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Volume 1630
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Martian Measurements of Time

Marking Time on Burroughs' Barsoom
by
Fredrik Ekman and Thomas Gangale
The planet Mars is one of our nearest neighbours in space, and therefore also one of the astronomical phenomena that has been most extensively studied. The length of its day and year in particular were some of the early subjects of inspection. The Dutch astronomer Christiaan Huyghens estimated the Martian day to 24 hours as early as 1659, and seven years later the Italian Giovanni Domenico Cassini suggested a rotation period of 24 hours and 40 minutes, only two and a half minutes too much.

By the time that Edgar Rice Burroughs wrote his Mars stories (the first one published in 1912), measurements regarding the rotation and revolution of Mars were highly accurate. Burroughs used that information to design a system for measuring time on Mars (or Barsoom, as it is known in the constructed language of the locals). He thereby became one of the first to design such a system (the first author on the subject known to us was Percy Greg, in his 1880 novel, Across the Zodiac). But, unfortunately, Burroughs' application of the measurements was inconsistent and sometimes incorrect.

There have been many attempts in the past to compile the information about the various time units used by Burroughs. The most well-known (and possibly the most successful) has been John Flint Roy's book A Guide to Barsoom (Chapter 5 in particular). But Roy's work, being of a general nature, has some flaws and omissions. This article attempts to move one step further and analyse the subject in depth. Even so, it will not be beyond argument. But, it is our hope that it can be a steady platform for further research.

The terms "day," "month" and "year" constitute a potential source of confusion if they are used both for the original terrestrial meanings, and for their Martian equivalents. Therefore we will mostly use the terms padan (day), teean (month) and ord (year) for the Barsoomian units. These terms were found in Burroughs' personal notes and were published in Roy's book. The terrestrial terms will be reserved for their original meanings and for general astronomical discussions.

Throughout this article we will use abbreviations when we reference Burroughs' books. Explanations of the abbreviations can be found at the end of the article.

Counting the Ages

In spite of many wars and a planet slowly dying, Barsoom in John Carter's time seems politically and socially stable. Dejah Thoris is said to be "the proud daughter of a thousand jeddaks" (PM/17) and science has "stagnated in a quiet pond of self sufficiency" (FMM/2). In such a cultural climate, it is safe to assume that the calendar has not changed significantly in the past few centuries or millennia. There has simply been no reason for change.

Historians tend to divide history into eras, each era representing some phase in a planet's or a society's development. The beginning of an era is called the epoch. For instance, the beginning of the Christian era is the year 1 A.D., which therefore denotes the epoch of that era and the first year of the Gregorian calendar.

Barsoom has an extremely long history, and consequently many eras. According to legend, the Tree of Life flourished "twenty-three million years ago" (GM/7). Even recorded history "reaches back more than one hundred thousand years" (MMM/10), possibly much more.

Unfortunately we know next to nothing about how these past eras are counted. Carter sometimes mentions past events, but always relative to his own present time. We are not even certain whether he counts Barsoomian ords or Earth years. In the entire series, only two Barsoomian dates are quoted. The first is in the following passage:

  Kam Han Tor looked at him in amazement. "You have been dead over five hundred years, Hor Kai Lan," he exclaimed, "and so has your brother. My brother succeeded the last jeddak in the year 27M382J4."
  "You have all been dead for ages," said Pan Dan Chee. "Even that calendar is a thing of the dead past."
(LG-1/9)
This quote reveals little. It does not even suggest what the different numbers relate to and what the letters mean, even ignoring the fact that the calendar is no longer used. Yet, assuming that the letters are abbreviations of unknown words, we can draw some conclusions.

For one thing, the epoch cannot be based on only the reign of the current jeddak. If it were so, then a date in the future would have been meaningless to Hor Kai Lan.

It seems probable that one number represents a cycle of some sort, so that every n ords (where n is the length of the cycle) that number is increased by one and the count of ords (one of the other numbers) is restarted from 1 or 0. That leaves one number, which could be either a cycle within the cycle (just as we have seconds of minutes of hours in a day) or a number that is not directly related to the others. Such a number could refer to, for instance, how long the current jeddak has ruled, or it could be a reference to aid memory in a complex system of leap ords. For example, the date could refer to the 382nd ord of the 27th cycle, the fourth ord of a separate leap ord cycle.

The second Barsoomian date is more informative, stating the current year as "the four hundred and thirty-third year of O-Tar, Jeddak of Manator" (CM/17). Here is a clear suggestion of the local epoch: either the birth or the ascension of the current ruler. Unfortunately, it says little about other contemporary nations, since Manator is described as scientifically and culturally retarded.

Traditionally, on Earth, calendars have chiefly taken two different approaches for deciding the epoch. One is the first reigning year of a ruler or a dynasty, the other some important religious event. Either one is possible from a Barsoomian perspective.

The epoch of the current Barsoomian calendar is probably set after the replacement of the Orovar calendar of the first quoted date above. This must have happened within the past one or two hundred thousand years: the period after the decline of the Orovars (PM/11).

If most of Barsoom shares the same era for the calendar, then two possibilities for the epoch are the birth of the first man from the Tree of Life (many millions of years ago) and the founding of the Issus cult (thousands of years ago at the very least).

If each Barsoomian nation, like Manator, has its own epoch, then some possibilities for Helium would be the ascension of the current jeddak (less than a thousand years ago); the founding of the city of Helium (possibly about a hundred thousand years ago); and the start of the current dynasty's reign (possibly coinciding with the founding of Helium).

For time periods shorter than epochs but longer than ords, at least some Barsoomian nations have a unit corresponding to our decade. This can be assumed from the custom to hold "decennial games" (CM/16) in Manator. It is not known to what extent this unit is incorporated in daily usage.

Counting the Years

Even though Barsoom (unlike the real Mars) does not have very marked seasons, its inhabitants count the years much the same as we do. One sign of this is that they have annually recurring events, just as we have holidays.

Most recurring events mentioned in the series are more of a tribute to the present than to the past. Some, such as the green men's annual visits to oversee their eggs (PM/7) or the debt notes, which are "redeemed twice yearly" (PM/20), are necessary to maintain society. Others, including the annual great games of green men (PM/16) and the monthly rites of Issus (GM/9), are festivities with no apparent reason beyond what they themselves represent. Only a single event is mentioned as a celebration of the past, as Carthoris explains to John Carter: "Each year that brings its anniversary of the day that saw you racing across a near dead world [...] a great festival is held in your honor" (GM/14).

Since there are apparently few celebrations of the past (no birthdays are mentioned, for instance), an annual event such as the new year (new ord) is probably marked by some natural event, such as an equinox or a solstice. (See below under "Counting the Months and Weeks" for a further discussion on this topic.)

The exact length of the ord is one instance where Burroughs has been inconsistent. Four different possibilities are described below.

Scientific Year

We may want to assume a scientifically correct tropical year for the ord, which is approximately 668.59 Martian solar days (686.97 Earth days). This is in fact the only alternative if we regard Barsoom and Mars as the same planet.

Approximate Scientific Year

Burroughs did not cite the exact scientific figure anywhere, but he did give the length of one half Barsoomian ord, which is "about three hundred and forty-four of [Earth's] days" (PM/20). This is almost in keeping with science; there is only a very trivial decimal error (686.97/2≈343.49). Burroughs may have started with a value found in Flammarion's Astronomy for Amateurs (a book which Burroughs had in his personal library), where the Martian year is said to be "687 days" (p. 132), to achieve his result (687/2=343.5≈344). An ord of 687 Earth days (approximately 668.62 padans, assuming the scientifically correct day) is therefore a possibility, which is close to science and which may have been used by Burroughs.

Calendar Year

As stated above, Burroughs never cited the scientific year, but he did come very close in his personal notes. Roy, in his book, quotes a table from Burroughs' personal notes saying that one ord is ten teeans, each of which in turn is 67 padans. This could be based on the scientific year (668.59/10≈67) or it could be based on the number of sidereal days (see below) in one ord, which is one more than the number of solar days (669.59/10≈67).

Ten teeans of 67 padans gives an ord of 670 padans, apparently the length of one calendar ord. Roy suggests that some teeans may be only 66 padans in order to achieve the scientific value, but Burroughs does not give any indications in that direction.

In order to account for the fact that there are not a whole number of padans in an ord, there must sometimes be "skip ords" (inverted leap years) containing fewer padans.

Incorrect Year

One Martian tropical year is 668.59 solar days, approximately equal to 686.97 Earth days. This simple fact apparently confused Burroughs (as well as many other designers of Martian calendars), for he seems to state in three different passages that one ord is 687 Barsoomian padans. The most obvious one is where Dejah Thoris is imprisoned for one ord in the Temple of the Sun, so that "Six hundred and eighty-seven Martian days must come and go before the cell's door would again come opposite the tunnel's end" (WM/1).

Although incorrect, this is repeated so many times that we must not ignore it completely. Even though the number of solar days on real-world Mars number 669, they may well be 687 on Burroughs' fantasy Barsoom. "Six hundred and eighty-seven Martian days" would be equal to 705.8865 scientifically correct terrestrial days.

Choosing a Year

Summing up, our four options for length of ord are:
  • Scientific year, as measured by astronomers (668.59 padans).
  • Scientific year, as may have been approximated by Burroughs (668.62).
  • Calendar year, as implied by Burroughs (670).
  • Incorrect year, as quoted by Burroughs (687).
  • We do not say that any one alternative is the only one, or even the best. Unfortunately, this is one of many inconsistencies in Burroughs' fantasy world, an inconsistency that can only be resolved by denying one or more facts as they are presented by Burroughs.
     

    Counting the Months and Weeks

    In his personal notes, as mentioned above, Burroughs specified the teean as 67 padans and the ord as ten teeans. But these figures were not mentioned in the novels. In fact, there is an indication in a different direction, as John Carter apparently equates "six long Martian months" with one half ord (WM/1). This, then, would seem to indicate a total of twelve teeans to the ord.

    Roy suggests, and we agree, that this can be disregarded. We see it as an extreme and misplaced (not to mention incorrect) example of Burroughs' oft-expressed aim to simplify terminology by using Earth terms at most times, so "six months" should read as "half a year" (Martian in this case).

    Teean length is also in question due to the distribution of the monthly rites of Issus. Judging from Ekman's article "A Chronology for the Princess of Mars Trilogy" there are 370 padans between the rite where John Carter participated (GM/11) and the one that was held on the padan before the battle of Omean (GM/20). This is not evenly divisible by anything even near 67. Nine 74-padan teeans would come quite close to solving the equation for a 669-padan ord, as would thirteen 53-padan teeans for a 687-padan ord.

    This, too, can be disregarded. It is unlikely that Burroughs, always more interested in telling a good story than paying attention to every detail, calculated the exact dates for each rite. Possible assumptions for circumventing the inconsistency are that either the rites are not always held on the same date, or the First Born use a different calendar. Nine teeans would not be unreasonable in such a calendar. Nine, the number of facets on the jewels worn by Holy Therns, may have some significance in the Issus cult.

    There is but a single passage in the books themselves where Burroughs specifies the length of the teean, stating that it "is equivalent to about seventy days of Earth time" (LG-3/3). The figure is not entirely correct (686.97/10≈68.7). Even so, this is the canonical confirmation that the ord does in fact have ten teeans, since no other number of teeans results in approximately seventy Earth days (the closest is 686.97/9≈76.3). Our guess is that Burroughs calculated correctly, then rounded to the nearest multiple of ten. As an interesting aside, the nearest solution to the equation comes from assuming a 687-padan year and a sidereal day (687*1.026/10≈70.49; see below for an explanation of the sidereal day).

    What we do not know is whether all teeans are of equal length or not. For an ord with 670 days they could be, but for other lengths of the ord they would have to be different, so that for instance some teeans would be 66 padans and others would be 67.

    The Barsoomian Week

    Another unknown of Barsoomian time reckoning is whether they have a unit corresponding to our week. The word "week" is frequent in the texts. But does it refer to a Barsoomian week of unknown length, or is it just a hybrid use of the Earth "week" to represent seven padans? The latter is probable, even in those books where the narrator is a native Barsoomian. In one such book, Burroughs (in the role of editor of the story) makes the following reflection: "Certain Martian words and idioms which are untranslatable, measures of time and of distance will be usually in my own words" (SMM/1).

    But this does not preclude the existence of a Barsoomian week. The inhabitants of Kamtol hold their Lesser Games "about once a week" (LG-2/7), suggesting a "week" unit. Roy argues that a Barsoomian week (if there is one) would probably be either seven or ten days long. Both these alternatives do find some weak support in the texts. Ten-day periods that could be indicative of a week are the Great Games in Warhoon (PM/19) and the period before the intended wedding between Salensus Oll and Dejah Thoris (WM/11). A seven-day period precedes another intended wedding, namely that between O-Tar and Tara (CM/20).

    One clue that strongly supports the existence of a week is the very terms padan and teean. Semantically, these appear to match another set of words, namely padwar (lieutenant), dwar (captain) and teedwar (colonel). Is it then not likely that there should also be an an term inserted into the padan and teean sequence to complete that set? If so, then we have our week.

    The literal meaning of dwar seems to be "officer", and the prefixes "pa[d]-" and "tee-" could have meanings such as "minor" and "major". But the word tee also means "ten" and Roy's conclusion that that a teedwar commands ten times as many men as a dwar suggests this as a more likely semantic option. Analogously, we suggest that one teean is ten times one an, and one tenth of 67 is approximately 7. It therefore seems possible that the an is seven padans (which also matches Roy's analysis).

    There is one thing we cannot guess: Are some ans shorter in order to make an even ten ans in a teean, or are weeks and months independent of each other as in the Gregorian calendar?

    Happy New Ord

    Knowing the lengths of Barsoomian ans and teeans may provide a clue to when the Barsoomian new ord (new year) is. The key here is the gigantic calendar called The Temple of the Sun (described in GM/20 and GM/22). The chambers of the temple, one for each padan, are placed in column below one another. Each opens only one padan every ord to the outer world. For ease of reference, it seems most probable that the chambers are organized so that the uppermost one opens on the first padan of the ord, the next on the second padan, and so on. The sloping tunnel that leads to the chambers is divided into "tiers of galleries" (GM/22), and it is likely that each gallery represents either one an or one teean.

    John Carter and Xodar passed half a dozen galleries before they reached the one that opened on that padan. If each gallery represented a teean they would have had to pass miles of galleries, and since Xodar seems to indicate that they could reach the surface in five minutes the six galleries passed probably correspond to six ans, or 42 padans. The seventh gallery (which was apparently entered but not passed) would end on the 49th door. Therefore, the first padan of the new ord should be between 42 and 48 padans before this event. In Ekman's chronology he has estimated Dejah's imprisonment to occur on March 23, 1887. The Barsoomian new ord could thus be in early February of that year (42*1.027≈43, 48*1.027≈49; the exact date is therefore between February 2 and February 8).

    During the flight from Omean, some 320 or 330 padans before this presumed new year (again according to Ekman's article), it was summer (GM/13). It therefore seems possible that the Barsoomian new year falls on the winter solstice (summer solstice on the northern hemisphere). However, if early February, 1887 was summer solstice on the northern hemisphere, then that is a clear indication that Mars and Barsoom are not the same planet. On the real Mars, February 16 of that year was actually winter solstice.
     

    Counting the Days

    Perhaps the most confusing inconsistency in the Martian books is the length of the padan. There are at least six different alternatives, depending on what source is used and how it is interpreted. Before we describe the various options at our disposal, it is important to understand that from an astronomical point of view there are different ways to measure the length of one day.

    In normal daily life, of course, one day is the time from one noon to the next noon, or in other words the time it takes for the planet to rotate once around its own axis, relative to the sun. Astronomers call this the solar day.

    However, physical scientists normally express measurements in terms of a single inertial reference system. Astronomers standing on a rotating, revolving reference point (Earth) measure the rotational period of other rotating, revolving objects such as Mars and the other planets. It makes sense to them to reference all of these various motions to the so-called "fixed" stars. A rotational period expressed in such a fixed inertial reference system is known as a sidereal day. The sidereal day of Earth is approximately 23 hours, 56 minutes.

    The illustration shown here is taken from the book Popular Astronomy (1894) by Camille Flammarion. Burroughs probably did not consult this particular book, but we will quote Flammarion's very clear description of the difference between solar and sidereal day:

      Let us consider the terrestrial globe at any moment. It revolves round the sun from left to right (fig.5) in a length of orbit which takes it a year to pass over, and at the same time turns upon itself every day in the direction indicated by the arrow. At noon the point A (left-hand position) is exactly in front of the sun; when the earth has accomplished a complete revolution, the next day, it will have been carried to the right-hand position, and the meridian A will be found exactly as it was the day before. But the transfer of the earth towards the right will cause the sun, by perspective, to move back towards the left, and in order that the point A may again return in front of the sun, and there may be noon again, it is necessary that the earth should still turn for 3 minutes 56 seconds; and this on every day of the year. It is this which makes the solar or civil day longer than the diurnal rotation of the globe (also termed the sidereal day).
    (p. 17)
    Mars takes nearly twice as long to orbit the sun, so the daily change in its angle to the sun is only about half that of Earth. This makes the difference between the sidereal day and the solar day about two minutes. For both planets, this angular discrepancy between the sidereal day and the solar day accumulates in the course of one revolution around the sun, so that there is exactly one more sidereal day in a year than there are solar days. The math is easy, but the underlying logic needs to be understood:
    For planets like Earth and Mars with relatively short days and long years, the difference between sidereal and solar day is small. Yet it is significant in calculations. The correct value to use for a local observer (such as John Carter) should always be the solar day, but in astronomical tables it is more common to find the sidereal day cited.

    Now we can go on to look at the various options for the length of the padan.

    Solar Day

    A couple of books that Burroughs may have consulted specified the Martian solar day, as well as the sidereal day. On Page 160 of Mars and Its Canals (1906) Percival Lowell states: "Mars turns on its axis in 24 h. 37 m. 22.65 s. with reference to the stars, and in 24 h. 39 m. 35.0 s. (as a mean) with regard to the Sun." Thus, Burroughs could have had access to this information. Whether he would have understood its proper application is another matter.

    If we believe that Burroughs' Barsoom is the same as Mars in our real universe, then we must assume the scientifically correct solar day of about 24.6597 hours, or approximately 24 hours, 39 minutes, 35 seconds.

    Approximate Solar Day

    Burroughs nowhere cites the solar day in the texts. But, an error in one of his calculations may provide a clue to how he used it. John Carter says: "The ten Earth years I had spent upon Barsoom had encompassed but five years and ninety-six days of Martian time" (GM/20). In reality, ten Earth years would be approximately 5 ords and 212 padans. So where did Burroughs go wrong?

    Let us assume that he first calculated how many Earth days John Carter was on Mars (3653, or 3650 if he forgot to consider leap years). The solar day of Mars can be expressed as approximately 1.027 Earth days long, so next, he may have calculated how many padans 3653 days would be on Mars (3653/1.027≈3557.0) and divided that with the length of one ord (3557.0/669≈5.3169). The result so far is correct. Burroughs now knew that John Carter was on Mars for over five ords.

    What he should have done next is to take the remainder of the division 3557.0/669 to arrive at 212 padans.

    What he possibly did was to subtract the number of padans from the number of Earth days (3653-3557=96). A simple sanity check proves that this is not correct. If 3557 padans is equal to 5 ords, 96 padans, then you would expect 96 subtracted from 3557 (3557-96=3461) to be exactly equal to five ords (669*5=3345), which is not the case.

    How, then, can we know for certain that Burroughs used this method? Well, we cannot. We have, however, tried many different approaches for arriving at the incorrect result 5 years, 96 days. Only this, using the exact value 1.027, works. Using the more precise value 1.0275 gives 98, while the lower precision value 1.03 gives 102. Using another ratio, such as the ratio between Mars' sidereal day and Earth's sidereal day, or between Mars' sidereal day and Earth's solar day (incorrect but possible), also gives a different result. The more obvious computational and arithmetic mistakes also yield other figures. Incidentally, using 1.027 for length of day results in 96 regardless of whether the three leap days are considered or not.

    This little game may seem to be a gloating over the mistakes of an author who is no longer alive to defend himself. However, by examining this error we have also learned that there is a possibility that Burroughs used exactly 1.027 Earth days for the length of the padan, or approximately 24 hours, 38 minutes, 53 seconds. This, then, would be the length to use if we want to stay close to the scientific truth, while using the values that Burroughs possibly used in his own calculations.

    Sidereal Day

    As has already been pointed out, it is incorrect to use the sidereal day from John Carter's perspective. Nevertheless, it was the most accessible figure in Burroughs' day and most of the sources he would be likely to use mention it in one form or another. Percival Lowell's Mars (1895) gives it as 24 hours, 37 minutes, 22.7 seconds, Flammarion, in Astronomy for Amateurs (1904), cites 24 hours, 37 minutes, 23.65 seconds and the 1910/11 edition of Encyclopædia Britannica says 24 hours, 37 minutes, 22.66 seconds.

    Approximate Sidereal Day

    The sidereal day was one of two lengths of day that Burroughs actually cited, although he used an approximation, writing that "the Martian day is a trifle over 24 hours 37 minutes duration (Earth time)" (GM/16). Therefore, a case could be made for using that approximation, or for using the scientifically correct sidereal day (see above), which was his source.

    Another reason to use either of these two alternatives is that both match the statement that "a zode [is] 2.462 earth hours" (FMM/2). That is not true for any other length of padan discussed in this article.

    If the fictional Barsoom is assumed to be the same planet as the real Mars, then the sidereal day must be disregarded as a mistake. But if Barsoom is a fantasy world similar to Mars but not the same, then Burroughs' quote could take precedence over any other scientific or calculated lengths.

    Erroneously Calculated Day

    As mentioned above, Burroughs cited two different lengths in the novels. The second one claims that Barsoom's "days are forty-one minutes longer than ours" (GM/20). In other words, a padan of 24 hours, 41 minutes. So where does this figure come from?

    One possibility is that he had access to an astronomical table citing the sidereal day of Earth (23 hours, 56 minutes) and that of Mars (24 hours, 37 minutes). The difference is 41 minutes, so the quote actually reflects the truth, although not in a sense that would be useful to John Carter. But it is also possible that the statement is based on a quote from Percival Lowell's Mars and Its Canals, stating that a Martian day "very closely counterparts in duration our own, being only one thirty-fifth the longer of the two" (p. 34). 1/35 is actually highly accurate when applied on the sidereal day, although Lowell did not go into the specifics at this point in his text. It would be understandable if Burroughs incorrectly applied it on the solar Earth day of 24 hours, which gives approximately 41 minutes, 9 seconds.

    At any rate, the 41 minutes citation is apparently another reflection of the sidereal day and we suggest that it can be disregarded as a mistake. Nevertheless, it is part of the canon and therefore deserves mention.

    "Five Years and Ninety-Six Days"

    We have already shown that the quote of "five years and ninety-six days" is based on an error. Yet, it is part of the canon, and unless we prefer to ignore it for the error it is, there are two ways in which we can make it fit in with at least some other facts. Either we can assume that John Carter was not quite ten years on Barsoom (it is nowhere stated on what date he returned) or we can assume a longer padan than any of the previous alternatives.

    The exact length here depends on other factors, especially the length of the ord. Assuming Burroughs' quoted 687 padans gives a padan of approximately 24 hours, 49 minutes, 45 seconds. As with the "erroneously calculated day" our opinion is that this should not be used at all. We discuss it only because Ekman mentioned it in the first version of his chronology for the Princess of Mars trilogy.

    Choosing a Day

    Just like the length of the ord, the length of the padan can only be set by ignoring some statements made by Burroughs. It must also be remembered that the length of the padan will affect the length of the ord, since for most alternatives we measured the ord in number of Martian solar days (which by definition is identical with padans). Therefore, the choice of ord should also govern the choice of padan.

    The scientific figures naturally belong together, as do the approximations that Burroughs may have used in his calculations. The calendar year appears based on correct scientific assumptions, so belongs with either of the solar day alternatives. Finally, the values cited in the novels, even though incorrect, also belong together. These connections are summarised in the following table:

    Choice of ord (padans) Choice of padan (solar Earth days) Length of ord (solar Earth days)
    Scientific tropical year (668.5921) Scientific solar day (1.02749) 668.5921*1.02749≈686.97
    Approximate scientific year
    (687/1.027≈668.94)
    Approximate solar day (1.027) 687
    Calendar year (670) and skip ords
    Approximate solar day, or
    scientific solar day
    Depends on skip ords
    Incorrect year (687) Approximate sidereal day (1.02569) 687*1.02569≈704.65

    Counting the Moments

    Throughout his first book, Burroughs uses the terms "hour," "minute" and "second" for smaller units of time. It seems that he thereby means the Earth units, so that one hour is 1/24th of an Earth day, not a subdivision of the padan. This nomenclature is used throughout the rest of the series in parallel with the Barsoomian terms, which causes a certain amount of confusion.

    The second book in the series contains an oft-cited footnote explaining the native terminology: "Martians divide [the day] into ten equal parts, commencing the day at about 6 A.M. Earth time. The zodes are divided into fifty shorter periods [xats], each of which in turn is composed of 200 brief periods of time [tals], about equivalent to the earthly second" (GM/16). Burroughs also writes that "at the 1st zode" it is "about 8:40 A.M. Earth time" (Ibid.), which seems to support this (although 16 minutes too late), and which would make "6 A.M." into zode 0. This is also consistent with the statement that the 8th zode is "About 1:00 A.M. Earth time" (CM/21).

    However, other quotes give a different picture. Noon is said to be "25 xats past the 3rd zode" (LG-1/7) and midnight is "the middle of the eighth zode" (SM/1 and LG-2/11). Others yet give the 4th zode as "about one P.M. Earth time" (LG-2/1), the 7th zode as "About 8:30 P.M. Earth time" (CM/20), the 8th zode as "10:48 P.M. Earth time" (LG-4/10) and finally the 9th zode as "1:12 A.M. E.T." (LG-3/10). All these "Earth times" are about a zode early compared with the original premise.

    So even though the sources are inconsistent, there seems to exist more canonical evidence that 6 A.M. is actually the first zode, which does make sense with the quote that the padan begins at that time. Zode 0, then, does not exist at all.

    The table below gives the zodes of the padan and the corresponding time of padan as if it was divided as the Earth day into 24 hours with 60 minutes (slightly stretched to fit the longer Martian day).

    Zode Corresponds to
    1 6:00 A.M.
    2 8:24 A.M.
    3 10:48 A.M.
    4 1:12 P.M.
    5 3:36 P.M.
    6 6:00 P.M.
    7 8:24 P.M.
    8 10:48 P.M.
    9 1:12 A.M.
    10 3:36 A.M.
    The exact lengths of the zode and its subdivisions follow, of course, from the length of one padan. Burroughs gives the zode as "2.462 earth hours" (FMM/2), which is consistent with the sidereal day. The tal is approximated to "about eight tenths of an earthly second" (LG-4/10), but that must be an error since it indicates a very short padan of less than 23 hours. It seems likely that Burroughs truncated the result after the first decimal.

    The table below sums up the various possibilities for length of the padan and its subdivisions.

      Scientific solar Approx. solar Scientific sidereal Approx. sidereal Erroneous "5 years, 96 days"
    Padan (hours) 24h, 39m, 35s 24h, 38m, 53s 24h, 37m, 23s 24h, 37m 24h, 41m 24h, 49m, 45s
    Padan (days) 1.027489 1.027 1.025957 1.025694 1.028472 1.034551
    Zode 2h, 27m, 57s;
    ≈2.465974h
    2h, 27m, 53s;
    ≈2.4648h
    2h, 27m, 44s;
    ≈2.462296h
    2h, 27m, 42s;
    ≈2.461667h
    2h, 28m, 6s;
    ≈2.476667h
    2h, 28m, 59s;
    ≈2.482923h
    Xat 2m, 57.6s 2m, 57.5s 2m, 57.3s 2m, 57.2s 2m, 57.7s 2m, 58.8s
    Tal 0.888s 0.887s 0.886s 0.886s 0.888s 0.894s
    It is easy to see that for the smaller units of time, the differences are insignificant. For our purposes, it is normally only when working with ords, or even larger units, that the choice of padan length becomes important.

    To begin the day halfway between midnight and midday seems somewhat impractical, since neither noon nor midnight falls on an even zode. It may be a leftover from an older, now abandoned, time-keeping system that was used before the current decimal system.

    Mysterious, Magic Moons of Mars

    Burroughs was apparently very fascinated with the concept of twin moons and their paths across the heavens. In some of his most poetic passages he describes their wild chase across the skies, and how even the Barsoomians themselves can never become used to this. On occasion, the Barsoomians use the moons as a natural chronometer. One such rare example is when Dejah Thoris proclaims that she may be dead "ere the further moon has encircled Barsoom another twelve times" (PM/13). Such statements, of course, are of little value unless we know the duration of the moons' respective orbits.

    Thuria (Phobos) would seem to be the less problematic case. Burroughs claims that it "makes a complete revolution around the planet in a little over seven and one-half hours" (PM/5) and in that time it moves "from horizon to horizon in less than four hours" (LG-3/1), following which it would be out of sight "for about three and three quarters Earth hours" (MMM/5) or for "more than three and a half hours" (CM/3). In spite of the minor deviances, it seems obvious that Burroughs simply used the scientifically correct sidereal orbit (7.65 hours) and divided by two to arrive at the rounded figures for its passage from horizon to horizon (3.83 hours).

    A number of problems are connected with these figures. To begin with, just as an observer standing on the planet would have no use for the sidereal day (see above), the same goes for the sidereal period of either of the moons. The planet's own orbit and rotation must also be taken into the equation, which gives the mean time from moonrise to moonrise of 11.10 hours (0.45 padans) for Phobos. Furthermore, Phobos is so close to the planet that it would not be visible for exactly half its orbital period. The visible arc of Mars beneath it is only 137.8 degrees instead of a full 180. Therefore it is above the horizon for only 4.25 hours at the equator. The farther one is from the equator, the less time Phobos remains above the horizon. Because it is so close to Mars, it is never visible above 70.4 degrees latitude (either north or south).

    The other moon, Deimos, has a sidereal orbit of 30.30 hours and a mean time from moonrise to moonrise of no less than 5 days, 12.50 hours (5.37 padans). Because of its proximity to Mars (it is, however, farther away than Phobos) it is visible for 2 days, 15.56 hours (2.58 padans) from the equator. Deimos is never visible above 82.7 degrees latitude.

    Burroughs, again quoting the sidereal orbit, claimed that Cluros (Deimos) "revolves about Mars in something over thirty and one-quarter hours" (PM/5). But he also writes that it travels across the sky in eight zodes, or "a trifle over nineteen and a half Earth hours" (CM/3), which implies an orbit of sixteen zodes (~39.5 hours). This is probably an arithmetic error, since half the sidereal orbit of Deimos would be a little more than six zodes (15.15 hours).

    This leaves us with the following options for the orbits of the Barsoomian moons, assuming a zode of 2.462 hours:

      Thuria Cluros
    Quoted 7.5 hours (3.05 zodes) 30.25 hours (12.29 zodes)
    Scientific, sidereal 7.65 hours (3.11 zodes) 30.30 hours (12.31 zodes)
    Scientific, moonrise to moonrise 11.10 hours (4.51 zodes) 5 days, 12.50 hours (53.82 zodes)
    Incorrect -- 39.39 hours (16 zodes)
    It may seem unnecessary to include the erroneous orbit of Cluros in the table, since it must be a mistake. However, a detailed study of all references to that moon throughout The Master Mind of Mars reveals that it is the only working option (Ekman, "Chronology", forthcoming revised version). All the other options fail to explain Ulysses Paxton's many observations of Cluros. This may be because Burroughs continued using the incorrect figures from The Chessmen of Mars, or it may be a coincidence if Burroughs randomly inserted moon observations into the text.

    In addition to the other incorrect statements Burroughs made regarding the Martian moons, they are in fact very small and dark. Deimos only appears the size and brightness of a star. Phobos is larger but only appears about one-fifth the diameter of our own moon. There would be no "gorgeous Martian night beneath the hurtling moons and the million stars" (TMM/3) as Burroughs envisioned.

    But if we accept Burroughs' words, then Thuria in particular would be very useful for time measurement, neatly dividing the padan into six parts, rising thrice and setting thrice. It is strange that Burroughs' Barsoomians did not use this amazing natural clock more frequently, but perhaps the ancient Barsoomians did, before deciding to move to a possibly more practical decimal system.
     

    A Suggested Calendar

    Based on what has been written above, we would like to lay out a suggestion for a possible Barsoomian calendar. The reader is hereby asked to understand that this is not meant for use in literary discussion of Burroughs' books, since it is based on a very shaky foundation. It is meant mostly as an example of how the concepts in this article can be combined. For more practical purposes it could be used, for example, in long role-playing campaigns set on Barsoom, where the players and the game master need to have a common reference of time.

    The Barsoomian calendar is based on the following assumptions:

  • The Barsoomian era is divided into cycles of 532 ords each. (See discussion below.)
  • The epoch (ord 1) is different for each Barsoomian state. Helium's epoch is based on the founding of Helium, 49,657 ords before John Carter's arrival. (This figure has no support in the canon and is an invention of our own.)
  • Dates are written as o O c HE, where o represents the current ord and c the current cycle of the Helium Era, e.g. "160 O 93 HE."
  • The new ord starts (on average) on the winter solstice. In 1887 this occurred on February 5. (This date is not in compliance with scientific facts.)
  • The astronomical ord is approximately 668.5921 padans long. This is the scientifically correct figure, which makes for more fun when fiddling with the skip ords.
  • The standard calendar ord is 670 padans.
  • To correct the difference between the calendar ord and the astronomical ord, seven padans are skipped every five ords at the end of the ord and seven more padans are skipped at the end of the first ord of every cycle. (See discussion below.)
  • The teeans are named First Teean (Ay Teean) through Tenth Teean (Tee Teean).
  • The week (an) is seven padans long. Its padans are named First Padan (Ay Padan) through Seventh Padan (Ov Padan).
  • Teeans and ans are independent of each other, but the ord always starts on the first padan of the an. Therefore the final an of the ord is only five padans long.
  • Barsoom has nothing that corresponds to our Sunday, but First Padan is generally set aside for various regular transactions and revisions, wherefore some institutions are closed on that day. Festivities can occur on any day of the an.
  • The padan is approximately 24.6597 Earth hours. If we use the scientifically correct ord, we must also use the scientifically correct padan.
  • The really delicate problem here is the skip padans. The simple solution would have been to just skip one entire an every ord that is evenly divisible by five. That would mean an average calendar ord of 668.6 padans. Very close to our chosen 668.5921. But not close enough. It would mean that the calendar would be more than one padan ahead after only 127 ords.

    So we could have a rule that skips an extra padan every 127th ord, except that such a rule would be impossible to remember. Easier to remember, and almost as accurate, would be to use a combination of an extra skip padan every 100 ords, but not every 500 ords. This is a practical solution that has been suggested for some Martian calendar designs, but a drawback from our perspective is that it would be inelegant to mix skip padans and skip ans. Also, we need near-perfect accuracy because of the high life expectancy, and consequently long eras, of the Barsoomians.

    The remaining error in our calendar with the skip an is 0.0079 (668.6-668.5921) padans too long in a year. If we want to use that with an improved skip an design we must find out when the error has grown to one whole an. This number can be found by dividing seven by our error, which leads to 886 (7/0.0079≈886.08). So we could have another skip ord every 886 ords, but then we are back to a rule that is very difficult to remember.

    Recall, on the other hand, that the Barsoomians may have used a system of cycles in the past. Such a system would be convenient here, too. It would both simplify skip ord remembrance, and shorten the long dates of the Barsoomian eras ("Our current jeddak ascended in the ord forty-nine-thousand-four-hundred-and-eighty-seven."). For convenience, we will term the five-ord skip ord cycles "primary cycles," and the longer cycles then become "secondary cycles."

    But we cannot use secondary cycles that are 886 ords long, because 886 is one ord after a skip ord and since the new cycle starts anew on one, with skip ords still falling on every ord evenly divisible by 5, this would carry an inaccuracy of 1.4 padans (1/5th of the seven-padan skip an) into the next cycle. Therefore we must take one step back to 885, which is itself a multiple of 5, with a marginal loss in accuracy.

    Alternatively, it is possible to take advantage of the inherent inaccuracy (1.4 padans) of the extra ord past the last complete primary cycle. So instead of going back one ord to 885, we can go back 175 ords (1.4/0.0079≈177.2 and round to the nearest multiple of five) to 711 ords (886-175=711). In fact, each extra ord past the latest complete primary cycle will, likewise, shorten the secondary cycle inversely proportionally. This is because the incorrectness of each extra calendar ord (which, as you will remember, is longer than the tropical ord) past the latest complete primary cycle will increase the error to be corrected by the secondary cycle, and correction must therefore be more frequent. This may seem like a shortcoming, but it is actually a feature. We are now allowed the luxury of choosing one alternative out of five:

    Extra ords Secondary cycle Average ord
    0 885 (885+0) 668.592090
    1 711 (710+1) 668.592124
    2 532 (530+2) 668.592105
    3 353 (350+3) 668.592068
    4 179 (175+4) 668.592179
    The 179-ord alternative is slightly too inaccurate to be useful, but the others are extremely close to the real astronomical ord. So what length of secondary cycle would the Barsoomians most likely use?

    One figure that is repeatedly mentioned throughout the novels is the expected life span of 1000 years (e.g. PM/4). We have assumed that this means 1000 Earth years, based on the statement that Barsoomian women "will still be desirable in the eyes of men after forty generations of Earth folk have returned to dust" (CM/2), supposing that this is meant to indicate that they are beautiful until the end of their days and that a generation in this context is 25 years (25*40=1000). Burroughs possibly intended 1000 Earth years to correspond to 500 ords, which is a nice and round figure. But, inverting the reasoning, this poses a potential problem. 500 ords does not round off well to 1000 years. It is closer to 900. So why would Carter say 1000 years in his manuscripts?

    One solution could be to assume that the secondary cycles were originally 500 ords long, but when the calendar needed revision to correct the drift from the astronomical year, 532 was chosen because it was closest to the original value. At length it came to represent not only the calendar cycle, but also the maximum life expectancy. By an amazing coincidence, this would explain Carter's quoted 1000 years extremely well. The ord is about 1.881 Earth years, so 1000 years is almost exactly 532 ords (1000/1.881≈531.6).

    We are aware that this is not what Burroughs intended, but it works both within the context of the novels and for our calendar design.

    Our cycle system has an extremely high degree of long-term accuracy, with a theoretical error of only a single padan in 200,000 ords. Furthermore, being a three-digit number, 532 is easy to learn, especially since 5=3+2. The drawback is that while the average accuracy is high, the precision for a single ord can be almost a full an off. We have chosen to go with this system anyway, mostly because it allows us to retain Burroughs' implied 670-padan ord while staying true to science.

    In practice, however, the length of the Martian year varies slightly over time. Therefore, even this high accuracy may not be enough over a period of 50,000 ords. A higher accuracy cannot be achieved with our current knowledge of how the solar system works. And, even though it is possible that the Barsoomian scientists have come further in this respect, it is not very likely that they bothered to give their calendar better accuracy since that would complicate a system such as presented here. It is more likely that skip ords would be added or deleted as needed. This could be decreed by a global community of scientists (such a community, formal or informal, probably exists since there is "a common scientific language understood by the savants of all nations" (SMM/6)), allowing many nations to use the same basic calendar even though they have different epochs.

    Such added or deleted skip ords would only have occurred a few times during the past 50,000 ords, wherefore we have chosen to not consider them in our own calculations.

    Below you can see the Barsoomian ord. Skip an is shown in red. Solstices and equinoxes (average) are shown in blue.

    Teean
    First
    Second
    Third
    Fourth
    Fifth
    Padan 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7
      1 2 3 4 5 6 7   1 2 3   1 2 3 4 5 6   1 2   1 2 3 4 5
    8 9 10 11 12 13 14 4 5 6 7 8 9 10 7 8 9 10 11 12 13 3 4 5 6 7 8 9 6 7 8 9 10 11 12
    15 16 17 18 19 20 21 11 12 13 14 15 16 17 14 15 16 17 18 19 20 10 11 12 13 14 15 16 13 14 15 16 17 18 19
    22 23 24 25 26 27 28 18 19 20 21 22 23 24 21 22 23 24 25 26 27 17 18 19 20 21 22 23 20 21 22 23 24 25 26
    29 30 31 32 33 34 35 25 26 27 28 29 30 31 28 29 30 31 32 33 34 24 25 26 27 28 29 30 27 28 29 30 31 32 33
    36 37 38 39 40 41 42 32 33 34 35 36 37 38 35 36 37 38 39 40 41 31 32 33 34 35 36 37 34 35 36 37 38 39 40
    43 44 45 46 47 48 49 39 40 41 42 43 44 45 42 43 44 45 46 47 48 38 39 40 41 42 43 44 41 42 43 44 45 46 47
    50 51 52 53 54 55 56 46 47 48 49 50 51 52 49 50 51 52 53 54 55 45 46 47 48 49 50 51 48 49 50 51 52 53 54
    57 58 59 60 61 62 63 53 54 55 56 57 58 59 56 57 58 59 60 61 62 52 53 54 55 56 57 58 55 56 57 58 59 60 61
    64 65 66 67   60 61 62 63 64 65 66 63 64 65 66 67   59 60 61 62 63 64 65 62 63 64 65 66 67  
      67     66 67    
    Teean
    Sixth
    Seventh
    Eighth
    Ninth
    Tenth
    Padan 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7
        1   1 2 3 4 1 2 3 4 5 6 7   1 2 3   1 2 3 4 5 6
    2 3 4 5 6 7 8 5 6 7 8 9 10 11 8 9 10 11 12 13 14 4 5 6 7 8 9 10 7 8 9 10 11 12 13
    9 10 11 12 13 14 15 12 13 14 15 16 17 18 15 16 17 18 19 20 21 11 12 13 14 15 16 17 14 15 16 17 18 19 20
    16 17 18 19 20 21 22 19 20 21 22 23 24 25 22 23 24 25 26 27 28 18 19 20 21 22 23 24 21 22 23 24 25 26 27
    23 24 25 26 27 28 29 26 27 28 29 30 31 32 29 30 31 32 33 34 35 25 26 27 28 29 30 31 28 29 30 31 32 33 34
    30 31 32 33 34 35 36 33 34 35 36 37 38 39 36 37 38 39 40 41 42 32 33 34 35 36 37 38 35 36 37 38 39 40 41
    37 38 39 40 41 42 43 40 41 42 43 44 45 46 43 44 45 46 47 48 49 39 40 41 42 43 44 45 42 43 44 45 46 47 48
    44 45 46 47 48 49 50 47 48 49 50 51 52 53 50 51 52 53 54 55 56 46 47 48 49 50 51 52 49 50 51 52 53 54 55
    51 52 53 54 55 56 57 54 55 56 57 58 59 60 57 58 59 60 61 62 63 53 54 55 56 57 58 59 56 57 58 59 60 61 62
    58 59 60 61 62 63 64 61 62 63 64 65 66 67 64 65 66 67   60 61 62 63 64 65 66 63 64 65 66 67  
    65 66 67       67    
    Below are the Barsoomian dates for some interesting events, as close as it has been possible to calculate them. Earth dates for most Barsoomian events are based on a revised version of Ekman's chronology for The Princess of Mars trilogy.


    ERBzine Volume 1630

    Bill Hillman
    BILL AND SUE-ON HILLMAN ECLECTIC STUDIO
    ERB & Barsoom Text and Images Copyright Edgar Rice Burroughs, Inc.