Time Portals or Annual Gates

A collection of axioms and formulas for resolving the courses of the Earth and Moon can be recited from certain passages of an early-written manuscript attributed to Enoch (one of the Bible patriarchs). In fact, an entire section of this respective book (from chapter 71 to chapter 82) has a focus upon "the revolutions of the heavenly luminaries". (The cited portion of text that attempts to mathematically quantify the spin and orbital phenomenon is known as Enoch's astronomical book).

Certain of Enoch's given adages or axioms for determining the orbital returns can ultimately be recognized to represent a quite plausible (or a rational) explanation for time cycles that are generated by the Earth and Moon. In essence, certain among the definitions and laws recorded in the astronomical book appear to correctly depict that rates of solar days, synodic months, and tropical years can all be identified together in the context of a rational model (an intelligent lunisolar system).

Enoch's considerable prowess (or ability) as a cosmological interpreter is well reflected from pages of ancient literature. For example, the book of Jubilees relates that Enoch was the first who "recounted the weeks of the jubilees, and ... set in order the months... " (refer to chapter 4, by Charles).

More about the major accomplishments of the cited astronomer can be understood from a historical sketch presented by Bar-Hebraeus. This medieval author's writings about the life and times of Enoch appear to represent a compendium that was drawn from a number of more ancient sources. According to this respective author, Enoch was also the first to have "discovered the knowledge of the Zodiac, and the course of the Planets".

The occupation of Enoch as a priest is only hinted at from amid the various texts attributed to Enoch's own authorship. However, some considerable degree as to the scope and effectiveness of his service in a priesthood office seems to be mirrored from certain passages of early-written literature. In example, Enoch is shown to have "... appointed festivals for sacrifices to the Sun, at each of the Zodiacal Signs". Enoch is further shown to have taught men "to worship God... to fast... pray... give alms, votive offerings, and tenths". Enoch "reprobated inappropriate foods and drunkenness" (Bar-Hebraeus).

Enoch; as an astronomer of note, and as a significant religious leader; seems to also be mirrored in certain Sumerian chronicles--where in "critical scholarship, Enoch is regarded as being a character based on the... myth of Enmeduranki" (Wikipedia). This title or name appears in the Sumerian king list. "[Surviving] records pre-date the authorship of the torah by some 1000 years, [and tell]... of a great priest... of the sun-god Utu. He, in the myth, was subsequently taken by the gods Shamash and Adad, to heaven, and taught the secrets of heaven and of earth. Enmeduranki was extemely significant to the Sumerians, as he was the ancestor from whom all priests had to be able to trace descent, in much the same way as Aaron was to the Aaronid priesthood of ancient Judaism... " (ibid).

Pages of history thus portray Enoch to have been both an accomplished astronomer, as well as a ranking cleric. It here seems of some certain significance that this respective priest-astronomer is unilaterally shown to have been the very first to interpret a lunisolar system on the basis of a set of laws pertaining to the spin and orbital rates.

As is further shown throughout subsequently presented sections and accompanying articles, some of the adages and axioms given by Enoch for resolving the courses of the Sun and Moon adequately describe/define an intelligently arranged system. Clear enough from the collection of Enoch texts is that even an early astronomer would have been capable of making an accurate forecast of the orbital returns of the Earth and Moon. In fact, some of the cosmological interpretations attributed to Enoch are so entirely valid that even a modern astronomer would find them of benefit.

Stations of the Sun and Moon

The collection of Enoch literature is unique in that a rather comprehensive description of tracking time stations is embedded in the astronomical section.

Early-held knowledge of the location of time stations for both the Sun and the Moon seems very apparent from the following selected portions of 'The Ethiopian Enoch', by Laurence:

[Chapter 71:] "The book of the revolutions of the luminaries of heaven, according to... their respective periods... and their respective months... according to every year of the world for ever... ." [Skipping to Chapter 73:] "... I beheld their stations... according to the fixed order of the months the Sun rises and sets... thirty days belonging to the Sun... [All the days belonging to each year can be correlated to a fixed number of days]... to the Sun and stars... thirty days belonging to them... The Moon brings on all the years exactly, that their stations may come neither too forwards nor too backwards a single day; but that the years may be changed with correct precision in [a fixed number of] days... The year then becomes truly complete according to the station of the Moon, and the station of the Sun... which rise and set in them for thirty days."

From the Enoch literature, it is apparent that the ancients did once time track a "station of the Sun"--probably in association with a cycle of 30 days. Portions of text from the astronomcial book also make it clear that a "station to the Moon" was time tracked inside of the year cycle.

Based upon an hypothesis that Enoch's numbers could pertain to a valid lunisolar system; and to better illustrate the use and definition of a station of the Sun; certain portions of Enoch's astronomical book (Chapter 73) can be interpreted/paraphrased--as follows:

• One in 30 days belongs to the Sun.
• To the Sun and stars, one in 30 days belongs to them.
• The station of the Sun (or one day) reappears in a cycle of 30 days.

The indicated description of a station or a day of the Sun seems significant, and the detail is ample enough to point to the ancient use of the following axiom or time formula:

The revolutions of the heavenly luminaries define a station or day that pertains to the Sun. This station or day reoccurs in a cycle of 30 days (an endless rate).

It is pertinent that--in addition to a station of the Sun--Enoch's astronomical book also describes an associated station of the Moon.

"The year then becomes truly complete according to the station of the Moon, and the station of the Sun" (ibid).

According to the astronomical book, in addition to a station of the Sun, a station of the Moon also belongs among (pertains to) the revolutions of the heavenly luminaries.

It is here of significance that other portions of the Enoch literature tend to indicate that the cited station or day of the Moon might have been tracked in place, or in position, with a sequence of the lunar quarters.

Note that the Moon travels through four distinct quarter phases in each orbital cycle. The four distinctly defined phases are: 1. New phase (when the Moon is fully dark); 2. First-quarter phase (when the Moon is half dark and half light); 3. Full phase (when the Moon is full of light); and 4. Last-quarter phase (when the Moon is half light and half dark). Each of the cited quarter phases of the Moon can be predicted to elapse in a time-span that is approximately equivalent to seven and one-third days.

This positioning of a station or day of the Moon in correspondence with a cycle of the lunar-quarter phases is easy to interpret from the following portions of the cited astronomical book: "(Chapter 72: verse 3)... [the Moon's] light is a seventh portion from the light of the Sun.... (verse 6) Half of it is in extent seven portions... its light is by sevens... (verse 8-10) On that night, when it commences its period... it is dark in its fourteen portions... During the remainder of its period its light increases to fourteen portions [or the Moon's light increases to fourteen portions]... (Chapter 73: verse 4) In each of its two seven portions it completes all its light [or the Moon reaches the phase of full illumination in two seven portions]... " (refer to 'The Ethiopian Enoch', by Laurence).

A more indepth research of Enoch's astronomical book leads to the ultimate conclusion that the cited station or day of the Moon was probably tracked in association with a cycle of 7 lunar quarters or 7 lunar weeks. The clue to coming up with a more explicit definition of the station of the Moon from the astronomical book can seemingly be found in Chapter 73 in the portion of text that provides detail of the Moon and its lag of 50 days. ("To the Moon alone... it has fifty days..."). It is here of considerable significance that a cycle of 7 lunar quarters or 7 lunar weeks can effectively be counted out in correspondence with a span of 50-days--as is further shown below.

It can thus ultimately be interpreted that primal priest-astronomers did once reckon lunar weeks and were knowledgeable of a station or day of the Moon (in addition to the cited station of the Sun). The station of the Moon appears to have been tracked in correspondence with a time-span of 7 lunar quarters or 7 lunar weeks.

The description of a station or a day of the Moon from the Enoch texts is then additionally significant and tends to indicate the early use of the following axiom or time formula:

The revolutions of the heavenly luminaries define a station or day that pertains to the Moon. This station or day reoccurs in a cycle of 7 lunar weeks (an endless rate).

Note that priest-astronomers throughout the ancient Middle East are indicated to have once specially reckoned a cycle of 7 weeks (probably 7 lunar weeks). For additional information concerning the early reckoning of a lunar-week cycle, refer to the following online publication: 'Significance of the Lunar Week'.

It here becomes most remarkable that "every year of the world forever" can effectively be determined by applying nothing more than the two cited axioms (those described in Enoch's astronomical book)! Essentially, it is demonstrable that the rate of the solar year can effectively (perfectly!) be measured and metered out through the time track of a station (a day) of the Sun and a station (a day) of the Moon.

Through the continual reckoning of the two cited stations, the rate of the solar year can precisely (perfectly!) be correlated to a specific number of day units.

Hint: If the rate of one day in each month-like cycle of 30 days is routinely reckoned apart from other days that comprise the time stream then this respective rate is inherently equal to 12.17474 days per year. Also, if the rate of one day in each cycle of 7 lunar weeks is routinely reckoned apart from other days that comprise the time stream then this respective rate is inherently equal to 7.0676 days per year. These two rates of set-apart days (stations) are then equivalent to a total of 19.24232 days per year (in average time). Thus, if 19.24232 days or stations per year (on average) are reckoned apart from all other days, it becomes a given conclusion that the limits of each passing solar year can effectively be measured and metered out in correspondence with a number count that is always equal to 346.000 of the other days. Note that the rate of the solar year of 365.242 days minus the cited rate of set-apart days (19.242 days) is equal to 346.000 days.

It then seems clear that certain among the axioms and time formulas written down in Enoch's astronomical book are remarkably accurate. The solar circle (365.24219 days) inherently does contain a station or day of the Sun (one in a 30-day cycle) and also a station or day of the Moon (one in a cycle of 7 lunar weeks).

Thus, it seems significant to a study of Enoch's astronomical book that--as long as the cited stations of the Sun and Moon are routinely tracked apart from the other days--the length of each passing solar year is inherently metered into 346 equal divisions--on average. (Note that each of the cited 346 divisions inherently corresponds with the boundary of an exclusively counted day).

It is here very significant that the reckoning of 346 specific divisions (as exclusively counted days) results in a time span that is exactly equivalent to the length of the annual circle or year (in average time). Essentially, 346 days--when counted in association with 19.24232 renewal days per year--is equal to 365.24232 days. Thus, the annual result of routinely leaping the count of each station (or day) of the Sun and each station (or day) of the Moon is a time span that is exactly equal to the length of the annual circle or solar year (on the average). The average annual result of tracking 346 days in correspondence with stations of the Sun and Moon is perfect to within an annual difference of only 11.2 seconds! Remarkable is that the annual result of tracking stations of the Sun and Moon can be recognized as fully or absolutely perfect relative to the rate of the solar year only several centuries before. Refer to the online publications 'Functional Time Design' and 'The Moon as a Time Meter' for specific information concerning the perfect accuracy inherent in tracking a station (or day) of the Sun and a station (or day) of the Moon.

A track of 346 time stations (not necessarily 364 days)

While some areas of text attributed to Enoch can clearly be recognized in the context of a correct lunisolar model, a number of passages appear to pertain to definitions of the spin and orbital phenomena that are incorrect.

The most logical conclusion for the disparate information is that a more original version of the astronomical book was in circulation among the ancients. The primal version of the astronomical book appears to have subsequently been modified--or possibly recompiled with other information--by intervening scribes. Essentially, those inconsistent areas of text now attributed to Enoch do probably reflect the action of scribal error (or addition).

One obviously incorrect definition appearing in current copies of the astronomical book is the fixed assignment of 364 stations for the length of the year. Because portions of the astronomical book detail a requirement to intercalate stations of the Sun and Moon (an average intercalation rate equal to 19.24 days per year) then it becomes a given conclusion that the original version would have shown 346 stations for the annual number--not 364 stations. In essence, each and every passing annual circle can perfectly be measured and metered out in correspondence with 346 time stations (plus the intercalation of 19 more days). Thus, current versions of Enoch--which now indicate 364 days--appear to not correctly reflect what was originally written (346 days plus intercalated days).

Based upon the clear indication that the rate of the solar year (365.24 days) can perfectly be measured and metered out through a combinational time track of a station (or day) of the Sun and a station (or day) of the Moon, current copies of Enoch's astronomical book seem to warrant the substituting of the originally written number of days (346) for the wrongly copied number of days (364). Consequently, it seems almost sure that a closer representation of the outline of the original version of Enoch's astronomical book is reflected in the following paragraph:

[Chapter 71:] "The book of the revolutions of the luminaries of heaven, according to... their respective periods... and their respective months... according to every year of the world for ever... ." [Skipping to Chapter 73:] "... I beheld their stations... According to the fixed order of the months the Sun rises and sets... one station or day in 30 days belongs to the Sun... All the remaining days belong to the year... It is the station (or day) of the Moon that brings on all the years exactly so that an annual count of 346 days can be assigned. This count does come neither too forwards nor too backwards by a single day. Through the intercalation of Sun and Moon stations, the years are changed with correct precision."

Regardless of which recreation of Chapter 73 is believed to more closely reflect the more original version, there is hardly any doubt but that primal priest-astronomers were knowledgeable of a station (or day) of the Sun and a station (or day) of the Moon. It seems remarkable that the Sun and Moon stations shown in early-written Enoch texts can be used to effectively (perfectly) measure and meter out the solar orbit. Even more remarkable is that these same stations can also be used to effectively (perfectly) measure and meter out the lunar orbit.

Refer to subsequent sections for pertinent information concerning the significance of reckoning Sun and Moon stations. By tracking the cited stations of the Sun and Moon, the solar orbit can effectively (perfectly) be represented in terms of a number of day divisions (346 metered divisions). Also by tracking the very SAME stations of the Sun and Moon, the lunar orbit can effectively (perfectly) be represented in terms of a number of day divisions.

This all means that certain of the axioms and formulas contained in portions of Enoch's astronomical book (the presumed more original version) appear to be remarkably valid. It is very clear that a nearly perfect definition of the solar year--or 365.24232 days in average time--can be achieved by accounting for the cited lunar and solar stations. (For additional information concerning the incredible accuracy inherent in the reckoning of months and weeks, refer to other online literature presented at www.creation-answers.com.)

Almost beyond belief is that the use of certain of Enoch's axioms and time-formulas would result in a perfect definition of the solar year. It is the literal truth that cycles of both the new month and the lunar week can be counted-out in correspondence with "every year of the world for ever". [Note that in this modern era, a simple count of months and lunar weeks can be used to define the limits of the solar year to within a difference of only 11.2 seconds too slow; however, due to the slowing spin of the Earth, astronomers who were alive at about 3000 years ago should have been able to define the solar year to within the limits of absolute or even perfect accuracy.]

Annual Quarters

Certain passages of the Enoch literature indicate that the ancients did track and celebrate a special day in correspondence with each passing annual quarter.

Explicitly clear from two separate sections is that a unique day would have been intercalated in correspondence with the turn of each quarter--where 4 equally-distributed days are shown to have been tracked per year. The respective 4 days that were routinely intercalated were described in detail by the author (or authors) of Enoch in ascending order (or in chronological sequence) with the previously cited count of annual stations (or world stations).

The definition of 4 specific days in pace with the 4 quarters of the year can be recited from portions of the astronomical section--as follows:

"... 4 intercalary days... belong to the reckoning of the year... owing to them men go wrong therein, for those luminaries truly render service on the world-stations, the 1st day in the 1st portal... the 2nd day in the 3rd portal... the 3rd day in the 4th portal... and the 4th day in the 6th portal, and the exactness of the year is accomplished through its separate 346 stations..." (Paraphrase of Chapter 75, by Charles. Note that 346 is here shown rather than 364 so as to better reflect the probable original number of world stations).

As in other passages of Enoch, this quoted portion of text continues to indicate that primal astronomers did track each passing solar year in pace with a fixed number of world stations. The cited quote--however--additionally shows 6 portal stations and 4 seasonal stations as being distributed along/among/amid the world stations.

The cited 4 days that were intercalated appear to have been understood to pertain to the "exactness of the year". In essence, early astronomers appear to have understood 4 specific days as dividing the year into quarter divisions (exactly).

The day-count guides stated by author (or authors) of Enoch can ultimately be recognized to represent a rather sophisticated method of modelling the tropical year (as further shown below).

The following diagram is presented to better illustrate the feasibility of tracking the revolution of each passing tropical year within the context of the day cycles indicated by Enoch:

In reference to the diagram shown above, it seems significant that each one of the annual quarters (4 per year) can EXACTLY be correlated (on the average) to only ONE specific day. Through this interpretation, one day unit (positioned right at the turn of each annual quarter) is typed or classed to stand out and apart from the month days.

The respective interpretation has considerable merit in the regard that each passing quarter of the tropical year can effectively (perfectly!) be measured and metered out within the context of a month count that alternates between 28 days (in one month) and 29 days (in the following month). The cited month sequence (that alternates between 28 and 29 days) can inherently be repeated throughout all 12 months of the year. In fact, the alternating month count of the shown calendar is so very precise that--from the very beginning of recorded history--the addition or omission of a calendar day has never been warranted. In essence, each calendar year of this respective model can be stated to ALWAYS contain 6 months of 28 days interleaved with 6 months of 29 days.

Of further significance concerning the recorded time track of a day positioned at each quarter division of the year is that a distribution of at least 6 portals or 6 gates was also shown by the author (or authors) of the Enoch literature. The first of these four days is shown as being positioned in the first portal, the second of the quarter days is shown at the position of the third portal, the third quarter day is shown in position in the fourth portal, and the last of the days (the 4th day) is shown in the sixth portal (as cited).

To more clearly illustrate how primal astronomers might have once reckoned 6 portal divisions in each annual circle, the replica of an early-used zodiac calendar is subsequently shown:

Note that the 6 portals--drawn in with yellow marker on the photograph--have been added in an attempt to better show the positioning of the portal divisions relative to the location of the 4 quaters.

If a quarter division of the year was positioned within the 1st, 3rd, 4th, and 6th of the cited gates or portals then a given conclusion is that one of the quarter divisions would have been reckoned from about the middle of the 1st portal. Subsequent quarter divisons would then inherently have commenced in correspondence with the beginning of the 3rd portal... and again the middle of the 4th portal... and yet again at the beginning of the 6th portal.

From the given positioning of the 6 portals relative to the 4 quarters it can be recognized that each of the portals would have been accounted for at the turn of every 29th day (or at the rotation of every alternate month).

The indicated effective time track of world stations with seasonal and with portal divisions points to the possibility that--on the average--some among the early astronomers may have been right on par with modern astronomers. Essentially, the limits of each passing solar year (on the average) could have been determined to within the limits of even perfect precision.

For additional information concerning the early time track of annual stations, refer to the following online publication: Tracking The Day-of-the-Sun

Signs for the 4 seasons

Certain priest-astronomers who flourished in the era of the Temple may have interpreted the turn of each annual quarter in correspondence with a unique portal division--as cited.

This possibility is perhaps most clearly mirrored from portions of Enoch's astronomical book which relate that "4 intercalary days... belong to the reckoning of the year". The cited 4 quarter signs appear to have been charted/tracked in corresponding (or ascending) sequence with 6 distributed time portals--as follows:

"These luminaries [the Sun and Moon] truly render service on the world-stations, the 1st quarter is in the first portal... the 2nd quarter is in the 3rd portal... the 3rd quarter in the 4th portal... and the 4th quarter is in the 6th portal, and the exactness of the tropical year is accomplished through its separate 346 world stations..." (paraphrase of Chapter 75, by Charles).

The author of Enoch also wrote that the other luminary (the Moon) rises in corresponding order with these same 6 time portals or annual divisions--as follows:

"And I saw six portals in which the Sun rises... and the Moon [also] rises... in these [same six] portals... " (Chapter 72).

The ancients thus appear to have understood that the synodic period of the Moon can somehow be accounted for right in association (or in cross-reference) with a uniform distribution of 6 portal divisions in each tropical year.

It here becomes rather amazing that Enoch's computation for the cited return of the tropical year (in 365.24219 days) can also be recognized to have incorporated the period of the Moon.

Significant about Enoch's cited method for determining the zodiac signs and the annual quarters is that the synodic revolution of the Moon can additionally be determined (as an inherent or an automatic definition of tracking portals and quarters).

The lunar period

A formal method for tracking the revolution of the Moon relative to the positioning of annual portals is very easy to document. This correspondence between the rate of the lunar month and the rate of 6 annual portals can perhaps best be recognized from the time span (in days) by which the Moon revolves through all its phases. [Note that the time for the synodic return is accomplished (on the average) in correspondence with a time span of 29.53059 days.]

Because the cycle of the lunar month is completed in a time interval that is NOT divisible by a whole-day rate then a count of the lunar month in terms of the solar day must be in correspondence with either a shorter span of 29 days or a longer span of 30 days. Essentially, because the lunar orbit completes in correspondence with a fractional day then at least every other lunar month must be counted to be longer than 29 days.

This respective additional lunar day was commonly interpreted among certain Jewish astronomers to correspond with a long or a full count of the lunar month (or a month that contained a 30th day). Long or full months of 30 days were those months that contained an intercalated (extra) day... a day counted in place right at the end or at the synodic return of the Moon.

However, in portions of Enoch's astronomical book, the ancients are shown to have observed the Moon and Sun to both appear together at a reoccurring rate of always 6 days per year.

"... [I saw a law for the luminary] named the Moon... [sometimes] her days are... together with the Sun... And the overplus of... [these days] amounts to 6 days [each year]... ".

From the detail of this annual distribution of 6 days it can ultimately be recognized that certain early astronomers understood or interpreted the synodic revolution of the Moon right in correspondence with the location of the cited 6 time portals (not necessarily in correspondence with a 30th day positioned at the end of the lunar period). Essentially, the requirement to track additional lunar days was probably understood in correspondence with 6 special days (time portals) located at fixed time positions (or at equally distant time spans) around the annual transit of the Sun.

The indicated understanding of the location of 6 portals (or uniformly positioned gates) in association with the tropical year is then significant in that this interpretation points to the possibility that some among the ancients applied a day count of no more than 29 days to each lunar month. In association with a fixed count of always 29 days, the cited annual portals (6 days per tropical year) may not have been applied to the count of the lunar month. Rather, the portal days were probably leaped from out of (or not included within) the count of the lunar month (a fixed count of 29 days). In essence, the additional day that was required to match the synodic return of the Moon was probably accounted for in pace with a separated time portal (not as a specifically numbered day of the lunar month).

It is here significant that shadowy passages of text embedded in the Enoch literature point to the possibility that the ancients would have understood yet another law for interpreting the synodic revolution of the Moon:

"And I saw another [time] course, a law for her, how according to [the track of an additional circuit, the Moon's monthly revolution can exactly be determined]... in 8 years there are... days. For the moon alone the days... in 8 years amount... all the days... in 8 years... ".

Enoch's 2nd law for resolving the Moon's monthly revolution thus appears to have been understood in the context of a time circuit equal to 8 tropical years.

Enoch's additional law is significant in regard that if the synodic return of the Moon is routinely accounted for in half-day units then an effective (perfect!) time track of the limits of 8 tropical years can ultimately be achieved. The cited time course of 8 years would have almost surely been understood among the ancients as also being synonymous with a fuller or longer count of 16 years (as is further shown below). In essence, Enoch's 2nd law--when stated in terms of whole days--is inherently equal to a double cycle of 8 tropical years, or is equal to a span of 16 tropical years.

To more clearly illustrate how primitive Hebrew astronomers might have computed the return of the Moon using Enoch's 2nd law, passages of text attributed to Anatolius of Alexandria seem to be pertinent. When writing "of the order of the times", this early Christian author made mention of a peculiar cycle of 16 years--as follows.

"[In] the books of the Hebrews and Greeks, we find not only the course of the Moon, but also that of the Sun, and, indeed, not... in the general, but even the separate and minutest moments... all calculated... Of these Hippolytus made up a period of 16 years with certain unknown courses of the Moon" ('The Paschal Canon').

From other passages of early-written literature, it can be recognized from the cited reference to Hippolytus that this early astronomer was both a learned scholar and a prolific writer. As a Christian theologian, Hippolytus became rather influential at Rome before finally suffering martyrdom in about the year 238 CE.

Based upon lunisolar accounting attributed to Hippolytus, it is clear that this ancient astronomer was also familiar with a long cycle of 112 years (refer to Easter Controversy at www.newadvent.org). Hippolytus is thus shown to have possessed the means of predicting the spin and orbital phenomenon in association with a long cycle comprised of both 16 years and 112 years. (Note that the stated great cycle of 112 years was almost surely time tracked in 7 segments of 16 years each).

What is significant concerning the stated great cycle of 112 years (and similar information contained in ancient "books of the Hebrews and Greeks") is that the spin and orbital rates (Earth and Moon) can be demonstrated to exactly keep pace with a time grid comprised of 16-year segments.

To more fully illustrate, it would be a true axiom to state that if the rate of the synodic month is always counted out in correspondence with a whole-day rate (29 days) then the difference (when counted apart as a day rate) inherently equals 105 additional days in every cycle of 16 tropical years. (This respective rate of additional days is also exactly equal to 735 days in a cycle of 112 years).

The indicated correspondence between the spin of the Earth and the synodic revolution of the Moon is then remarkable in the regard that 105 days in 16 years... or 735 days in 112 years... is quite perfectly equal to the rate of 0.53059 days per lunar month.

Note in reference to the shown diagram that the modern rate of lunar-month days in excess of 29 days (105 days in 16 tropical years) inherently bounds with the epoch of each 16th year to within an average difference of only 30 seconds. (This is a difference of less than 2 seconds per year!) The cited rate of 105 days can almost perfectly be scribed relative to the rate of 16 tropical years; however, because the spin of the Earth appears to be slowing with time then it can be recognized that this respective solar-day count would have been absolutely perfect in the relatively recent past.

The cited rate of lunar-month days in excess of 29 days is then of considerable significance in the regard that the number of days in each synodic revolution CAN systematically be scribed relative to always 29 days (as a rate of whole days). Of further significance is that the stated rate of days in excess of 29 days can also be recognized to exactly (perfectly!) interface with the rate of the tropical year.

Thus, the astronomer-priest who wrote the Enoch texts appears to have been fully correct in citing the requirement to leap a portal day from out of the lunar-month count (of always 29 days). This respective leap day can exactly be accounted for in correspondence with a separated or a secondary rate of days (as shown). Because the required secondary rate of days is all but perfectly equal to 105 days in every time segment of 16 tropical years then it is clear that the ancients did probably track the reoccurrence of the leap day in cross-reference (or in correlation) with the rate of the tropical year.

If the apparent orb of the Moon returned at a rate exactly equal to 29.5 days per synodic month then a 30th day could effectly be intercalated every alternate month. However, the actual synodic revolution in 29.53059 days is 44 minutes and 3 seconds slower than 29.50000 days. This respective difference--if prorated on a straight-line basis--would mandate that an additional day always be intercalated every 55.65614 days (on the average). [Note that each tropical year inherently contains 12.368267 lunar months. This number of months when multiplied by an excess over 29 days of 0.53059 days per month is equal to 6.56248 additional days per tropical year--on the average. (This rate is also equal to 1 additional day every 55.65614 days... or is equal to 104.99965 additional days every 16 tropical years).]

The clear possibility then is that the ancients did time track at least 6 portals or gates throughout each passing tropical year (Enoch's 1st law). It is here additionally significant from the information passed down by Hippolytus that a cycle of 112 years would have additionally been tracked in 16 year segments (Enoch's 2nd law). This long cycle--and the requirement to always leap 6 portals relative to the rate of the tropical year--ultimately indicates that an additional lunar-month day would have been leaped at the frequency of every 7th season.

      _________________________________________


       NUMBER OF MOON DAYS IN EXCESS OF 29 DAYS
           ACROSS A LONG-CYCLE OF 112 YEARS

      _________________________________________


        49   +   49   +   49   +   49   +   49
        49   +   49   +   49   +   49   +   49
        49   +   49   +   49   +   49   +   49
        49   +   49   +   49   +   49   +   49
        49   +   49   +   49   +   49   +   49

        --------------------------------------

         Total extra Moon days  =  735 Days

        ___________________________________

           A SEASONAL TRACK OF JUBILEES
        ___________________________________

            First cycle of 25 years:
            ------------------------
              7 cycles of 7 seasons
              7 cycles of 7 seasons
              ---------------------
               Jubilee celebrated
                (summer and fall)


            Second cycle of 25 years:
            -------------------------
              7 cycles of 7 seasons 
              7 cycles of 7 seasons
              ---------------------
               Jubilee celebrated
               (winter and spring)

        ___________________________________

        Total Time = 200 seasons (50 years)

                             ..
                             ..
      4th of month, 11 parts obscured,  Moon enters Day.
      5th of month, 12 parts obscured,  Moon enters Day.
      6th of month, 13 parts obscured,  Moon enters Day.
      7th of month, 14 parts obscured,  Moon enters Day.
      8th of month, 14 + half obscured, Moon rules all Day.

        When the Sun sets, the light of the Moon is no
        longer obscured. Thus, the Moon begins to be
        revealed again on One-to-Sabbath [Echd BShbt],
        the 8th of the month). *

      9th of month,  1 part  revealed,  Moon enters Night.
     10th of month,  2 parts revealed,  Moon enters Night.
     11th of month,  3 parts revealed,  Moon enters Night.
     12th of month,  4 parts revealed,  Moon enters Night.
     13th of month,  5 parts revealed,  Moon enters Night.
     14th of month,  6 parts revealed,  Moon enters Night.
     15th of month,  7 parts revealed,  Moon enters Night.
     16th of month,  8 parts revealed,  Moon enters Night.
     17th of month,  9 parts revealed,  Moon enters Night.
     18th of month, 10 parts revealed,  Moon enters Night.
     19th of month, 11 parts revealed,  Moon enters Night.
     20th of month, 12 parts revealed,  Moon enters Night.
     21st of month, 13 parts revealed,  Moon enters Night.
     22nd of month, 14 parts revealed,  Moon enters Night.
     22nd of month, 14 + half revealed, Moon rules all Night.

       When the Sun sets, the light of the Moon is no
       longer revealed. Thus, the Moon begins to be
       obscured again on One-to-Sabbath [Echd BShbt],
       the 22nd of the month). *

     23rd of month,  1 part  obscured,  Moon enters Day.
     24th of month,  2 parts obscured,  Moon enters Day.
     25th of month,  3 parts obscured,  Moon enters Day.
                             ..
                             ..

     ------------------------------------------------------

   * -- Note  the  peculiar  reference  to 'Echad Bshbt'.
        This respective occasion [One-to-Sabbath] appears
        to  have been celebrated twice in the lunar month
        (once at the epoch of the new Moon, and again  at
        the epoch of the full Moon).

      _________________________________________________

       INDICATED FORMAL DEFINITION FOR THE LUNAR MONTH
      _________________________________________________

       14 Waxing Stages
       ----------------

        1st stage of Moon waxing (nighttime + daytime)
        2nd stage of Moon waxing (nighttime + daytime)
        3rd stage of Moon waxing (nighttime + daytime)
        4th stage of Moon waxing (nighttime + daytime)
        5th stage of Moon waxing (nighttime + daytime)
        6th stage of Moon waxing (nighttime + daytime)
        7th stage of Moon waxing (nighttime + daytime)
        8th stage of Moon waxing (nighttime + daytime)
        9th stage of Moon waxing (nighttime + daytime)
       10th stage of Moon waxing (nighttime + daytime)
       11th stage of Moon waxing (nighttime + daytime)
       12th stage of Moon waxing (nighttime + daytime)
       13th stage of Moon waxing (nighttime + daytime)
       14th stage of Moon waxing (nighttime + daytime)

       -----------------------------------------------

             One-to-Sabbath celebrated at nighttime
           (The Moon "rules all night" this evening) 

       -----------------------------------------------

       14 Waning Stages
       ----------------

        1st stage of Moon waning (daytime + nighttime)
        2nd stage of Moon waning (daytime + nighttime)
        3rd stage of Moon waning (daytime + nighttime)
        4th stage of Moon waning (daytime + nighttime)
        5th stage of Moon waning (daytime + nighttime)
        6th stage of Moon waning (daytime + nighttime)
        7th stage of Moon waning (daytime + nighttime)
        8th stage of Moon waning (daytime + nighttime)
        9th stage of Moon waning (daytime + nighttime)
       10th stage of Moon waning (daytime + nighttime)
       11th stage of Moon waning (daytime + nighttime)
       12th stage of Moon waning (daytime + nighttime)
       13th stage of Moon waning (daytime + nighttime)
       14th stage of Moon waning (daytime + nighttime)

       -----------------------------------------------

             One-to-Sabbath celebrated at daytime
           (The Moon "rules the daytime" this day)

           365.24219 days (rate of the tropical year)
    minus   19.24232 days (rate of Sun-Moon stations)
           --------------
   equals  346.000 days   (a specific number of days)

         INDICATED DAY COUNT FOR THE TROPICAL YEAR *
        ---------------------------------------------
          Season  Quarter  Zodiac   Zodiac   Portal
          Number  Station  Month   Stations  Station
          ------  -------  ------  --------  -------
             1       1        1     7 7 7 7     1
                              2     7 7 7 7
                              3     7 7 7 7     1
             2       1        4     7 7 7 7
                              5     7 7 7 7     1
                              6     7 7 7 7
             3       1        7     7 7 7 7     1
                              8     7 7 7 7
                              9     7 7 7 7     1
             4       1       10     7 7 7 7
                             11     7 7 7 7     1
                             12     7 7 7 7
        ---------------------------------------------
                     4                  336     6

            Year Total  =  346 World Stations

        * - This count equals 365.2423 days per year
               when paced by Sun-Moon stations.

        INDICATED DAY COUNT FOR THE LUNAR MONTH *
        -----------------------------------------
             Month   Counted    Turn of
             Days     From       Month
             -----   -------   ----------
              14     evening   (half day)
              14     morning   (half day)
        -----------------------------------------
              28 Month Days   (1 whole day)   

         * - This count equals 29.53 days a month
                when paced by portals and seasons.