 Month 2 of the Inundation, Day 1 (from Lepsius). |
M. G. Reader D.S.C., a confectionary technologist, is also a specialist in marine navigation. His earlier contribution to SISR on Egyptian astronomy dealt with mythological/astronomical ceiling decoration.
Information recorded on astronomical tables in the Ramesside tombs can be charted to show the movements of stars across the sky over the course of a year. From the consistent variation of the resultant star-tracks from the expected vertical lines, it must be concluded that the year of the tables' compilation - provisionally, ca. 700 BC - was marked by considerable disruption of the orderly motions of the skies.
THE "RAMESSIDE STAR TABLES" comprise sets of 24 tables of stars, each table naming 13 stars. Each table is headed by a date, the dates being spaced at 15-day intervals through the year, a set of 24 tables thus making up a year of 360 days - the general form of the table headings is: Month 1, Day l; Month 1, Day 16/15; Month 2, Day 1 ... Month 11, Day 16/15; Month 12, Day 1; Month 12, Day 16/15. The 13 stars in a table are each allocated to an hour of the night, starting with "Hour 0" [1] - apparently sunset - and ending with "Hour 12" - apparently sunrise.
Four sets of such tables have been found - two in the tomb of Ramesses VI, one in the tomb of Ramesses VII and one in the tomb of Ramesses IX (NEUGEBAUER & PARKER, 1964). In each case, the tables appear as a sort of "appendix" to a larger and more pictorial design which bears a family likeness to the astronomical (or "astro-theological") ceilings in the tomb of Senmut, Seti and Ramesses II (dated 300-600 years earlier, described in detail in READE, 1977). No set of tables is absolutely complete and there are minor differences between the individual ones, but it is clear that they are all at least trying to tell the same story. In order to get anything approaching a complete tabulation, it is necessary to consult tables in more than one tomb, but it is only seldom that they disagree with one another; some tables are omitted or are incomplete in individual sets and there are also some gaps in the tables which remain as gaps in all four versions.
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Month 2 of the Inundation, Day 1 (from Lepsius). |
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Each table is further accompanied by a crossword-like "grid" of 8 x 13 squares (except for one isolated case in the tomb of Ramesses IV, apparently accidental, where the grid is 7 x 13; there are also some anomalous grids in the tomb of Ramesses IX, where grids of 8 x 12 sometimes combine two stars on a single line). One, or very occasionally more than one 5-pointed star sign is positioned on each of the 13 horizontal rows of a normal grid. These star signs are obviously intended to indicate the precise position of the star which is named (in hieroglyphs) in the adjoining line of the text. Much speculation has been directed to the significance of the figure of a squatting man who is drawn immediately under each grid, with whom is obviously also associated the hieroglyphic instructions which accompany each star name and which read "on the right eye", "on the left ear", "on the left hip" and so on. The present author is satisfied that these are simply directions to the scribe as to where he is to place the particular star sign on the grid [2] - the scribes were presumably not numerate - but even this device was apparently not enough to save them from making mistakes: there are quite a few discrepancies between the written instruction and the actual depiction (see Appendix IV). However, if one follows the rules derived by HEINRICH BRUGSCH (1883) and places each star on its grid in accordance with the written text, rather than as shown by the scribe, the results are distinctly more satisfactory. (This is despite the apparent incongruity of some of Brugsch's instructions - e.g., he actually describes a figure which is a mirror image of most of the ones reproduced photographically by Neugebauer and Parker; he claims that the left hip of the figure lies alongside its right arm; and he produces a transcript of the tables which differs in some important respects from the ones assembled in the later study.)
The present writer is also satisfied that each of the eight vertical lines of a grid represents a time interval of two days. Thus, a star which is described as "in the middle of the breast" belongs on the 4th vertical line and was observed on either the 8th or the 23rd day of the month (according to whether the table concerned was for the first or the second half of the month). The scribes did occasionally manage to place a star between two lines, as would seem reasonable, but there does not seem to have been any corresponding textual instruction - though it is not inconceivable that there could have been one, as variant writings of both the instructions and the star names abound. No star ever appears on the 8th line of a grid, and appearances on the first line are extremely rare, possibly only accidental. It is also possible to argue almost indefinitely whether the "middle of the breast" should properly be lined up with the 6th or the 8th day of a half-month; the available evidence is at least to some extent self-contradictory, but the point does not appear to be of much practical importance.
Brugsch has also derived a most useful translation of the hieroglyphic descriptions which identify the individual stars; there are several indications that it cannot be a perfect translation, but the present writer finds his classification much preferable to anything of a similar nature that he has so far been able to find in the literature. Brugsch lists 44 potential star names, but it soon becomes obvious that one or two of them, at least, must be duplications (that is, single stars which have more than one possible description). The serious student will need to refer to Brugsch's full account of his reading of the tables, which is given on pp. 185-194 of his Thesaurus.
The accompanying graphical presentation of the observations recorded in the Ramesside tables summarises the available material in what appears to be the most convenient form for further analysis. The individual stars are identified by letter symbols, based on Brugsch's classification (set out in more detail below). The special advantage of this style of presentation is that stars which are behaving normally will produce straight-line tracks which run truly vertical on the plot [3]; the amount of any deviation of a track from the vertical is a direct measure of the change in the apparent longitude of the star concerned.
Style of Compilation
To be able to make any viable interpretation at all, it is essential first to be reasonably confident of how the tables were compiled. The Asyut coffin lids (POGO 1932; Neugebauer & Parker 1960) display not dissimilar star patterns, but they are invariably "perfect", at least in the sense that each star produces a straight and vertical line on a plot of this type. The reason is clearly that the hours of the night were defined at that era by the positions of particular stars: the "hours" may well have been unequal and uneven in any absolute sense, but they cannot but come out "right" on a diagram of this sort if the interval between the rising (or setting, or any other transit) of two named stars is the only recognised definition of an "Hour". The present tables obviously do not follow this pattern and an "hour" must therefore have been defined (and measured) in some independent manner at the era when the present tables were compiled. The only independent timing device which we know of as being available to the ancient Egyptians is the water clock, and we must therefore suppose that the time of transit of these stars was recorded with the help of such a clock. No doubt the water clock was itself originally calibrated by observations of intervals between stars (probably the sun, moon and planets as well); what the present tables principally show, therefore, is that the calibration was no longer working as it once did. It was evidently still working during much of the first two to three months of the year, however (assuming that the minor aberrations of stars Jj/Jk in Tables 1-5 can safely be neglected for the present), and one can establish from this that stars Jd to Na were genuine hour stars; careful averaging of the intervals between them (omitting Jj/Jk) shows average intervals of 61 minutes, 121 minutes, 55 minutes, 62 minutes, 62 minutes, 57 minutes, 60 minutes and 61 minutes [4]. Thus, though the individual stars were evidently slightly erratically spaced, the accumulated time error after nine stars had passed (= 9 hours) was only 1 minute. Clearly, some of the stars may have had to be quite minor ones to make this degree of precision possible, and one should not be too surprised if it turns out to be all but impossible to identify individual stars with certainty.
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As yet, however, we are barely at the start of the problem, for water clocks do not appear to have been designed to run for more than twelve hours or so. They could he kept going indefinitely by topping them up with fresh water of course, but it is very questionable whether their accuracy was such that they could keep good time for twelve hours let alone twenty-four hours or a 1-year period (as these tables appear to require). A good dissertation on the time-keeping characteristics of Egyptian water clocks is that by R. W. SLOLEY (1931): it should be consulted by anybody who wants to try to draw precise conclusions from observations recorded in these tables.
In practice, there must clearly have been some system of daily checking and adjustment of the clock. The simplest possible technique - wait for a known star to appear and then start the clock - was clearly not used; if it had been, the general pattern of the tracks on the diagram would have been even more erratic than it actually is. The next "simple" suggestion might be to start the clock at sunset, but the time of sunset varies through the year (up to approx. plus or minus 47 minutes from the equinoctial time for an observer on the latitude of Thebes) and the stars still visible at sunrise should then have shown a distinct cyclic pattern through the year (the sunset stars could also show some cyclic variation). This effect can be avoided by using a specially calibrated clock, however, and there are grounds for thinking that the Egyptians of this era did have such a clock (further discussed below): but, were the clock always started at sunset, one would not expect to find irregular gaps in the sunset observations, even if there might well be some in the sunrise observations. Actually, there are some quite well-defined gaps in the star lists for both the sunset and the sunrise hours, and they are remarkably evenly distributed: the shorter nights, when stars were either "missing" or obviously unusually difficult to observe with any degree of precision at both sunset and sunrise, appear to have occurred principally in Month 6, though there are also some rather more minor indications of short nights a month or two before and after this. The gaps are essentially similar at both ends of the night, though perhaps tending to be rather more conspicuous at sunset than at sunrise [5]. This indicates that the clock must have been re-set by some method other than those so far suggested.
 Summary of the data recorded in the Ramesside star tables. If the motions of the stars had been normal and stable, all the star tracks on this diagram would have been straight and vertical lines, whilst the tracks in the triangle at bottom left would have lined up with those in the parts of the main diagram directly above it (and similarly, the tracks at top right would have aligned with those directly beneath). Note also that there is a slight difference of alignment between the scales of right ascension (see APPENDIX I) at top and bottom of the diagram, but that these scales are not and cannot be precise. (The error varies erratically between about plus and minus 1 hour - see text and APPENDIX VI.) Solid connecting lines are intended to indicate identifications which are reasonably firm, supported by more than one version of the tables (whenever possible), and also reasonably plausible; broken connecting lines denote correspondences which are either less firm or less plausible, but only very few of the "tracks" included on the diagram can really be accepted as being free from taint of any kind. Serious students who think they may be able to improve on the picture presented here are recommended to plot their own diagrams, but are warned that quite a large number of diagrams can be required to cope with all the uncertainties in the available evidence. They should also bear in mind that a possible further consequence of the disturbances, one not easily isolable from the other effects, would be a drift in the apparent latitude of the observing station. Rather more observations are available than have been included on the diagram, and these should be taken into consideration by anyone seriously trying to advance the analysis further; but it has seemed advisable to exercise at least some selectivity for the purposes of the present article: almost none of the available data could be described as "beyond controversy and much of it is quite certainly "doubtfully sound" (even contradictory). |
Faced with this problem, a modern astronomer would probably start his clock at mid-day, which he could observe fairly accurately by means of shadow lengths and directions (subject to the qualification that he would still have no automatic method of correcting for the equation of time, which is the error to which all sundials are subject, sun time and mean time getting as much as 14 to 16 minutes apart at certain seasons of the year). We do not think the ancient Egyptians had sundials which could be used reliably at all times of the day and at all seasons of the year, but it is certainly conceivable that they might have used some form of sundial for starting the clock at a pre-determined "sun time" in the later part of the afternoon; the potential errors due to the equation of time would probably not have been known to them, and a further uncertainty of 30 minutes or so due to the use of an unsophisticated type of sundial would be unlikely to show up at all clearly in a table of this sort. (If the tables were precise in all other respects, there would be the same "kink" in every star track which was affected by a particular night's observations. Because of the system of construction of the tables, not every available star is recorded on the same night, but there are some instances where there are matching "kinks" which could be attributed to variable setting of the clock on particular evenings or at particular seasons.)
Before we can attempt any real interpretation of the data actually recorded, however, there is still another problem to be cleared. At one time, it seems to have been true that day hours were different in length from night hours, each being one twelfth of the period between sunrise and sunset (e.g., 68 minutes per day hour, 52 minutes per night hour at midsummer in Thebes). In the case of the Asyut coffin diagrams, it is generally thought that the night hours were defined as hours of total darkness - that is, "night" officially started some time after sunset and ended some time before sunrise - and the same might apply here. The ultimate test is the number of "hour stars" actually needed to see a year through: if there are 13 hour stars observed on an "average" night (i.e. one which has been corrected for the purely seasonal effects of summer and winter) and 24 hour stars suffice to see the year through, then the stars are definitely spaced at "genuine" 1-hour intervals - i.e., equinoctial, or equal hours for both day and night; if 13 stars are observed each "average" night but there are more than 24 hour stars in all, the night hours are shorter than the day hours. (In the case of the Asyut coffins, there are 12 stars listed for each night but 36 are required to see the year through.)
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For a variety of reasons, we cannot compute precisely how many hour stars do complete the present diagram, but it appears to be very close to 24; if anything, the number appears to be nearer 25 than 24 [6]. On the whole, therefore, it appears probable that the hours in the present tables are genuine equinoctial ones - the nine hours listed above certainly set this pattern, and the symmetrical "gaps" at sunrise and sunset during an apparent summer season also support this conclusion - but it cannot be absolutely excluded that the night hours may have been slightly shorter on average than the day ones; the effect, if any, can only have been very slight (nothing approaching the 40-minute night hours of the Asyut tables).
This still does not fully clear the possibilities, however, for we also know that at least some Egyptian water clocks were calibrated with "seasonal" hours rather than genuinely equal hours, as noted above. A clock calibrated with seasonal hours indicates rather more than 60 "true" minutes per hour in the long winter nights and rather less in the summer. The arguments of the last paragraph show that the average hour, computed over the year, was at least very close to a genuine equinoctial one, but they do not entirely exclude the possibility of shorter night hours in summer which were balanced up by longer night hours in winter. This possibility will be further reviewed in the concluding part of this article.
It can be noted in passing that the angular distances between "summer hour stars" and "winter hour stars" have to be different if a seasonal hour clock is used. This would be a distinct disadvantage today, but not necessarily so in the ancient world: the seasonal hour system would permit the same number of "hour stars" to be recorded in a short summer night as in a long winter night and no significant other anomaly would arise so long as "summer stars" always remained summer stars. There is a comparatively minor snag in that each "hour star" will actually be visible for approximately six months of the year (starting as a morning star, visible all through the night three months later, and finishing as an evening star) and the implications of this behaviour are further amplified in Appendix VI; but there is an essentially more serious long-term problem in that all stars must actually slowly drift away from any initial correspondence with the seasons, due to the precession of the equinoxes. Leap year corrections do not halt this drift, in fact they only make it more obvious to the man in the street, and this seems to have been a principal reason for the general Egyptian antipathy to leap-year corrections (see also Appendix III). It is impossible to devise a calendar system which keeps both the sun and the stars to precisely the same positions in the heavens at the same season year after year, but the antique "seasonal hour" system outlined here appears to have been a compromise which genuinely suited the customs of the age. It ceased to he maintainable when constant-rate timing mechanisms, unsuited to seasonal adjustment to match the vagaries of either the sun or the stars, were finally introduced; it also implies that different "time" would have been kept in places of differing latitude, but this also would have been of no great consequence in a pre-railway age. It is much better suited to localities of low latitude than ones of high latitude.
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The suggestion is, therefore, that a water clock would have been started running, probably at some time in the late afternoon, and that a signal would have been given once an hour through the hours of darkness (such as strokes on a ship's bell), whereupon the duty watch would have to decide whether any recognised hour star was to be recorded as rising (or setting, or transiting some other pre-arranged mark). One should probably also enquire whether this seems a reasonable procedure, or whether practical observers might not have been expected to pick on some better or easier method of recording star motions (or calibrating water clocks, as would most probably have been the original purpose of the procedure). If the present "Tables" are actually only edited abstracts from some much fuller set of observations, which would include records of stars within a measurable distance of the transit point (to be shown as approaching or receding from the point itself), probably also at more than one transit point, with corresponding observations of the motions of the planets and the moon as well, it does seem to make good sense, for it would then have been possible at least partially to compensate for missed observations (such as must have occurred at times, if only due to temporary bad visibility), as well as other aberrations such as those caused by human error (observer half asleep?) or by variable atmospheric refraction.
We would obviously like to know which particular transits were observed, and it is frequently suggested that what was recorded was the moment of rising of each star. This does not make practical sense, however, as it is obviously much easier to observe a setting with precision than a rising: one has ample time in which to locate a setting star in the sky and focus one's eyes on it, also to observe it particularly closely as it nears the transit point (in this case, the western horizon). Comparison of the Asyut coffin lids with the hour angle diagram published with the author's "Senmut and Phaeton" article (READE, 1977) can incidentally also be made to suggest that they record settings rather than risings. Experienced observers would soon have discovered that neither risings nor settings are really very practical from the observer's point of view, however, being subject to considerable distortions of position due to atmospheric refraction (also intermittent fading, shimmering and strange colour effects). Modern observers invariably take the meridian transit of a star, which occurs when the star is at its highest point in the sky, but it is a virtual certainty that the Egyptians of this era did not, for the simple reason that there is no known trace of any instrument in ancient Egypt which could be used for this type of observation. Meridian passage is usually all but impossible to judge with any degree of accuracy with the unaided eye; a transit telescope must be used, but it is not the telescope which is the essential part of this instrument - it is the accurately aligned pivots on which it is mounted. A pair of simple sights mounted on rigidly aligned pivots would be quite adequate for many observing purposes, but any such device is conspicuous by its absence from ancient Egyptian records. We know that thee Egyptians used plumb-line instruments, however, and these are quite adequate for observing the bearings of low-altitude stars, perhaps ones rising as high in the sky as the pole star (25-30° above the horizon in Egypt); but they become all but unusable on stars which rise much higher than this, and it is obvious that in Egypt one would choose stars which rise high in the sky for hour measuring purposes. (The ideal would usually be equatorial stars, but it does look from the tables as though there may have been some bias in favour of stars which pass even more nearly overhead in Egypt.)
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Assuming observers of 1000-500 BC to have been reasonably practical, as they must have been, it seems obvious that they would sooner or later have adopted observation of transits across an artificial horizon, most likely one set at a height of 5° or so above the eastern or western horizon, very probably the eastern one. Such horizons (e.g. the top of a wall) are easily levelled with the help of water; one might well specify a castellated wall, as the gaps in it could then he used to locate rising stars with certainty before they actually reached the transit point, and they would also be serviceable as bearing indicators [7]; but there are plenty of possible configurations which would be well suited to particular observatory sites. The ancients must also have discovered and can hardly have failed to make use of the circumstance that a star rises (and sets) on the same compass bearing throughout the year, whatever the time of its rising or setting (the sun, moon and planets are more variable in this respect); it even appears that some of the seeming mis-identifications in the present tables could have been due to usurpation of the regular point of rising of one star by another.
The Constellations Observed
The constellations of the ecliptic, with celestial longitude marked for 700 BC and 1980 AD, to take into account the precession. (0° is conventionally the vernal equinox or "first point of Aries".) The letters along the base of the figure were added by the Editor, and mark Brugsch's constellations, as designated in the article, according to the identifications suggested by Petrie (Wisdom of the Egyptians, London, 1940, pp. 12ff. and Plates 7 & 8). Image by Rosemary Burnard |
The letter symbols for the individual stars have been devised by the present writer and derive from Brugsch's classification outlined above. They are as follows:-
| A | - | "The star of the triangle" (The star of the triangle is generally supposed to have been Sirius; Brugsch recognises Aa as the star of the triangle itself, Ab as "What follows the triangle".) |
| B | - | "The double star" (Ba = Bb = "The peak (or head) of the double star", Bc = "The double star"); |
| C | - | "The stars of the water"; |
| D | - | "The Lion" (Da = "The head of the lion", Db = "His tail") |
| E | - | "The many stars"; |
| F | - | "The beautified boy"; |
| G | - | "The (upright) knife" (or the dagger? the hieroglyphs concerned appear to have been read by others as "the mooring post"; see also Appendix II); |
| H | - | "The female hippopotamus" (see also Appendix II); |
| J | - | "The giant" (see also Appendix II); |
| K | - | "The star Aryt" |
| L | - | "The bird (or goose?)" (La = "The crest (or hood) of the bird", Lb = "The head of the bird", Lc = "Its rear part"); |
| M | - | "The thousand star"; |
| N | - | "The star of Orion" (Na = "The point (or peak) of Orion", Nb = "The star of Orion".) |
| SAR | - | This is a designation which has been introduced by the present writer (and others), located between M and Na. It is a simple transcript of hieroglyphic symbols which occur repeatedly in the tables (usually with additional symbols). In Brugsch's original classification, this star was seen as a close relative of K, but it is obvious that the two are at least spatially well separated, despite their apparent confusion in Tables 22-24 [8]. |
On the diagram, two scales of approximate (modern) right ascension have been included. The upper one is seen as applicable to stars in the upper part of the plot, and has been aligned on the basis of a supposition that M represents the Pleiades and SAR the Aldebaran/Hyades complex; it does also give reasonable approximations for the likely position of the constellations Orion, Sirius, the Lion and the Hippopotamus. One must suppose that these identifications are essentially only a guide, and that the hour star itself may have been some quite minor star which was situated somewhere in the general vicinity of the commonly recognised celestial figure. Note also that there are comparatively few stars which produce tracks which extend consistently through several hours of the night: one might suppose that these are the brighter and more easily identifiable ones - e.g. SAR, Nb, C, Da, Db, E, Ga, Hf Hg, Ja, etc. - but it must also be recognised that some stars were apparently deliberately replaced by others when it became obvious that they were deviating from their original hour star status. (It is worth noting that stars which suffer a major change of declination, such as would be caused by a shift of the world's axis which affects some stars more severely than others, are those most likely to be substituted.)
Also, if one inspects the excellent reproduction of 36 original tables presented in LEPSIUS' Denkmäler (Band VII, Abt. III, pp. 227, 228 & 228 bis), comprising various tables from the tombs of Ramesses VI and Ramesses IX, one must inevitably come to suspect that the tables were still in course of being "corrected" when work on them was discontinued: there are various indications that individual lines of hieroglyphs had been over-painted or were in course of revision. This suspicion is only heightened when one also observes that different tables appear to be the work of different scribes - the way in which the hour of the night is written is different in some tables, and it is also somewhat variable between corresponding tables in the different "sets". All in all, it is a very major task to establish what is dependable about these observations and what is not. The present writer even questions whether the original observations were necessarily Egyptian, as the representations in the tombs could conceivable have been an "Egyptianisation" of data obtained from Babylon (or even Greece). It could well be helpful if a reasonable identification can be suggested for Brugsch's constellation J: it appears to be an exceptionally large and rambling constellation, covering at least six hours of right ascension, but the present writer knows of no system of division of the heavens which ever countenanced such a large single constellation [9]. That it is a single constellation appears near certain, for the symbols for "the giant" form a part of most of the hieroglyphic renderings of its individual stars.
The second and lower scale of right ascension is intended to apply to stars in the lower part of the plot. It is even less well secured than the upper scale and rests on the supposition that the isolated mention of star Jd in Table 21 is a reliable record. Star Jd has distinctive hieroglyphic symbols and then are recorded fairly fully on each occasion (some other identifications have to be based on what appear to be abbreviated forms of hieroglyphic renderings); Tables 21 and 22 are also the only ones in the lower half of the diagram which show a pattern of genuine "hour stars" which track properly, and Jd, though isolated, fits well into this pattern. On this basis therefore, the scale of right ascension at the bottom of the diagram has been aligned on the assumption that Jd had the same right ascension in Month 11 as it had in Month 1 [10]. A weak feature of this supposed correspondence is that Jd and Jk appear two hours apart at the start of the year but three hours apart in Table 21; all that can be said about this at present is that the Jk identifications are distinctly more precarious than the Jd ones. (There are also questionable identifications of K and M in Table 24 which support the Jd correspondences - the tables actually teem with uncertainties of this kind.) Note also that there are distinct limitations to the uses which can legitimately be made of the present scales of right ascension; this subject is amplified in Appendix VI, but the comment there does also embrace some further considerations which arise from the concluding parts of this article.
When attempting identifications with known modern stars, it should be borne in mind that the celestial equator of 700 BC (currently assumed to be the probable era of these disturbances) was differently placed in the sky from the present celestial equator. The choice of the Pleiades and the Aldebaran group as key markers, for instance, is partly dictated by their respective declinations of 12.4° and 7° N, relative to the equator of 700 BC - i.e., appreciably closer to an equatorial position than they are today. (Also, these stars could have appealed especially to the Egyptians because of their associations with earlier traditions; and this would be reasonable, for 1500 years earlier they would have been even more nearly equatorial.) Sirius in 700 BC would have been 17.7° south of the equator (comparing with 16.7° today). On this basis, the stars of constellation J could be expected to have a modern declination of around 5° to 20° N, the Ja end being rather more southerly than the Jm/Jn end. Note also, however, that J appears to have contained two principal sequences of hour stars and that there may have been quite a large difference of declination between the two.
Implications
If nothing more, the Ramesside star tables show fairly convincingly that something had gone wrong with the orderly motions of the stars in this year. It appears difficult to advance any single hypothesis as to the exact nature of the disturbance which does not require an uncomfortably large proportion of the observations to be deemed "erroneous", but one can probably get a bit further yet before having to concede defeat. Unfortunately, however, there seems to be no internal evidence of an astronomical nature which can date the tables at all closely. The 700 BC provisionally assumed here derives from other considerations; a century or more earlier than this is also not inconceivable - i.e., the assumed period when Mars was displacing Venus as the principal disturber of terrestrial peace [11].
Previous commentators (GENSLER 1872; MACNAUGHTON 1932)[12] have sought to make much of the claim that Sirius (Aa) was rising with the sun (i.e. heliacally) in Month 1, as it was expected to do in the first month of the inundation. Our diagram - which essentially derives from a new interpretation of the function of the "squatting man" [2] - dates the sunrise hour transit of Sirius as occurring (none too reliably) on the 29th day of Month 1. If the observer was actually recording transits across an artificial horizon set about 20° higher than the true eastern horizon, we could certainly agree that Sirius rose heliacally on the first day of Month 1. The evidence will also tolerate postulation of a generally lower and more convenient horizon without materially affecting the claim that the heliacal rising of Sirius did mark the start of the Egyptian year at this era [13]. Note, however, that the "shortest night" appears to have occurred around 6 months after the start of the year, and that this is distinctly contrary to expectations.
Retrospective calculation indicates that the heliacal rising of Sirius at Thebes in 700 BC should have occurred about 90 days after the vernal equinox (on a 360-day year basis - but see also Appendix V). The equivalent date by a modern style of calendar (that is, one with years which begin on January 1st and which come to the vernal equinox at about March 21st) would be approximately June 21st, i.e. the mid-summer day of the northern hemisphere - in Egypt, the first day of the year at the Ramesside era, the day following the last day of the "summer season" and the first day of the "inundation season" [14]. If the shortest night did actually occur some six months after the start of the year, one must clearly suspect an association with the supposed Ramesside text which claims, "winter is come in summer, the months are reversed, the hours in confusion" (Papyrus Anastasi IV, as quoted in Gardiner, 1961, p. 64) [15].
The tables principally suggest a "midsummer day" near the end of Month 6 (approve December15th by a modern style of calendar), though there is also some evidence of short nights a month or two before and after this. Apart from the question of long or short nights, however, the tables also offer abundant evidence that the stars were repeatedly tending to transit earlier than expected. As our supposition is that the water clock was daily re-set by the sun, and the sun itself would have been affected similarly to the stars, it seems inescapable that the world must have been accelerating its rate of spin. This acceleration would incidentally be associated with an increasing count of days per year so long as the earth was not simultaneously reducing its average distance from the sun. Another essential side-effect of spin acceleration is that more than the "proper" number of hour stars must be seen each night (whether recorded or not); and this also appears to be supportable by the evidence. The special effects of Months 2 and 3, when only the early morning stars were disturbed and not the evening ones, if genuine, could only be explainable on the basis that the earth had rolled somewhat in the general direction of Sirius, so bringing Sirius and its neighbours rather higher in the sky than normal and making them rise earlier (but set later - note also that if it was transits at setting which were actually observed, the rolling of the earth would have had to be in the opposite direction). A further automatic consequence of this supposed "roll" is that stars of right ascension twelve hours different from Sirius - those in the transitional zone between constellations H and J - would simultaneously have moved lower in the sky and so be late in rising: this also is not inconceivable, for when they next rise during the night, some four to five months later, they have the effect of halting the previous accelerated motion of the heavens, at least temporarily.
It would presumably have been this "roll" which principally caused the apparent inversion of winter and summer, but there are some anomalies which suggest that there could have been a still earlier "roll" which occurred before the start of these fables. If the year actually started with Sirius at heliacal rising on June 21st, the sun would already have been at its maximum normal northerly declination; but Table 1 does not actually suggest a shorter than average night (though an explanation for this which does not involve an earlier roll is offered below). The roll indicated by Tables 2, 3 and 4 would then have increased the sun's northerly declination still further, causing some exceptionally short nights at Thebes (occurring more or less simultaneously with the roll). Moreover, Papyrus Anastasi IV reads "winter is come in summer", not "summer is come in winter", which is more nearly what the tables of Months 1 to 7 would suggest, if not pre-biased by an earlier roll which produced long nights immediately prior to June 21st. The writer doubts whether there was any earlier roll, however, and Papyrus Anastasi IV could equally well be interpreted as referring to an occurrence of winter conditions in Months 10, 11 and 12, which (with Month 9) formed the official "summer" of the Egyptian calendar, whatever this season turned out to be in reality (which it does not seem to be at all easy to judge with any degree of reliability from the tables). Note, however, that both "climate" and "length of night" can be affected in quite a complex manner by a roll of the earth towards Sirius, and not entirely predictable if the roll could also be associated with a change in the apparent latitude of the observing station. The present writer considers the latitude of the original observing station still too uncertain to allow pushing of arguments based on either climate or length of night to their ultimate limit. Note also that if tilting of the earth's axis should cause a significant change in the apparent latitude of the observing station (provisionally assumed to be Thebes, in 25° 42' N latitude), the rising and setting times of a star such as Sirius (presumed finally to have stabilised at 17.7° S declination) could be affected in a more complex manner than has so far been suggested. It actually seems improbable that the earth rolled far enough to produce such effects in other than a comparatively minor degree.
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It may be helpful at this stage to run briefly through some "rules" which must be satisfied by any interpretation of the star motions, as follows:-
(1) If the earth rolls towards a certain star, its declination becomes more northerly and stars 12 hours distant from it suffer an equal and opposite change in their declinations, whilst stars 6 hours distant from it remain unaffected. It is thus at least conceivable that an earlier roll could have occurred which, like the one indicated in the tables, did not materially affect the stars actually visible in the earlier parts of the nights of Months 1, 2, 3 and 4. Such a roll would incidentally have had to be in almost exactly the opposite direction to the one indicated in the tables.
(2) If the heliacal rising of Sirius marked the start of the year, the sun would still have been reasonably close to Sirius in Months 1 and 2, so that its declination would have been affected similarly to that of Sirius. The sun's right ascension normally increases about 2 hours per month (plus or minus 10 to 12 minutes - the movement is fastest at the solstices and slowest at the equinoxes). The sun would actually already have had 1 hour 24 minutes greater right ascension than Sirius at the time of the latter's heliacal rising at Thebes in 700 BC, the actual declinations of the sun and Sirius being very different at this time of year and leading to their rising on very different bearings - the sun at N 64° E, Sirius at S 70° E, or 46° between the two. The sun should therefore have been rather less affected by the roll than Sirius, if we assume the roll to have been directly towards Sirius [16].
(3) The right ascension of a heavenly body is normally slightly affected by changes in its declination but is independent of the rate of rotation of the earth (that is, if days are always subdivided into 24 hours, irrespective of the absolute duration of either a day or a year).
(4) The seasons are principally caused by regular cyclic changes in the declination of the sun; but they can also be affected to some extent by the actual dates and distances of perihelion and aphelion. The prime cause of any unexpected shift in the seasons must be sought in an unexpected change in the declination of the sun; changes in the declinations of stars can only be symptoms, not causes.
If there was no earlier "roll" and if the normal complement of 13 hour stars is to be equally visible at normal mid-summer as at normal mid-winter, then there is a strong probability that the water clock in use was one graduated with "seasonal hours" - i.e. short night hours in summer and long night hours in winter. In this particular year, the seasons obviously went "wrong", but the observers would presumably have continued to try to use their normal expected clock settings, at least at first. The effect would be that the "short nights" of these tables, principally in Months 6 and 7, would get recorded in somewhat exaggerated form: if the clock is set for longer nights than actually occur, fewer than the "proper" number of hour stars will be recorded before the sun again appears [17]. Tables 8-10 (Months 4-5) appear to see the highest counts of hour stars per night, but really precise counts are scarcely practicable - it could be that the nights lengthened again at this season, and it could also be that this was the season when the earth experienced its greatest acceleration of spin rate. Lengthening of the nights cannot be the sole explanation of the higher count, however, for some of the hour stars concerned slipped through without being properly recorded (i.e. they had already passed the transit point before the hour signal came up - this would not have been so obvious to the observers as might appear at first sight: even when things were going normally, they would only be expecting to record any particular star on one night in every fifteen).
What was happening in the later months of the year becomes increasingly difficult to divine with any real certainty. There could well have been more "rolls" than the initial one which is indicated with some clarity; and there was quite probably a continuing progressive "sway" of the earth's axis which would have gradually changed the declinations of all the stars in quite a complex manner. A considerable further disturbance seems to be called for if the short nights of Months 6-7 are to be succeeded by long nights only 3 months later but the very considerable confusion associated with constellation J does open up quite a wide range of alternative explanations. If the clock was actually set for the expected medium-short summer hours of Months 9-12, up to 14 or 15 hour stars could have been recorded in a long night, but it could hardly be claimed that this is substantiated by Tables 16 to 24 (subject to a consideration that it is uncertain what the observers would have done with Hour 13 or Hour 14 observations). Most probably the observers would by this time have recognised that something had gone very wrong with the lengths of the nights and would have long since abandoned trying to keep to "expected" clock settings. They might well have tried setting the clock in accordance with the indications of the immediately preceding nights, but one could also guess that they would have opted for equinoctial settings until it was clear which way things were developing. What course they actually adopted does not appear to make much difference to our conclusions; beyond the question of whether there was an earlier roll or not, it also would not significantly affect our present interpretation if an equinoctial clock were actually in use throughout the year. That a clock of some kind was used is indisputable.
Tables 23 and 24 are unfortunately very defective, and it may have to remain an open question whether the disturbances had ceased by the end of the year or whether the sky had been brought into such confusion that further observations were abandoned as useless. Table 13 is also exceptionally defective in all versions, but there seems to be no immediately obvious reason for this; it could simply be that Table 13 was in course of revision when work on the tables was discontinued. The present writer is certainly firmly of the opinion that these tables must be edited abstracts from some much fuller set of observations, also that the editing process may never have been seen through to final completion.
Brugsch's data for the last two months of the year actually suggest near stability but, short of confirmation of a sound source for this data (the only source he cites is Gensler 1872), they must be suspected of having been "smoothed", for Brugsch's Table 13 is also consistent with its having been interpolated between the tables on either side. Brugsch also specifically states that his comments are made from "a philological standpoint" and that he leaves evaluation of their astronomical import to others. Neugebauer and Parker's data, corrected by Brugsch's "rules" (as elaborated in Appendix IV), which are what are actually plotted on the accompanying diagram, suggest sheer chaos in Month 12, with the earth apparently both rocking violently and also changing its rate of spin, but there is no suggestion that the earth ever rocked so far as to become inverted. Tables 23 and 24 are only presented in reasonably complete form in the tomb of Ramesses VII, however, and there are some indications that Table 23 must be out of its proper place in the sequence (it is a near duplication of Table 24). The Ramesses VII set is unfortunately deficient in some of the earlier tables; but it does generally agree with the others when comparisons are possible.
There still remains a doubtful point which can be finally resolved, however, and this is the question of whether the observers were recording the transits of rising or setting stars. Some secondary parts of the evidence favour a supposition that they were observing stars which were in the west, rather than in the east, but they almost certainly were not. If settings were being recorded, the effect would be to displace the rising Sirius from its traditional position as marker of the start of the Egyptian year, and this seems scarcely justifiable; even worse, however, would be that one would have to admit that the observers of the first three months of this year had turned a blind eye to the ever-growing disorder of stars Ba to X, all of which would have been visible in the sky when Sirius was setting at the end of the night in the first months of the year; and this seems all but inconceivable, at least to one who views the question from an "astronometrical standpoint" and who leans on others for advice as to the actual customs and the philology of the Egyptians.
The principal single outcome of the present study appears to be a fairly well confirmed hypothesis that the axis of the earth was forced out of its hitherto normal alignment with the stars at a season shortly after the summer solstice, that the displacing force was a sustained one rather than a shock one, and that it was associated with an acceleration in the spin rate of the earth. It is also worth observing that evidence from other sources is currently suggesting that the effects of the disturbance were in many respects only temporary, and that the axis of the earth did eventually drift back to the same attitude with respect to the fixed stars (subject to a minor discontinuity in the precession of the equinoxes) as it had prior to the disturbance.
The present conclusions must be regarded as distinctly tentative, and some degree of speculation as to precisely when the tables were first prepared and precisely what was going on in the heavens at that time may be inevitable; it must also be admitted that it is possible to make quite a good case for claiming that the evidence is altogether too hazy and too unreliable really to substantiate some of the possibilities which have been aired here. However, it has seemed worthwhile to attempt a coherent account of what these tables possibly show and also to try to open up a road for others who have hypotheses which they need to test out against the available data or who can see ways of developing the analysis further.
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APPENDIX I DECLINATION AND RIGHT ASCENSION
Declination is the celestial equivalent of terrestrial latitude; Right Ascension is the celestial equivalent of terrestrial longitude. Both are measured relative to the celestial equator (which is always located directly above the terrestrial equator at the era concerned). The apparently more rational terms "Celestial latitude" and "Celestial longitude" were unfortunately pre-empted many centuries ago for measurements made relative to the ecliptic rather than to the celestial equator. The "zero point" of terrestrial longitude is the meridian of Greenwich (by international convention); the corresponding zero point" of both Right Ascension and celestial longitude is the vernal equinox intersection of the celestial equator and the ecliptic (also by convention): hence the far-reaching importance of the precise location of the "vernal equinox" in almost all astronomical computations. The vernal equinox is also termed "The first point of Aries" in some texts, but this tends to be misleading as it was only in the constellation of Aries at a particular epoch (now past history, as this epoch ended some centuries ago).
The summer solstice is 90°, or 6 hours or 3 months, distant from the vernal equinox; the autumnal equinox and the winter solstice are similarly "fixed" in relation to the vernal equinox.
One hour of Right Ascension is equivalent to 15° of terrestrial longitude.
APPENDIX II - BRUGSCH'S CLASSIFICATION OF THE STARS OF CONSTELLATIONS G, H AND J.
| * G: THE CONSTELLATION OF THE KNIFE | ||
| Ga | - | "'The drawer at the beginnings of the knife" |
| Gb | - | "The knife" |
| Gc | - | "The drawer of the knife" |
| * H: THE CONSTELLATION OF THE FEMALE HIPPOPOTAMUS | ||
| Ha | - | "The two feet of the hippopotamus figure" |
| Hb | - | "Its leg" |
| Hc | - | "The middle of the knife" |
| Hd | - | "Its kidneys (or loins)" |
| He | - | "Its incision (?)" |
| Hf | - | "Its genitals" |
| Hg | - | "Its udder" |
| Hh | - | "Its tongue" |
| Hj | - | "Its double feather" |
| * J: THE CONSTELLATION OF THE GIANT | ||
| Ja | - | "The tip of the double feathers of the giant" |
| Jb | - | "The double feathers of the giant" |
| Jc | - | "The head of the giant" |
| Jd | - | "Its throat" |
| Je | - | "The nape of its neck" |
| Jf | - | "Its collar (or necklace)" |
| Jg | - | "Its breast" |
| Jh | - | "Its knee" |
| Jj | - | "Its shin bone" |
| Jk | - | "Its foot" |
| Jl | - | "The sole of its foot" |
| Jm | - | "Its plinth" |
| Jn | - | "Its footstool (?)" |
APPENDIX III - SYNODIC "DRIFT" AND THE CALENDAR YEAR
The sole purpose of the modern leap year correction is to keep the sun from drifting away from correspondence with the seasons as indicated by the calendar. If there were a whole number of days in the year, leap year corrections would not be needed, but there are actually 365.2422 days in the modern solar year. The ordinary four-yearly correction of February 29th ensures that the calendar cannot drift more than one day before it gets "pulled back"; the less frequent century leap year correction roughly compensates the remaining 0.0078 days per year of "mismatch".
When this "general drift" arising from the impracticability of operating a calendar which does not contain a whole number of days per year is eliminated, there remain two principal styles or drift relative to the sun. Firstly there is the regular annual motion which repeats itself every year, according to which the "fixed" stars appear to overtake the sun by about 1° (or 4 minutes) per day; at the end of the year, the advance of the stars amounts to 360° (or 24 hours), so that the stage is once again set for a repeat performance. An alternative way of describing the same effect is to say that the sun completes a circuit of the zodiac in a year. Secondly there is the 25,800-year cycle, generally known as "the precession of the equinoxes", which causes the "fixed" stars to slip back by comparison with the sun, but this "slip back" only amounts to 0.014° per year and the "repeat performance" is not reached until 25,800 years have passed. Man has no way open to him for halting this long slow drift of the stars relative to the sun (and thus relative to the seasons as well when the calendar is constructed in such a way that the sun is prevented from drifting with respect to the seasons). In ancient days, when there was no automatic correction for the drift of the sun through the seasons, the drift of the stars could be kept hidden from the populace at large for periods of up to several hundred years, as the drift in position of any one star at any one particular calendar date only amounts to 1° every 72 years, whilst the sun can in practice drift quite a large number of degrees (or days of the calendar) before it becomes obvious to all that summer is no longer recurring at the same dates as it once did.
As Dr Velikovsky has pointed out (perhaps none too clearly) in his article "Astronomy and Chronology" (Pensée IVR IV, pp. 38ff.; also Peoples of the Sea, supplement), this situation was aggravated for the ancient Egyptians by the somewhat faster drift of the festivals of Venus relative to the sun, these drift similarly to the festivals of the stars, but in the opposite direction and at an average rate of 0.292° per year.* Whilst a drift rate of this magnitude is quite a lot faster than the 0.014° of the fixed stars, it is slow enough not to have been very conspicuous when the sun could also "drift" by comparison with the seasons; it is only when the sun is deliberately anchored to the seasons that the drift of the festivals of Venus quite speedily becomes obvious (say, by the time of the 3rd or the 4th significant conjunction with the sun, or after 8-12 years, instead of maybe after 50 years or even more). It would seem that only two of the ten conjunctions of Venus with the sun in an eight-year period were regarded as significant and marking the "festivals", presumably because every fifth conjunction always recurs in the same part of the sky, very likely one which was defined by reference to the position of Sirius. Arrivals of Venus in the vicinity of Sirius would presumably have been a cause for alarm, more or less irrespective of whether they were also associated with a conjunction with the sun or not, and it was possibly a near (visible) approach of Venus to Sirius which marked the actual "festival", rather than any associated conjunction with the sun: this is a subject which might well repay a deeper investigation. It is also worth noting that the "initial roll" of these tables, towards both the sun and Sirius, could conceivably have been associated with a Venus or a Mars conjunction, thus possibly marking the starting point for the cycle of the Olympiads (and/or the "Era of Nabonassar" - see W in C II, i: "The year -747"). It must also be considered surprising that all references to planets seem to have been deliberately excluded from these tables. The only reasonably satisfying explanation so far advanced appears to be that the tables are a "re-discovery" from ancient records and that the finder either neglected or even deliberately discarded planetary data. If the full story behind this omission ever comes to light, it could prove a fascinating one.
[* Calculated on the basis of a synodic period of Venus of 583.92 days, as given in Allen 1973; at Glasgow, April 1978, Professor A. E. Roy quoted a synodic period of 583.96 days, giving a yearly drift of 0.268°. These are, however, modern computations. Dr Velikovsky has suggested that the rate could have been even less than this in ancient times. It could also be significant that the one-time Egyptian habit of counting 365 days per year instead of 365¼ has the effect of stabilising the festivals of Venus in the calendar, though not in the seasons.]
APPENDIX IV - DESCRIPTION VS. DEPICTION
A provisional count based on Neugebauer and Parker's reproduction of the star tables indicates 423 tabulations in which the star depiction does not differ from the text by more than one day and 84 tabulations in which the difference is greater than this. Only a handful of the 84 differ by more than 2 to 4 days (that is, when Brugsch's "rules" are interpreted as already described). The count of correct depictions decreases rapidly when any of the more obvious alternative readings of Brugsch's rules are tried (such as an assumption that Brugsch had got the figure back to front by accident), but it should also be noted that it is questionable whether an expression such as "on the left eye" was originally intended to apply to the apparent left eye of the illustration or the true left eye of the figure. The rather strange construction of the figure, with "left hip" alongside "right arm", appears to have been planned to indicate that "the true left eye of the figure" is the correct reading, but this does not really help all that much, and it would appear that one or other figure must actually be arranged back-to-front; the "hip" or "knee" also always adjoins the trailing ends of the lines of text - most of which read right-to-left, but a few of which are reversed - and so might be expected to mark the first day of the period, but all other circumstances combine to suggest that it actually marks the last day of the period. Nor has the present writer been able to ascertain what grounds Brugsch had for claiming that certain stars - especial some in Tables 13, 23 and 24 - were included in any of the original lists; nevertheless, the simple fact is that Brugsch's "rules" applied to Neugebauer and Parker's textual data give distinctly more plausible results than either separately.
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These apparent inconsistencies are tiresome and somewhat unsettling; however, there are other respects as well in which absolute agreement between all authorities appears unlikely ever to be attainable. If nothing else, Neugebauer and Parker produce a few star depictions which differ very widely from those shown by Lepsius, though the vast majority of such depictions are in agreement. Neugebauer and Parker's reproductions of the texts also differ in minor respects from those shown by Lepsius. The above count refers to those of Neugebauer and Parkers texts which are reasonably clearly understandable and which are also accompanied by a star depiction. There are many more texts which are not accompanied by a star depiction, and there are also quite a few star depictions without an accompanying text. There can naturally also be more than one opinion as to whether any particular text should be rated "reasonably understandable" or not, there being a wide variety of doubtful readings of one sort or another. If there were no gaps at all in the four sets of tables of which we know, there would be 1248 texts in all. Neugebauer and Parker have themselves identified their texts with individual constellations and stars, generally similar to Brugsch's, but the present writer finds their compilation doubtfully acceptable as rather a high proportion of their "corrections" derive from an assumption that the arrangement of the heavens must be absolutely immutable. Their corresponding "diagram" does not differ at all widely from the one presented here, however, and some of their deductions based on the length of a missing phrase or similar philological detail give every appearance of being very worthwhile.
APPENDIX V - THE HELIACAL RISING OF SIRIUS
A more precise calculation than that on which the dating in the text of this paper is based indicates that the sun would have been 91.9° from the vernal equinox, measured along the ecliptic, at heliacal rising of Sirius for an observer at Thebes (25° 42' N latitude) in 700 BC. The calendar date indicated is about 2 days later than the June 21st date used in the main text. If the observers were using a low artificial horizon for all purposes (as they could even have been forced to do if their actual land horizon was a hilly one), heliacal rising occurs slightly earlier (only 0.2 days earlier when the zenith distance at rising is reduced from 90° 34' - a typical value for sea horizons and marine observations - to 85°). It seems pointless to attempt such a level of precision, however, partly because the calculation itself involves assumptions which could be out of place in this article (e.g. continuity of the precession of the equinoxes and constancy of the obliquity of the ecliptic), and partly because the assumed dating of 700 BC is itself only very provisional. In 800 BC, heliacal rising would have occurred a bare 1 day earlier in the calendar (sun at 91.0° from the vernal equinox instead of 91.9°). These calculations are based on the usual assumption that "sunrise" occurs when the centre of the sun is level with the horizon; if "sunrise" is seen as occurring when the upper limb of the sun is level with the horizon, as is perhaps more natural, the heliacal risings occur about 0.3 days later than stated above. (Sirius is slowly "overtaking" the sun: at first the sun is rising ahead of Sirius, but eventually Sirius catches up first with its lower limb, then with its centre, and finally with its upper limb, after which it can be seen - at least in theory - as rising before the sun.) True precision in calculation would incidentally call for adoption of a still further correction if the observer and his horizon were not both at precisely the same altitude above sea level, but the correction is a very small one under all ordinary circumstances. Direct observation of the moment when Sirius "overtook" the sun must actually have been far from easy in practice, though the circumstance that the sun rose on a very different compass bearing from Sirius would have made it easier to observe the heliacal rising of Sirius than that of almost any other star; on the whole, however, Sirius is not likely to have been seen at all clearly until some days after the theoretical moment when both could have been simultaneously level with the horizon. The writer has unfortunately never heard of any modern attempt to observe the heliacal rising of Sirius in Egypt and would like to know how easy or difficult it turns out to be in practice; he questions whether the more or less theoretical accounts which have been given elsewhere are necessarily sound.
The calibration marks on the water clock of Amenhotep III (as reproduced in PARKER, 1950) incidentally confirm that too much reliance should not be placed on retrospective calculation. These marks indicate rather plainly that the start of the Egyptian year was occurring some 2 months after the summer solstice at the era when this clock was set up (believed to be about 850 BC). If the indications of the water clock are preferred to retrospective calculation, as they probably should be, the "modern" dates quoted in the present article need moving back by 2 months or so (i.e. heliacal rising of Sirius occurring about August 21st, shortest night about February 15th). Though these potential corrections may appear large (and there could be more such "corrections" yet to come) their neglect does not appreciably affect the conclusions drawn in the text. These appear only to be conspicuously affected if the earth actually "rolled" a great deal further than the tables suggest.
If the actual observatory site was such that Sirius rose behind a range of hills whilst the sun rose through a natural horizon of lower altitude, the discrepancy between retrospective calculations and actual observation as indicated by the water clock would be quite sharply reduced; the difference between the two also reduces if the observatory was actually in a higher latitude than Thebes (though only at a rate of about 1 day per degree of latitude). Enquiries to date have also suggested that astronomically satisfactory horizons are hard to find in the Nile Valley; this could even have been a part of the reason for the eventual move of the temple observatories out to the desert oases.
Until somebody has actually tried observing the heliacal rising of Sirius in Egypt and reported the results (which could include an observation that early-morning mists are a major hazard), we cannot be too sure what the result will be, but it does seem that the "observable" date will be somewhat later than the 21st June used in the present article, though hardly as late as the August 21st indicated by Amenhotep III's water clock. Dr Velikovsky's recent comment that a possible discontinuity of 1 month in the precession of the equinoxes in 700 BC or thereabouts has been investigated by Dr. B. VAN DER WAERDEN (SISR III:2, 1978, p. 40) looks to be to the point; if such a discontinuity can be confirmed, it will have a significant effect on the dating of a great many earlier events, including the dating of the Phaeton episode and the various megalithic monuments so thoroughly studied by DR A. THOM.
APPENDIX VI - IDENTIFICATION OF THE HOUR STARS
The implications of the choice of particular hour stars can be extensive. We have confirmed that it was rising stars which were being observed - whether this was "true" rising (i.e. time of rising through a sea horizon, with or without corrections for refraction, height of eye of observer and semi-diameter of the sun) or "apparent" rising (as when a land horizon other than a level and featureless desert has to be substituted for a sea horizon) need not concern us; further, there was an evident preference for hour stars of quite widely varying declinations. The result is that the angular spacing of these hour stars (as viewed on almost any ordinary map of the heavens) may appear quite extraordinarily erratic, the time of rising of a star at any given geographical location being markedly affected by its declination. This is well illustrated by the example of the sun and Sirius at heliacal (i.e. simultaneous) rising at Thebes: Sirius could be more than 1 hour ahead of the sun in terms of right ascension, yet still rise after it. The opposite effect would apply for a star of greater northerly declination than the sun. The only reasonably quick and simple way of narrowing down the identification of potential hour stars is to mark up a star globe with a series of great circles which join the positions of points on the celestial sphere which rise simultaneously at the geographical location of the observing station. The intercepts of these curves with the celestial equator then mark the time differences between the individual risings. When this technique is applied to the positions of the Pleiades and Aldebaran, as it must be in order to get a starting point, their suitability for employment as key "markers" on Theban diagrams of about 700 BC becomes even more evident. The next step in refining the identification of the individual stars would be to replace the present scales of right ascension on the diagrams by slightly modified ones which would show the (ancient) right ascension of the points on the (ancient) celestial equator which rise simultaneously with each star at Thebes; it then becomes practicable to calculate precise combinations of right ascension and declination for each of Brugsch's stars and check up on whether they tally with the position of any known star or not. There are, of course, a very large number of possible such combinations for each of these stars, which speedily become impossibly numerous if there should be any real uncertainty as to the precise latitude of the observing station. The labour of the computation, if not the uncertainties as well, is made worse by the independent drift in position of individual stars with time - which, though slow, is large enough to make a significant difference to their actual right ascensions and declinations of some 2500 years ago.
There does not appear to be any real difficulty about computing the differences in (equatorial) spacing of summer and winter hour stars with quite a high degree of precision, but there is an inevitable uncertainty as to whether any particular pair of stars will be found correctly spaced as morning stars, night stars or evening stars. The most critical pair are Orion and Sirius (which start as summer stars and finish as winter stars), together with their counterparts of 6 months later (Hf and Ja); a more precise observer, if obliged to use such a system, would presumably try to choose some stars for use as "evening hour stars" and others for use as "morning hour stars", but it is clear that this was not done by the present observers. Sloley's comments on the systematic errors of Egyptian water clocks can also tempt one into some slightly hair-splitting calculations on the effects of calibrating a clock with stars which are only "properly spaced" at one season of the year. In practice, one must obviously start from an assumption that the hour stars were correctly spaced at midnight, the sectors of the sky in which such stars will be found being fixed by the position of the vernal equinox at the era concerned, though one must also bear in mind that it is unlikely that the Egyptians would have selected their stars quite as ideally as this. When selecting stars in practice, it is also self-evident that one would tend to avoid picking on stars which rise on abruptly differing bearings: the smooth progression of the Pleiades, Aldebaran, Orion and Sirius actually seems a natural one to select if one particularly wishes to include Sirius in the succession (actually a not very desirable star for clock calibration purposes), but the choice in other sectors of the celestial sphere is still quite an open one. The main point of this discussion of detail, however, is that it is of some importance to be able to check up on the effect which these considerations have on assessment of the "roll" of the earth towards Sirius in the first months of the year - the tables actually show Orion and Sirius as rather more widely spaced in the mornings than they are in the evenings some months later, which is the wrong way round for a uniformitarian solution. It also appears certain that the effects of the "disturbance" far outweigh the built-in defects of the seasonal hour system.
It would seem that, given the time and the computing power, a programme of successive approximations with progressive refinement of the detail can take the analysis rather further than it has been taken in the present article, though any real uncertainty as to the true latitude of the observing station could produce a stumbling block which might take a great deal of time and labour to circumvent. It must also be expected that individual stars may have changed so much in brightness in the last 2500 years as always to leave some residue of "doubtful" identifications.
Also, it appears possible to go on to derive some reasonably firm conclusions as to what was happening in the later parts of the year; but it has seemed advisable to limit the detailed coverage of the present article. The principal key appears to lie in the alternate compression and expansion of constellation J and its immediate neighbours. There is a further question which will have to be resolved before a complete decode becomes possible, however, and this is the actual technique used by the observers to specify new hour stars when old ones become unserviceable; there appear to be several possibilities, amongst them one that Table 13 marks the start of a transition period when new hour stars were being specified. It is even conceivable that there could be a connection with the "Anu, Enlil and Ea" paths (see W in C II, viii: "The reforming of the calendar") Much worthwhile work could still also be done on the reliability of individual observations recorded in these tables.
References
Acknowledgments
The inspiration for this article, together with the first documentary data on the subject matter, came from Geoffrey Gammon; the writer also acknowledges considerable help on Egyptological subjects from Malcolm Lowery. However, the author bears sole responsibility for the views expressed.
Postscript
THE ANALYSIS of the Ramesside star tables presented above is based on an assumption that the spin axis of the earth can be deflected with respect to the fixed stars whilst the latitude of the observing station remains constant, though a caution is expressed that a drift in the apparent latitude of the observing station would also be conceivable. The WARLOW "Tippe-top" mechanism of precessional disturbance, described in SISR III:4, 100-112 [and further discussed elsewhere in this issue - Ed.], requires that the spin axis of the earth remain fixed with respect to the fixed stars whilst the apparent latitude (and longitude) of the observing station can drift. These two mechanisms produce a slightly differing pattern of dislocation of the apparent motions of hour stars in the course of a minor but prolonged disturbance, such as the present one, and the trend of the Ramesside data currently appears to be to favour the first mechanism (that is, a deflection of the spin axis of the earth with respect to the fixed stars). It must be borne in mind that an "improved" analysis of the Ramesside data will probably be feasible at some time, however, the more so as the Warlow hypothesis embraces far too many satisfying features to be easily dismissed. An initial roll of the earth in the general direction of Sirius is equally acceptable with either mechanism; it is in what follows around 6 months later that most of the potential differences lie, but these differences can be comparatively slight when a low-latitude observer is recording reasonably well chosen hour stars and when the actual angle of roll is not too great. It should also be noted, however, that the present form of the Warlow hypothesis probably cannot accommodate the difference in degree of disturbance of morning and evening stars which is such a conspicuous feature of the first four months of the Ramesside tables. The analysis presented above is in many respects dominated by this feature, the resolution of which for a long time presented a major stumbling-block to completion of any viable analysis at all.
It is worth noting that Warlow's paper contains an observation that the effects of a minor disturbance, such as the present one, might not fully die away for as much as 100 years afterwards, which could explain many of the known anomalies of latitude and length of day or night, though possibly only if the actual dislocation of the motion of the earth was rather more complex than either of the idealised and almost certainly over-simplified mechanisms cited here suggests. Some oscillation of the spin axis of the earth with respect to both the fixed stars and points on the earth's surface seems probable, for instance (and is positively indicated, by the legends which attest a "War of the Gods"), in place of the unidirectional drift allowed it by the elementary form of the Warlow hypothesis, and this may some day be demonstrable from analysis of the apparent motions of the individual hour stars of these tables, if not from other considerations as well. The elementary Warlow hypothesis in any case requires some elaboration to accommodate it to a situation in which the final spin rate exceeds the initial one and, short of a claim that the Ramesside tables are fictional and bear no relationship to actual observation, the finding that these tables relate to an era when the spin rate of the earth was being accelerated looks to be a near certainty (but not yet an absolute one, as a "roll" can cause an apparent acceleration where no true acceleration exists; this roll did undoubtedly also do this, but the evidence in favour of an associated genuine increase in the spin rate looks to be very strong).
One must also observe that a mechanism for controlling the spin rate of the earth, other than the purely inertial one which has been assumed ever since NEWTON's time, is still missing from the teachings of orthodox science. Currently, the best hope of an ultimate solution appears to lie in the relativistic explanation of electrical forces in a magnetic field recently cited by CHRIS S. SHERRERD (Kronos IV:4, 1979, 55-58) and deriving from a paper read to the Institution of Electrical Engineers in 1961 by DR K. J. R. WILKINSON (Proc. Inst. Electr. Eng. 109B, 1962, 244-248). If the earth should move through an electrical field in space, electrical conductors (and/or charged non-conductors) on opposite sides of the earth could experience different forces, thus producing a torque which could affect spin rate and also cause inversion of the earth, depending principally on the strength of the particular forces but to some extent also on their geometry. The same hypothesis can also suggest how the earth can recover from the effects of a temporary "disturbance" and eventually settle back to the same orientation and spin rate as it had previously, as appears to have happened on at least some occasions. A reasonably simple test of this theory might lie in its potential applicability to the well known violence of tropical storms; another potentially interesting side effect is the possibility that bodies such as the moon are in a metastable state and are capable of resuming an axis tilt with independent spinning in the event of another catastrophe.
Notes
1. It should be observed that a zero digit does not exist in ancient Egyptian scripts. In the present case, it is clear that the first hour of each list is actually "an hour before Hour 1", though the hieroglyphs concerned are often read as "the sunset hour". This reading could be confusing, however, as one should not assume in advance of a detailed examination of the astronomical evidence that "the sunset hour" and "the moment of sunset" are necessarily the same thing.
