Uriel's Time-keeping Legions: Does the book of Enoch precisely account for the differences between the solar year and a 364-day calendar?
The above is based on the first of 2 interpretations of Enoch 82:4-20.
(The above is based on the second of 2 interpretations for Enoch 82:4-20.)
Copyright 2021 Ebionite Revival
Copyright 2021 P.J. Oh
(ebioniterevival@gmail.com)
License CC BY-NC-ND 4.0
The Enoch-based eschatology project can be found at this link:
https://www.researchgate.net/projec...-its-calendar-and-its-laden-Messianic-message
The book of Enoch is nominally a calendar having 364 days, which includes 12 months, each invariably 30 days in length along with 4 single day seasonal markers that lead each of the four seasons.
According to a system of intercalation deduced by John P. Pratt (PhD, Astronomy), which has been slightly modified by me, this calendar would be considerably more accurate than the Gregorian and Mayan calendars if intercalated by a system that adds a week every seven years, and an additional week every 28 years, except for 2 instances every Great Year quintet (one Great Year cycle is 364 years long; so 5 Great Year cycles would be 1820 years long) when a 28th year additional week isn't added.
It appears very probable that such a method of intercalation was practiced, especially in light of the book of Jubilees, which highlights the importance of the numbers 4, 7 and 28, especially when a 7 year "week" is multiplied by 4, which is the first whole number greater than half of 7; furthermore 28 is the total number of "days" (when weeks are counted as years) that constitutes the first whole number of weeks that equals the greater part of seven "weeks", which equals 49. The spiritual significance of these anniversaries of "weeks" and quartets of same, as well as quartets of weeks of Jubilees (1400 years), is demonstrated in the narratives of Jubilees such that they marked times when the following were called for: remorse over past sin; repentance; reflection on lessons learned; rededication to the Elohiym's ways of righteousness; and renewal of one's purity.
Although such a "sabbatical" cycle of intercalation probably allowed time for such remorse, repentance, reflection, rededication, and renewal; it appears that the amount of time accrued by the disparity between the 364-day cycle and the solar cycle of 364.2422 days was being precisely accounted for before effectively doing such resets by means of intercalating.
For example, in the 74th chapter, Enoch explains that the point where 5 years worth of months (i.e. 1800 days) elapses in addition to 6 days for each of those past five years, equally 30 days, thereby totalling 1830 days, is when the moon is exactly a month behind the sun. I have verified this to be true by performing the following calculations:
"And (if) five years are added together, the sun has an excess of thirty days ; but aII the days (which) accrue to it for one year of those five years, when they are complete, amount to three hundred and sixty-four days. And the excess of the sun and the stars comes to six days; in five years, six (days) each (year), they have an excess of thirty days, and the moon falls behind the sun and the stars by thirty days." (Enoch 74:10-11) (Knibb & Ullendorff, 1978, pp. 173-174).
If we divide 1830 by the number of solar days in a lunar month:
1830 / 29.5305956 = 61.969627189 in number of lunar cycles
(By comparison, there are exactly 61 thirty-day month cycles within a 1830 day period.)
In order to figure out when the incompleted lunar cycle started, we multiply the remainder, which is 0.969627189, by the length of the lunar cycle in solar days before subtracting the result from 1830:
0.969627189 * 29.5305956 = 28.6336684011
1830 - 28.6336684011 = 1801.3663316
If we add a full lunar month, in solar days, i.e. 29.5305956 to 1801.3663316:
1801.3663316 + 29.5305956 = 1830.8969272
(Thus the lunar cycle in progress would end 0.8969272 days after the 1830 day mark.)
By contrast, if we add a full Enoch month, 30 days to the result:
1801.3663316 + 30 = 1831.3663316
If we subract the number of days equivalent to a full lunar cycle from 1831.3663316:
1831.3663316 - 29.5305956 = 1801.835736
1831.3663316 - 1801.835736 = 29.5305956, which is exactly the length of a lunar cycle in solar months!
To corroborate, let's see how much the difference of 1831.3663316 and 1801.3663316 is in solar days:
1831.3663316 - 1830.8969272 = 0.4694044
0.4694044 * 30 = 14.082132
14.082132 / 29.5305956 = 0.476865830637
0.4694044 / 0.476865830637 = 0.984353186667
0.984353186667 * 30 = 29.5305956, which is exactly the length of a lunar cycle in days
Besides knowing when the moon would be exactly a full month behind the sun; it seems possible that even more precise knowledge might have been revealed to Enoch; and this would only have been possible if Enoch received it directly from YHVH, because he had no access to the likes of Hubble space telescopes!
I believe that there is a way of interpreting a passage found in Enoch in such a way that we can calculate the length of the solar day to 8 or more decimals places.
The following calculations are based on the passage found in Enoch 82:4-20:
This is from the translation by Knibb & Ullendorff (1978, pp. 178-192):
[begin quote]
82. 4 Blessed are all the righteous, blessed are all those who walk in the way of righteousness, and do not sin like the sinners in the numbering of all their days in which the sun journeys in heaven, coming in and out through the gates for thirty days with the heads over thousands of this order of stars, (and) with the four which are added and divide between the four parts of the year, which lead them and appear with them on four days. 82. 5 Because of them men go wrong, and they do not reckon them in the reckoning of the whole (course of the) world; for men go wrong in respect of them, and do not know them exactly. 82.6 For they belong in the reckoning of the year, and are truly recorded (therein) for ever, one in the first gate, and one in the third, and one in the fourth and one in the sixth. And the year is completed in three hundred and sixty-four days. 82. 7 And the account of it (is) true, and the recorded reckoning of it (is) exact, for the lights, and the months, and the feasts, and the years, and the days Uriel showed me, and he inspired me— he to whom the Lord of the whole created world gave commands about the host of heaven for me. 82. 8 And he has power in heaven over night and day to cause light to shine on men: the sun, and the moon, and the stars, and all the powers of heaven which rotate in their orbits. 82. 9 And this is the law of the stars which set in their places, at their times, and at their feasts, and in their months. 82. 10 And these (are) the names of those who lead them, who keep watch that they appear at their times, and in their orders, and at their proper times, and in their months, and in their periods of rule, and in their positions. 82. 1 1 Their four leaders who divide the four parts of the year appear first; and after them the twelve leaders of the orders who divide the months and the years into three hundred and sixty-four (days), with the heads over thousands who separate the days; and for the four (days) which are added to them there are the leaders who separate the four parts of the year. 82. 12 And as for these heads over thousands, one is added between the leader and the led behind a position, but their leaders make the separation. 82. 13 And these (are) the names of the leaders who separate the four appointed parts of the year: Melkiel, Helemmelek, Meleyal, and Narel. 82. 14 And the names of those whom they lead (are) Adnarel, lyasusael, and lylumiel; these three follow behind the leaders of the orders, and (each) one follows behind the three leaders of the orders who follow behind those leaders of positions who separate the four parts of the year. 82.1 5 In the beginning of the year Melkiel rises first and rules, (the one) who is called the southern sun; and all the days of his period of rule during which he rules (are) ninety-one. 82. 16 And these (are) the signs of the days which are to be seen on earth in the days of his period of rule: sweat, and heat, and calm; and all the trees bear fruit, and leaves appear on all the trees, and the wheat harvest, and rose flowers, and all the flowers bloom in the field, but the trees of winter are withered. 82. 1 7 And these (are) the names of the leaders who (are) under them: Berkeel, Zelebsael, and another one who is added, a head over a thousand named Heloyaseph. And the days of the period of rule of this one are complete. 82. 18 The second leader after htm (is) Helemmelek whom they call the shining sun; and all the days of his light (are) ninety-one. 82. 19 And these are the signs of the days on earth: heat, and drought; and the trees bring their fruit to ripeness and maturity, and make their fruit dry; and the sheep mate, and become pregnant; and men gather all the fruits of the earth, and everything which is in the fields, and the vats of wine. And (these things) occur in the days of his period of rule. 82. 20 And these are the names and the orders and the leaders .. . of these heads over thousands: Gedaeyal, Keel, and Heel; and the name of the head over a thousand who is added to them (is) Asfael. And the days of his period of rule are complete
[end quote] (references to original Ethiopic reprinted in the first volume are removed).
Based on one possible interpretation of this passage, such as described in the above subheading, I have reasoned that there are 3-4 levels of leaders, with each leader successively lower in the hierarchy managing a progressively lower gradation of time, going from downwards by negative exponents from the value of 10 to 1 to 0.1 to 0.01:
The chief is Uriel, under whose charge the authority to manage time has been vested.
Under Uriel are the following four “leaders”: Melkiel, Helemmelek, Meleyal, and Narel, each of which manages their own dedicated season - Spring, Summer, Autumn, and Winter respectively.
Based on one possible way of interpreting these texts:
These four "battalion leaders” (which August Dillman called "toparchs") which are represented by the four single-day seasonal markers prior to each season 90-day season, are representatively administered by, along with the leaders that follow them, by three order-makers (or “ministers” (Hebrew "sharatat")) named Adnarel, Iyasusael, and Iylumiel, while each successive order-maker manages progressively smaller gradations of time: thus Adnarel administers directly on behalf of (or above) the four "toparchs"; Iyasusael administers the 12 substations under the four stations called seasons (Dillman calls this level the "taxiarch" level; and Iylumiel presumably manages the stars, planets, tides, moons, and orbits that finely govern all subunits of time. These three ordermakers appear during the first season in order to set the pattern for the rest of the seasons, I deduce. During the second season (summer), three other time governors appear: Berkeel, Zelebsael, Heloyasef; and in the third season (autumn), three more: Gedaeyal, Keel, and Heel; and Asphael for the fourth season [along with presumably two unmentioned others, unless Asphael is managing all months of the winter season].
The text says that Heloyasef was "added to manage the small gradations of time, referred to as "thousands"; and like Heloyasef, Asfael has been "added" later to oversee the small(est) increments of time, and I believe that the roles of Heloyasef and Asfael are thus linked. Perhaps they've been added due to the expansion of the universe and the lengthening of the solar day, which are measured in fractions of milliseconds per decade).
(Interestingly, the name Iylumiel (along with the name Narel[1]appears to be the etymological root for the Latin root illuminare[2] from which derives the English word "illumination"! Could Iylumiel be an angel employing some sort of photonic energy?)
In order to calculate how many solar hours (from the perspective of the modern 24 hour clock system) each of the 18 divisions of the Enoch day, we divide the number of hours in a solar day by the number of divisions in the Enoch day:
23.9345 hours / 18 = 1.32969444444 hours
Since there are four levels from Uriel to the level of leaders (which Dillman calls 'chiliarchs') by Iylumiel, who oversees those managing increments of time measuring in the thousands - which I presume include the hours, minutes and seconds that constitute days, weeks, months and years - I assume that 10 EDUs should be assigned to Uriel.
10 EDUs * 1.32969444444 hours = 13.29693444444 hours.
Next we add a gap equivalent to 1 EDU, which is 1.32969344444 hours. This is 1/10 the amount of time allotted to Uriel, and it could represent the rank of Adnarel, the administrator of the four toparchs:
13.29693444444 + 1.32969444444 = 14.6266288889 hours
Next, we multiply 1 EDU by four so that we can see how many hours accrue on top of each season on account of the four "leaders" named "Melkiel, Helemmelek, Meleyal, and Narel" (Enoch 82:13; Knibb & Ullendorff, 1978, pp. 189–190).
1.32969444444 hours × 4 = 5.31877777776 hours
But I deduce that each of these four leaders are separated from those they lead by another gap of hours equal to one-eighteenth of an Enoch day, each of which is equivalent to 1.32969444444 hours, so we need to double the above number of hours in order to account for both the number of hours dedicated to each "leader" in addition to the humber of hours separating from the ones they are leading:
5.31877777776 hours × 2 = 10.6375555555 hours
Additionally, since each of these seasonal leaders are leading the three substations respectively dedicated to each of the three months of each season, we need to multiply one-tenth of the 24-hour clock equivalent (in hours per solar day) of each one-eighteenth of an Enoch day by twelve in order to figure out how much time is separating each of the leaders from the monthly "leaders" following them:
0.132969444444 hours × 12 = 1.59563333333 hours
There appear to be 11 gaps of time each equivalent to each of the taxiarch-level additional durations of time dedicated to the 12 stations, and these separate the 12 months:
0.132969444444 hours × 11 = 1.46266388888 hours
(Will the 12th taxiarchal level gap be added later when the heavens and earth are renewed?)
Or perhaps the 11th gap represents the position filled by Iylumiel, who apparently administers the chiliarch level which is the level two and three negative exponents' worth of value from Uriel, i.e. hundredths and thousandths.
Let's add the above number of accumulated hours to get a running total before we add the remaining amount of hours based on those following these first two levels of "leaders", and their respective stations and substations, below Uriel:
14.6266288889 hours + 10.6375555555 hours + 1.59563333333 hours + 1.46266388888 hours = 28.3224816666 hours
Next, we multiply one-tenth of one-tenth of the original value of 1.329694444 hours, which would determine how much time would be dedicated to each of the 53 weeks:
53 × 0.013296944444 hours = 0.704738055532 hours
If we add an additional gap of equivalent size:
0.704738055532 hours * 2 = 1.40947611106 hours
There is no more time we need to add on account of all levels of "leaders" associated with years (led by Uriel); seasons (led by "Melkiel, Helemmelek, Meleyal, and Narel"); and the 12 [presumed, with the last one apparently not fully divided] substations under these four.
Let's add up all the totals:
28.3224816666 hours + 1.40947611106 hours = 29.7319677775 hours
Now we just need to calculate how many hours are remaining after all this time has been accounted for, if we subtract from a 23.9345 hour day.
29.7319677775 - 23.9345 = 5.7974677766 hours
In order to figure out what fraction of a day is represented by 5.7974677766 hours, we divide by 23.9345 hours:
5.7974677766 ÷ 23.9345 = 0.242222222173
That is an interesting fraction, because if we add the full day accounted for by the above 29.7319677775 hours, along with the 364 days of the Enoch calendar
364 + 1 + 0.242222222173 = 365.242222222173 days
365.242222222173 days is probably almost exactly the length of a solar year in solar days!
In summary, here is the entire calculation in one long equation:
10 + 1 + (4 * 1.3296944444) + (4 * 1.3296944444) + (12 * 0.13296944444) + (11 * 0.132969444444) + (53 × 0.013296944444) + (53 × 0.013296944444)) = 29.7450111111 hours
(continued below)
(The above is based on the second of 2 interpretations for Enoch 82:4-20.)
Copyright 2021 Ebionite Revival
Copyright 2021 P.J. Oh
(ebioniterevival@gmail.com)
License CC BY-NC-ND 4.0
The Enoch-based eschatology project can be found at this link:
https://www.researchgate.net/projec...-its-calendar-and-its-laden-Messianic-message
The book of Enoch is nominally a calendar having 364 days, which includes 12 months, each invariably 30 days in length along with 4 single day seasonal markers that lead each of the four seasons.
According to a system of intercalation deduced by John P. Pratt (PhD, Astronomy), which has been slightly modified by me, this calendar would be considerably more accurate than the Gregorian and Mayan calendars if intercalated by a system that adds a week every seven years, and an additional week every 28 years, except for 2 instances every Great Year quintet (one Great Year cycle is 364 years long; so 5 Great Year cycles would be 1820 years long) when a 28th year additional week isn't added.
It appears very probable that such a method of intercalation was practiced, especially in light of the book of Jubilees, which highlights the importance of the numbers 4, 7 and 28, especially when a 7 year "week" is multiplied by 4, which is the first whole number greater than half of 7; furthermore 28 is the total number of "days" (when weeks are counted as years) that constitutes the first whole number of weeks that equals the greater part of seven "weeks", which equals 49. The spiritual significance of these anniversaries of "weeks" and quartets of same, as well as quartets of weeks of Jubilees (1400 years), is demonstrated in the narratives of Jubilees such that they marked times when the following were called for: remorse over past sin; repentance; reflection on lessons learned; rededication to the Elohiym's ways of righteousness; and renewal of one's purity.
Although such a "sabbatical" cycle of intercalation probably allowed time for such remorse, repentance, reflection, rededication, and renewal; it appears that the amount of time accrued by the disparity between the 364-day cycle and the solar cycle of 364.2422 days was being precisely accounted for before effectively doing such resets by means of intercalating.
For example, in the 74th chapter, Enoch explains that the point where 5 years worth of months (i.e. 1800 days) elapses in addition to 6 days for each of those past five years, equally 30 days, thereby totalling 1830 days, is when the moon is exactly a month behind the sun. I have verified this to be true by performing the following calculations:
"And (if) five years are added together, the sun has an excess of thirty days ; but aII the days (which) accrue to it for one year of those five years, when they are complete, amount to three hundred and sixty-four days. And the excess of the sun and the stars comes to six days; in five years, six (days) each (year), they have an excess of thirty days, and the moon falls behind the sun and the stars by thirty days." (Enoch 74:10-11) (Knibb & Ullendorff, 1978, pp. 173-174).
If we divide 1830 by the number of solar days in a lunar month:
1830 / 29.5305956 = 61.969627189 in number of lunar cycles
(By comparison, there are exactly 61 thirty-day month cycles within a 1830 day period.)
In order to figure out when the incompleted lunar cycle started, we multiply the remainder, which is 0.969627189, by the length of the lunar cycle in solar days before subtracting the result from 1830:
0.969627189 * 29.5305956 = 28.6336684011
1830 - 28.6336684011 = 1801.3663316
If we add a full lunar month, in solar days, i.e. 29.5305956 to 1801.3663316:
1801.3663316 + 29.5305956 = 1830.8969272
(Thus the lunar cycle in progress would end 0.8969272 days after the 1830 day mark.)
By contrast, if we add a full Enoch month, 30 days to the result:
1801.3663316 + 30 = 1831.3663316
If we subract the number of days equivalent to a full lunar cycle from 1831.3663316:
1831.3663316 - 29.5305956 = 1801.835736
1831.3663316 - 1801.835736 = 29.5305956, which is exactly the length of a lunar cycle in solar months!
To corroborate, let's see how much the difference of 1831.3663316 and 1801.3663316 is in solar days:
1831.3663316 - 1830.8969272 = 0.4694044
0.4694044 * 30 = 14.082132
14.082132 / 29.5305956 = 0.476865830637
0.4694044 / 0.476865830637 = 0.984353186667
0.984353186667 * 30 = 29.5305956, which is exactly the length of a lunar cycle in days
Besides knowing when the moon would be exactly a full month behind the sun; it seems possible that even more precise knowledge might have been revealed to Enoch; and this would only have been possible if Enoch received it directly from YHVH, because he had no access to the likes of Hubble space telescopes!
I believe that there is a way of interpreting a passage found in Enoch in such a way that we can calculate the length of the solar day to 8 or more decimals places.
The following calculations are based on the passage found in Enoch 82:4-20:
This is from the translation by Knibb & Ullendorff (1978, pp. 178-192):
[begin quote]
82. 4 Blessed are all the righteous, blessed are all those who walk in the way of righteousness, and do not sin like the sinners in the numbering of all their days in which the sun journeys in heaven, coming in and out through the gates for thirty days with the heads over thousands of this order of stars, (and) with the four which are added and divide between the four parts of the year, which lead them and appear with them on four days. 82. 5 Because of them men go wrong, and they do not reckon them in the reckoning of the whole (course of the) world; for men go wrong in respect of them, and do not know them exactly. 82.6 For they belong in the reckoning of the year, and are truly recorded (therein) for ever, one in the first gate, and one in the third, and one in the fourth and one in the sixth. And the year is completed in three hundred and sixty-four days. 82. 7 And the account of it (is) true, and the recorded reckoning of it (is) exact, for the lights, and the months, and the feasts, and the years, and the days Uriel showed me, and he inspired me— he to whom the Lord of the whole created world gave commands about the host of heaven for me. 82. 8 And he has power in heaven over night and day to cause light to shine on men: the sun, and the moon, and the stars, and all the powers of heaven which rotate in their orbits. 82. 9 And this is the law of the stars which set in their places, at their times, and at their feasts, and in their months. 82. 10 And these (are) the names of those who lead them, who keep watch that they appear at their times, and in their orders, and at their proper times, and in their months, and in their periods of rule, and in their positions. 82. 1 1 Their four leaders who divide the four parts of the year appear first; and after them the twelve leaders of the orders who divide the months and the years into three hundred and sixty-four (days), with the heads over thousands who separate the days; and for the four (days) which are added to them there are the leaders who separate the four parts of the year. 82. 12 And as for these heads over thousands, one is added between the leader and the led behind a position, but their leaders make the separation. 82. 13 And these (are) the names of the leaders who separate the four appointed parts of the year: Melkiel, Helemmelek, Meleyal, and Narel. 82. 14 And the names of those whom they lead (are) Adnarel, lyasusael, and lylumiel; these three follow behind the leaders of the orders, and (each) one follows behind the three leaders of the orders who follow behind those leaders of positions who separate the four parts of the year. 82.1 5 In the beginning of the year Melkiel rises first and rules, (the one) who is called the southern sun; and all the days of his period of rule during which he rules (are) ninety-one. 82. 16 And these (are) the signs of the days which are to be seen on earth in the days of his period of rule: sweat, and heat, and calm; and all the trees bear fruit, and leaves appear on all the trees, and the wheat harvest, and rose flowers, and all the flowers bloom in the field, but the trees of winter are withered. 82. 1 7 And these (are) the names of the leaders who (are) under them: Berkeel, Zelebsael, and another one who is added, a head over a thousand named Heloyaseph. And the days of the period of rule of this one are complete. 82. 18 The second leader after htm (is) Helemmelek whom they call the shining sun; and all the days of his light (are) ninety-one. 82. 19 And these are the signs of the days on earth: heat, and drought; and the trees bring their fruit to ripeness and maturity, and make their fruit dry; and the sheep mate, and become pregnant; and men gather all the fruits of the earth, and everything which is in the fields, and the vats of wine. And (these things) occur in the days of his period of rule. 82. 20 And these are the names and the orders and the leaders .. . of these heads over thousands: Gedaeyal, Keel, and Heel; and the name of the head over a thousand who is added to them (is) Asfael. And the days of his period of rule are complete
[end quote] (references to original Ethiopic reprinted in the first volume are removed).
Based on one possible interpretation of this passage, such as described in the above subheading, I have reasoned that there are 3-4 levels of leaders, with each leader successively lower in the hierarchy managing a progressively lower gradation of time, going from downwards by negative exponents from the value of 10 to 1 to 0.1 to 0.01:
The chief is Uriel, under whose charge the authority to manage time has been vested.
Under Uriel are the following four “leaders”: Melkiel, Helemmelek, Meleyal, and Narel, each of which manages their own dedicated season - Spring, Summer, Autumn, and Winter respectively.
Based on one possible way of interpreting these texts:
These four "battalion leaders” (which August Dillman called "toparchs") which are represented by the four single-day seasonal markers prior to each season 90-day season, are representatively administered by, along with the leaders that follow them, by three order-makers (or “ministers” (Hebrew "sharatat")) named Adnarel, Iyasusael, and Iylumiel, while each successive order-maker manages progressively smaller gradations of time: thus Adnarel administers directly on behalf of (or above) the four "toparchs"; Iyasusael administers the 12 substations under the four stations called seasons (Dillman calls this level the "taxiarch" level; and Iylumiel presumably manages the stars, planets, tides, moons, and orbits that finely govern all subunits of time. These three ordermakers appear during the first season in order to set the pattern for the rest of the seasons, I deduce. During the second season (summer), three other time governors appear: Berkeel, Zelebsael, Heloyasef; and in the third season (autumn), three more: Gedaeyal, Keel, and Heel; and Asphael for the fourth season [along with presumably two unmentioned others, unless Asphael is managing all months of the winter season].
The text says that Heloyasef was "added to manage the small gradations of time, referred to as "thousands"; and like Heloyasef, Asfael has been "added" later to oversee the small(est) increments of time, and I believe that the roles of Heloyasef and Asfael are thus linked. Perhaps they've been added due to the expansion of the universe and the lengthening of the solar day, which are measured in fractions of milliseconds per decade).
(Interestingly, the name Iylumiel (along with the name Narel[1]appears to be the etymological root for the Latin root illuminare[2] from which derives the English word "illumination"! Could Iylumiel be an angel employing some sort of photonic energy?)
In order to calculate how many solar hours (from the perspective of the modern 24 hour clock system) each of the 18 divisions of the Enoch day, we divide the number of hours in a solar day by the number of divisions in the Enoch day:
23.9345 hours / 18 = 1.32969444444 hours
Since there are four levels from Uriel to the level of leaders (which Dillman calls 'chiliarchs') by Iylumiel, who oversees those managing increments of time measuring in the thousands - which I presume include the hours, minutes and seconds that constitute days, weeks, months and years - I assume that 10 EDUs should be assigned to Uriel.
10 EDUs * 1.32969444444 hours = 13.29693444444 hours.
Next we add a gap equivalent to 1 EDU, which is 1.32969344444 hours. This is 1/10 the amount of time allotted to Uriel, and it could represent the rank of Adnarel, the administrator of the four toparchs:
13.29693444444 + 1.32969444444 = 14.6266288889 hours
Next, we multiply 1 EDU by four so that we can see how many hours accrue on top of each season on account of the four "leaders" named "Melkiel, Helemmelek, Meleyal, and Narel" (Enoch 82:13; Knibb & Ullendorff, 1978, pp. 189–190).
1.32969444444 hours × 4 = 5.31877777776 hours
But I deduce that each of these four leaders are separated from those they lead by another gap of hours equal to one-eighteenth of an Enoch day, each of which is equivalent to 1.32969444444 hours, so we need to double the above number of hours in order to account for both the number of hours dedicated to each "leader" in addition to the humber of hours separating from the ones they are leading:
5.31877777776 hours × 2 = 10.6375555555 hours
Additionally, since each of these seasonal leaders are leading the three substations respectively dedicated to each of the three months of each season, we need to multiply one-tenth of the 24-hour clock equivalent (in hours per solar day) of each one-eighteenth of an Enoch day by twelve in order to figure out how much time is separating each of the leaders from the monthly "leaders" following them:
0.132969444444 hours × 12 = 1.59563333333 hours
There appear to be 11 gaps of time each equivalent to each of the taxiarch-level additional durations of time dedicated to the 12 stations, and these separate the 12 months:
0.132969444444 hours × 11 = 1.46266388888 hours
(Will the 12th taxiarchal level gap be added later when the heavens and earth are renewed?)
Or perhaps the 11th gap represents the position filled by Iylumiel, who apparently administers the chiliarch level which is the level two and three negative exponents' worth of value from Uriel, i.e. hundredths and thousandths.
Let's add the above number of accumulated hours to get a running total before we add the remaining amount of hours based on those following these first two levels of "leaders", and their respective stations and substations, below Uriel:
14.6266288889 hours + 10.6375555555 hours + 1.59563333333 hours + 1.46266388888 hours = 28.3224816666 hours
Next, we multiply one-tenth of one-tenth of the original value of 1.329694444 hours, which would determine how much time would be dedicated to each of the 53 weeks:
53 × 0.013296944444 hours = 0.704738055532 hours
If we add an additional gap of equivalent size:
0.704738055532 hours * 2 = 1.40947611106 hours
There is no more time we need to add on account of all levels of "leaders" associated with years (led by Uriel); seasons (led by "Melkiel, Helemmelek, Meleyal, and Narel"); and the 12 [presumed, with the last one apparently not fully divided] substations under these four.
Let's add up all the totals:
28.3224816666 hours + 1.40947611106 hours = 29.7319677775 hours
Now we just need to calculate how many hours are remaining after all this time has been accounted for, if we subtract from a 23.9345 hour day.
29.7319677775 - 23.9345 = 5.7974677766 hours
In order to figure out what fraction of a day is represented by 5.7974677766 hours, we divide by 23.9345 hours:
5.7974677766 ÷ 23.9345 = 0.242222222173
That is an interesting fraction, because if we add the full day accounted for by the above 29.7319677775 hours, along with the 364 days of the Enoch calendar
364 + 1 + 0.242222222173 = 365.242222222173 days
365.242222222173 days is probably almost exactly the length of a solar year in solar days!
In summary, here is the entire calculation in one long equation:
10 + 1 + (4 * 1.3296944444) + (4 * 1.3296944444) + (12 * 0.13296944444) + (11 * 0.132969444444) + (53 × 0.013296944444) + (53 × 0.013296944444)) = 29.7450111111 hours
(continued below)
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