The current sequence of numbersfor years was first introduced byDionysius Exiguus in c.525 whenpreparing a new table of the datesof Easter (Colgrave and Mynors1969). Dionysius developed a cycleof 532 years, made up of 28 peri-ods of 19 years each. He produceda calendar for another 95 years, butnumbered the years, “from theIncarnation of the Lord”. He start-ed the new cycle with the leap year532 so that the preceding cycle con-sisted of the year of the Incarnationfollowed by the years 1 to 531.

“When Bede came to write hisHistory he ... soon came to the con-clusion that the system introducedby Dionysius Exiguus ... was notonly the simplest way but also themost appropriate for a book deal-ing with the history of the ChristianChurch,” (Levison 1935). Bede alsorealized that the year of the Incar-nation was not the year 1, but thepreceding year. He referred to “theyear of Rome 693, that is in theyear 60 before our Lord”. Colgraveand Minors thought that this wasan error for they pointed out that“the year of Rome 693 is 61 BC”.Dionysius had counted forwardsfrom a year that had a name but nonumber and Bede had later fol-lowed the same practice in countingbackwards from the year of theIncarnation. Nearly 1000 yearslater, the astronomer Jacques Cassi-ni (1740) formalized the system bydenoting the year of the Incarnationas zero and treating the precedingyears as negative numbers. Thisastronomical system is not onlyconsistent with the intentions ofDionysius and Bede, but the rulesof arithmetic apply in calculatingtime intervals and for leap years,positive and negative.

Unfortunately, the current system,in which the year AD 1 is precededby the year 1 BC, had already comeinto use. This erroneous system hadbeen introduced by anotherastronomer, Denis Petau, while lec-turing at the College de Clermontin Paris in 1627 (Duncan 1998p99). Cassini’s system passed unno-ticed and now astronomers as wellas historians believe that in count-ing “ab incarnatione domini nostriJesu Christi” Dionysius had intend-ed that the year 1 should be regard-ed as the year of the birth of Christ,rather than as the year after. Thisfalse assumption is the origin ofstatements that the third millenium

will not begin until 2001. Fother-ingham (1931) drew attention tothe 532-year cycle in the dates ofEaster, but it appears that he didnot wonder why Dionysius hadstarted his Easter table with theyear 532. The editor of the first edi-tion of the Explanatory Supplementto the Astronomical Ephemeris wasnot then aware of the coincidenceand so published erroneous state-ments about the start of the Christ-ian era and of the 20th century(NAO 1961 p411).

It seems reasonable to speculatethat Dionysius realized that he wasunable to determine an accuratedate for birth of Christ and that heconsidered it appropriate to useinstead the start of a 532-year cycleof the dates of Easter. This choicewas accepted by Bede, whose use ofit led to its widespread adoptionwithin the Christian Church andthroughout the world for generaluse. The notations CE, for CommonEra, and BCE, for Before the Com-mon Era, (MLA 1985) have beenintroduced to make this systemappropriate for people of any or noreligious faith. It would, however,be more appropriate to use the sim-ple, language-independent notationof the astronomical system, especial-ly with the further advantage thatthere would then be no doubt aboutwhen the next century will begin.George A Wilkins, Sidford, Devon.

References and other sourcesAveni A F 1990 Empires of Time Tauris, London.Borst A 1993 The ordering of time Polity, Cambridge(translated from German edition, 1990).Colgrave B and Mynors R A B 1969 Bede’s ecclesi-astical history of the English people Oxford UP.Cannon J (ed.) 1997 The Oxford companion to BritishHistory OUP.Cassini J 1740 Tables astronomi... Paris (not seen).Doggett L E 1992 Calendars Ch. 12 of Seidelmann(ed) 1992.Fotheringham J K 1931 In the Explanation to theNautical Almanac and Astronomical Ephemeris for theyear 1931 p734–747 HMSO.Grun B 1982 The timetables of history New York,Simon and Schuster.Levison W 1935 Bede as a historian In Hamilton A(ed) Bede, his life, times and writings OUP.MLA 1985 Achtert W S and Gibaldi J The MLA StyleManual Modern Language Association of America,New York.NAO 1961 Issued by HM Nautical Almanac OfficeExplanatory Supplement to the AstronomicalEphemeris and the American Ephemeris ... HMSO,London.O’Neil W M 1975 Time and the calendars Sydney UP(also Manchester UP).Seidelmann P K (ed.) 1992 Explanatory Supplementto the Astronomical Almanac University Science Books,California.

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I thought that the argument aboutthe start of the third millenniumhad been terminated, but I see it isstill rumbling on. Part of the prob-lem stems from two different num-bering system which use the samesymbols – namely the ordinal sys-tem for ordering and the cardinalsystem for measuring.

The numbers used in the Gregori-an, Julian, Muslim and Jewish cal-endars are ordinal numbers, e.g.first, second, third etc years of theChristian era, with no place for azero. The term “first year of theChristian era” expresses an extend-ed period of time, one civil year.Civil years do not all have the samelength. Months and days are fur-ther examples of extended periodsof time. We correctly talk of daysas being the first, second, third etc,even though we write 1, 2, 3. Thefact that years and months do notall have equal lengths is of no con-cern in an ordinal system – after all,the person who is second in a racecan be half an inch or half a milebehind the winner.

When astronomers used –2 for3 BC, I thought that this was littlemore than a change of nomencla-ture and that –2 was still an extend-ed period. But with the introductionof decimals to denote days orinstants of time, it is now clear thatan ordinal system is being draggedscreaming into a cardinal system

where the whole numbers no longerrepresent a civil year – they nowdenote the exact instant of timewhen one year turns into the next.

Unfortunately, the civil years werenot necessarily all the same length,so the conversion is a misfit: theessential feature of a cardinal sys-tem is that the spacings betweenwhole numbers must be equal.Banks know to their cost that a dayis a different fraction of a leap yearthan it is of an ordinary year.

We are asked if –54.246 refers to1 April in the year –54 or to 3October –55. This is a superbexample of the confusion resultingfrom the mixing of systems. Toobtain the solution 1 April –54, the54 is treated as negative while the–0.246 is treated as positive. Thesymbol for this is —54.246 not–54.246. But has the terminologyany validity at all? The –54 is beingsimultaneously used for two differ-ent purposes: first, it is being usedto denote an instant of time andsecondly, it is being used to denotean extended part of that time.

No wonder the younger Scaligerand his contemporaries devised theJulian Period and numbered everyday from 1 January 4713 BC. I havealways believed that each generationhas to find out for itself (sometimesthe hard way) that some of our pre-decessors really knew their stuff. Bill Dow, Carnoustie, Angus.

The Editor exhorts astronomers toexplain the calendar (A&G 40/61999). Any explanation will beincomplete if it does not include thefact that the AD/BC calendar doesnot have a year zero and it wasdevised when only Roman numeralswere in use. The so-called Arabicnumerals with the wonderful inven-

tion of zero appeared in India in the6th century and did not reachnorthern Europe until the early 16thcentury. So we don’t need zero tocount days, months, years, centuriesor millennia and the third Millenni-um CE will begin on I/I/MMI.Ian Elliott, Dunsink Observatory,Dublin 15.

Ian Elliott

Zeroing in on the calendar problem

Bill Dow

April Foolishness?

past future

civil years

‘astronomical’years

measurement system

1: An illustration of how confusion arises through turning an ordinalcalendar system into a cardinal system.

George A Wilkins

The year without a number

4 BC 3 BC 2 BC 1 BC AD 1 AD 2

–3 –2 –1 0 AD 1 AD 2

–2 –1.6 –1 0 1 2

–2.4

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I read with interest the letter in theFebruary edition of A&G by NigelHenbest and Heather Couper, inwhich they attempted to answercritics of the alleged American biasin the TV series Universe, whichwas jointly produced by their ownUK-based Pioneer Productions, andthe American Discovery cable chan-nel. I would like to comment in thelight of some inside knowledge.One of the key members of theUniverse production team, who hassince left Pioneer, told me that theDiscovery channel had dictatedwhat should be in the final pro-grammes – and they wanted pre-dominantly American scientists.

This illustrates the fallacies inHenbest and Couper’s letter toA&G, which states that Pioneerpaid for half of the series but17.5% of the interviewees shownwere British. The authors claim thatsince this represents the IAU prorata membership, this is somehow“fair”. Why did they not insist on a50:50 US:UK ratio, in proportionto their respective financial inputs?

It is also interesting that theauthors think that Americans arebetter at “sound-bites” than usBrits. I thought that New Labourhad dispelled that myth! But seri-ously, if the interviewees did notprovide what the producers want-ed, then they should have beentold. My own experience is that themedia sees scientists and scientificfacilities as a free resource for theirown use, as and when they see fit,and in this case Pioneer simplycaved in to American pressure.

Pioneer is by no means alone inthis. The BBC is usually even moreguilty, although there are hon-ourable exceptions. A BBC Wales

film crew covering aspects of theBA meeting in Cardiff, on a shoe-string budget, managed to make aslick half-hour programme, whichwas clearly explained and easilyaccessible to a wide audience.

Should British astronomers refuseto co-operate with TV companiesthat do not give a fair showing forBritish science? Surely this is not inany of our best interests. Instead weshould support British TV ventures,but this support needs to be recip-rocated. The BBC and Pioneer Pro-ductions could play a key role inpublicizing British astronomy ifthey wished to. They could joinwith PPARC’s public understandingof science ventures, or provideinnovative ways of show-casingBritish astronomy to the public.Who knows, even the Americansthemselves might want to buy pure-ly British productions! We cannotafford to continue letting the Britishpublic (including those who workat the OST) think, as they currentlydo, that the only astronomy impor-tant enough to be shown on Britishtelevisions is American astronomy.

So my final request to Henbestand Couper is simply this: stand upto the Americans. Do not settle for17% when you’ve paid for 50%. Ifnecessary, refuse to make joint ven-tures with the Discovery channel ifyou lose control of the final pro-gramme production. If this meansyou can only afford a one- or two-programme series, rather than four,then I’m sure we would all agreethat is a small price to pay for see-ing British astronomy fairly por-trayed by a British TV company. Derek Ward-Thompson, Departmentof Physics & Astronomy, CardiffUniversity, Wales.

I am engaged in research onEdward Walter Maunder (1851–1928). Although I have been fortu-nate in obtaining access to severalarchives with correspondence to orfrom Edward, his wife Annie ScottDill or his brother Thomas Frid, Iwould like to ask if any readercould inform me of any collections,including private collections.

So far I have been able to obtain orconsult copies of letters fromarchives in the USA, France and Eng-

land (including the RAS). However,it is almost certain that many existelsewhere. Therefore if any readerscan help I would be grateful.

In particular I would appreciatephotocopies of any letters and theappropriate permission to depositthese copies in the RAS archiveswhen finished with. If necessary Ican be contacted by e-mail atanthony.kinder@lineone.net.A J Kinder, 16 Atkinson House,Catesby Street, London SE17 1QU.

I am writing to tell you of progresswith our commemmoration ofThomas Wright. The stained glasswindow to his memory is now inplace in the parish church of StPeter the Apostle, Byers Green.Thanks to all who contributed. Thememorial was unveiled last year, bythe Bishop of Durham, the RevdMichael Turnbull. A brass platebeneath it describes Wright(1711–1786) as “a local man offaith and science ... mathematician,astronomer and natural philoso-pher, who first gave the form of theMilky Way”.

We hope to continue to raisemoney in our Reach for the StarsAppeal, to start up a permanentexhibition, a telescope and equip-ment to help school groups, visitorsand astronomy groups to learnmore about Thomas Wright and todevelop an interest in astronomyfor themselves. I am writing to askif readers would like to make acontribution to this appeal. Alldonations will be acknowledged aspart of the display.Revd Captain Paul T Allinson, StPeter’s Rectory, Byers Green,Spennymoor, Co Durham DL16 7NL.

It probably won’t add much to thisdebate to go into a point-by-pointrebuttal of Derek’s comments –though we must correct his assertionthat Universe was jointly funded byPioneer Productions and Discovery.Channel 4 was the co-funding part-ner in the UK, as was made clear inour original article.

We certainly didn’t mean our pre-vious article to be “apologetic”. We– and all at Pioneer – are proud ofUniverse. We believe it is a wonder-

ful showcase for British astronomyon the international stage. Howmany astronomy documentaries oninternational release feature anyBritish researchers at all? Yet now alarge number of American viewershave been exposed to the paradigm-shifting sight of cutting edgeresearch being conducted byastronomers from Britain.Nigel Henbest and Heather Couper,Pioneer Productions,Voyager House,32 Galena House, London W6 0LT.

Derek Ward-Thompson

The ‘American bias on TV’ debate

Nigel Henbest and Heather Couper

Defending the UniverseA J Kinder

In search of E W Maunder

Revd Captain Paul T Allinson

Thomas Wright’s window

The Thomas Wright Window, Church of St Peter the Apostle, Byers Green.