 580 p.(GERMAN)
 Monnaies, poids, mesures et usages commerciaux de tous les états du monde. – 2e éd. – Paris [etc.] : Hachette, 1875. – VIII, 386 p.Arranged geographically by French name. Appendix: Tableaux de conversion des monnaies, poids et mesures d’Angleterre en monnaies, poids et mesures de France et réciproquement. (FRENCH)
 NTC’s encyclopaedia of international weights and measures / William D. Johnstone. – Lincolnwood (Illinois) : NTC Publishing group, 1966. – 329 p. ; 15 cm. – ISBN 0-8442-0850-7Section on units of length 57 pp. Includes ancient linear units (ENGLISH)
 Spravochnik mer / sostaviteli V.A.Sokolov i L.M.Krasavin ; Nauchno-issledovatel’skij konyunkturnyj institut ministerstva vneshnej torgovli soyuza SSR. – Vtoroe, dopolnennoe izdanie [Handbook of measurements / compilers: V.A.Sokolov and L.M.Krasavin ; Scientific Market Conditions Research Institute of the Ministry of Foreign Trade of the USSR. – 2nd, augmented ed.] – Moskva : Vneshtorgizdat, 1960. – 246 p.Linear measures encountered in the alphabetical listing are in Russian, with the Latin given in parenthesis in those cases where the Russian transliterates differently from the original. Some exotic measures are encountered, like the British ‘nail’ (5.71 cm) and American ‘place’ (76.2 cm). Measures arranged by country and alphabetically. (RUSSIAN)
 For good measure : a complete compenduim of international weights and measures / William D. Johnstone. – New York : Holt, Rinehart and Winston, [ca. 1975]. – XXII, 329 p. – ISBN 0-03-013946-5Part one: Units of length (pp. 1-57)
Part five: the metric system and conversion tables (pp. 208-212) (ENGLISH)
CLASSICALByzantinische Metrologie [Byzantian metrology] / von Erich Schilbach. – München : C.H. Beck’sche Verlagsbuchhandlung, 1970 . – XXIX, 291 p. – ISBN 3-406-01424-0P. 13-55: longitudinal measures (GERMAN)
 Griechische und römische Metrologie [Greek and Roman metrology] / von Friedrich Hultsch. – 2. Bearb. – Graz : Akademische Druck- u. Verlagsanstalt, 1971. – XIV, 745 p.P. 27-39: longitudinal measures (GERMAN)
ISLAMIC WORLDIslamische Masse und Gewichte : umgerechnet ins metrische System [Islamic measures and weights : converted to the metric system] / von Walther Hinz. – Leiden : E.J. Brill, 1955. – 66 p.P. 54-64: longitudinal measurements (GERMAN)
BELGIUMOude maten, gewichten en muntstelsels in Vlaanderen, Brabant en Limburg [Old measures, weights and monetary systems in Flanders, Brabant and Limburg] / Paul Vandewalle. – Gent : Belgisch Centrum voor Landelijke Geschiedenis, 1984. – 70 p.Arranged by municipality, refering to a table of 17 geographical entities with their measures. (DUTCH)
DANMARKDe gamle danske længdeenheder [The old danish units of distance] / N.E. Nørlund. – København : Munskgaard, 19 44. – 80, [12] p.A history of Danish units of distance (DANISH)
 Mål og vægt [Measures and weights] / Poul Rasmussen. – København : Danish Association of Historical Societies, 1967. – 87 p.A handbook of medieval weights and measures (DANISH)
FRANCEFrench weights and measures before the revolution : a dictionary of provincial and local units / Ronald Edward Zupko. – Bloomington : Indiana University Press, 1978. – XLVII, 208 p. – ISBN 0-253-32408-7(ENGLISH)
GERMANYBi-Lexicon alten Masse, Münzen und Gewichte / Helmut I. Kahnt und Bernt Knors. – Leipzig : Bibliographisches Institut, 1986. – 380 p. : ill. – ISBN 3-323-00013-7(GERMAN)
ITALYItalian weights and measures from the Middle Ages to the nineteenth century / Ronald Edward Zupko. – Philadelphia : American Philosophical Society, 1981. – LXXXIV, 339 p. – ISBN 0-87169-973-8(ENGLISH)
THE NETHERLANDSDe oude Nederlandse maten en gewichten / J.M. Verhoeff. – 2nd ed. – Amsterdam : P.J. Meertens-Instituut, 1983. – XIII, 131 p. – (Publicaties van het P.J. Meertens-Instituut ; Deel 3). – ISBN 90-70389-07-XContains: Dutch measures for weight, lenght, contents and volume, from the Middle Ages till the present, arranged by area and by name (DUTCH)
 Vergelijkingstafels van lengetematen en landmaten / J.H. van Swinden ; uitg. en ingel. door R. Rentenaar. – Wageningen : PUDOC, 1971. – 2 dl. (153 + 170 p.); 30 cm. – Met lit. opg. – ISBN 90-220-0352-3Contains reprints of the Dutch parts of Van Swinden’s Vergelijkings-tafels tusschen de Hollandsche lengte-maten en den mètre en Vergelijkings-tafels tusschen de Hollandsche land-maten en de hectare, (both from 1812), and his notes (DUTCH)
NORTH AMERICAArchaeological metrology: English, French, American and Canadian systems of weights and measures for North American historical archaeology / Lester A. Ross. – [Ottawa, Ont.] : National Historic Parks and Sites Branch, Parks Canada, 1983. – 123 p. – (History and archaeology, ISSN 0225-0101 ; 68). – ISBN 0-660-11336-8English systems: linear systems (pp. 5-54). Measures are given in two historical tables, 1305-1826 and 1826-present. Metric equivalent is given.
French systems (New France): linear systems (pp. 75-80). This gives the time periods in which the systems were in use, with metric equivalents.
American systems: pp. 87-90.
Canadian systems: pp. 91-100, giving measures used in the Dominion as well as in the provinces.
(ENGLISH)
 Métrologie archéologique : systèmes de poids et mesures anglais, français, américain et canadien pour l’archéologie historique de l’Amérique du Nord / Lester A. Ross. – [Ottawa, Ont.] : Direction des lieux des parcs historiques nationaux, Parcs Canada, 1983. – 115 p. – (Histoire et archéologie, ISSN 0227-3551 ; 68). – ISBN 0-660-91044-6Systèmes anglais: Longeur: pp. 46-50
Systèmes français: pp. 71-76
Systèmes américain: p. 86
Systèmes canadiens: pp. 95-97
UNITED KINGDOMBritish weights and measures : a history from a ntiquity to the seventeenth century / R.E. Zupko. – Madison : University of Wisc onsin Press, 1977. – 248 p ; 16 cm. – ISBN 0-299-07340-888 pp. of tabl es; includes old British and European measures; extensive bibliography and index es (ENGLISH)
 A dictionary of english weights and measures from Anglo-Saxon times to the nineteenth century / R.E. Zupko. – Madison : University of Wisconsin Press, 1968. – 224 p. ; 15 cmDictionary arrangement; extensive bibliography (ENGLISH)
 The weights and measures of England / R.D. Connor. – London : Her Majesty’s Stationery Office, 1987. – XXVI, 422 p. – ISBN 0-11-290435-1Includes classical and Celtic measures (ENGLISH)

Geographical co-ordinates
Though Greek philosophers like Pythagoras, Aristoteles, and Erathosthenes already posed that the earth was spherical it was the famous Greek astronomer Hipparchos (ca. 190 – 125 B.C.) who thought to cover this sphere with a grid of meridians and parallels. Following the Babylonian use of dividing circles and angles according to the sexagesimal system he created a grid of 360 lines running from the North to the South Pole and 180 lines running parallel to the equator. The lines running from the North to the South Pole later were called meridians, because when two places had the same time at noon they were on the same meridian, after the Latin ‘meridies’.

For a general and mathematical overview there is the Coordinate Systems Overview by Peter H. Dana of the Department of Geography, University of Texas at Austin.

Looking for ways for coordinate conversion and transformation the site Cartographic links for botanists compiled by Raino Lampinen, Botanical Museum, Finnish Museum of Natural History, contains mapping software packages, which have various utilities for coordinate conversion.

For geographic coordinate transformation pertaining to the Dutch grid and vice versa one can use the website Transformatie van RD-coördinaten en geografische coördinaten created by Ed. Stevenhagen. (There is also a Java-script with maps where the location is indicated). Besides it automatically gives the coordinates in WGS84 and the meridian-convergence.

In 1761 John Harrison (1693-1776) solved the longitude problem when his Model No. 4 or “H. 4” chronometer was used on a nine-week trip from London to Jamaica. During this trip his clock only lost five seconds, or about 1.25 minutes of longitude. His “K. 1” clock was successfully tested by James Cook on his second voyage around the world, beginning in 1772. (Boorstin, Daniel J. (1991). The discoverers. Vol. 1, p. 86.).
Connected to the problem of the prime-meridian is that of it’s opposite, the date line. From a Western point of view this was always situated somewhere at its antipode, as fictitionally treated by Umberto Eco in his The island of the day before (originally published as L’isola del giorno prima, 1994). A more scientific treatment of this problem can be found on A History of the International Date Line by Robert H. van Gent.

As the position of prime meridians is not always known I reproduce here a table in use with the CCK (Dutch Union Map Catalogue), ammended with information from other sources, among others Cartographic materials : a manual of interpretation for AACR2. The position is given with respect to the (Greenwich) International Prime Meridian, adopted at the 1884 International Meridian Conference at Washington DC, USA.

For those having trouble calculating bounding-box coordinates for maps the tool from Klokantech.com comes in very handy, especially since the coordinates are given in any MARC- or other description-format one is working with.

LOCATION OF PRIME MERIDIANS

CityCountryPosition
AlexandriaEgyptUsed by Albert Hermann in 1930 for a reconstruction of a map of Marinus of Tyrus. The meridians are hours west or east of Alexandria
AmersfoortNetherlandsE 005º23′
AmsterdamNetherlandsE 004º53’01”
AntwerpBelgiumE 004º22’50”
AthensGreeceE 023º42’59”
Batavia (Jakarta)IndonesiaE 106º48’28”
BerlinGermanyE 013º23’55”
BerneSwitzerlandE 007º26’22”
BogotaColombiaW 074º04’53”
BombayIndiaE 072º48’55”
BrusselsBelgiumE 004º22’06”
BucharestRomaniaE 026º07′
CádizSpainW 006º17’42”
CanberraAustraliaE 149º08′
CapetownSouth-AfricaE 018º28’41”
CaracasVenezuelaW 066º55’50”
Celebes, Middle Meridian ofIndonesiaE 121º48′
Christiana (Oslo)NorwayE 010º43’23”
CopenhagenDenmarkE 012º34’40”
CórdobaArgentinaW 064º12’03”
FerroCanary IslandsW 017º39’46”
GreenwichUnited KingdomE 000º00’00”
GenoaItalyE 008º55′
HelsinkiFinlandE 024º57’17”
IstanbulTurkeyE 028º58’50”
JakartaIndonesiaSee: Batavia
JulianehaabGreenlandW 046º02’22”
KaliningradRussiaSee: Köningsberg
KöningsbergRussiaE 020º29’47”
LeningradRussiaSee: St. Petersburg
LissabonPortugalW 009º11’10”
LondonUnited KingdomW 000º05’43”
MadrasIndiaE 080º14’50”
MadridSpainW 003º41’15”
Mexico CityMexicoW 099º11’40”
MoscowRussiaE 037º34’15”
MunichGermanyE 011º36’32”
NaplesItalyE 014º15’42”
New York City (Manhattan)United StatesW 074º00’29”
OldenburgGermanyE 008º12′
OsloNorwaySee: Christiana
Padang, SumatraIndonesiaE 100º22’01”
ParisFranceE 002º20’14”
PekingChinaE 116º28’10”
PhiladelphiaUnited StatesW 075º08’55”
Pulkovo (St. Petersburg)RussiaE 030º19’39”
QuitoEcuadorW 070º30′
Rio de JaneiroBrazilW 043º01’21”
RomeItalyE 012º29’05”
RotterdamNetherlandsE 004º29’46”
San FernandoSpainW 006º12′
San FranciscoUnited StatesW 122º27′
SantiagoChileW 070º41’00”
Singkawang, BorneoIndonesiaE 108º59’41”
South SumatraIndonesiaE 103º33′
St. PetersburgRussiaE 030º18’59”
StockholmSwedenE 018º03’30”
SucreBoliviaW 065º15′
SydneyAustraliaE 151º12’23”
TenerifeCanary IslandsW 016º35′
TiranaAlbaniaE 019º46’45”
TokyoJapanE 139º44’40”
Washington (D.C.)United StatesW 077º00’34”

When not taking into account which prime meridian is used the following situation might occur.

HUMOR: Teaching Coordinates

The geography teacher was lecturing on map reading. After explaining about latitude, longitude, degrees, minutes, and seconds, the teacher asked, “Suppose I asked you to meet me for lunch at 23 degrees, 4 minutes, 30 seconds north latitude and 45 degrees, 15 minutes, zero seconds east longitude.”

After a confused silence, a voice volunteered, “I guess you’d be eating alone.”

(Ken Everard, on Maphist, 8 February 2001)

When the teacher meant GMT as prime meridian he would have been lunching somewhere in the Arabian Desert called Dawasir. Had the teacher meant e.g. the San Francisco prime meridian he would have been lunching on a boat on the Great Bahama Bank near Channel Rock!

Centesimal system of co-ordinates

(derived verbatim from: Cartographic materials : a manual of interpretation for AACR2)
The sexagesimal division of the circle is now virtually universal in cartographic work. However, in the 18th century French scientists, using the metric system, devised the centesimal division of the circle. Today there exist large numbers of maps of France and its former colonial territories based on such a system. It can be quite confusing due to the relative closeness of the values.
The centesimal division of the circle is extremely simple. The entire circle is divided into 400 grads (a right angle in 90º in the sexagesimal system, 100 grads in the centesimal system). Each grad is in turn divided into 100 minutes and each minute into 100 seconds. The centesimal values can be expressed in regular decimal form or as minutes and seconds. The grad is shown as “G” and the centesimal minutes and seconds have the same marks as the sexagesimal ones, but with the slopes of the marks in the opposite direction.

Sexagesimal notation: 37º23’12”
Centesimal notation: 41G.5407 or 41G54`07“

The process of conversion is very simple.
It is known that 90º equals 100G and that 60 sexagesimal minutes or seconds equals 100 centesimal minutes or seconds. Through a simple proportion multiply the centesimal values by 0.9 to obtain sexagesimal degrees and the remainders are multiplied by 60 to obtain sexagesimal minutes and seconds.

The latitude of downtown Saigon is 11G.9727 N or 11G97`27“ N.

Therefore:
11.9727 x .9 = 10.77543
 .77543 x 60 = 46.5258
 .5258 x 60 = 31.5480
A centesimal value of 11G.9727 N or 11G97`27“ N equals a sexagesimal value of 10º46’32” N.

A Decimal To Degrees Converter or Degrees to Decimal Degrees Converter is made available by Gary J. Park of the Earth Observation Group.

Equinox
The equinox is one of the two points of intersection of the ecliptic and the celestial equator, occupied by the sun when its declination is 0º. This for most map curators intangible phenomenon has been well described in Cartographic materials : a manual of interpretation for AACR2 paragraph 3D2, p. 62-65. I refer those who are interested to this text as no other source is available to me.